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Multifaceted Quadruplet of Low-Lying Spin-Zero States in Ni 66 : Emergence of Shape Isomerism in Light Nuclei
Abstract
A search for shape isomers in the Ni66 nucleus was performed, following old suggestions of various mean–field models and recent ones, based on state-of-the-art Monte Carlo shell model (MCSM), all considering Ni66 as the lightest nuclear system with shape isomerism. By employing the two-neutron transfer reaction induced by an O18 beam on a Ni64 target, at the sub-Coulomb barrier energy of 39 MeV, all three lowest-excited 0+ states in Ni66 were populated and their γ decay was observed by γ-coincidence technique. The 0+ states lifetimes were assessed with the plunger method, yielding for the 02+, 03+, and 04+ decay to the 21+ state the B(E2) values of 4.3, 0.1, and 0.2 Weisskopf units (W.u.), respectively. MCSM calculations correctly predict the existence of all three excited 0+ states, pointing to the oblate, spherical, and prolate nature of the consecutive excitations. In addition, they account for the hindrance of the E2 decay from the prolate 04+ to the spherical 21+ state, although overestimating its value. This result makes Ni66 a unique nuclear system, apart from U236,238, in which a retarded γ transition from a 0+ deformed state to a spherical configuration is observed, resembling a shape-isomerlike behavior.
... So far, for only two cases of 0 + states, deexciting via hindered E2 decays, the retardation has been clearly attributed to a significant change of shape, involving configurations located in well-defined minima of the PES. They are the 0 + 4 states in 64 Ni and 66 Ni with half-lives >1 ps and ∼20 ps (corresponding to HF values >63 and 24), respectively [11,12]. We refer to them as "shapeisomer-like" structures, due to their much-reduced hindrances with respect to the fission-shape isomers in the actinides. ...
... In contrast, a series of measurements performed in Bucharest, ALTO IPN-Orsay, ILL and Argonne, guided by predictions from the MCSM, confirmed the existence of a complex scenario of excitations based on different spherical, oblate and prolate shapes also in A=62, 64, 66 Ni isotopes. Such results were obtained with the employment of different reaction mechanisms, e.g., sub-Coulomb barrier transfer reactions with heavy-ion stable beams, neutron-capture reactions with intense thermal-neutron beams, and Coulomb excitation [11,12,61,62]. In the case of 66 Ni, the two-neutron transfer reaction induced by an 18 O beam on a 64 Ni target, at the sub-Coulomb barrier energy of 39 MeV, was first used to populate all excited states up to ∼4.1 MeV excitation energy [11]. ...
... Such results were obtained with the employment of different reaction mechanisms, e.g., sub-Coulomb barrier transfer reactions with heavy-ion stable beams, neutron-capture reactions with intense thermal-neutron beams, and Coulomb excitation [11,12,61,62]. In the case of 66 Ni, the two-neutron transfer reaction induced by an 18 O beam on a 64 Ni target, at the sub-Coulomb barrier energy of 39 MeV, was first used to populate all excited states up to ∼4.1 MeV excitation energy [11]. Furthermore, lifetime measurements of all three 0 + excited states, located at 2443-, 2671-and 2974-keV excitation energies, performed with a plunger setup, yielded B(E2) transition rates of 4.3(5), 0.09(1), and 0.21(7) W.u., for the 0 + 2 , 0 + 3 , and 0 + 4 states, corresponding to HF factors of 1.2, 56 and 24, respectively. ...
The paper reviews the searches for shape isomers, which are “extreme” example of shape-coexistence phenomena in nuclei. They may appear when highly deformed structures, well localized in the nuclear Potential Energy Surface (PES) in the deformation space, undergo a significant change in shape to match the final state shape, thus leading to a substantially hindered $$\gamma$$ γ decay. This is in sharp contrast to the vast majority of shape-coexistence phenomena, where significant mixing in the initial and final state wave functions is found. So far, the most spectacular examples of shape isomerism are known in fissioning systems in the actinides, although only scarce experimental information is available from experiments conducted more than 20 years ago. Searches in lighter mass regions, guided by theory predictions based on different approaches and experimental investigations on superdeformed systems, are also presented. They point to $$^{64,66}$$ 64 , 66 Ni as additional examples of prolate deformed shape-isomer-like structures, although with much reduced hindrance with respect to the actinides. Their origin is strictly related to the action of the monopole component of the tensor force of the nucleon-nucleon interaction, which is expected to favor the appearance of deep secondary minima also in the PES of Sn nuclei with masses 112–118. Perspectives in current searches of shape isomerism with modern detection systems, in the actinides regions and in lighter masses, are discussed.
... Shape coexistence, i.e., existence of eigenstates with similar energies but characterized by distinct geometrical shapes, presents an intriguing phenomenon in atomic nuclei [1]. Over the past few decades, the studies of shape coexistence have been extensively performed in experiments [2], and nuclei with shape coexistence continue to be discovered in new mass regions [3][4][5] thanks to the rapid development of worldwide rare isotope beam facilities (for recent progress on shape coexistence, readers are referred to a collection of articles in Ref. [6]). ...
... platform to study the interplay among these configurations in a single nucleus. After the discovery of the first example in 186 Pb [20], several additional candidates are suggested throughout the nuclear chart [5,[21][22][23][24][25][26][27]. ...
... By taking the moderate criterion, i.e., d 123 or d 124 > 0.06, the main mass regions of multiple shape coexistence displayed in Fig. 6(b) are summarized in Table I. Many of them lie in the vicinity of closed shells or subshells, and this feature is also consistent with corresponding experimental suggestions [5,[21][22][23][24][25][26][27]. Moreover, the present calculations also predict multiple shape coexistence in the transitional regions, e.g., the region near (N, Z) = (110, 70), where the coexistence of an oblate shape and two prolate shapes was also studied in detail previously [40]. ...
Shape and multiple shape coexistence of nuclei are investigated throughout the nuclear chart by calculating the low-lying spectra and the quadrupole shape invariants for even-even nuclei with $10\leq Z\leq 104$ from the proton drip line to the neutron one within a five-dimensional collective Hamiltonian based on the covariant density functional PC-PK1. The quadrupole shape invariants are implemented to characterize the quadrupole deformations of low-lying $0^+$ states and predict nuclear mass regions of shape and multiple shape coexistence. The predicted low-lying spectra and the shape or multi-shape coexisting nuclei are overall in good agreement with the available experimental results. In addition, the present work predicts a wealth of nuclei with shape or multiple shape coexistence in the neutron-rich regions. The connection between the strong $E0$ transition strength and the occurrence of shape coexistence is analyzed systemically. It is found that nuclei with pronounced shape coexistence generally have strong $E0$ transition strengths, while the reverse may not be true. The present results can serve as useful guidelines for experimental searches and theoretical studies of shape and multiple shape coexistence, especially in neutron-rich regions.
... In the N = 81 isotones of 132 Sb and 133 Te [54,64], characterized by two and three valence particles, excitations were explained in terms of proton-neutron hole states, as well as 2p-2 h excitations (in 132 Sb). In the N = 84 two-valence-neutron nucleus 134 Sn, the ( f 7/2 ) 2 multiplet was identified up to a 6 + isomeric state at 1246 keV [65], while yrast states in the two-and three-proton N = 82 isotones 134 Te and 135 I, located up to above 5.5 MeV, were interpreted in terms of valence proton and particle-hole core excitations [66]. By employing fusion-and transfer-induced fission of 238 U at 6.2 MeV/u the structure of 132 Te (N = 80), with two proton particles and two neutron holes outside of the 132 Sn doubly magic core, has been recently extended up Partial level schemes of one-valence particle/hole nuclei around doubly magic 132 Sn. ...
... Examples of empirical values of residual pn interactions for three particular configurations having j p = j n , with l p = l n + 1. Experimental results for 88 Rb, 134 Sb and 210 Bi are given by filled symbols, while open symbols refer to values obtained by applying the Pandya transformation (bringing particleparticle into particle-hole and viceversa). Similar studies are also reported in Refs. ...
... [37,73]). Examples of empirical values of V res (I ) for the g 7/2 f 7/2 configuration of 134 Sb, in comparison with values extracted from analogous configurations in 88 Rb and 210 Bi, are given in the middle panel of Fig. 9 (see discussion below). These types of empirical two-nucleon interactions have been extensively used to perform shell model calculations especially designed to give a good representation of experimental level energies in N = 82 isotones, from Sb to Ba, as discussed for example by Blomqvist in Ref. [44]. ...
The paper reviews recent developments in $$\gamma $$ γ -ray spectroscopy of the neutron-rich fragments produced in nuclear fission. This subject has been an intensive area of study spanning more than five decades. Here we highlight key results and describe the evolution of the associated experimental techniques since the last review papers in 1995 (I. Ahmad and W.R. Phillips, Rep. Prog. Phys. 58(11), 1415 (1995); J. H. Hamilton et al., Prog. Part. Nucl. Phys. 35, 635(1995)). Research themes in nuclear structure will be explored along with the fission reaction mechanism and the links to nuclear astrophysics and applications.
... Let us take an example. Figure 12 [64] depicts the PES of 66 Ni with the same Hamiltonian as in Figure 10. The small circles on the PES are the T-plot. ...
... Type-II shell evolution occurs in various cases, especially in a number of shape coexistence cases, providing deformed states with stronger deformation, lower excitation energies, and more stabilities. It is an appearance of the monopole-quadrupole interplay and plays crucial roles in various phenomena including the first-order quantum phase transition (Zr isotopes [65][66][67]), the second-order quantum phase transition (Sn isotopes [68]), the multiple even-odd quantum phase transitions (Hg isotopes [69]), as well as the raising of the intruder band due to the suppression of the type-II shell evolution (lighter Ni isotopes [64,70]). As the involvement of the monopole interaction in this manner had not been recognized, type-II shell evolution appears to be among the emerging concepts of nuclear structure. ...
... where e is the unit charge; e p (e n ) denotes proton (neutron) effective charge induced by inmedium (or core-polarization) effects; and R 0 stands for the radius parameter of the droplet model (spherical background) (see [73] for some detailed explanation). The relations in Equations (18) and (19) worked very well in many works, for instance [64,[69][70][71]. Figure 14c,d shows the T-plot for the original interaction, where the PES is shown by using β 2 and γ as coordinates (see Figure 14a). Figure 14e,f depicts the T-plot for the monopole-frozen interaction obtained with the spherical HF state. ...
Some emerging concepts of nuclear structure are overviewed. (i) Background: the many-body quantum structure of atomic nucleus, a complex system comprising protons and neutrons (called nucleons collectively), has been studied largely based on the idea of the quantum liquid (à la Landau), where nucleons are quasiparticles moving in a (mean) potential well, with weak “residual” interactions between nucleons. The potential is rigid in general, although it can be anisotropic. While this view was a good starting point, it is time to look into kaleidoscopic aspects of the nuclear structure brought in by underlying dynamics and nuclear forces. (ii) Methods: exotic features as well as classical issues are investigated from fresh viewpoints based on the shell model and nucleon–nucleon interactions. The 70-year progress of the shell–model approach, including effective nucleon–nucleon interactions, enables us to do this. (iii) Results: we go beyond the picture of the solid potential well by activating the monopole interactions of the nuclear forces. This produces notable consequences in key features such as the shell/magic structure, the shape deformation, the dripline, etc. These consequences are understood with emerging concepts such as shell evolution (including type-II), T-plot, self-organization (for collective bands), triaxial-shape dominance, new dripline mechanism, etc. The resulting predictions and analyses agree with experiment. (iv) Conclusion: atomic nuclei are surprisingly richer objects than initially thought.
... In 70 Ni, a prolate 0 þ 2 state is found at 1567 keV above the spherical ground state [22]. Finally, four 0 þ levels are known below a 4-MeV excitation energy in 66 Ni, where the ground state and the 2664-keV 0 þ 3 level are interpreted as spherical, while the 0 þ 2 , 2445-keV and the 0 þ 4 , 2945-keV states are of oblate and prolate character [23]. ...
... It should be emphasized that this level is not populated in 64 Co β decay [30], in contrast to all other 0 þ states, up to 0 þ 6 , which are fed in this process. This observation already points to a marked difference in structure for this excitation, and is reminiscent of that occurring in 66 Ni [23], where the prolate-deformed 0 þ 4 state at 2974 keV was also the only 0 þ excitation not fed in the β decay of the spherical 66 Co ground state [40]. Further inspection of the ILL data revealed three 2 þ states (firmly established in this work) at 3647.9, 3749.1, and 3798.7 keV, which complement four such excitations, at 1345.8, 2276.6, ...
... The right-hand side of Fig. 3 presents the level scheme from MCSM calculations, performed with significantly extended MCSM basis vectors as compared to earlier studies of 66-78 Ni [11,23]. The model space includes protons and neutrons in the full fp shell with, in addition, the g 9=2 and d 5=2 orbitals, and the Hamiltonian is based on the A3DA-m effective interaction [11]. ...
... In 70 Ni, a prolate 0 þ 2 state is found at 1567 keV above the spherical ground state [22]. Finally, four 0 þ levels are known below a 4-MeV excitation energy in 66 Ni, where the ground state and the 2664-keV 0 þ 3 level are interpreted as spherical, while the 0 þ 2 , 2445-keV and the 0 þ 4 , 2945-keV states are of oblate and prolate character [23]. ...
... It should be emphasized that this level is not populated in 64 Co β decay [30], in contrast to all other 0 þ states, up to 0 þ 6 , which are fed in this process. This observation already points to a marked difference in structure for this excitation, and is reminiscent of that occurring in 66 Ni [23], where the prolate-deformed 0 þ 4 state at 2974 keV was also the only 0 þ excitation not fed in the β decay of the spherical 66 Co ground state [40]. Further inspection of the ILL data revealed three 2 þ states (firmly established in this work) at 3647.9, 3749.1, and 3798.7 keV, which complement four such excitations, at 1345.8, 2276.6, ...
... The right-hand side of Fig. 3 presents the level scheme from MCSM calculations, performed with significantly extended MCSM basis vectors as compared to earlier studies of 66-78 Ni [11,23]. The model space includes protons and neutrons in the full fp shell with, in addition, the g 9=2 and d 5=2 orbitals, and the Hamiltonian is based on the A3DA-m effective interaction [11]. ...
The low-spin structure of the semimagic Ni64 nucleus has been considerably expanded: combining four experiments, several 0+ and 2+ excited states were identified below 4.5 MeV, and their properties established. The Monte Carlo shell model accounts for the results and unveils an unexpectedly complex landscape of coexisting shapes: a prolate 0+ excitation is located at a surprisingly high energy (3463 keV), with a collective 2+ state 286 keV above it, the first such observation in Ni isotopes. The evolution in excitation energy of the prolate minimum across the neutron N=40 subshell gap highlights the impact of the monopole interaction and its variation in strength with N.
... Recently, large-scale shell-model calculations predicted the appearance of shape coexistence in 78 Ni and its link to a new island of inversion around 74 Cr [8], similar to that observed around 64 Cr [9]. The shell evolution [6,10] and the shape coexistence driven by type-II shell evolution [5,7] have been experimentally identified in the Ni and Cu isotopes as consequences of the varying occupation of the neutron g 9/2 orbital, not only in lighter isotopes [11][12][13][14][15][16][17][18][19][20] but also in heavier Cu isotopes towards N = 50 [21,22]. In fact, the data for the lowest states of 77,79 Cu seem to suggest that their neutron shell structure is dominated by the filling scheme with the closed p f shell and valence neutrons in the g 9/2 orbital. ...
... Finally, it is worth noting that the reduction of the Q s (2 + 1 ) in 74 Zn could be also attributed to shape coexistence and mixing. Indeed, the shape-coexistence phenomenon seems to be prevalent in the vicinity of 68 Ni and 78 Ni [17,24,79,80] and the energies of the 0 + 2 states in 66,68,70,72,74 Zn nuclei follow a parabolic trend characteristic for intruder configurations, as discussed in Sec. II. ...
The first experiment using radioactive beams post-accelerated by the HIE-ISOLDE facility has enabled to obtain a precise set of B(E2) transition probabilities in neutron-rich Zn74,76 isotopes. The resulting B(E2; 21+→01+) values are consistent with those determined in earlier REX-ISOLDE measurements. While the B(E2; 41+→21+) transition probability in Zn76 is also in agreement with earlier Coulomb-excitation results, the value obtained for Zn74 is considerably lower. For the first time, a spectroscopic quadrupole moment of the 21+ state was measured for an exotic nucleus in this mass region. A detailed comparison is presented with large-scale shell-model and Monte Carlo shell-model calculations.
... The "parabolic" energy trend suggests interactions with neutrons across the shell with a characteristic energy minimum near the mid-shell point (N = 66), as indicated. Note the severe deficiency of data for electromagnetic decay strengths: there is one half life, for the 589 keV state in 117 In, and the E2/M1 mixing ratio for the decay of this state is ambiguous. Data for 107 In are from [111] and for 131 In are from [112]; other data are taken from ENSDF [22]. ...
... However, this is an incomplete view, as details in Figure 33 imply; the structure of 70−76 Ni is also addressed in detail in this Section. 66 Ni at 2443 and 2671 keV are assigned spin-parity 0 + and are taken from [117]; other data are taken from ENSDF [22]. 68,70 Ni, from [126] for 72 Ni and from [127] for 74 Ni. ...
The present review takes steps from the domain of the shell model into open shell nuclei. The question posed in the title is to dramatize how far shell model approaches, i.e., many nucleons occupying independent-particle configurations and interacting through two-body forces (a configuration interaction problem) can provide a description of nuclei as one explores the structure observed where neither proton nor neutron numbers match closed shells. Features of doubly closed and singly closed shell nuclei and adjacent nuclei are sketched, together with the roles played by seniority, shape coexistence, triaxial shapes and particle–core coupling in organizing data. An illuminating step is taken here to provide a detailed study the reduced transition rates, B(E2;21+→01+), in the singly closed shell nuclei with doubly closed shell plus or minus a pair of identical nucleons, and the confrontation between such data and state-of-the-art shell model calculations: this amounts to a review of the effective charge problem. The results raise many questions and point to the need for much further work. Some guidance on criteria for sharpening the division between the domain of the shell model and that of deformation-based descriptions of nuclei are provided. The paper is closed with a sketch of a promising direction in terms of the algebraic structure embodied in the symplectic shell model.
... In order to prepare plunger targets with a large surface, special care must be attributed to avoid cracks and holes -a thermal treatment is recommended after every 3 microns thicknesses decrease, k) 65 Cu foils were obtained by rolling. To improve the measurements for the proposed experiment, which was a transfer reaction, a thermal treatment was applied for oxygen decontamination in order to obtain clear γ-spectra [23]; l) The adhesion between Ni and Fe is very poor; to enhance the adhesion between these two materials, the Fe surface used as backing was scratched with a Ted Pella, Pelco Bell Jar Kleen polishing cleaner powder and then washed, thus the surface roughness allowed adhesion of the Ni layer. ...
... According to [22], high purity 64 Ni targets were prepared for two neutron transfer reactions of an 18 O beam on 64 Ni targets at sub-barrier energies [23]. Target preparation considers the Ni chemical activity in air, as oxygen layers are incorporated and formed on the target surface. ...
Target manufacturing is one fundamental issue in nuclear physics experiments using accelerators. A variety of targets are required, each having to satisfy specific conditions related to the experimental particularities. In this context, a brief description of the target preparation laboratory developed at IFIN-HH is presented in this paper. To fulfill the specific requirements, the laboratory is endowed with high performance equipment for evaporation-condensation (thermal resistance, e-based systems, sputtering) and cold rolling. During the last years, consistent technological improvements were achieved. Target characteristics, quality and reliability are important for our experiments’ feasibility in the first place, but also for the degree of confidence in the assumed accuracy. Consequently, XRD, AFM, SEM/EDX and RBS analyses are performed in collaboration with specialized departments from our institute and from other research centers.This paper is meant to synthetize our work so far.
... The Monte Carlo Shell Model (MCSM) 42 allows to incorporate more SPOs into the calculation. For the MCSM predictions presented here, the A3DA-m Hamiltonian 43 was employed for [64][65][66][67][68][69][70][71][72][73][74][75][76] Ni, which encompasses the full pf shell as well as the 0g 9/2 and 1d 5/2 SPOs for protons and neutrons. To enable more detailed calculations for 78 Ni, the A3DA-m Hamiltonian was extended to the full proton and neutron pf and sdg shells. ...
... Using the doubly magic 40 Ca nucleus as an inert core, 8 protons and up to 32 neutrons were left to actively interact in a much larger model space as compared to conventional configuration interaction calculations. The A3DA-m interaction 43 in the model space of 6 SPOs (pf shell, 0g 9/2 and 1d 5/2 orbitals) both for protons and neutrons was used for [64][65][66][67][68][69][70][71][72][73][74][75][76] Ni. This interaction was extended to a model space of 9 SPOs (pf and sdg shells) for 78,80 Ni where upper SPOs in the sdg shell become more important. ...
Nuclear magic numbers, which emerge from the strong nuclear force based on quantum chromodynamics, correspond to fully occupied energy shells of protons, or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. While the sequence of magic numbers is well established for stable nuclei, evidence reveals modifications for nuclei with a large proton-to-neutron asymmetry. Here, we provide the first spectroscopic study of the doubly magic nucleus $^{78}$Ni, fourteen neutrons beyond the last stable nickel isotope. We provide direct evidence for its doubly magic nature, which is also predicted by ab initio calculations based on chiral effective field theory interactions and the quasi-particle random-phase approximation. However, our results also provide the first indication of the breakdown of the neutron magic number 50 and proton magic number 28 beyond this stronghold, caused by a competing deformed structure. State-of-the-art phenomenological shell-model calculations reproduce this shape coexistence, predicting further a rapid transition from spherical to deformed ground states with $^{78}$Ni as turning point.
... Recent studies have shown that shape changes may be linked to multiple particle-hole excitations of both protons and neutrons [22][23][24][25][26]. However, a precise and accurate excitation energy measurement of the 1=2 þ isomer to confirm claims of shape coexistence in 79 Zn is missing from the above-mentioned work. ...
Isomers close to doubly magic Ni502878 provide essential information on the shell evolution and shape coexistence near the Z=28 and N=50 double shell closure. We report the excitation energy measurement of the 1/2+ isomer in Zn493079 through independent high-precision mass measurements with the JYFLTRAP double Penning trap and with the ISOLTRAP multi-reflection time-of-flight mass spectrometer. We unambiguously place the 1/2+ isomer at 942(10) keV, slightly below the 5/2+ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with discrete nonorthogonal shell-model calculations which are used here for the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other N=49 isotones. The 1/2+ isomer is interpreted as the bandhead of a low-lying deformed structure akin to a predicted low-lying deformed band in Zn80, and points to shape coexistence in Zn79,80 similar to the one observed in Ni78. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart.
... While the jj45pn interaction has a limited valence space and does not allow for particle excitation across Z = 50 or N = 82, it has been successfully used to explain the structure of excited states in the isotopes lying the vicinity of 100,132 Sn doubly magic nuclei [24,25,46,75,76]. At the same time, it has been previously observed that an increase of valence space and excitation across magic numbers were necessary to explain experimental phenomena observed around the nickel (Z = 28) [77][78][79][80][81][82] and the lead (Z = 82) [83,84] neutron midshell regions. However, further theoretical studies on indium isotopes are needed for a better understanding of the measured species. ...
Neutron-rich In120–124 isotopes have been studied utilizing the double Penning trap mass spectrometer JYFLTRAP at the IGISOL facility. Using the phase-imaging ion-cyclotron-resonance technique, the isomeric states were resolved from ground states and their excitation energies measured with high precision in In121,123,124. In In120,122, the 1+ states were separated and their masses were measured while the energy difference between the unresolved 5+ and 8− states, whose presence was confirmed by post-trap decay spectroscopy, was determined to be ≤15 keV. In addition, the half-life of Cd122, T1/2=5.98(10)s, was extracted. Experimental results were compared with energy density functionals, density functional theory, and shell-model calculations.
... Recent studies have shown that shape changes may be linked to multiple particle-hole excitations of both protons and neutrons [22][23][24][25][26]. However, a precise and accurate excitation energy measurement of the 1/2 + isomer to confirm claims of shape coexistence in 79 Zn is missing from the above-mentioned work. ...
Isomers close to doubly-magic nickel-78 provide essential information on the shell evolution and shape coexistence near the Z = 28 and N = 50 double shell closure. We report the excitation energy measurement of the 1/2+ isomer in zinc-79 through independent high-precision mass measurements with the JYFLTRAP double Penning trap and with the ISOLTRAP Multi-Reflection Time-of-Flight Mass Spectrometer. We unambiguously place the 1/2+ isomer at 942(10) keV, slightly below the 5/2+ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with Discrete Non Orthogonal shell-model calculations which are used here for the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other N = 49 isotones. The 1/2+ isomer is interpreted as the band-head of a low-lying deformed structure akin to a predicted low-lying deformed band in 80Zn and points to shape coexistence in 79,80Zn similar to the one observed in 78Ni. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart.
... The Ni (Z = 28) Isotopes SC in this region has first been observed in 68 Ni 40 [741][742][743][744][745][746][747] and 70 Ni 42 [742,748,749], attributed to proton 2p-2h excitations across the Z = 28 shell. The early implications [750] that configuration mixing is needed in order to interpret the spectra of 64,66 Ni 36,38 was followed by the observation of SC in these two isotopes, see [751,752] for 66 Ni 38 and [532,753] for 64 Ni 36 . Existing evidence for SC in these isotopes is reviewed in [754], in which it is seen (in Figure 7 of [754]) that the 0 + 2 states in [64][65][66][67][68][69][70] Ni 36-42 resemble the left branch of a parabola reaching a minimum/plateau at N = 40, 42 (see Figure 13c). ...
The last decade has seen a rapid growth in our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle–hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell-model and mean-field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts that can help in improving our understanding of the details of the nucleon–nucleon interaction, as well as of its modifications occurring far from stability.
... A. The Ni (Z=28) isotopes SC in this region has first been observed in 68 Ni 40 [133,150,175,233,235,630,726] and 70 Ni 42 [134,150,618], attributed to proton 2p-2h excitations across the Z = 28 shell. The early implications [78] that configuration mixing is needed in order to interpret the spectra of 64,66 Ni 36,38 was followed by the observation of SC in these two isotopes, see [433,556] for 66 Ni 38 and [450,473] for 64 Ni 36 . Existing evidence for SC in these isotopes is reviewed in [252], in which it is seen (in Fig. 7 of [252]) that the 0 + 2 states in 64−70 Ni 36−42 resemble the left branch of a parabola reaching a minimum/plateau at N = 40, 42 (see Fig. 7(c)). ...
The last decade has seen a rapid growth of our understanding of the microscopic origins of shape coexistence, assisted by the new data provided by the modern radioactive ion beam facilities built worldwide. Islands of the nuclear chart in which shape coexistence can occur have been identified, and the different microscopic particle-hole excitation mechanisms leading to neutron-induced or proton-induced shape coexistence have been clarified. The relation of shape coexistence to the islands of inversion, appearing in light nuclei, to the new spin-aligned phase appearing in N=Z nuclei, as well as to shape/phase transitions occurring in medium mass and heavy nuclei, has been understood. In the present review, these developments are considered within the shell model and mean field approaches, as well as by symmetry methods. In addition, based on systematics of data, as well as on symmetry considerations, quantitative rules are developed, predicting regions in which shape coexistence can appear, as a possible guide for further experimental efforts, which can help in improving our understanding of the details of the nucleon-nucleon interaction, as well as of its modifications occurring far from stability.
... Such 0 + states are effectively populated and studied using two-particle transfer reactions such as (t, p) or ( 3 He,n). An alternative and very powerful probes are the ( 18 O, 16 O) and ( 14 C, 16 O), two-neutron (2n) [203,204] two-proton (2p) [205] transfer reactions, respectively. Pioneering studies at Orsay employed this reaction to discover the first excited 0 + state in 68 Ni through the selectivity of the reaction and the measured angular distributions of 16 O ejectiles, allowing the identification of the momentum transfer [205]. ...
The next years will see the completion of the radioactive ion beam facility SPES (Selective Production of Exotic Species) and the upgrade of the accelerators complex at Istituto Nazionale di Fisica Nucleare – Legnaro National Laboratories (LNL) opening up new possibilities in the fields of nuclear structure, nuclear dynamics, nuclear astrophysics, and applications. The nuclear physics community has organised a workshop to discuss the new physics opportunities that will be possible in the near future by employing state-of-the-art detection systems. A detailed discussion of the outcome from the workshop is presented in this report.
... We present a recent work on this subject from a modern viewpoint combined with state-of-the-art configuration interaction (CI) calculations with a realistic effective nucleonnucleon (NN) interaction. The CI calculation in nuclear physics is called shell model, and some introductory details 5.17 (21) 217 (5) Q= -1.9 (4) Q= 2.13 (15) [20][21][22][23], which enabled us to carry out CI calculations far beyond the limit of the conventional CI approaches, on contemporary challenges [24][25][26][27][28][29][30][31][32][33][34]. Some details of the MCSM are presented in Appendix B. A large number of single-particle orbits are taken so that the ellipsoidal deformation can be described, 8 for protons and 10 for neutrons. ...
Virtually any object can rotate. While the rotation provides various intriguing physics cases, the primary picture for atomic nuclei was simple. Rotational bands have been observed for many nuclei, and their basic picture is considered to have been established in 1950s. We, however, show that this traditional picture is superseded with a novel picture arising from basic characteristics of the nuclear forces. In the traditional view, as stressed by Aage Bohr in his Nobel lecture, most of heavy nuclei are like axially-symmetric prolate ellipsoids (i.e., with two shorter axes of equal length), rotating about one of the short axes, like a rod. In the present picture, however, in many cases, the lengths of these three axes are all different, called triaxial. The triaxial shape yields more complex rotations, which actually reproduce experimental data as shown by state-of-the-art Configuration Interaction calculations, on supercomputers. The key to differentiate the two pictures is the nuclear tensor force, which is known to produce the shell evolution in exotic nuclei, a major agenda of Rare-Isotope physics. We now demonstrate that the same tensor force generates, in many nuclei, the triaxiality, fading the prolate-ellipsoid dominance away. The tensor force is a direct consequence of one $\pi$ meson exchange between nucleons, and the present finding is regarded as the first explicit or visible case that elementary particles directly affect nuclear shapes. The importance of the explicit tensor force is in the same line as Weinberg's modeling of nuclear forces. This feature makes the new picture robust, and may cast challenges for other many-body systems having spin-dependent forces. Substantial impacts on superheavy nuclei and fission are anticipated. This study sheds lights on the earlier suggestion of dominant triaxiality by Davydov, a Ukrainian physicist.
... Moreover, a significant occupancy of the neutron g 9/2 and d 5/2 orbitals, which appear above the energy gap for N = 40, was necessary to reproduce the measured transition probabilities in 64,66 Fe [12][13][14]. The ground states of magic Z = 28 Ni nuclei are dominated by normal-ordered 0p0h configurations, while a multitude of low-lying 0 + states were identified in 64−70 Ni [15][16][17][18][19][20][21][22][23][24]. Based on their decay properties combined with transferreaction cross sections [25,26], these excited 0 + states were interpreted as resulting from either neutron promotion across the energy gap for N = 40 or proton excitation across the energy gap for Z = 28, and tentatively assigned as intruder structures with various shapes. ...
The excited states of $N=44$ $^{74}$Zn were investigated via $\gamma$-ray spectroscopy following $^{74}$Cu $\beta$ decay. By exploiting $\gamma$-$\gamma$ angular correlation analysis, the $2_2^+$, $3_1^+$, $0_2^+$ and $2_3^+$ states in $^{74}$Zn were firmly established. The $\gamma$-ray branching and $E2/M1$ mixing ratios for transitions de-exciting the $2_2^+$, $3_1^+$ and $2_3^+$ states were measured, allowing for the extraction of relative $B(E2)$ values. In particular, the $2_3^+ \to 0_2^+$ and $2_3^+ \to 4_1^+$ transitions were observed for the first time. The results show excellent agreement with new microscopic large-scale shell-model calculations, and are discussed in terms of underlying shapes, as well as the role of neutron excitations across the $N=40$ gap. Enhanced axial shape asymmetry (triaxiality) is suggested to characterize $^{74}$Zn in its ground state. Furthermore, an excited $K=0$ band with a significantly larger softness in its shape is identified. A shore of the $N=40$ ``island of inversion'' appears to manifest above $Z=26$, previously thought as its northern limit in the chart of the nuclides.
... A large number of MCSM calculations have been performed as exemplified in refs. 32,33,45,[52][53][54][55][56][57][58] . Most of these applications feature the adoption of an inert core with valence nucleons for the description of the nuclear properties. ...
A long-standing crucial question with atomic nuclei is whether or not α clustering occurs there. An α particle (helium-4 nucleus) comprises two protons and two neutrons, and may be the building block of some nuclei. This is a very beautiful and fascinating idea, and is indeed plausible because the α particle is particularly stable with a large binding energy. However, direct experimental evidence has never been provided. Here, we show whether and how α(-like) objects emerge in atomic nuclei, by means of state-of-the-art quantum many-body simulations formulated from first principles, utilizing supercomputers including K/Fugaku. The obtained physical quantities exhibit agreement with experimental data. The appearance and variation of the α clustering are shown by utilizing density profiles for the nuclei beryllium-8, -10 and carbon-12. With additional insight by statistical learning, an unexpected crossover picture is presented for the Hoyle state, a critical gateway to the birth of life.
... Type II shell evolution occurs in various cases, especially in a number of shape coexistence cases, providing deformed states with stronger deformation, lower excitation energies and more stabilities. It is an appearance of the monopolequadrupole interplay, and plays crucial roles in various phenomena including the first order phase transition (Zr isotopes [61][62][63]), the second order phase transition (Sn isotopes [64]), the multiple even-odd phase transitions (Hg isotopes [65]) as well as the raising of the intruder band due to the suppression of the type II shell evolution (lighter Ni isotopes [59,66]). As the involvement of the monopole interaction in this manner had not been recognized, Type II shell evolution appears to be among the emerging concepts of nuclear structure. ...
Some emerging concepts of nuclear structure are overviewed. (1) Background: the many-body quantum structure of atomic nucleus, a complex system comprising protons and neutrons (called nucleons collectively), has been studied largely based on the idea of the quantum liquid (a la Landau), where nucleons are quasiparticles moving in a (mean) potential well, with weak "residual" interactions between nucleons. The potential is rigid in general, although it can be anisotropic. While this view was a good starting point, it is time to look into kaleidoscopic aspects of the nuclear structure brought in by underlying dynamics and nuclear forces. (2) Methods: exotic features as well as classical issues are investigated from fresh viewpoints based on the shell model and nucleon-nucleon interactions. The 70-year progress of the shell-model approach, including effective nucleon-nucleon interactions, enables us to do this. (3) Results: we go beyond the picture of the solid potential well by activating the monopole interactions of the nuclear forces. This produces notable consequences in key features such as the shell/magic structure, the shape deformation, the dripline, etc. These consequences are understood with emerging concepts such as shell evolution (incl. type-II), T-plot, self-organization (for collective bands), triaxial-shape dominance, new dripline mechanism, etc. The resulting predictions and analyses agree with experiment. (4) Conclusion: atomic nuclei are surprisingly richer objects than initially thought.
... However isomers can also occur in light nuclei, for example, 66 Ni (γ-decay, t 1/2 = 134 ± 9 ps) [9]. ...
This PhD thesis reports on works towards laser cooling and trapping caesium isotopes and nuclear isomers. The main outcome of the research was the installation of an experimental facility for obtaining ∼100 µK samples of 135mCs, and in the test of the facility with 133Cs+ ionic beams neutralised and trapped in MagnetoOptical Traps (MOTs). The work can be divided into three related experiments, instrumental for obtaining ultra-cold isomers of caesium atoms. The first part was conducted in the laser cooling laboratory at University College London. The task consisted of designing and setting up a laser and imaging systems for a dual-chamber MOT of 133Cs atoms. The laser systems comprise of two main lasers, cooling and repumping lasers, each equipped with frequency stabilisation and amplification stages. The second part of the work took place in the Accelerator Laboratory of the University of Jyvaskyla (Finland). Here, the systems created at UCL were transferred and installed within the existing Ion Guide Isotope Separation On-Line (IGISOL) facility. The reassembled system was tested again with the 133Cs MOT and optimised for stability and robustness in a new, uncontrolled, and noisy environment. In the third part of the experiment, the system in Finland was upgraded for neutralisation and laser cooling of an incoming +1 ions beam produced by IGISOL. This required the installation of a new experimental chamber, equipped with a thin Y foil for ion implantation and neutralisation, and coated with a low-desorption energy coating to increase the trapping efficiency. In parallel, the ions’ delivery system and connection to the IGISOL electrostatic transport line were also created. In this phase, the implantation of 135mCs+ beams was tested. In order to monitor the production and transport of the desired ions, the gamma decay of 135mCs implanted in a Ge detector was observed. The life-time of 135mCs atoms was measured to confirm the implanted species. Moreover, trapping of 135Cs was attempted. The long term goal of the research started with this thesis is to employ the facility to realise Bose-Einstein condensate of 135mCs. The realisation would have numbers of applications, most notably paving the path for investigations on multibody physics in ultra-cold nuclear matter, and the demonstration of the generation of coherent gamma photons.
... This island, at its boundary, also harbors the * Present address: Lawrence Livermore National Laboratory, Livermore, California 94550, USA. noteworthy case of triple shape coexistence in 68 Ni [15,16], just four protons north of 64 Cr, with such coexistence also reported in the neighboring Ni isotopes [17][18][19]. A recent prediction extends this island of inversion to N = 50 [20], and includes nuclei that will only be reached at next-generation rare-isotope beam facilities. ...
... Similar studies were also performed in the case of the 65 Cu and 67 Cu nuclei, where Ni cores were considered [59,60]. This neutron-rich region around Z =28 is characterized by the coexistence of different nuclear shapes [61][62][63][64][65][66], the emergence of which is intimately related to proton-neutron correlations and shell structure. ...
We present recent results on the structure of the one-valence-particle Ca41 and Ca49 nuclei and the one-valence-hole Ca47 nucleus. The isotopes of interest were populated via the cold-neutron-capture reactions Ca40(n,γ), Ca48(n,γ), and Ca46(n,γ), respectively. The experiments were performed at the Institut Laue-Langevin, within the EXILL campaign, which employed a large array of high-purity germanium (HPGe) detectors. The γ decay and level schemes of these nuclei were investigated by γ-ray coincidence relationships, leading to the identification of 41, 10, and 6 new transitions in Ca41, Ca47, and Ca49, respectively. Branching ratios and intensities were extracted for the γ decay from each state, and γ-ray angular correlations were performed to establish a number of transition multipolarities and mixing ratios, thus helping in the spin assignment of the states. The experimental findings are discussed along with microscopic, self-consistent beyond-mean-field calculations performed with the hybrid configuration mixing model, based on a Skyrme SkX Hamiltonian. The latter suggests that a fraction of the low-spin states of the Ca41, Ca49, and Ca47 nuclei is characterized by the coexistence of either 2p-1h (two-particle–one-hole) and 1p-2h excitations, or couplings between single-particle or single-hole degrees of freedom and collective vibrations (phonons) of the doubly-magic “core.”
... magic Ni nuclei (Z = 28) and close to the neutron midshell between N = 28 and N = 50, these nuclei provide ideal opportunities to study the interplay of microscopic and macroscopic degrees of freedom in nuclear matter, particularly with respect to shape coexistence and shape transition phenomena. The former has been established in the neighboring Se, Ge, and Ni isotopes [1][2][3][4][5], while no clear evidence has yet been reported in the Zn isotopic chain. The only exception is 68 Zn, where the 0 2 + state has been suggested to be the bandhead of a more deformed structure than that built on the ground state [6]. ...
The electromagnetic structure of Zn66 at low excitation energy was investigated via low-energy Coulomb excitation at INFN Legnaro National Laboratories, using the Gamma Array of Legnaro Infn Laboratories for nuclEar spectrOscopy (GALILEO) γ-ray spectrometer coupled to the SPIDER (Silicon PIe DEtectoR). A set of reduced E2, E3, and M1 matrix elements was extracted from the collected data using the gosia code, yielding 12 reduced transition probabilities between the low-spin states and the spectroscopic quadrupole moment of the 21+ state. The B(E2) values for transitions depopulating the 02+ state have been determined for the first time, allowing for the lifetime of this state to be deduced and, consequently, the ρ2(E0;02+→01+) monopole transition strength to be extracted. In addition, the B(E3;31−→01+) value has been determined for the first time in a Coulomb excitation experiment. The obtained results resolve the existing discrepancies between literature lifetimes and demonstrate that Zn66 cannot be described by using simple collective models. Therefore, new state-of-the-art beyond-mean-field and large-scale shell-model calculations were performed in order to interpret the structure of this nucleus. Both the experimental and theoretical results suggest that the triaxial degree of freedom has an important impact on electromagnetic properties of Zn66, while the unique features of the 02+ state indicate its distinct and rather isolated structure.
... This phenomenon, called "shape coexistence," arises from the subtle interplay between macroscopic (collective) and microscopic (individual nucleons) effects [1], and occurs in almost all nuclei (see, e.g., Refs. [1][2][3][4][5][6]). Adding any new information on nuclear shape-coexistence phenomena is important, as it provides guidance to nuclear structure theory which aims at a unified description of atomic nuclei. ...
Medium and high spin states of the Y96 nucleus, located in the shape-coexistence region near Z=40 and N=60, were populated in thermal-neutron-induced fission of U233 and U235 targets, diluted in a scintillator. γ rays were measured with the FIssion Product Prompt γ-ray Spectrometer (FIPPS) high-purity germanium (HPGe) detector array, using double and triple γ-ray coincidence techniques and taking advantage of the efficient fission tag provided by the scintillating target material. A complex level scheme, extending up to 5.2 MeV and including excitations above the 8+β-decaying isomer, was investigated, and firm spin and parity assignments were given to a number of states, on the basis of angular correlation analysis and considerations on the γ-decay patterns. While the structures built on the 0− ground state and the 8+ isomer show irregular patterns typical for spherical shapes, the (6+) isomeric state at 1655 keV [with half-life of 181(9) ns], and the rotational band built on it [with spin-parity values between (6+) and (9+)], can be explained by Hartree-Fock-Bogoliubov calculations, if an oblate deformation is assumed. This is the first observation of a deformed structure in an N=57 isotone, lying three neutrons away from the N=60 line. An important finding is also the 115-keV transition which connects the (6+) 181(9)-ns isomer to the β-decaying 8+ spherical isomer, allowing us to firmly place the latter at 1541 keV excitation energy. This may be relevant for calculations of electron and antineutrino spectra from fission of actinides, for which Y96 is a prominent product.
... Similar studies were also performed in the case of the 65 Cu and 67 Cu nuclei, where Ni cores were considered [59,60]. This neutron-rich region around Z =28 is characterized by the coexistence of different nuclear shapes [61][62][63][64][65][66], the emergence of which is intimately related to proton-neutron correlations and shell structure. ...
We present recent results on the structure of the one-valence-particle $^{41}$Ca and $^{49}$Ca, and one-valence-hole $^{47}$Ca, nuclei. The isotopes of interest were populated via the cold-neutron capture reactions $^{40}$Ca(n,$\gamma$), $^{48}$Ca(n,$\gamma$) and $^{46}$Ca(n,$\gamma$), respectively. The experiments were performed at the Institut Laue-Langevin, within the EXILL campaign, which employed a large array of HPGe detectors. The $\gamma$ decay and level schemes of these nuclei were investigated by $\gamma$-ray coincidence relationships, leading to the identification of 41, 10, and 6 new transitions in $^{41}$Ca, $^{47}$Ca, and $^{49}$Ca, respectively. Branching ratios and intensities were extracted for the $\gamma$ decay from each state, and $\gamma$-ray angular correlations were performed to establish a number of transition multipolarities and mixing ratios, thus helping in the spin assignment of the states. The experimental findings are discussed along with microscopic, self-consistent beyond-mean-field calculations performed with the Hybrid Configuration Mixing model, based on a Skyrme SkX Hamiltonian. The latter suggests that a fraction of the low-spin states of the $^{41}$Ca, $^{49}$Ca, and $^{47}$Ca nuclei is characterized by the coexistence of either 2p-1h and 1p-2h excitations, or couplings between single-particle/hole degrees of freedom and collective vibrations (phonons) of the doubly-magic "core".
... One area where data are still particularly lacking is a characterization of E0 transition strengths between states of J > 0 in spherical nuclei. This deficiency is the motivation for the present study of the nickel isotopes [11][12][13]. Detailed muonic X-ray measurements [14] and optical spectroscopy [15] indicate that the ground states of these isotopes are spherical with little variation. ...
Excited states in $^{58,60,62}$Ni were populated via inelastic proton scattering at the Australian National University as well as via inelastic neutron scattering at the University of Kentucky Accelerator Laboratory. The Super-e electron spectrometer and the CAESAR Compton-suppressed HPGe array were used in complementary experiments to measure conversion coefficients and $\delta(E2/M1)$ mixing ratios, respectively, for a number of $2^+ \rightarrow 2^+$ transitions. The data obtained were combined with lifetimes and branching ratios to determine $E0$, $M1$, and $E2$ transition strengths between $2^+$ states. The $E0$ transition strengths between $0^+$ states were measured using internal conversion electron spectroscopy and compare well to previous results from internal pair formation spectroscopy. The $E0$ transition strengths between the lowest-lying $2^+$ states were found to be consistently large for the isotopes studied.
Small-scale facilities play a significant role in the landscape of nuclear physics research in Europe. They address a wide range of fundamental questions and are essential for teaching and training personnel in accelerator technology and science, providing them with diverse skill sets, complementary to large projects. The current status and perspectives of nuclear physics research at small-scale facilities in Europe will be given.
Lifetime measurements of the (3−), (4−), and (6−) intraband states in the neutron-rich, odd-odd Rb96 nucleus were performed at the LOHENGRIN spectrometer of Institut Laue-Langevin, using thermal-neutron-induced fission of U235 and fast-timing techniques with LaBr3:Ce scintillator detectors. The nanosecond isomeric nature of the (3−) bandhead was established as well as the β2=0.39(3) deformation parameter of the band, pointing to a robust deformation in Rb96. Moreover, a hindered B(E2) value of 3.9−13+19×10−2 W.u. was found for the γ decay of the deformed (4−) state to the spherical 2− ground state. A retardation was also found for the (3−) → 2− transition, possibly due to the shape change and giving strong support to a shape coexistence scenario in this nucleus, at the borders of the island of deformation at N=60. Analogies with the structure of the Y98 isotone are discussed.
The excited states of N=44 Zn74 were investigated via γ-ray spectroscopy following Cu74 β decay. By exploiting γ−γ angular correlation analysis, the 22+, 31+, 02+, and 23+ states in Zn74 were firmly established. The γ-ray branching and E2/M1 mixing ratios for transitions deexciting the 22+, 31+, and 23+ states were measured, allowing for the extraction of relative B(E2) values. In particular, the 23+→02+ and 23+→41+ transitions were observed for the first time. The results show excellent agreement with new microscopic large-scale shell-model calculations, and are discussed in terms of underlying shapes, as well as the role of neutron excitations across the N=40 gap. Enhanced axial shape asymmetry (triaxiality) is suggested to characterize Zn74 in its ground state. Furthermore, an excited K=0 band with a significantly larger softness in its shape is identified. A shore of the N=40 “island of inversion” appears to manifest above Z=26, previously thought as its northern limit in the chart of the nuclides.
Shape and multiple shape coexistence of nuclei are investigated throughout the nuclear chart by calculating the low-lying spectra and the quadrupole shape invariants for even-even nuclei with 10≤Z≤104 from the proton drip line to the neutron one within a five-dimensional collective Hamiltonian based on the covariant density functional PC-PK1. The quadrupole shape invariants are implemented to characterize the quadrupole deformations of low-lying 0+ states and predict nuclear mass regions of shape and multiple shape coexistence. The predicted low-lying spectra and the shape or multishape coexisting nuclei are overall in good agreement with the available experimental results. In addition, the present work predicts a wealth of nuclei with shape or multiple shape coexistence in the neutron-rich regions. The connection between the strong E0 transition strength and the occurrence of shape coexistence is analyzed systemically. It is found that nuclei with pronounced shape coexistence generally have strong E0 transition strengths, while the reverse may not be true. The present results can serve as useful guidelines for experimental searches and theoretical studies of shape and multiple shape coexistence, especially in neutron-rich regions.
The lifetime of the 11/21+ state in the Sb131 nucleus was measured at the LOHENGRIN spectrometer of the Institut Laue-Langevin via neutron-induced fission of U235 using γ-ray fast-timing techniques. The obtained value of T1/2=3(2) ps, at the edge of the sensitivity of the experimental method, is the first result for the 11/21+ state half-life in neutron-rich Sb isotopes. The corresponding quadrupole reduced transition probability to the ground state is B(E2)=1.4−0.6+1.5W.u., indicating a noncollective nature of this state. Realistic shell-model calculations performed in a large valence space reproduce well the experimental value and point to a dominant 2+(Sn130)⊗πg7/2 configuration for the 11/21+ state, as expected in a weak-coupling scenario. At the same time, the sum of the quadrupole strength of the multiplet states is predicted to exceed the one of the Sn130 core as a consequence of the equal contribution of the proton and the proton-neutron quadrupole matrix elements, pointing to possible development of collectivity already in the close neighborhood of Sn132.
The atomic nucleus comprises protons and neutrons, with complex quantum many-body structure, arising from these two kinds of constituents and also from complicated forces binding them (nuclear forces). Nevertheless, atomic nuclei exhibit simple and beautiful features, unexpected from the complexities. The gap between the complexity and the simplicity/beauty can be filled by the shell model, the nuclear physics terminology of configuration Interaction (CI) approach. This article presents basic ideas and formulations of the shell model, up to recent developments. The computational aspect is quite crucial for the shell model, because the Schrödinger equation has to be solved with the nuclear forces and the two kinds of fermions. The traditional approach based on direct diagonalization of Hamiltonian matrix has been used since the 1950s with technical improvements. Besides this approach, a different CI methodology, Monte Carlo shell model (MCSM), was proposed in the 1990s and has been developed. These methodologies are explained in a pedagogical way. Ni and Cu isotopes are discussed as examples of various appearances of low-lying deformed states coexisting with spherical ground states. The T-plot analysis is explained as a unique way to unveil nuclear shapes contained in the MCSM wave functions. The original version of the shell model was conceived by Mayer and Jensen. Recent studies show definite departures from this picture: the evolution of the shell structure, or the shell evolution, in exotic nuclei. The shell evolution is briefly sketched, with a certain emphasis on the prominent role of the tensor force. The shell evolution is extended from a single-particle-type feature to highly correlated many-body features such as the collective motion leading to surface deformation, as referred to as type II shell evolution. Thus, this article overviews the basic and contemporary facets of the nuclear shell model in simple terms.
The structure of Ni64, the heaviest stable Ni isotope, has been investigated via high-statistics, multistep safe Coulomb excitation to search for shape coexistence, a phenomenon recently observed in neutron-rich Ni66 and Ni70 as well as in doubly magic, N=40, Ni68. The study was motivated by recent, state-of-the-art Monte Carlo shell-model calculations (MCSM), where a Hamiltonian with effective interactions incorporating the monopole tensor force predicts the existence of shape coexistence, also in the lower-mass Ni62,64 isotopes. A set of transition and static E2 matrix elements for both yrast and near-yrast structures was extracted from the differential Coulomb excitation cross sections. From comparisons between the new results and MCSM as well as other shell-model calculations, a clearer picture of the structure of Ni64 emerges. Specifically, the low-spin states are shown to be dominated by proton and neutron excitations mainly within the fp shell, with minimal contribution from the g9/2 shape-driving neutron orbital. The agreement between experimental data and MCSM results indicates a small oblate deformation for the 02+ level and a spherical shape for the 03+ state. In addition, the small upper limit determined for the B(E2) probability of a transition associated with the decay of the recently observed 3463-keV, 04+ state agrees with its proposed assignment to a prolate shape, herewith providing first evidence for triple shape coexistence in a stable Ni isotope.
The ground-state properties of neutron-rich exotic Na and Mg isotopes with even numbers of neutrons, N, are studied up to drip lines. The shell-model calculations with an ab initio effective nucleon-nucleon interaction reported by Tsunoda, Otsuka, Takayanagi et al. [Nature (London) 587, 66 (2020)] are extended to observables such as magnetic dipole and electric quadrupole moments, and charge and matter radii. Good agreements with experimental data are found, and predictions are shown up to drip lines. A prescription to extract the deformation parameters for the eigenstates of the Monte Carlo shell model is presented, and the obtained values are used to calculate charge and matter radii. The increase of these radii from the droplet model is described as the consequences of the varying deformation of the surface and the growing neutron excitations or occupations in the pf shell, consistent with the drip-line mechanism presented in the above reference. The neutron skin thickness is shown to be about 0.1 fm for N=20, which can be compared to the value for Pb208 in an A1/3 scaling. The relation of the neutron skin thickness to the electromagnetic moments is discussed for an exotic nucleus, Na31.
Excited states in the Zn66 nucleus were populated via a Fe56(C12,2pγ) fusion-evaporation reaction at a beam energy of ≈62 MeV. The deexciting γ rays were detected using the Indian National Gamma Array (INGA). The level scheme of the Zn66 nucleus has been updated by placing several new γ rays as well as by assigning the spin and parity of various excited states from the present spectroscopic results. The microscopic structure of the observed states have been investigated in the light of large shell-model calculations. The shape of this nucleus in the low-spin regime has been studied under the framework of total Routhian surface (TRS) calculations. The lifetime of first 3− state at 2826 keV is experimentally measured using the Doppler-shift attenuation method and the deduced B(E1) value indicates the presence of octupole collectivity in this nucleus.
A workshop on The Next Generation Gamma-Ray Source sponsored by the Office of Nuclear Physics at the Department of Energy, was held November 17-19, 2016 in Bethesda, Maryland. The goals of the workshop were to identify basic and applied research opportunities at the frontiers of nuclear physics that would be made possible by the beam capabilities of an advanced laser Compton beam facility. To anchor the scientific vision to realistically achievable beam specifications using proven technologies, the workshop brought together experts in the fields of electron accelerators, lasers, and optics to examine the technical options for achieving the beam specifications required by the most compelling parts of the proposed research programs. An international assembly of participants included current and prospective γ -ray beam users, accelerator and light-source physicists, and federal agency program managers. Sessions were organized to foster interactions between the beam users and facility developers, allowing for information sharing and mutual feedback between the two groups. The workshop findings and recommendations are summarized in this whitepaper.
A systematic study of shapes in Ni [Formula: see text] isotopes has been made in the Relativistic–Hartree–Bogoliubov (RHB) formalism with two types of density-dependent NN interactions which are based on the range of meson-exchange. The constraint calculations assuming the axial and triaxial-symmetry predict the shape isomerism in the case of [Formula: see text] isotopes. Significant jumps at [Formula: see text] in the binding energy per nucleon (BE/A) and in the [Formula: see text] correspond to the neutron shell closure, and [Formula: see text] as doubly magic nuclei. The present calculation supports the recently reported calculations using the non-relativistic Hartree–Fock (HF) Skyrme SIII [1] interaction predicting the importance of tensor parameter in order to reproduce the experimental findings of the proton level crossing at [Formula: see text]. The results obtained are in agreement with experiment and with other theoretical studies.
The triaxial nature of low-lying rotational bands of Er166 is presented from the viewpoint of the Bohr Hamiltonian and from that of many-fermion calculations by the Monte Carlo shell model and the constrained Hartree-Fock method with projections. A recently proposed novel picture of those bands suggests definite triaxial shapes of those bands, in contrast to the traditional view with the prolate ground-state band and the γ-vibrational excited band. Excitation level energies and E2 transitions can be described well by the Bohr Hamiltonian and by the many-fermion approaches, where rather rigid triaxiality plays vital roles, although certain fluctuations occur in shell-model wave functions. Based on the potential energy surfaces with the projections, we show how the triaxial rigidity appears and what the softness of the triaxiality implies. The excitation to the so-called double γ-phonon state is discussed briefly.
The region of neutron-rich Cr isotopes has garnered much attention in recent years due to a rapid onset of collectivity near neutron number N=40. We report here on the first γ-ray spectroscopy beyond the (41+) state in Cr62,64, using nucleon removal reactions from several projectiles within a rare-isotope beam cocktail. A candidate for the 6+ state in Cr64 is presented as well as one for, possibly, the second excited 0+ state in Cr62. The results are discussed in comparison to the LNPS shell-model predictions that allow for neutron excitations across the N=40 harmonic oscillator gap into the g9/2 and d5/2 orbitals. The calculated level schemes for Cr62,64 reveal intriguing collective structures. From the predicted neutron particle-hole character of the low-lying states in these Cr isotopes, Cr62 emerges as a transitional system on the path to the center of the N=40 island of inversion.
An extended investigation of the low-spin structure of the Ni65 nucleus was performed at the Institut Laue-Langevin, Grenoble, France, via the neutron capture reaction Ni64(n,γ)Ni65, using the Fission Product Prompt Gamma-Ray Spectrometer High-Purity Ge array. The level scheme of Ni65 was significantly expanded, with two new levels and 87 newly found transitions. Angular correlation analyses were also performed, allowing us to assign spins and parities for a number of states and to determine multipolarity mixing ratios for selected γ transitions. The low-energy part of the experimental level scheme (up to about 1.4 MeV) was compared with Monte Carlo shell-model calculations, which predict spherical shapes for all states, apart from the 9/2+ and the second excited 1/2− states of oblate deformation.
The g factor of the \(12^+\) K-isomer in \(^{174}\)W has been measured by means of the time-differential perturbed angular distribution technique as \(g(12^+)=+0.304(11)\). In addition, the half-life of the isomer has been remeasured as \(T_{1/2}(12^+)=124(8)\) ns, in agreement with the literature value and confirming the anomalous hindrance F of the E2 transition to the \(10^+\) level of the ground state band with respect to the \(\gamma \)-tunnelling model prediction. The measured g factor has been compared with estimates based on experimental g factors from odd-mass isotopes in the same mass region and with Nilsson model calculations. The results establish unique features of the \(12^+\) K-isomer in \(^{174}\)W, which can possess a non-pure intrinsic configuration and/or can be characterised by values of the intrinsic quadrupole moment \(Q_0\) and the rotational g factor \(g_R\) significantly different with respect to the majority of K-isomers at mass \(A \approx 180\).
Strongly correlated many-body systems often display the emergence of simple patterns and regular behaviour of their global properties. Phenomena such as clusterization, collective motion and appearance of shell structures are commonly observed across different size, time, and energy scales in our universe. Although at the microscopic level their individual parts are described by complex interactions, the collective behaviour of these systems can exhibit strikingly regular patterns. This contribution provides an overview of the experimental signatures that are commonly used to identify the emergence of shell structures and collective phenomena in distinct physical systems. Examples in macroscopic systems are presented alongside features observed in atomic nuclei. The discussion is focused on the experimental trends observed for exotic nuclei in the vicinity of nuclear closed-shells, and the new challenges that recent experiments have posed in our understanding of emergent phenomena in nuclei.
New physics opportunities are opening up by the Advanced Gamma Tracking Array, AGATA, as it evolves to the full 4\(\pi \) instrument. AGATA is a high-resolution \(\gamma \)-ray spectrometer, solely built from highly segmented high-purity Ge detectors, capable of measuring \(\gamma \) rays from a few tens of keV to beyond 10 MeV, with unprecedented efficiency, excellent position resolution for individual \(\gamma \)-ray interactions, and very high count-rate capability. As a travelling detector AGATA will be employed at all major current and near-future European research facilities delivering stable and radioactive ion beams.
Two-neutron transfer reactions serve as an important tool for nuclear-structure studies in the neutron-rich part of the nuclear chart. In this paper, we report on the first experimental attempt to populate the excited states of¹⁴⁰Ba employing the 2n-transfer reaction¹³⁸Ba(¹⁸O,¹⁶O)¹⁴⁰Ba. ¹⁴⁰Ba is highly important, as it is placed on the onset of octupole correlations and the lifetimes of its excited states are completely unknown, with the sole exception of the first state. The experiment was carried out at the Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN–HH) in Magurele, Romania. Lower limits on the lifetimes of the ground state band up to the state are reported. Furthermore, relative cross-sections regarding the 2n-transfer reaction with respect to the fusion and the total inelastic reaction channels have been deduced. Further investigation directions of the nuclear structure of ¹⁴⁰Ba are also discussed.
In a two–neutron transfer experiment, performed in Bucharest in July 2016 at sub–Coulomb barrier energy,a photon decay hindered – solely – by a nuclear shape change was identified in the ⁶⁶ Ni nucleus. Such a rare process, at spin zero, was clearly observed before only in actinide nuclei in the 1970’s,where fission isomers were found. The experimental findings on ⁶⁶ Ni have been well reproduced by the Monte Carlo Shell Model Calculations of the Tokyo group, which predict a multifaceted scenario of coexistence of spherical, oblate and prolate shapes in neutron–rich Ni isotopes. The results on ⁶⁶ Ni encouraged a comprehensive gamma–spectroscopy investigation of neutron–rich Ni isotopes, in particular ⁶² Ni and ⁶⁴ –Ni, at IFIN–HH (Bucharest), IPN Orsay and ILL (Grenoble), employing different reaction mechanisms to pin down the wave function composition of selected excited states. The aim is to shed light on the microscopic origin of deformation in neutron–rich Ni nuclei, possibly locating other examples of “shape–isomer–like” structures inthis region.
The couplings between particles and vibrations in atomic nuclei play a key role in the understanding of various nuclear properties, as it has been highlighted along several decades. In this contribution, after a short survey of the early discoveries of particle-phonon multiplets around the ²⁰⁸Pb region, we review recent experiments and theoretical attempts to understand low-energy spectra of odd-nuclei close to magic and semi-magic cores, where particle-phonon coupling phenomena play a significant role. The focus will be on nuclei around ⁴⁸Ca , ¹³²Sn , ²⁰⁸Pb and neutron-rich Ni isotopes. Special emphasis will be given to experimental techniques based on high-resolution \( \gamma\)-spectroscopy and to recent theoretical developments aimed at disentangling particle-phonon coupled states and other more hybrid configurations, using the Hybrid Configuration Mixing model that has been recently proposed by the Milano group.
The underlying structure of low-lying collective bands of atomic nuclei is discussed from a novel perspective on the interplay between single-particle and collective degrees of freedom, by utilizing state-of-the-art configuration interaction calculations on heavy nuclei. Besides the multipole components of the nucleon-nucleon interaction that drive collective modes forming those bands, the monopole component is shown to control the resistance against such modes. The calculated structure of Sm154 corresponds to the coexistence between prolate and triaxial shapes, while that of Er166 exhibits a deformed shape with a strong triaxial instability. Both findings differ from traditional views based on β/γ vibrations. The formation of collective bands is shown to be facilitated from a self-organization mechanism.
The level structures of ⁷⁰Co and ⁷⁰Ni, populated from the β decay of ⁷⁰Fe, have been investigated using β-delayed γ-ray spectroscopy following in-flight fission of a ²³⁸U beam. The experimental results are compared to Monte-Carlo Shell-Model calculations including the orbitals. The strong population of a state at 274 keV in ⁷⁰Co is at variance with the expected excitation energy of ∼1 MeV from near spherical single-particle estimates. This observation indicates a dominance of prolate-deformed intruder configurations in the low-lying levels, which coexist with the normal near spherical states. It is shown that the β decay of the neutron-rich isobars from the new island of inversion to the closed-shell regime progresses in accordance with a newly reported type of shell evolution, the so-called Type II, which involves many particle-hole excitations across energy gaps.
Shape coexistence near closed-shell nuclei, whereby states associated with deformed shapes appear at relatively low excitation energy alongside spherical ones, is indicative of the rapid change in structure that can occur with the addition or removal of a few protons or neutrons. Near ⁶⁸Ni ( , ), the identification of shape coexistence hinges on hitherto undetermined transition rates to and from low-energy states. In 68,70Ni, new lifetimes and branching ratios have been measured. These data enable quantitative descriptions of the states through the deduced transition rates and serve as sensitive probes for characterizing their nuclear wave functions. The results are compared to, and consistent with, large-scale shell-model calculations which predict shape coexistence. With the firm identification of this phenomenon near ⁶⁸Ni, shape coexistence is now observed in all currently accessible regions of the nuclear chart with closed proton shells and mid-shell neutrons.
We first review the shell evolution in exotic nuclei driven by nuclear forces. We then demonstrate that the underlying mechanism played by the balance of the tensor and central components in the effective nucleon–nucleon interaction is crucial when describing shape coexistence. This effect will be referred to as type II shell evolution, while the shell evolution passing through a series of isotopes or isotones is denoted as type I. We describe type II shell evolution in some detail for the case of the 68Ni nucleus as an example. We present how the fission dynamics can be related to enhanced deformation triggered by type II shell evolution, at its initial stage. It is suggested that the island of stability may be related to the suppression of this mechanism.
The internal-conversion and internal-pair-production decays of the first excited 0+ state in Ni68 are studied following the β decay of Co68. A novel experimental technique, in which the ions of Co68 were implanted into a planar germanium double-sided strip detector and which required digital pulse processing, is developed. The values for the energy of the first excited 0+ state and the electric monopole transition strength from the first excited 0+ state to the ground state in Ni68 are determined to be 1605(3) keV and 7.6(4)×10-3, respectively. Comparisons of the experimental results to Monte Carlo shell-model calculations suggest the coexistence between a spherical ground state and an oblate first excited 0+ state in Ni68.
The shapes of neutron-rich exotic Ni isotopes are studied. Large-scale shell
model calculations are performed by advanced Monte Carlo Shell Model (MCSM) for
the $pf$-$g_{9/2}$-$d_{5/2}$ model space. Experimental energy levels are
reproduced well by a single fixed Hamiltonian. Intrinsic shapes are analyzed
for MCSM eigenstates. Intriguing interplays among spherical, oblate, prolate
and gamma-unstable shapes are seen including shape fluctuations, $E$(5)-like
situation, the magicity of doubly-magic $^{56,68,78}$Ni, and the coexistence of
spherical and strongly deformed shapes. Regarding the last point, strong
deformation and change of shell structure can take place simultaneously, being
driven by the combination of the tensor force and changes of major
configurations within the same nucleus.
We present a newly enhanced version of the Monte Carlo shell-model (MCSM) method by incorporating the conjugate gradient method
and energy-variance extrapolation. This new method enables us to perform large-scale shell-model calculations that the direct
diagonalization method cannot reach. This new-generation framework of the MCSM provides us with a powerful tool to perform
very advanced large-scale shell-model calculations on current massively parallel computers such as the K computer. We discuss
the validity of this method in ab initio calculations of light nuclei, and propose a new method to describe the intrinsic
wave function in terms of the shell-model picture. We also apply this new MCSM to the study of neutron-rich Cr and Ni isotopes
using conventional shell-model calculations with an inert 40Ca core and discuss how the magicity of N=28,40,50 remains or is broken.
The neutron-rich nuclei, 66Co, 68Co, and 70Co were produced using a laser-ionization isotope-separation
on-line method. The resulting �-delayed � decay was studied. The half-life of 66Co is measured to be 0.18�1�
s. Two �-decaying states are identified in 68Co with half-lives of 0.23�3� and 1.6�3� s. In addition, two
�-decaying states are observed in 70Co with half-lives of 0.12�3� and 0.50�18� s. From the � decay of these
states in 66,68,70Co, many new excited levels are established in 66Ni, 68Ni, and 70Ni. These results are compared to the valence mirror nuclei in the N�50 region as well as with shell-model calculations. It can be concluded that collective excitations appear to play an increasingly important role with increasing occupation of the � g9/2 orbital.
We discuss a variational calculation for nuclear shell-model calculations and
propose a new procedure for the energy-variance extrapolation (EVE) method
using a sequence of the approximated wave functions obtained by the variational
calculation. The wave functions are described as linear combinations of the
parity, angular-momentum projected Slater determinants, the energy of which is
minimized by the conjugate gradient method obeying the variational principle.
The EVE generally works well using the wave functions, but we found some
difficult cases where the EVE gives a poor estimation. We discuss the origin of
the poor estimation concerning shape coexistence. We found that the appropriate
reordering of the Slater determinants allows us to overcome this difficulty and
to reduce the uncertainty of the extrapolation.
We propose an extrapolation method utilizing energy variance in the Monte Carlo shell model in order to estimate the energy eigenvalue and observables accurately. We derive a formula for the energy variance with deformed Slater determinants, which enables us to calculate the energy variance efficiently. The feasibility of the method is demonstrated for the full $pf$-shell calculation of $^{56}$Ni, and the applicability of the method to a system beyond current limit of exact diagonalization is shown for the $pf$+$g_{9/2}$-shell calculation of $^{64}$Ge. Comment: 4 pages, 4figures
Understanding the fundamental excitations of many-fermion systems is of significant current interest. In atomic nuclei with even numbers of neutrons and protons, the low-lying excitation spectrum is generally formed by nucleon pair breaking and nuclear vibrations or rotations. However, for certain numbers of protons and neutrons, a subtle rearrangement of only a few nucleons among the orbitals at the Fermi surface can result in a different elementary mode: a macroscopic shape change. The first experimental evidence for this phenomenon came from the observation of shape coexistence in 16O (ref. 4). Other unexpected examples came with the discovery of fission isomers and super-deformed nuclei. Here we find experimentally that the lowest three states in the energy spectrum of the neutron deficient nucleus 186Pb are spherical, oblate and prolate. The states are populated by the alpha-decay of a parent nucleus; to identify them, we combine knowledge of the particular features of this decay with sensitive measurement techniques (a highly efficient velocity filters with strong background reduction, and an extremely selective recoil-alpha-electron coincidence tagging methods). The existence of this apparently unique shape triplet is permitted only by the specific conditions that are met around this particular nucleus.
Large-scale shell-model calculations predict that the region of deformation which comprises the heaviest chromium and iron isotopes at and beyond N=40 will merge with a new one at N=50 in an astonishing parallel to the N=20 and N=28 case in the neon and magnesium isotopes. We propose a valence space including the full pf shell for the protons and the full sdg shell for the neutrons, which represents a comeback of the the harmonic oscillator shells in the very neutron- rich regime. The onset of deformation is understood in the framework of the algebraic SU(3)-like structures linked to quadrupole dominance. Our calculations preserve the doubly magic nature of the ground state of Ni78, which, however, exhibits a well-deformed prolate band at low excitation energy, providing a striking example of shape coexistence far from stability. This new IOI adds to the four well-documented ones at N=8, 20, 28, and 40.
The ROmanian array for SPectroscopy in HEavy ion REactions (ROSPHERE) has been designed as a multi-detector setup dedicated to γ-ray spectroscopy studies at the Bucharest 9 MV Tandem accelerator. Consisting of up to 25 detectors (either Compton suppressed HPGe detectors or fast LaBr3(Ce) scintillator detectors) together with a state of the art plunger device, ROSPHERE is a powerful tool for lifetime measurements using the Recoil Distance Doppler Shift (RDDS) and the in-beam Fast Electronic Scintillation Timing (FEST) methods. The array's geometry, detectors, electronics and data acquisition system are described. Selected results from the first experimental campaigns are also presented.
The rapid shape change in Zr isotopes near neutron number $N$=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its $0g_{9/2}$ orbit, and is shown to be a quantum phase transition. Monte Carlo shell-model calculations are carried out for Zr isotopes of $N$=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in a good agreement with experiments, depicting various shapes in going from $N$=50 to 70. Novel coexistence of prolate and triaxial shapes is suggested.
Background: Type II shell evolution has recently been identified as a microscopic cause for nuclear shape coexistence. Purpose: Establish a low-lying rotational band in 96-Zr. Methods: High-resolution inelastic electron scattering and a relative analysis of transition strengths are used. Results: The B(E2; 0_1^+ -> 2_2^+) value is measured and electromagnetic decay strengths of the secdond 2^+ state are deduced. Conclusions: Shape coexistence is established for 96-Zr. Type II shell evolution provides a systematic and quantitative mechanism to understand deformation at low excitation energies.
In recent models, the neutron-rich Ni isotopes around N=40 are predicted to exhibit multiple low-energy excited 0+ states attributed to neutron and proton excitations across both the N=40 and Z=28 shell gaps. In Ni68, the three observed 0+ states have been interpreted in terms of triple shape coexistence between spherical, oblate, and prolate deformed shapes. In the present work a new (02+) state at an energy of 1567 keV has been discovered in Ni70 by using β-delayed, γ-ray spectroscopy following the decay of Co70. The precipitous drop in the energy of the prolate-deformed 0+ level between Ni68 and Ni70 with the addition of two neutrons compares favorably with results of Monte Carlo shell-model calculations carried out in the large fpg9/2d5/2 model space, which predict a 02+ state at 1525 keV in Ni70. The result extends the shape-coexistence picture in the region to Ni70 and confirms the importance of the role of the tensor component of the monopole interaction in describing the structure of neutron-rich nuclei.
The development and limitations of the conventional shell model
calculations are mentioned. In order to overcome the limitations, the
Quantum Monte Carlo Diagonalization (QMCD) method has been proposed. The
basic formulation and features of the QMCD method are presented as well
as its application to the nuclear shell model, as referred to as Monte
Carlo Shell Model (MCSM). The MCSM provides us with a breakthrough in
the shell model calculation: the structure of low-lying states can be
studied with realistic interactions for a wide, nearly unlimited
basically, variety of nuclei. Thus, the MCSM will contribute
significantly to the physics to be developed by means of Radioactive Ion
Beams. Applications to 56Ni, Ba isotopes and N ~ 20 exotic
nuclei far from the β stability line are mentioned.
Excited states in 64Ni, 66Ni, and 68Ni were populated in quasielastic and deep-inelastic reactions of a 430-MeV 64Ni beam on a thick 238U target. Level schemes including many nonyrast states were established up to respective excitation energies of 6.8, 8.2, and 7.8 MeV on the basis of γ-ray coincidence events measured with the Gammasphere array. Spin-parity assignments were deduced from an angular-correlation analysis and from observed γ-decay patterns, but information from earlier γ-spectroscopy and nuclear-reaction studies was used as well. The spin assignments for nonyrast states were supported further by their observed population pattern in quasielastic reactions selected through a cross-coincidence technique. Previously established isomeric-state decays in 66Ni and 68Ni were verified and delineated more extensively through a delayed-coincidence analysis. A number of new states located above these long-lived states were identified. Shell-model calculations were carried out in the p3/2f5/2p1/2g9/2 model space with two effective interactions using a 56Ni core. Satisfactory agreement between experimental and computed level energies was achieved, even though the calculations indicate that all the states are associated with rather complex configurations. This complexity is illustrated through the discussion of the structure of the negative-parity states and of the M1 decays between them. The best agreement between data and calculations was achieved for 68Ni, the nucleus where the calculated states have the simplest structure. In this nucleus, the existence of two low-spin states reported recently was confirmed as well. Results of the present study do not indicate any involvement of collective degrees of freedom and confirm the validity of a shell-model description in terms of neutron excitations combined with a closed Z = 28 proton shell. Further improvements to the calculations are desirable.
We study the development of collectivity in the neutron-rich nuclei around N=40, where the experimental and theoretical evidence suggest a rapid shape change from the spherical to the rotational regime, in analogy to what happens at the island of inversion surrounding ³¹Na. Theoretical calculations are performed within the interacting shell-model framework in a large valence space, based on a Ca core, which encompasses the full pf shell for the protons and the 0f, 1p, 1p, 0g, and 1d orbits for the neutrons. The effective interaction is based on a G matrix obtained from a realistic nucleon-nucleon potential whose monopole part is corrected empirically to produce effective single-particle energies compatible with the experimental data. We find a good agreement between the theoretical results and the available experimental data. We predict the onset of deformation at different neutron numbers for the various isotopic chains. The maximum collectivity occurs in the chromium isotopes where the large deformation regime already starts at N=38. The shell evolution responsible for the observed shape changes is discussed in detail, in parallel to the situation in the N=20 region.
The existence of the ..gamma.. branch in the decay of the ²³â¸U shape isomer is confirmed by the observation of an E0 transition between the isomer and the ground state. The data are consistent with the excitation energy of 2558 keV, spin of 0/sup +/, and half-life of roughly-equal200 ns of the isomer.
First experimental evidence for a low-lying Jpi=0+ excited state in 192-198Pb is obtained by study of the beta decay of mass-separated Bi isotopes. It is shown that such excited states correspond to deformed two-particle, two-hole configurations.
Experimental and theoretical investigations of recent years point to the existence of a new type of isomerism of atomic nuclei, due to the strong difference between the shapes of the nuclei in the initial and final stages.
The low-energy level structures for the neutron-rich Co isotopes at N = 39 and N = 41 are constructed following the beta decay of the respective even-even Fe isotopes. Spin and parity assignments of the lowest energy populated state in 66Co and 68Co are consistent with a 1+ spin and parity assignment and attributed to the coupling of the deformed proton configurations identified in 67Co and deformed neutron configurations inferred from neighboring Fe isotones. Comparisons along the N = 39 and N = 41 isotonic chains reveal a similarity in the structures of the Co and Mn isotopes.
The low-spin level scheme of 68Ni was investigated with the Gammasphere array following reactions between a 70Zn beam and 238U, 208Pb, and 197Au targets. Spin assignments for some states have been verified through γ-ray angular correlations, including the 0+ assignment for the 2511-keV level. Two previously unknown states at 3302 and 3405 keV have been identified. No evidence was found for a recently reported 216-ns, 0+ isomer at 2202 keV that was attributed to a proton two-particle, two-hole intruder configuration, despite experimental conditions similar to those used in the measurement reporting its discovery.
A small proportion of atomic nuclei can form highly excited metastable states, or isomers. Of particular interest is a class of isomers found in deformed axially symmetric nuclei; these isomers are among the longest-lived and have the potential to reach the highest energies. By probing their properties, insights into nuclear structure have been gained. The possibility of stimulated isomer decay may ultimately lead to new forms of energy storage and |[gamma]|-ray lasers.
Delayed gamma -particle coincidences following the reaction 235U(d,p)236U at Ed=11 MeV were recorded in order to search for a gamma decay of the 236U( tau =165 ns) shape isomer. An experimental upper limit was determined for the branching ratio ranging from Gamma gamma / Gamma f<4.5 at Egamma =0.5 MeV to gamma gamma / Gamma f<1.5 at Egamma =2.5 MeV for a single gamma cascade. This result for 236U appears to be at variance with the observed gamma branching intensity of the 238U shape isomer.
The experimental techniques of measuring the mean lifetimes tau of excited nuclear states is reviewed. Emphasis is put on direct measurements of tau in the region 10-18-10-6 s, especially on techniques involving the observation of Doppler energy shifts of gamma -rays. Indirect methods of obtaining tau by measuring the widths or partial widths are discussed. Comparisons are made of the applicability, accuracy and reliability of the different experimental techniques.
Shape coexistence in doubly even nuclei is reviewed. Two main theoretical approaches are presented. The first is essentially the shell model with the excitation of pairs of protons and/or neutrons across closed shells or subshells together with a residual proton-neutron interaction. The second is the deformed mean-field approach. The first is broadly defined so that it includes various truncation schemes to the shell model including generalized seniority and the interacting boson model. The presentation of the theory has two main aims: to provide a framework into which the majority of theoretical studies of shape coexistence can be placed and to provide a framework within which a unified view can be discussed. Selected experimental data are shown from 16O to 238U. Our criteria for selection emphasize detailed spectroscopic evidence (“fingerprints”) for coexisting shapes.
A new internal conversion coefficient database, BrIcc has been developed which integrates a number of tabulations on internal conversion electron (ICC) and electron–positron pair conversion coefficients (IPC), as well as Ω(E0) electronic factors. A critical review of general formulae and procedures to evaluate theoretical ICC and IPC values are presented, including the treatment of uncertainties in transition energy and mixing ratio in accordance with the Evaluated Nuclear Structure Data File. The default ICC table, based on the Dirac–Fock calculations using the so called “Frozen Orbital” approximation, takes into account the effect of atomic vacancies created in the conversion process. The table has been calculated for all atomic shells and to cover transition energies of 1–6000 keV and atomic numbers of Z=5–110. The software tools presented here are well suited for basic nuclear structure research and for a range of applications.
The (t, p) reactions on the even isotopes of nickel have been studied at a bombarding energy of 12 MeV using the Aldermaston multiangle magnetic spectrograph and tandem Van de Graaff. States of the final nuclei were identified up to excitation energies of about 6 MeV and Q-values were measured.From the shapes of the proton angular distributions a number of states with Jπ = 0+, 2+, 3− and 4+ were identified. Where comparison is possible the agreement with previous spin and parity assignments is good.The present results on 66Ni represent the first investigation of the states of this nucleus. We have identified 59 levels up to an excitation energy of 6.7 MeV and have made 13 assignments of spin and parity.The (t, p) cross sections to the nickel ground states are larger by factors of 5 to 10 than the yields to any of the excited states. The 2+ and 3− vibrational states receive an appreciable strength. As expected, no strongly populated 0+ excited states were observed.
Microscopic Hartree-Fock plus BCS calculations in three-dimensional coordinate space are performed to obtain potential energy surfaces in order to analyse shape isomerism in mass regions other than the well-documented fission isomers in the actinides. Many isotopes of platinum, mercury and osmium exhibit a second minimum with a large deformation and are thus candidates for shape isomerism. The same feature also occurs around the 68Ni nucleus. The most promising candidates for experimental verification are delineated.
The development, present status and future perspectives of the Monte Carlo shell model are discussed. The development and limitation of the conventional shell model calculations are shown, and stochastic approaches are introduced. As one of such approaches, the Quantum Monte Carlo Diagonalization (QMCD) method has been proposed. The formulation of the QMCD method is presented with an illustrative example. While the QMCD method is a general method for solving the quantum many-body interacting systems, its application to the nuclear shell model is referred to as the Monte Carlo Shell Model (MCSM). A test of the MCSM is presented, confirming the feasibility of the MCSM. The MCSM represents a breakthrough in shell model calculations: the level structure of low-lying states can be studied with realistic interactions for a wide, probably basically unlimited, variety of nuclei. The MCSM has two major characteristic features: the feasibility of including many single-particle orbits and the capability of handling many valence nucleons. We present some applications for which these features played essential roles. Such applications include the structure of exotic nuclei around the neutron number 20, a unified description of spherical to superdeformed states in nuclei around 56Ni, a new effective interaction for pf-shell nuclei and their unified description, and microscopic studies on the spherical-deformed shape phase transition and on the γ-unstable deformation.
Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ2(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ2(E0) and isotopic shifts.
The boundary between the grazing deep inelastic collisions and the quasi-fission or fusion reactions is studied though classical, semiclassical and WKB approximations. Although transfer reactions are responsible for the main part of the large energy loss in grazing collisions that come close to the barrier, the excitation energy is more than compensated by an additional attraction, due to polarization, so that the projectile reaches the barrier almost as if no reactions had taken place. At some distance outside the Coulomb barrier an instability occurs towards a merging of the surfaces, which also appears if no Coulomb barrier exists. Fluctuations in energy, partly due to transfer reactions, but mainly to the zero-point motion of the low-lying surface modes give an important spread in the capture angular momentum.
To determine which nuclei may exhibit shape isomerism, we use a well-benchmarked macroscopic-microscopic model to calculate potential-energy surfaces as functions of spheroidal (epsilon{2}), hexadecapole (epsilon{4}), and axial-asymmetry (gamma) shape coordinates for 7206 nuclei from A=31 to A=290. We analyze these and identify the deformations and energies of all minima deeper than 0.2 MeV. These minima may correspond to characteristic experimentally observable shape-isomeric states. Shape isomers mainly occur in the A=80 region, the A=100 region, and in an extended region centered around (208)Pb. We compare our model to experimental results for Kr isotopes. Moreover, in a plot versus N and Z we show for each of the 7206 nuclei the calculated number of minima. The results reveal one fairly unexplored region of shape isomerism, which is experimentally accessible, namely the region northeast of (82)(208)Pb.
This theoretical work represents the first stage in our efforts to establish an extensive list of nonfissile even-even nuclei located inside or near the valley of stability which might develop shape isomers. Our selection relies upon whether a secondary minimum takes place along an elongation axis in the potential energy surfaces of nuclei spread over the mass region A<208. These surfaces are determined through a joint use of the Hartree-Fock-Bogoliubov and Strutinsky methods. More than seventy nuclei located inside the region 40<A<208 are suggested as possible candidates for shape isomerism.
Secondary minima in the potential-energy surfaces of even-even nuclei are searched for through nonaxial Hartree-Fock-Bogoliubov calculations based on a finite-range, density-dependent effective force. This study covering the mass region 64/lt//ital A//lt/208 is intended to select nonfissile nuclei which would develop shape isomers. Results are presented for nuclei which seem to be the most interesting candidates for experimental investigations.
A new isomeric 0(+) state was identified as the first excited state in the self-conjugate (N=Z) nucleus 72Kr. By combining for the first time conversion-electron and gamma-ray spectroscopy with the production of metastable states in high-energy fragmentation, the electric-monopole decay of the new isomer to the ground state was established. The new 0(+) state is understood as the band head of the known prolate rotational structure, which strongly supports the interpretation that 72Kr is one of the rare nuclei having an oblate-deformed ground state. This observation gives in fact the first evidence for a shape isomer in a N=Z nucleus.
We present fission-barrier-height calculations for nuclei throughout the periodic table based on a realistic macroscopic-microscopic model. Compared to other calculations (i) we use a deformation space of a sufficiently high dimension, sampled densely enough to describe the relevant topography of the fission potential, (ii) we unambiguously find the physically relevant saddle points in this space, and (iii) we formulate our model so that we obtain continuity of the potential energy at the division point between a single system and separated fission fragments or colliding nuclei, allowing us to (iv) describe both fission-barrier heights and ground-state masses throughout the periodic table.
- C M Dobson
- A Šali
- M Karplus
C. M. Dobson, A. Šali, and M. Karplus, Angew. Chem. Int.
Ed. 37, 868 (1998).
- B Singh
- R Zywina
- R Firestone
B. Singh, R. Zywina, and R. Firestone, Nucl. Data Sheets
97, 241 (2002).