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Proton and neutron excitations in superdeformed Tb 150
Abstract
Two new superdeformed (SD) bands have been observed in 150Tb using the reaction 31P+124Sn and the GAMMASPHERE detector array. These new bands are interpreted as being excited SD configurations involving a proton and a neutron particle-hole excitation, respectively. The configurations are discussed in terms of the occupancy of high-N intruder orbitals. These data are used to provide information on (i) the contribution to the dynamic moments of inertia due to the occupation of specific orbitals, (ii) the deformation driving effects of the particle-hole states, and (iii) the consequences of these effects on pairing and band-crossings.
... SD states have been observed across a wide variety of nuclei. They were first observed in 152 Dy [114], and the mass region near A ≈ 150 has seen considerable experimental interest [114][115][116][117][118][119][120][121][122][123][124][125][126]. Even more study has been dedicated to the A ≈ 190 region, for example Refs. ...
In this work, the Dyson's equation formalism is outlined and applied to
several open quantum systems. These systems are composed of a core,
quantum-mechanical set of discrete states and several continua,
representing macroscopic systems. The macroscopic systems introduce
decoherence, as well as allowing the total particle number in the system
to change. Dyson's equation, an expansion in terms of proper self-energy
terms, is derived. The hybridization of two quantum levels is reproduced
in this formalism, and it is shown that decoherence follows naturally
when one of the levels is replaced by a continuum. The work considers
three physical systems in detail. The first, quantum dots coupled in
series with two leads, is presented in a realistic two-level model.
Dyson's equation is used to account for the leads exactly to all orders
in perturbation theory, and the time dynamics of a single electron in
the dots is calculated. It is shown that decoherence from the leads
damps the coherent Rabi oscillations of the electron. Several regimes of
physical interest are considered, and it is shown that the difference in
couplings of the two leads plays a central role in the decoherence
processes. The second system relates to the decay-out of superdeformed
nuclei. In this case, decoherence is provided by coupling to the
electromagnetic field. Two, three, and infinite-level models are
considered within the discrete system. It is shown that the two-level
model is usually sufficient to describe decay-out for the classic
regions of nuclear superdeformation. Furthermore, a statistical model
for the normal-deformed states allows extraction of parameters of
interest to nuclear structure from the two-level model. An explanation
for the universality of decay profiles is also given in that model. The
final system is a proposed small molecular transistor. The Quantum
Interference Effect Transistor is based on a single monocyclic aromatic
annulene molecule, with two leads arranged in the meta configuration.
This device is shown to be completely opaque to charge carriers, due to
destructive interference. This coherence effect can be tunably broken by
introducing new paths with a real or imaginary self-energy, and an
excellent molecular transistor is the result.
This document is part of Subvolume B3 'Tables of Excitations from Reactions with Charged Particles. Part 3: Z = 63 - 99' of Volume 19 'Nuclear States from Charged Particle Reactions'. It provides energy level parameters and branching ratios for atomic nuclei with atomic number Z = 65 (Terbium). The isotopes Tb-149, Tb-150, Tb-151, Tb-152, Tb-153, Tb-154, Tb-155, Tb-156, Tb-157, Tb-158, Tb-159, Tb-160, Tb-161, Tb-162, Tb-163 are considered.
The superdeformed bands in the A - 190 and 150 regions are systematically analyzed using four-parameter rotational spectra formula of Bohr-Mottelson's I(I+1) expansion. The result shows that the superdeformed bands in the A - 190 and 150 regions can be described very well with four-parameter ABCD-formula. The theoretical values of J(2) of most of nuclei accord with the experimental extracted values. The four-parameter value relation doesn't support the theoretical expected values of ab and Harris formula, but comparatively the theoretical expected value of ab formula agrees with the experimental extracted values better than that of Harris formula.
A high statistics experiment performed on Gd nuclei with the use of the EUROGAM II array resulted in the discovery of twelve new superdeformed (SD) bands. Three of them have been assigned to 148Gd and seven to 149Gd giving a total of thirteen SD bands now known in this last nucleus. The close relationship in transition energies between these bands and those in neighboring nuclei has been used to suggest configurations. Most of the new bands exhibit more or less pronounced irregularities in their dynamical moments of inertia with consequences on their identities with other bands.
In a recent experiment carried out with theEurogam Phase II γ-ray spectrometer three new superdeformed (SD) bands have been established in153Ho. The properties of these SD bands are discussed in terms of proton particle-hole excitations and are compared to the SD bands in the adjacent nuclei. This is the first observation of SD structures in aZ=67 nucleus.
The experimental results from the various reaction and decay studies leading to nuclides in the A=150A=150 mass chain have been reviewed. These data are summarized and presented, together with the adopted level schemes and properties, for the nuclides from Cs(Z=55) through Lu(Z=71). This evaluation replaces the previous evaluation by E. der Mateosian and J. K. Tuli (1995De28), which appeared in Nuclear Data Sheets 75, 827 (1995).
A detailed study of known and new SD bands in Tb isotopes has been performed with the use of the EUROBALL IV γ-ray array. The high-statistics data set has allowed for the extension of known SD bands at low and high spins by new γ-ray transitions. These transitions, as it turns out, correspond to the rotational frequencies where the principal superdeformed gaps (Z=66,N=86) close giving rise to up- or down-bending mechanisms. This enables to attribute the underlying theoretical configurations with much higher confidence as compared to the previous identifications. Five new SD bands have been discovered, three of them assigned to the 152Tb and the two others to the 151Tb nuclei. Nuclear mean-field calculations have been used to interpret the structure of known SD bands as well as of the new ones in terms of nucleonic configurations.
An enhanced population of the 149Gd yrast superdeformed band has been observed in the reaction 124Sn(31P,p5n) using the EUROBALL IV multidetector associated with an inner ball. This effect is explained as the consequence of a higher probability of trapping residual nuclei into the superdeformed well whose depth has been increased due to favorable temperature and of total energy and angular momentum selection with the inner ball.
Five superdeformed (SD) bands have been observed in 149Tb, using the Gammasphere spectrometer. The measurement was performed with a backed target to obtain lifetime information from a Doppler-shift attenuation method analysis. It is proposed that the yrast SD band corresponds to the 148Gd(yrast)⊗π63 intruder configuration. The first excited band (band 2) is found to be identical to the 150Tb yrast SD band. Band 3 is proposed to correspond to the π[301]1/2(α=-1/2)→[651]3/2(α=-1/2) proton-hole excitation coupled to the π64ν71(ν[651]1/2)-1 intruder configuration. Bands 4 and 5, the weakest SD bands seen in the present work, show similarities with band 3 and are most likely associated with a similar intruder configuration.
A method that generalizes the definition of identical bands was established. More than 100 available superdeformed bands were analyzed by means of the method and the number of identical bands as a function of criteria is presented. It is found that the quantization of incremental alignments depends very sensitively on the tolerance of the criterion for identical bands. The relation between the particle-rotor model and the present method is given.
In a recent experiment performed with the EUROGAM II γ-ray spectrometer three superdeformed (SD) bands have been established in 153Ho. The properties of these bands are discussed in terms of single-particle proton excitations and are compared with respect to the SD magic nucleus 152Dy. These results represent the first observation of SD structures in a holmium nucleus and provide further information on the proton orbitals lying above the Z=66 shell gap.
A high statistics experiment performed on Gd nuclei with the use of the EUROGAM II array resulted in the discovery of twelve new superdeformed (SD) bands. Three of them have been assigned to 148Gd and seven to 149Gd giving a total of thirteen SD bands now known in this last nucleus. The close relationship in transition energies between these bands and those in neighboring nuclei has been used to suggest configurations. Most of the new bands exhibit more or less pronounced irregularities in their dynamical moments of inertia with consequences on their identities with other bands.
The influence of band interaction on the spin predictions and the J (2) pattern of superdeformed (SD) bands are investigated. To make a reliable spin prediction using the best-fit method, the transitions with significant band mixing should be excluded from the least-squares fitting. Spin predictions for 15 SD bands in the A ~150 region are made. In particular, the spin of the lowest level of the first discovered high-spin SD band 152 Dy(1) is predicted to be I 0 = 26. A two-band mixing model is used to describe the irregular behaviour of J (2) with angular momentum. Two types of J (2) patterns are discussed. For the band-crossing case, the J (2) pattern in the band-crossing region is of a V (or inverse-V) type, which has been observed in both the A ~190 and 150 regions. For the band-mixing case characterized by a relatively weak band interaction, the J (2) pattern in the band-mixing region is of a W (or inverse-W) type, which was observed only in some SD bands in the A ~150 region.
Alpha particle spectra in coincidence both with normal deformed (ND) and superdeformed (SD) bands of 150Tb have been measured using the reaction 120Sn(37Cl,α3n) at 187 MeV bombarding energy. A clear difference is observed between the two spectra, that in coincidence with the SD states being shifted to lower energies. This effect is understood in terms of different angular momentum regions from which the ND and SD states orginate. The standard statistical model fails to describe the angular momentum dependence of the alpha particle energies.
One hundred and sixty-one rotational bands of superdeformed states in nuclei are considered on the basis of a model that admits
triplet Cooper pairing in superfluid nuclear matter. The behavior of the dynamical moment of inertia for such states is investigated
within this model, which is shown to comply well with available experimental data and to describe successfully the rotational
spectra of superdeformed states.
The cranked relativistic mean field approach is applied for a systematic investigation of superdeformed rotational bands observed in the A ∼ 140–150 mass region. The present investigation covers yrast and in some cases also excited superdeformed bands of all nuclei of this mass region in which such bands have been observed so far. Using the parameter set NL1, which has been adjusted ten years ago to a few spherical nuclei, reasonable agreement with experimental data is obtained throughout the mass region under investigation. It is shown that the calculated properties of superdeformed rotational bands such as the dependence of the dynamic moment of inertia J(2) with respect to the rotational frequency and the absolute value of the charge quadrupole moment Q0 depends sensitively on the number of occupied high-N intruder orbitals. This is agreement both with previous investigations within the cranked Nilsson-Strutinsky and the cranked Woods-Saxon-Strutinsky approaches and with available experimental data.
Single-particle properties at superdeformation are investigated within the Cranked Relativistic Mean Field (CRMF) theory on the example of superdeformed rotational bands observed in the A ∼ 140–150 mass region. Applying the effective alignment approach it is shown that CRMF theory provides a reasonable description of the alignment properties of the single-particle orbitals. The agreement with experiment is good in most of the cases. This suggests that many features of the observed superdeformed bands can be well understood in terms of an almost undisturbed single-particle motion. The stability of the results with respect to the parameterizations used in Relativistic Mean Field (RMF) theory is also investigated, employing some frequently used non-linear effective forces. It turns out, with the exception of the single-particle ordering in superdeformed minimum, that the dependence of the calculated observables on the parameterization is rather small.
The cranked relativistic mean field theory is applied for a detailed investigation of eight superdeformed rotational bands observed in151Tb. It is shown that this theory is able to reproduce reasonably well not only the dynamic moments of inertiaJ
(2) of the observed bands but also the alignment properties of the single-particle orbitals.
One of the superdeformed rotational bands in Hg194 has transition energies (rotational frequencies) that are equal within about 0.1% to those of the (only known) band in Hg192. This excited (two-quasiparticle) band in Hg194 has an aligned spin of (1.00±0.04)Latin small letter h with stroke relative to the very similar band in Hg192, suggesting an interpretation in terms of aligned pseudo (intrinsic) spin. The implied pseudospin symmetry may be a clue as to why the rotational frequencies are so similar.
Nine superdeformed bands in several nuclei of the mass-190 region all have transitions of the same or equivalent energies to within an average of about 1 keV almost identical. Furthermore, it is found that transitions of the same energy do not always connect levels of the same spin, indicating noncollective angular momentum alignments that are all very nearly integers (0, 1Latin small letter h with stroke, or 2Latin small letter h with stroke). Possible explanations involving pseudospin are discussed.
GAMMASPHERE is one of a new generation of gamma ray detector arrays. It consists of 110 Compton-supressed large volume Ge detectors. The design goal is to achieve high efficiency and peak-to-total value for four to five fold coincidence experiments. Such high-fold coincidence capability will provide new physics opportunities in areas such as high spins, transfer reactions, giant resonances, and astrophysics. The design of the detector and shield has been developed through extensive simulation calculations and an "electronic honeycomb" design was chosen. The electronics and computer systems are capable of operating at 50,000 event/sec. The design and development tasks are being carried out at several laboratories in the U.S. The project is expected to be funded in the fall of 1990. The first experiment is planned in the summer of 1992.
A rotational band of nineteen transitions with a moment of inertia scrIband(2) of 84h2 MeV-1 has been observed in 152Dy. The band feeds into the oblate yrast states between 19- and 25- and it is proposed that the lowest member of the band has a spin of 22+ and thus the band extends up to 60h. It is identified as the yrast superdeformed band and its intensity accounts for the whole of the ridge structure seen previously in continuum Egamma-Egamma correlations.
A Doppler shift attenuation measurement has been carried out to determine the collectivity of the superdeformed band in 150Gd. The data was found to be consistent with a constant inband quadrupole moment of 17 +/- 3 eb. This corresponds to a quadrupole deformation of ß2~0.58. In addition the measurement has resolved important questions regarding the de-excitation of the band, confirming the rapid de-excitation of the superdeformed band in 150Gd with more than 80% of the band intensity being lost over one transition.
It is investigated how particles in high-N shells affect the moment of inertia, (2), and the quadrupole moment, Q0, of superdeformed high-spin states. The different behaviour of (2) versus the rotational frequency observed for superdeformed states in 152Dy and 149Gd is explained in terms of different occupations of a few high-N orbits. Predictions for (2) and Q0 for the neighbouring nucleus 148Eu are presented.
Five excited superdeformed bands have been observed in the doubly closed-shell superdeformed nucleus 152Dy. Three of the new bands are interpreted in terms of single neutron excitations across the N = 86 shell gap. One of these bands appears to partly decay into the yrast superdeformed band. Another band involves a single proton excitation across the Z = 66 shell gap into the N = 7 hyper-intruder orbital. This is the first evidence of the influence of this deformation driving orbital on superdeformed structures in any mass region.
Candidates for two excited superdeformed (SD) bands based on unfavoured signature partners of proton particle-hole excitations in the 152Dy core have been observed in the 151Tb nucleus with the EUROGAM spectrometer. In the framework of cranked shell model calculations, one of these bands is interpreted as the signature partner of the 151Tb yrast band. It is suggested that the second band is either the signature partner of the 151Tb first excited band with a proton π[301] configuration or is an excitation from the π[303] into the [651] intruder orbitals. There is a disagreement between the data and the predictions of self-consistent relativistic Hartree-Fock calculations.
Candidates for two excited superdeformed (SD) bands based on unfavoured signature partners of proton particle-hole excitations in the Dy-152 core have been observed in the Tb-151 nucleus with the EUROGAM spectrometer, In the framework of cranked shell model calculations, one of these bands is interpreted as the signature partner of the Tb-151 yrast band. It is suggested that the second band is either the signature partner of the Tb-151 first excited band with a proton pi[301]1/2 configuration or is an excitation from the pi[303]5/2 into the [651]3/2 intruder orbitals. There is a disagreement between the data and the predictions of self-consistent relativistic Hartree-Fock calculations.
The structure of superdeformed rotational bands recently discovered around 152Dy is discussed within the deformed shell model based on an average Woods-Saxon potential with a monopole pairing force. A comparison with available experimental data is provided and detailed predictions for yet unobserved cases are given. Pronounced variations in the observed rotational pattern are attributed to the angular momentum alignment of the high-N intruder (quasi)particles.
Rotational bands, characteristic of a superdeformed prolate shape (ε≈0.6) and extending to above spin , have been observed in both 150Gd and 151Tb. The magnitudes of the moments of inertia (2) were found to vary with frequency and the variation greatly exceeded that seen in 148,149Gd and 151,152Dy. The differences in the (2)'s are attributed to the occupation of particular high-N orbitals. Moreover, contrary to the previous examples the bands in both 150Gd and 151Tb de-excited at a much higher rotational frequency of and this may indicate that the pair gap extends to higher frequencies in 150Gd and 151Tb.
A rotational band of 19 (possibly 20) transitions extending to spin ∼ has been observed in 151Dy with an average dynamic moment of inertia . This band is identified as a superdeformed band in 151Dy. The value of agrees with cranked Strutinsky calculations. Similarities as well as striking differences with the superdeformed bands of neighboring nuclei are observed.
One of the four new excited superdeformed bands found in 151Dy is characterized by transition energies that lie midway between the γ-ray energies of the yrast superdeformed band in 152Dy. This result adds significant new information on the issue of “identical” bands, as it confirms predictions based on the strong coupling model and the pseudospin coupling scheme.
Two excited superdeformed bands in {sup 149}Gd have been observed in {gamma}-ray spectroscopy. Based on the behavior of the dynamical moments of inertia, we assign one band to a neutron excitation and the other to a proton excitation. The proton-excited-band {gamma}-ray energies are nearly identical to those already known in {sup 150}Tb. In addition, two new members of the {sup 149}Gd yrast cascade have been observed, extending the band to spin 135/2{h bar}. The results are discussed in terms of high-{ital N} intruder orbitals in the cranked-shell model.
A discrete superdeformed band was found in /sup 148/Gd, and was produced both in Ca- and Si-induced compound-nucleus reactions. It is the third band found in the mass-150 region and its properties provide the clearest indication that /sup 152/Dy is a ''magic'' superdeformed nucleus
The structure of recently discovered identical superdeformed bands in $^{151}\mathrm{Tb}$ and $^{152}\mathrm{Dy}$, and in $^{150}\mathrm{Gd}$ and $^{151}\mathrm{Tb}$ are discussed in terms of the strong-coupling approach. Based on the experimental evidence that the superdeformed core of $^{152}\mathrm{Dy}$ is extremely insensitive to the polarization effects induced by the odd particle, the bands are shown to exhibit the presence of the pseudo SU(3) symmetry at extreme conditions of large elongations and high spins.
Excited superdeformed bands have been observed in the N=86 isotones 150Gd and 151Tb. The properties of these bands were found to closely resemble those of the yrast superdeformed bands in their Z+1 N=86 isotones (151Tb and 52Dy) such that, on average, the transition energies are identical to an accuracy of 1:1000. It is proposed that these excited superdeformed bands are based on single-proton excitations from the [301]1/2 orbital into the [651]3/2 intruder orbital and thus they are the first obsrevation of proton excitations in superdeformed nuclei.
Eight superdeformed rotational bands have been observed in the [sup 149]Gd nucleus. Several excited bands have partners in neighboring nuclei which differ by up to four nucleons, with nearly identical dynamic moments of inertia and quantized [gamma]-ray phasing. These observations cannot be easily explained by theoretical models including an intrinsic scaling with mass of the moment of inertia. A paired backbend and an interaction due to an accidental degeneracy between two superdeformed levels have also been observed.
A discrete superdeformed rotational band has been discovered in [sup 144]Gd following the reaction [sup 100]Mo([sup 48]Ti, 4[ital n])[sup 144]Gd at 221 MeV. The dynamical moment of inertia shows a sharp irregularity at [h bar][omega]=0.45 MeV. The intensity of the [gamma]-ray transitions suggests that the irregularity can be associated with a backbend, which is interpreted in terms of the [ital N]=6 proton band crossing. The experimental results are in good agreement with cranked mean field calculations, which indicate the presence of large shell gaps for both protons and neutrons.
An excited superdeformed (SD) band in [sup 150]Gd is associated with a two-particle--two-hole proton excitation and provides the first evidence for collective proton pair excitations in a SD nucleus. This band is seen to exhibit a discontinuity in the [gamma]-ray transition energies (backbending), which is interpreted as a band crossing associated with the alignment of a pair of [ital N]=6 protons. There is further evidence that this excited SD band decays into the yrast SD band.
- F.S. Stephens