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In quadrantI, the deformation parameter β and power index parameter bAV sharply rises as N increases from 86 to 92. For N>92, both parameters show uniform trend and saturates in fig. 2.1(a and b). In quadrantII, the Er and Yb nuclei show same trend for both parameters for N=88 104. The β rises for Hf and W nuclei when N
increases from 88 to 98 and decreases towards N=100 and again rises on increasing N. The bAV rises for ErOs nuclei when N increases from 88 to 104. The Pt has different behavior. In quadrantIII, the Pt nuclei shows same trend with both parameters whereas after N>108, the W and Os nuclei shows same trend. In quadrantIV, the nuclei Ba, Ce, Nd and Sm shows same trend, whereas the Xe nuclei has a dip at Z=66 in power index
parameter and a up in deformation parameter.
Proceedings of the DAE Symp. on Nucl. Phys. 59 (2014) 298 http://sympnp.org/proceedings/59/A125.pdf, BHU, INDIA; 12/2014

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Result and Discussions: The variation of E state (in MeV) versus neutron number (N) is shown in Fig. 1 for N=86122. The data points are joined for same element so the N dependence of E is visible. The value of E is having maximum scattering (0.7 to 1.6 MeV) at N=104 for Yb to Pt isotopes corresponβ nuclei[9] The fig. 1 is reproduced from [9]. The variation of E2γ versus proton number (Z) is shown in Fig. 2 for Z = 60 80. The data points are joined for each isotones for N =86– 116. The value of E2γ is suddenly increasing from 0.8 to 1.6 MeV for a fixed value of Z= 70 when N is changing from 90 to 104. The E2γ decreases sharply on increasing Z from 60 to 68 for each isotones i.e. N= 8898 indication shape phase transition from Vibration to Rotation i.e. SU(5) to SU(3) limits of IBM. The slope for N= 88 and 90 are same and there is no indication for subshell effect in this fig. The variation of asymmetric parameter (γ) versus proton number (Z) for N= 82 96 isotones for Z= 5872 region is shown in Fig.3. The gap is maximum i.e. 7.6 at Z= 64 when N changes from 88 to 90 indication the subshell effect at Z=64 for N<90. Since the γ is evaluated from E2g and E2γ. However the Z=64 subshell effect is not evident in E2γ (see fig. 2) and in E0β (see fig.4 ref. [9]). It is evident only in E2g [4] and R4 [4 and see fig. 12 of ref. 10].
Proceedings of the DAE Symp. on Nucl. Phys. 59 (2014) 234 http://sympnp.org/proceedings/59/A93.pdf, BHU, INDIA; 12/2014

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Result and Discussion
The values of root mean square deviation (RMSD) of the reproduced level energies are obtained using PL and SRF from experimental level energies [5]. It is observed that the RMSD values are small using power law in comparison to the SRF. Most of the nuclei having RMSD value lie below 40 KeV using power law except N=88 whereas using SRF it is lie below 100 KeV. The variation of RMSD versus N using SRF and PL is shown in Fig. 1(a, b). The MOI from SRF for βband and ground band is studied with energy ratio of both the bands and shown in Fig. 2(a, b). It is observed from the diagrams that as the energy ratio rises from spherical behavior to deformed limit, the MOI increases except 150Sm in βband and 150Nd out of the fit of smooth curve. The systematics of softness parameters of both the bands also has same correlation with energy ratios.
Conclusion:
It is evident from variation of RMSD vs. R4 curve that the level energies of βband are well reproduced in PL and the values of RMSD ≤ 40 KeV except N=88 isotones (RMSD≈ 50 KeV). The variation of MOI (θ) vs. R4 for g band and β band show a strong correlation.
Proceedings of the DAE Symp. on Nucl. Phys. 59 (2014) 238 http://sympnp.org/proceedings/59/A95.pdf, BHU, INDIA; 12/2014

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There are various empirical formulae to study the level structure of ground band of medium mass nuclei. The expression for rotational spectra is: E(I) = (ħ2 /2θ) I(I+1). (1)
Where θ and I are the moment of inertia and spin respectively [1]. The deviation from eq. 1 has been observed for almost all the nuclei because of centrifugal stretching etc. which can be taken into account only up to some extent [2, 3] (3.1 ≤R4 ≤3.33) by apply an expansion in power of I(I + 1), i.e.
E(I) = A I(I+1) + B[I(I+1)] 2 + C[I(I+1)] 3 +··· (2)
where A, B and C have their usual meaning. For harmonic vibrator, the energy can be written as:
E(I) = a I. (3)
Das et. al. [4] suggested the energy expression for anharmonic vibrator:
E(I) = aI + bI(I2). (4)
The energy spectrum of ground band in well deformed nuclei (R4≈3.33) exhibit rotational characteristics and for shape transitional nuclei large deviations have been observed. In the literature, one finds quite a few variants, which involve two, three or more terms in terms of spins. Gupta et al [5] observed that the values of fitting parameters often depended on the number of levels used for calculation. They [5] suggested a very different form of energy expression in the form of a single term energy formula called power law:
E(I) = a Ib (5)
where the coefficient “a” and index “b” are the constants for the band. Also b is a noninteger. The
values of aI and bI are given below: bI = log(RI)/ log(I/2) and aI = EI / Ib.
This is the mostsimple expression among all the other formulae. The validity of this formula was well proved for the medium mass nuclei. Recently, it was also tested for the light N < 82 region. This formula was equally successful in expressing the ground band energies in the A=150200 region [5]. Mittal et. al [6] verified its validity for light mass Xe Sm nuclei. Recently, Kumar et. al [7] and Kumar [8] presented correlation of kinetic moment inertia with power formula index in 100≤A ≤150 region. Gupta and Hamilton [9] also illustrated the use of this formula to determine the degree of deformation of shape transitional nuclei.
Proceedings of the DAE Symp. on Nucl. Phys. 59 (2014) 250 http://sympnp.org/proceedings/59/A101.pdf, BHU, INDIA; 12/2014

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Introduction:Correlation of average scaling coefficient with asymmetric parameter and average power index with quadrupole deformation parameter
DAE SYM 2014 BHU, BHU; 12/2014

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ABSTRACT:
The level energies of ground band of even Z, even N nuclei may be reproduced well with good accuracy by using the single term power index formula E=a Ib. In an earlier study of the dependence of the kinetic moment of inertia J(1) on spin I, a possible correlation of the moment of inertia J(1) with power index ‘b’ was suggested. Here we illustrate that the slope of the kinetic Moment of Inertia (MoI) versus spin I corresponds to the magnitude of the index ‘b’ for several isotopes in the A=100150 region. A correlation of the change in slope of the MoI versus spin with change in power index ‘b’ is exhibited. This provides a meaningful alternative to the Dynamic moment of inertia plots. Its use to study the shape phase transition is illustrated for the N=60 region. Correspondence with B(E2)↑ is also illustrated.
Read More: http://www.worldscientific.com/doi/abs/10.1142/9789814525435_0081?queryID=%24%7BresultBean.queryID%7D&
Fission and Properties of NeutronRich Nuclei, Proceedings of the Fifth International Conference on ICFN5 Sanibel Island, Florida, USA, 4 – 10 November 2012; 09/2014

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J. B. Gupta
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The Xe isotopes in the A=130A=130 region, with low quadrupole deformation β , are good examples of the γ soft nuclei. Recent data of 124Xe exhibit well developed K bands of ground, Kπ=21+, 02+, 03+ and 41+. Its spectrum is studied in relation to the underlying dynamic symmetries The absolute intra and inter band B(E2) values and the B(E2) ratios are compared with the theoretical predictions of the dynamic pairing plus quadrupole model in the microscopic approach, and the interacting boson model IBM1. The potential energy surface illustrates the γ soft character. The variation of inertia tensor over the (β,γβ,γ) space is studied, and the spread of the wave functions of three Iπ=0+Iπ=0+ and two 2+2+ states over the (β,γβ,γ) space illustrate their varied character. Comparison is done with the dynamic symmetries of IBM for different bands. The O(6) symmetry breaking and preservation of the O(5) and O(6) symmetry are reviewed.
Nuclear Physics A 07/2014; 927. DOI:10.1016/j.nuclphysa.2014.03.002 · 2.50 Impact Factor

J. B. Gupta
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166,168Hf are the lightest isotopes of Hf, for which the spectral information for nonyrast levels is now available from recent experiments. The algebraic Interacting Boson Model IBM1 is employed to reproduce their level structures and to predict the E2 transition probabilities. The pairing plus quadrupole model is used to predict their spectra and E2 transition rates and the static moments in a microscopic approach. The spin assignments I
π
of new levels and their Kband structures are studied. The validity of the inclusion of 166,168Hf as members of a U(12) super group is studied using various empirical observables. The potential energy surfaces for the two isotopes are compared and the filling of the nucleons in Nilsson orbits is analyzed, to yield a consistent comprehensive view of the spectra of the two Z = 72 isotopes.
European Physical Journal A 10/2013; 49(10). DOI:10.1140/epja/i2013131264 · 2.42 Impact Factor

J. B. Gupta
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The anharmonity in shape transitional nuclei, observed earlier, is studied and an alternative form is derived. The dichotomy of a constant anharmonicity along with a changing nuclear structure is resolved. The evolution of the collective nuclear structure from the spherical vibrator to the deformed rotor is studied through the variation of energy ratio R10/2(E10/E2) with R4/2, for Ba–Dy and for Dy–Hf(N<104) and R12/2. The role of the Z = 64 subshell and the N = 88–90 shape phase transition are illustrated in the Mallmann plot. The relative merits of the empirical formulae: rotation–vibration linearity model, the soft rotor formula and the power index formula are compared.
International Journal of Modern Physics E 09/2013; 22(08). DOI:10.1142/S021830131350064X · 0.84 Impact Factor

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The use of soft rotor formula (SRF) for the level energies of K = 2 γband for the shape transitional even Z even N nuclei in the medium mass region is illustrated. With proper treatment, we obtained positive values of the moment of inertia and softness parameter, as opposed to negative values reported in literature. The moments of inertia of the γband are almost equal to the ground state band values. The systematic dependence of the softness parameter on energy ratio R4/2 is studied. The effect of the odd–even spin staggering on these parameters is studied in detail. In deformed nuclei, the same parameters for odd and even spin members yield fair energy values.
Pramana 07/2013; 81(1). DOI:10.1007/s1204301305530 · 0.72 Impact Factor

J. B. Gupta
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Background: The shapephase transition at N = 88–90, and the role of Z = 64 subshell effect therein has been a subject of study on empirical basis and in the context of the NpNn scheme, but a microscopic view of the same has been lacking.Purpose: A microscopic view of the N = 88–90 shapephase transition is developed. The Z = 64 subshell effect is viewed in terms of the Nilsson singleparticle orbitals in this region.Method: The dynamic pairing plus quadrupole model is employed to predict the occupation probabilities of the neutron and proton deformed, singleparticle orbitals. The nuclear structure of Ba–Dy (N > 82) nuclei is studied and the shape equilibrium parameters derived.Results: The filling of neutron orbitals at N = 86, 88, and 90 plays an important role in the shapephase transition. The filling of the proton Nilsson orbitals of varying slopes leads to the variation of nuclear structure with varying Z, which leads to the Z = 64 subshell effect, which disappears at N=90.Conclusions: The effect of the np interaction of the πh11/2 and νh9/2 orbitals, along with the contribution of the νi13/2 orbital leads to the shapephase transition at N=88−90. The slopes of proton Nilsson orbitals explain the Z = 64 subshell effect.
Physical Review C 06/2013; 87(6). DOI:10.1103/PhysRevC.87.064318 · 3.88 Impact Factor

J. B. Gupta
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ABSTRACT:
A linear relation for the level energy ratios in the ground band of
eveneven nuclei, based on the rotationvibration expression, is derived
and its application on a universal scale, including the O(6), E(5) and
X(5) symmetries, is illustrated. A microscopic view of this relation and
of the collective model is given. Also, an approximate relationship with
single term power index formula E = aIb is demonstrated.
International Journal of Modern Physics E 05/2013; 22(5):50023. DOI:10.1142/S0218301313500237 · 0.84 Impact Factor

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The neutron rich Pt isotopes with only 4 proton holes (two proton bosons) have been studied for long. For example, 196 Pt is cited as the best example of an O(6) nucleus [1]. Gupta et al. [2], in empirical studies of ground band energies of medium mass shape transitional nuclei, calculated the vibrational content of the low spin I=2 state in 182196 Pt isotopes and noted a phase transition at N=110 (A=188), with lighter isotopes showing significant deformation effects. The deformation for Pt is maximum at N=104, (A=182). With the advance in nuclear reaction and detection technology, the level structure of lighter Pt isotopes is being pursued down to N=92. In a recent experiment [3], the level structure of 170172 Pt, the lightest ones, was studied using the Gammasphere detector array. The isotopes of interest were selected through recoildecay tagging. The yrast band in 170 Pt is extended up to I=10 and in 172 Pt up to I=14, besides the nonyrast side bands. There is interest in these isotopes to study the effect of side bands on the yrast band, inducing the shape coexistence phenomenon. To start with, we have studied the level structure of Pt isotopes N=92104, by plotting the level energies against the spin I, to see the evolution of nuclear structure with N and to search for irregularity in the slope with varying spin I, if any. Further, we have calculated the kinetic Moment of inertia J (1)
DAE SYM, DU; 12/2012

J. B. Gupta
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The N = 90 isotones of Nd, Sm, Gd and Dy, with almost similar deformed level structure and associated with X (5) symmetry, form the isotonic multiplet in Z = 50–66, N = 82–104 quadrant. This is explained microscopically in terms of the Nilsson level diagram. Using the Dynamic PairingPlusQuadrupole model of KumarBaranger, the quadrupole deformation and the occupancies of the neutrons and protons in these nuclei in the Nilsson orbits have been calculated, which support the formation of N = 88, 90 isotonic multiplets. The existence of the Fspin multiplets, with almost identical spectra, recognized in earlier works, in Z = 66–82, N = 82–104 quadrant, is also explained microscopically in our study.
European Physical Journal A 12/2012; 48(12). DOI:10.1140/epja/i2012121773 · 2.42 Impact Factor

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In quadrantI, the B(E2, 01+ →21+) versus N data for XeDy lie on a smooth curve (Fig. 1). At N=8890, there is sharp phase transition. B(E2)↑ saturates for N>92. At N=88, 90, 92, value rises with increasing Z.
The plot of B(E2)↑ versus NpNn (figure 2) provides a smooth dependence on NpNn with somewhat lesser spread, but the sharp phase change is less evident. The B(E2)↑ for DyW (Z=6674, N<104) in
Quadrant–II (Fig. 3), rise with N, but each Z has it own smooth curve, for higher Z being lower. If one plots the same data versus NpNn a smooth single curve (with some spread) is obtained (Fig. 4). This is similar to the Fspin multiplets observed in Quadrant2 earlier. The B(E2, 01+→21+) for YbPt (N> 104) in quadrant3) (Fig. 5) plotted versus N yield a different pattern, values falling with increasing N. Each Z has it own slope. The same data on a plot versus NpNn (figure 6) yields a smooth rising curve. In all three regions (Q IIII), B(E2, 01
+→21+) values have a systematic dependence on NpNn. but having different patterns.
Proceedings of the DAE Symp. on Nucl. Phys. 57 (2012), MUMBAI; 12/2012

A. Dhal,
R. K. Sinha,
D. Negi,
T. Trivedi,
M. K. Raju,
D. Choudhury,
G. Mohanto,
S. Kumar,
J. Gehlot,
R. Kumar,
[...],
J. J. Das,
S. Muralithar,
N. Madhavan,
J. B. Gupta,
A. K. Sinha,
A. K. Jain,
I. M. Govil,
R. K. Bhowmik,
S. C. Pancholi,
L. Chaturvedi
Central European Journal of Physics 10/2012; · 1.08 Impact Factor

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Available from: Dr. Rajesh Kumar
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ABSTRACT:
The level energies of ground band of even Z, even N nuclei may be
reproduced well with good accuracy by using the power index formula E =
aIb. In an earlier study of the dependence of the kinetic
moment of inertia (MoI) J(1) on spin I, a possible
correlation of the MoI J(1) with power index "b" was
suggested. Here we illustrate that the slope of the kinetic MoI versus
spin I corresponds to the magnitude of the index "b" for several
isotopes in the A = 100150 region. The validity of the formula is
illustrated for light nuclei in A = 100 region and its use for studying
shape phase transition at N = 60.
International Journal of Modern Physics E 10/2012; 21(10):50082. DOI:10.1142/S0218301312500826 · 0.84 Impact Factor

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ABSTRACT:
The level structures of 130–136Ce are analyzed with the available experimental data. The level energies, E2 moments and the B(E2)B(E2) ratios for transitions from the K=2K=2 and 02 bands are compared with the values from the Dynamic Pairing plus Quadrupole model and the Interacting Boson Model1. In 130Ce, the recently assigned 1.672 MeV I=(2,3,4)+I=(2,3,4)+ state is tentatively associated with I=4I=4 on the basis of the predicted Kcomponents and the decay mode. The 2.068 MeV I=(4,5,6)+I=(4,5,6)+ state is associated with 52+ of this K=4K=4 band. In 132Ce, the 1932 keV I=4I=4 level is associated with Kπ=02+ band. Variation of the nuclear structure with neutron number N is studied visàvis the O(6)O(6) symmetry and critical point symmetries X(5)X(5) and E(5)E(5). The effect of filling of upsloping Nilsson orbitals on the decreasing deformation with increasing N is illustrated.
Nuclear Physics A 05/2012; 882:21–43. DOI:10.1016/j.nuclphysa.2012.03.006 · 2.50 Impact Factor

A. Dhal,
R.K. Sinha,
D. Negi,
T. Trivedi,
M.K. Raju,
D. Choudhury,
G. Mohanto,
S. Kumar,
J. Gehlot,
R. Kumar,
[...],
R.P. Singh,
J.J. Das,
S. Muralithar,
N. Madhavan,
J.B. Gupta,
A.K. Sinha,
A.K. Jain,
I.M. Govil,
R.K. Bhowmik,
S.C. Pancholi and L. Chaturvedi
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ABSTRACT:
The odd mass nucleus 137Pm has been studied to high spins through the 109Ag(32S, 2p2n)137Pm reaction at an incident beam energy of 150 MeV. The deexciting γrays were detected using an array of 18 Compton suppressed clover detectors. The level scheme of 137Pm has been extended up to
$J^\pi = \tfrac{{43}}
{2}^ $
and excitation energy of E
x
≅ 6 MeV with the observation of 42 new gamma transitions. The linear polarization (IPDCO) measurements for the γray transitions have been done for the first time. The spin and parity assignments for most of the reported levels have been made using these results and the coincidence angular anisotropy (RDCO) measurements. The nuclear shape evolution is discussed in the light of Total Routhian Surface (TRS) and Cranked Shell Model (CSM) calculations.
European Physical Journal A 03/2012; 48:28. DOI:10.1140/epja/i2012120283 · 2.42 Impact Factor