Projected Shell Model Calculations Research Articles

Level structures of 96Tc and their microscopic description

High spin states in the 96Tc nucleus were populated in the 75As(28Si, 4p3n) fusion-evaporation reaction at E lab = 120 MeV and the de-excitations were investigated through in-beam γ-ray spectroscopic techniques using indian national gamma array spectrometer consisting of 18 clover Ge detectors. The present level scheme of the 96Tc nucleus has been extended substantially with the addition of about forty five new γ transitions. The level structures in 96Tc have been established up to excitation energy ∼10 MeV and angular momentum ∼25ℏ. Level structures of 96Tc nucleus are discussed in the framework of triaxial projected shell model calculations.

Evidence for prolate-oblate shape coexistence in the odd- ABr383573 nucleus

The excited states in $^{73}\mathrm{Br}$ nucleus have been investigated through the fusion evaporation reaction $^{50}\mathrm{Cr}(^{28}\mathrm{Si}$, $\ensuremath{\alpha}p)^{73}\mathrm{Br}$ at a beam energy of 90 MeV using the Indian National Gamma Array. The $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence technique has been used to add eight new $\ensuremath{\gamma}$-ray transitions in the level scheme. The mixing ratio of $\mathrm{\ensuremath{\Delta}}I=0$ (mixed with $E2$ and $M1$) transitions have been determined using angular distribution and ${R}_{\mathrm{DCO}}$-polarization measurement. The half-life of the ${9/2}^{+}$ isomeric state has been measured to be ${\ensuremath{\tau}}_{1/2}=52(2)$ ns from the variation in the intensity of delayed $\ensuremath{\gamma}$-ray transition as a function of coincidence time window. The two state mixing model calculations were performed to obtain the mixing amplitude, and mixing interaction of two different configurations of $^{73}\mathrm{Br}$. The calculated mixing amplitudes along with the deformations of two different configurations provide the monopole transition strength ${\ensuremath{\rho}}^{2}(E0)$ for Se, Br, and Kr isotopes in a semiempirical approach. These results support a prolate-oblate shape coexistence in the odd-$A\phantom{\rule{4pt}{0ex}}^{73}\mathrm{Br}$ nucleus. The observed structural properties have been discussed in terms of projected shell model calculations.

Effect of nuclear deformation on the observation of a low-energy super-Gamow-Teller state

A well-known structure with concentrated Gamow-Teller (GT) transitions is the Gamow-Teller resonance, which has been observed at higher-energy regions (usually $>6$ MeV) of nuclear excitation. It has been found that the GT strength can also concentrate in the lowest ${J}^{\ensuremath{\pi}}={1}^{+}$ GT state named the ``low-energy super-GT (LeSGT) state'' when the initial even-even nucleus has the structure of ``LS-closed-shell core nucleus $+$ 2 neutrons (or 2 protons)'' and the final nucleus ``LS-closed-shell core nucleus $+$ 1 proton and 1 neutron.'' Such concentrations are realized with the core nuclei $^{4}\mathrm{He}$, $^{16}\mathrm{O}$, and $^{40}\mathrm{Ca}$, corresponding to the shell closures of $s$, $p$, and $sd$ shells, respectively. It is natural to speculate that the LeSGT state may also be observed in the $A=82$ systems if the $N=Z=40$ shell gap is significant and $^{80}\mathrm{Zr}$ represents a good core nucleus corresponding to the $pf$ shell closure. Possible conditions that allow the formation of the LeSGT state in the $^{82}\mathrm{Zr}\ensuremath{\rightarrow}^{82}\mathrm{Nb}$ charge-exchange reaction (or $^{82}\mathrm{Mo}\ensuremath{\rightarrow}^{82}\mathrm{Nb}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$ decay) are discussed by evaluating the results of projected shell model calculations, which are based on deformed model space. Our calculations show that with increasing deformation, the LeSGT feature found in the spherical limit (zero deformation) evolves gradually into a broad distribution in the higher-energy region. This lets us conclude that no LeSGT state is expected in $^{82}\mathrm{Nb}$ because the shape of the $^{80}\mathrm{Zr}$ core nucleus is ellipsoidal.

Chiral vibrations and collective bands in Mo104,106

High spin states of the neutron-rich $^{104}\mathrm{Mo}$ nucleus have been reinvestigated by analyzing the $\ensuremath{\gamma}$ rays in the spontaneous fission of $^{252}\mathrm{Cf}$ with Gammasphere. Both $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ and $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence data were analyzed. A new $\mathrm{\ensuremath{\Delta}}I=1$ band has been discovered with a tentative ${5}^{\ensuremath{-}}$ band head, and is proposed to form a class of chiral vibrational doublets with another ${4}^{\ensuremath{-}}$ band previously found. Angular correlation measurements have been performed to determine the spins and parities. A new ${3}^{\ensuremath{-}}$ level has been added to one of the chiral doublet bands in $^{106}\mathrm{Mo}$. The origin of the chiral doublet bands in $^{104,106}\mathrm{Mo}$ is interpreted as a neutron ${h}_{11/2}$ particle and mixed ${d}_{5/2}, {g}_{7/2}$ hole coupled to the short and long axis, respectively. Triaxial projected shell model calculations have been performed for the chiral doublet bands in $^{104,106}\mathrm{Mo}$. The results show reasonably good agreement with the experimental data.

Theoretical Study of Signature-splitting and Signature-inversion in Doubly-odd Nuclei in A∼80 Mass Region

Projected Shell model calculations have been performed using the angular-momentum projected two-quasiparticle states with the employment of a simple quadrupole-quadrupole + monopole–Pairing + quadrupole-pairing Hamiltonian to study the nuclear structure properties of doubly-odd 80Br and 82Rb isotones. The present calculations reproduce reasonably well the available experimental data on the yrast bands and also predict the new high spin states in these nuclei, where current data are still sparse. The phenomena of Signature-splitting and Signature–inversion have also been studied in detail within the context of Projected Shell Model.

Microscopic study of ground state bands in N = 45 and 46 isotones in mass region A ∼ 70–80

Using the angular-momentum projected quasiparticle states and a simple quadrupole–quadrupole + monopole–pairing + quadrupole-pairing type Hamiltonian, Projected Shell Model calculations have been performed to study the nuclear structure properties of some N = 45, 46 isotones in the mass region A = 70–80. The results are obtained for the yrast energy spectrum, rotational alignments, back-bending and reduced transition probabilities [B(M1) and B(E2)]. Results of our calculations exhibit satisfactory agreement with experimental data. Signature splitting and signature inversion which are the characteristics of this mass region have also been reproduced and discussed for these nuclei.

Superdeformed band in the N = Z + 4 nucleus 40Ar : A projected shell model analysis

40Ar is among the few sd -shell nuclei known to exhibit superdeformation. An interesting question is whether the experimentally identified superdeformed rotational band in 40Ar has an axially or triaxially deformed shape. Projected shell model calculations assuming an axially deformed basis are performed up to high spins for this nucleus. Our detailed analysis of the wave functions reveals that the high-spin states are dominated by mixed 0-, 2-, and 4-quasiparticle configurations with different K-components. The calculated electric quadrupole transition probabilities reproduce well the known experimental data and suggest a reduced but still significant collectivity in the high spin region. Due to the mixing of various multi-quasiparticle K-configurations, axial asymmetry emerges in the calculation. Throughout the entire rotational band, the extracted triaxial deformation parameters are small but non-zero. Relations of triaxiality and unnatural spin-parity states of the superdeformed side-band are discussed.

Systematic study of two-quasiparticle structure of the neutron-rich odd-odd rubidium nuclei

A theoretical study of the nuclear structure of odd-odd 88–96Rb nucleus in the A∼100 mass region is carried out by using the angular-momentum-projection technique implemented in the Projected Shell Model (PSM). For these isotopes, PSM calculations are performed to obtain the yrast spectra and the description of the formation of the yrast level structure from multi-quasi-particle configurations is also presented. The back-bending in moment of inertia and transition energies have also been calculated and compared with the available experimental data. In addition, the reduced transition probabilities, i.e. B(E2) and B(M1), are also obtained for the yrast band of these isotopes for the first time by using PSM wave-functions.

Study of the structure of yrast bands of neutron-rich 114-124Pd isotopes

The projected shell model calculations have been carried out in the neutron-rich 114-124Pd isotopic mass chain. The results have been obtained for the deformation systematics of \(E(2^{+}_{1})\) and \(E(4^{+}_{1})/E({2}^{+}_{1})\) values, BCS subshell occupation numbers, yrast spectra, backbending phenomena, B(E2) transition probabilities and g-factors in these nuclei. The observed systematics of \(E(2^{+}_{1})\) values and \(R_{42}\) ratios in the 114-124Pd isotopic mass chain indicate that there is a decrease of collectivity as the neutron number increases from 68 to 78. The occurrence of backbending in these nuclei as well as the changes in the calculated B(E2) transition probabilities and g -factors predict that there are changes in the structure of yrast bands in these nuclei. These changes occur at the spin where there is crossing of g-band by 2-qp bands. The predicted backbendings and predicted values of B(E2)s and g-factors in some of the isotopes need to be confirmed experimentally.

Study of shape evolution and electromagnetic properties in neutron-rich Zr and Sr isotopes

The projected shell model calculations have been carried out in neutron-rich 100–108Zr and 98–102Sr isotopes. The shape evolution and electromagnetic properties have been examined in neutron-rich Zr and Sr isotopes around N = 60. The structure of yrast states, backbending phenomena, g-factors and B(E2) transition probabilities are calculated and compared with corresponding observable quantities. The present calculations predict the occurrence of coexistence of prolate-oblate shapes at 0+ state in 100,102Zr and 98,100Sr. Nuclei beyond N = 62 are predicted to have prolate deformation in the ground-state.

Study of odd mass 115−125Sb isotopes with the projected shell model calculations

The projected shell model (PSM) with the deformed single-particle states, generated by the standard Nilsson potential, is applied to study the negative-parity high spin states of [Formula: see text] nuclei. The nuclear structure quantities like band structure and back-bending in moment of inertia have been calculated with PSM method and are compared with the available experimental data. In addition, the reduced transition probabilities, i.e., B[Formula: see text] and B[Formula: see text], are also obtained for the yrast band of these isotopes for the first time by using PSM wave function. A multi-quasiparticle structure has been predicted for [Formula: see text] isotopes by the present PSM calculations.

Possible very anharmonic one- and two-phonon γ-vibrational bands in 103Mo

High-spin levels of [Formula: see text]Mo have been reinvestigated by analyzing the high statistics [Formula: see text]-[Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] coincidence data from the spontaneous fission of [Formula: see text]Cf taken with the Gammasphere detector array. Two bands and 30 new transitions have been identified. A potential energy surface calculation has been performed. The calculation confirmed the 3/2[Formula: see text][411] configuration of the ground state band and 5/2[Formula: see text][532] for the 346[Formula: see text]keV excited band, as assigned in the previous work. The two newly established bands were proposed to be one- and two-phonon [Formula: see text] vibrational bands coupling to the 5/2[Formula: see text][532] Nilsson orbital, respectively. Triaxial projected shell model calculations have been applied to explain the level structure and are found in good agreement with experimental data.

Reinvestigation of two-phonon γ-vibrational band in neutron-rich 114Pd

The level structure in neutron-rich [Formula: see text]Pd nucleus has been reinvestigated by measuring prompt [Formula: see text] rays emitted in the spontaneous fission of [Formula: see text]Cf. A two-phonon [Formula: see text]-vibrational band built on the 1639.3[Formula: see text]keV level is observed, which confirms the previous suggestion from a [Formula: see text]-decay experiment. Systematical comparison supports the assignment for a two-phonon [Formula: see text]-vibrational band in [Formula: see text]Pd. Triaxial projected shell model calculations for the multi-phonon [Formula: see text] bands of [Formula: see text]Pd are in good agreement with the experimental data.

Quasi-particle structure of proton–hole cobalt isotopes

Projected Shell Model calculations have been employed for the description of the ground band in odd mass 57–67Co isotopes. In the present work, quadrupole and monopole pairing interactions as well as quadrupole–quadrupole interactions are effectively included in the Hamiltonian for obtaining various nuclear structure properties using the angular momentum projection technique. The yrast spectra of these isotopes are described as interplay between the angular momentum projected states around the Fermi level. The quasi-particle structure of these nuclei is found to be comprised of different intrinsic K-quantum numbers. Rotational alignments in terms of kinetic moment of inertia (ℑ(1)) have also been discussed. The electromagnetic transition probabilities [B(E2) and B(M1)] are also obtained in the present work and are found to be in good agreement with the available experimental as well as the other theoretical data, which tests the consistency of the applied projected shell model. The present PSM calculations also report the existence of low lying deformed structure along with the spherical structure at N=40.

Description of rotational properties of the superheavy nucleus 256,258,260Rf by projected shell model

Band structure of the Z = 104 nucleus 256Rf has been a recent research focus in nuclear physics. We performed projected shell model calculations for this and some other neighboring Rf isotopes. Specifically, we studied rotational properties of these nuclei and showed that variations in dynamic moment of inertia were sensitive to single-particle structures, which may be useful information for locating the anticipated island of stability. Electromagnetic transition properties were also calculated, and measurable quantities were predicted for further experimental test.

Identification of multi-phononγ-vibrational bands in odd-Z105Nb

Background: The odd-$Z$ ${}^{105}$Nb nucleus is located in the $A=100$ neutron-rich region. The study of multi-phonon vibrational band structures is important for understanding nuclear structure in this region.Purpose: To search for multi-phonon $\ensuremath{\gamma}$-vibrational bands in ${}^{105}$Nb.Methods: The high spin states of ${}^{105}$Nb have been studied by measuring the prompt $\ensuremath{\gamma}$ rays emitted in the spontaneous fission of ${}^{252}$Cf. The data analysis is carried out using triple- and four-fold $\ensuremath{\gamma}$ coincidence methods.Results: A new level scheme of ${}^{105}$Nb is established. The yrast band has been confirmed, and three new collective bands have been identified. Compared with previous results, a total of 14 new levels and 36 new $\ensuremath{\gamma}$ transitions are observed. Two bands built on 625.9 keV and 1231.9 keV levels are proposed as one-phonon- and two-phonon $\ensuremath{\gamma}$-vibrational bands, respectively. The evidences for supporting assignments of the multi-phonon $\ensuremath{\gamma}$-vibrational bands have been discussed. Triaxial projected shell model calculations for the $\ensuremath{\gamma}$-vibrational band structures are found in good agreement with the experimental data, thus further supporting the $\ensuremath{\gamma}$-vibrational interpretations for the experimental results in ${}^{105}$Nb.Conclusions: The one-phonon- and two-phonon $\ensuremath{\gamma}$-vibrational bands have been identified in ${}^{105}$Nb. Our results provide new data to systematically understand the characteristics of the multi-phonon $\ensuremath{\gamma}$-vibrational bands in the $A=100$ neutron-rich region.

Collectivity of neutron-rich magnesium isotopes investigated by projected shell model calculations

The abnormally large collectivity of neutron-rich magnesium isotopes in the “island of inversion” has not been well understood. It has been commented that the unexpectedly large deformations observed in the magnesium isotopes are attributed to the neutron f7/2 intruder orbits involved remarkably even in the ground states, which points to nuclear force directly. Recently, a new isospin-dependent Nilsson potential was suggested to improve the calculations of the ground states of magnesium isotopes. With the improved Nilsson potential, in the present work we investigate the collectivity of excited states by using the projected shell model. To avoid the collapse of the BCS pairing, which occurs in weak pairing, we improved pairing calculations by using the Lipkin-Nogami approach. The collectivity and the erosion of the N = 20 shell in neutron-rich magnesium isotopes are discussed by calculating spectra and electric quadrupole transitions. The gyromagnetic factors are calculated and compared with existing data to get insight into the configurations of collective states at different spins. A two-quasineutron K π = 6 + state in 38 Mg is predicted to be a possible isomer with an excitation energy lower than the I π = 6 + member of the ground-state band.

Multiphononγ-vibrational bands in theγ-soft nucleus138Nd

The low spin states of ${}^{138}$Nd have been reinvestigated via the ${}^{124}$Te(${}^{19}$F,$4n1p$) reaction at a beam energy of 103 MeV. The quasi-one-phonon $\ensuremath{\gamma}$-vibrational band based on the 1013.7 keV level has been expanded and the quasi-two-phonon $\ensuremath{\gamma}$-vibrational band built on the 1842.7 keV level has been proposed. A systematic comparison supports our assignments for multiphonon $\ensuremath{\gamma}$-vibrational bands in ${}^{138}$Nd. The characteristics of $\ensuremath{\gamma}$ softness in ${}^{138}$Nd have been discussed. Triaxial projected shell model calculations can well describe the rotational feature of the bands, but they fail to reproduce simultaneously the bandhead energies of the two $\ensuremath{\gamma}$-vibrational bands if a fixed triaxial deformation is assumed.

Microscopic analysis of band structures in odd mass 79–89Y isotopes

The positive-parity yrast bands of 79, 81, 83, 85, 87, 89Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.

THEORETICAL INVESTIGATION OF POSITIVE PARITY BAND STRUCTURE OF Y AND Nb ISOTOPES

The positive parity band structure of odd mass neutron-rich 97 – 103 Y and 99 – 105 Nb nuclei has been studied using microscopic technique known as the projected shell model (PSM) with the deformed single-particle states generated by the standard Nilsson potential. The nuclear structure properties like yrast spectra, energy splitting, moment of inertia, rotational frequencies and reduced transition probabilities B(M1) and B(E2) have been calculated and their comparison with the available experimental data has been made. A shape evolution has also been predicted in these isotopes as one moves from 97 Y to 99 Y and 99 Nb to 101 Nb . The PSM calculations also demonstrate the multi-quasiparticle structure in these nuclei.