Projected Shell Model Research Articles

Microscopic study of structure of light- and medium-mass even-even cadmium isotopes

The potential-energy surfaces (PESs) for ground states of even-even $^{102--112}\mathrm{Cd}$ isotopes are obtained by using the three-dimensional relativistic Hartree-Bogoliubov model with the density-dependent meson exchange interaction. The quadrupole deformation parameters are extracted from the PES calculations and employed in the beyond mean-field projected shell model to study the yrast and excited states of these isotopes. Besides, the $E2$ transition probabilities and $g$ factors are obtained and compared with the experimental data. The present calculations support the experimental finding that yrast ${8}^{+}$ states of light Cd isotopes are of ${(\ensuremath{\pi}{g}_{9/2})}^{2}$ character whereas the yrast ${10}^{+}$ states of medium-mass Cd isotopes are found to possess ${(\ensuremath{\nu}{h}_{11/2})}^{2}$ character.

Systematic investigation of γ-band structure of triaxial even-even neutron-deficient Os nuclei

Highlights of Manuscript on 180-192 Os nuclei • TPSM study of nuclear structure of even-even 180-192 Os nuclei. • The projected states are a mixture of 0-,2- and 4-qp configurations. • Transition probabilities for the yrast band by using TPSM wave-functions. • High spin states predicted in 180-192 Os isotopes. • Prediction of triaxial nature of 180-192 Os nuclei. γ -bands built on triaxial deformation of neutron-deficient even-even Os isotopes in the A ~180 region, are well investigated in the present work within the self-consistent quantum mechanical framework known as triaxial projected shell model (TPSM). The TPSM results on yrast, γ -, 2 γ -bands provide a reasonable description about the triaxial nature of the isotopes. Moreover, the deformation systematics, back-bending in moment of inertia, energy ratios, transition probabilities and g -factors have also been calculated and compared with the known experimental data and, a considerable good agreement has been achieved between the two.

Study of the nucleon-rich effect in 158Er and 185Os rare-earth nuclei using the projected shell model

In this paper, the structure evolution in 158Er and185Os isotopes is calculated using the projected shell model (PSM) framework. The yrast spectrum, nucleon-rich effects, back-bending phenomenon, and the ratio of reduced electromagnetic transition probabilities, B(M1)/B(E2), are calculated in the spins ranges 8+–22+ and 17/2+–45/2+ for the mentioned isotopes, respectively. In the yrast spectrum, band crossing of one, two, and three quasi-particle bands at spins around 12+ and 41/2+, which is a sign of nucleon alignments, is investigated and 27 additional nucleons are found to be the reasons for back bending at lower spins in 158Er than 185Os, which is coincident with two great drops in the B(M1)/B(E2) ratio plots.

Investigation of the alignment mechanism and loss of collectivity in Pm135

High-spin excited states of $^{135}\mathrm{Pm}$ have been investigated using the $^{107}\mathrm{Ag}(^{32}\mathrm{S}$, $2p2n$) reaction at 145-MeV beam energy. Three negative-parity bands have been investigated up to $\ensuremath{\sim}9.0\ensuremath{-}$, $7.6\ensuremath{-}$, and $6.9\ensuremath{-}\mathrm{MeV}$ excitation energies with spin parities $(55/{2}^{\ensuremath{-}})$, $(49/{2}^{\ensuremath{-}})$, and $(47/{2}^{\ensuremath{-}})\phantom{\rule{4pt}{0ex}}\ensuremath{\hbar}$, respectively. The experimental results have been interpreted using the triaxial projected shell model. It is shown that the observation of the parallel band structures can be explained in terms of crossing of two $s$ bands with the yrast band, which is a rare phenomenon for an odd-$A$ nucleus. Further, the lifetimes of levels in yrast band have been extracted using Doppler shift attenuation method. The evaluated $B(E2)$ values of yrast states show the loss of collectivity at higher spin, attributed to the alignment process.

Investigation of Alignment Effects of Neutron and Proton Pairs in High Spin States of Band Crossing for <sup>159,160</sup>Sm Isotopes Using Projected Shell Model (PSM)

Energy spectrum of nucleus is one the important information for better recognition of nuclear force and interaction of nucleon inside of the nucleus. Energy levels of nucleus are measured by detecting gamma- ray energy spectrum when a target nucleus bombarded with a special projectile to excite it in to levels higher than ground state. On the other hand, there are several models to calculate nuclear energy levels. Solution of the Schrödinger equation by considering a suitable potential is direct method to obtain energy levels of a quantum mechanical system like nucleus. Projected shell model is a model of this type that is developed by solving the Schrödinger equation for a set of potentials along with role of spin. Band structure and yrast bands for even-even and odd-even isotopes of Samarium (^159,160Sm) are calculated using a Fortran code founded based on the projected shell model (PSM). Energy levels of negative and positive parity bands of ¹⁵⁹Sm and ¹⁶⁰Sm isotopes of Samarium nucleus are obtained separately for each spin. Kinetic and dynamic moments of inertias are also calculated for these isotopes. The acquired results are compared with the experimental data. The electromagnetic reduced transition probabilities, B(M1)/B(E2) the behavior of dynamic moment of inertia J², rotational kinetic energy and moment of inertia J¹ as a function of spin have also been investigated and proper comparison is made between the calculated results and the experimental data. The alignment phenomena of neutron-proton pairs in view of the rotational movement in high spin states has also been studied with reference to band crossing.

A detailed study of nuclear structure of odd-mass Pm isotopes near N = 82 shell closure

A systematic study of the positive as well as negative parity yrast structure for the odd-mass 145−149Pm isotopes is carried out by using the angular momentum projection technique implemented in the projected shell model (PSM). By assuming an axial symmetry in the deformed basis, we have been able to calculate the yrast states up to a maximum spin of 47/2 for both positive and negative parity, and as a result, a good agreement is obtained with available experimental data for all isotopes. The intrinsic structure of positive and negative parity yrast states has been found to be built on πg7/2 $$ \otimes $$ νh11/2 and πh11/2 $$ \otimes $$ νh11/2 configurations, respectively. The phenomenon of back-bending has also been discussed in the present work. Reduced electric and magnetic transitions probabilities [B(E2) and B(M1)] are also calculated using the PSM wave functions. Since experimental data on B(E2) and B(M1) are not available, these results can serve as motivation for experimentalists to look for these data. However, the theoretical values of transition strength ratio B(M1)/B(E2) have been found to be matching excellently with the experimental ones.

Structural evolution of yrast and near-yrast bands in even–even Pd isotopes using a self-consistent approach

With the proton number just below the magic number Z = 50, the palladium isotopes are known to exhibit rich nuclear structure phenomena. Inspired by the extensive experimental as well as theoretical structural investigations of Pd isotopes, we have performed the detailed study of band structures of 108–118 Pd isotopes using triaxial projected shell model approach employing the multi-quasiparticle configuration space. As the mass region A ~ 110 depicts well-developed yrast, γ - and 2γ -bands, the present work demonstrates the reliable description of these bands by performing exact three-dimensional angular-momentum projection technique. The results obtained are also consistent with the global predictions of non-axial shapes for these isotopes. Besides this, the present study predicts the involvement of 2-quasiparticle neutron bands in describing various structural properties of these isotopes up to high spin states and has also achieved an excellent agreement of theoretical results with the known experimental data.

Microscopic study of band structures of neutron-rich 153,155,157Sm isotopes

A systematic study of band structures of some odd mass Samarium isotopes with neutron numbers 91 ≤ N ≤ 95 is carried out by employing projected shell model. The theoretical results have been obtained for band head energies, energy spectra, transition energies and moment of inertia. The calculations on comparison with the experimental data show a reasonably good agreement. The band spectra and transition energies for higher spin states are also predicted in these isotopes. The calculations successfully provide good understanding of the change in structure of the yrast bands and excited bands in terms of single and multi-quasiparticle configurations. The future experimental work will test the predictions made in this paper.

Systematic study of odd-mass 151-161Pm and 154,156Pm isotopes using projected shell model * * One of the authors, Suram Singh, acknowledges the financial support from University Grants Commission (UGC), MHRD, Govt. of India, under UGC BSR Start up grant no. F.30-412/2018(BSR)

Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass 151-161Pm and odd-odd 154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.

Basis-dependent measures and analysis uncertainties in nuclear chaoticity

Chaoticity in nuclei is usually measured by the information entropy through analyzing wave functions, or by spectral statistics with the spectral rigidity and the nearest neighbor level spacing (NNLS) distribution. We show that although information entropy (or localization length) is a basis-dependent quantity, it is helpful for understanding the complexity of wave functions, especially when the corresponding levels lie in a highly-excited, dense region. On the other hand, although nuclear levels used for spectral statistics are quantum-mechanically observable, one has to treat them through a model- (and parameter-) dependent unfolding procedure, which may introduce large uncertainties for drawing a conclusion. By applying the projected shell model, we address these problems with an ensemble of ∼ 20,000 Jπ=1/2+ levels calculated for the well-deformed, odd-mass nucleus 153Nd. Residual interactions that are responsible for nuclear chaoticity are discussed as well.

High-spin doublet band structures in odd–odd $$^{194-200}$$Tl isotopes

The basis space in the triaxial projected shell model (TPSM) approach is generalized for odd-odd nuclei to include two-neutron and two-proton configurations on the basic one-neutron coupled to one-proton quasiparticle state. The generalization allows to investigate odd-odd nuclei beyond the band crossing region and as a first application of this development, high-spin band structures recently observed in odd-odd $^{194-200}$Tl isotopes are investigated. In some of these isotopes, the doublet band structures observed after the band crossing have been conjectured to arise from the spontaneous breaking of the chiral symmetry. The driving configuration of the chiral symmetry in these odd-odd isotopes is one-proton and three-neutrons rather than the basic one-proton and one-neutron as already observed in many other nuclei. It is demonstrated using the TPSM approach that energy differences of the doublet bands in $^{194}$Tl and $^{198}$Tl are, indeed, small. However, the differences in the calculated transition probabilities are somewhat larger than what is expected in the chiral symmetry limit. Experimental data on the transition probabilities is needed to shed light on the chiral nature of the doublet bands.

Microscopic study of nuclear structure of odd-odd 128–138I nuclei within the framework of projected shell model for positive- and negative-parity states

We have done the microscopic study of neutron-rich odd-odd iodine isotopes within the framework of projected shell model. Odd-odd nuclei are the best candidates for studying possible structure variations away from the valley of stability. We used the projected shell model, in which the deformed Nilsson single-particle states are being used for the construction of model basis. We studied the band properties of odd-odd I[Formula: see text](Z [Formula: see text] 53) isotopes with neutron numbers N [Formula: see text] 75, 77, 79, 81, 83 and 85. Using model analysis, we presented the low-lying positive- and negative-parity states of these nuclei. In these isotopes, the band structures have been analyzed in terms of quasi-particle configurations and comparative presentation of yrast levels is discussed. The phenomenon of yrast energy splitting is also studied in this work.

Quasi- γ band in Te114

The low-lying non-yrast states in $^{114}$Te have been investigated using the Indian National Gamma Array through the fusion-evaporation reaction $^{112}$Sn($^{4}$He, 2n) at a beam energy of 37 MeV. Eight new $\gamma$-transitions have been placed in the level scheme to establish the quasi-$\gamma$ band in this nucleus. Spin and parity of several excited states have been assigned from the present spectroscopy measurements. The comparison of experimental results on the observed bands with the Interacting Boson Model (IBM) and Triaxial Projected Shell Model (TPSM) confirming the existence of the quasi-$\gamma$ band structure in the $^{114}$Te nucleus.

Microscopic study of nuclear structure dynamics of neutron-deficient even–even 100–110Cd isotopes within the framework of projected shell model

We have studied the deformation systematics of [Formula: see text] and [Formula: see text] values, yrast spectra, band structure and backbending phenomena in the neutron-deficient even–even [Formula: see text]Cd isotopes within the projected shell model (PSM) framework. The observations of the systematics of [Formula: see text] and [Formula: see text] values for [Formula: see text]Cd isotopes are well reproduced in present calculations. Our observations show that, as we move from [Formula: see text]Cd to [Formula: see text]Cd, the deformation increases and then it reduces up to [Formula: see text]Cd. This gives us a confirmation that [Formula: see text]Cd is the most deformed nucleus in this set of isotopic mass chain. The backbending phenomena is also observed in these isotopes, which can be related to the crossing of ground band (g-band) by 2-quasiparticle (qp) bands or s-bands. The pseudomagic character of [Formula: see text]Cd has also been observed.

Study of light tellurium isotopes along the yrast line

The projected shell model is employed to study the light tellurium isotopes along the yrast line. The results are obtained for yrast bands, moment of inertia and B(E2) transition probabilities. Besides this, the systematics of E21+,E41+/E21+ and B(E2;21+⟶01+) and BCS subshell occupation numbers are investigated in light 106−112Te isotopes. The results on moment of inertia predict the occurrence of phenomenon of backbending around the band crosssing region due to the alignment of a pair of neutrons in the neutron 1h11/2 subshell. The maximum collectivity is observed at N = 60 due to the large neutron-proton (n-p) interaction between spin-orbit partner (SOP) [(g9/2)π, (g7/2)ν] orbits and occupation of down slopping components of νh11/2 subshell.

Phenomenological description of non-axial shapes of some doubly even neutron deficient barium isotopes

The evolution of non-axial shapes and rotational structure in even–even 122–132Ba isotopes has been investigated microscopically with the application of a triaxial projected shell model (TPSM). Based on calculations, the shape instability and softness towards γ deformation are predicted for these isotopes. In the present work, the application of three-dimensional angular-momentum projection on multi-quasiparticle configurations, constructed from the triaxially deformed mean field, provides a reliable description of the yrast and near yrast structure in these nuclei. The theoretically obtained backbends demonstrate the importance of decoupling of multi-quasiparticle states for these nuclei. The uniform behaviour of transition probabilities B(E), shown by the present calculations, authenticate the global validity of Grodzin’s product rule. Besides this, the deformation systematics and odd–even staggering in γ bands have also been discussed in the present work.

Evolution of intrinsic nuclear structure in medium mass even-even Xenon isotopes from a microscopic perspective * * Arun Bharti acknowledges the financial support from the Science and Engineering Research Board, under the project file no. CRG/2019/001231 and Ridham Bakshi acknowledges the financial support from The Department of Science and Technology, Government of India, INSPIRE Fellowship under sanction no. DST/INSPIRE Fellowship/2018/IF180368

In this study, the multi-quasiparticle triaxial projected shell model (TPSM) is applied to investigate -vibrational bands in transitional nuclei of . We report that each triaxial intrinsic state has a -band built on it. The TPSM approach is evaluated by the comparison of TPSM results with available experimental data, which shows a satisfactory agreement. The energy ratios, B(E2) transition rates, and signature splitting of the -vibrational band are calculated.

Identification of new transitions and levels in Gd163 from β -decay studies

Background: Neutron-rich nuclei in the mass region around A=160 have been and will continue to be of interest for the study of nuclear structure because of the rapid onset of deformation between 88 and 90 neutrons. The observation of detailed changes in nuclear structures within this mass region has provided and will continue to provide insight into the nuclear force. Purpose: Investigations of γ rays emitted following Eu163 β-decay to Gd163 have been performed for evaluation of the nuclear structure of Gd163. Method: Data were collected at the LeRIBSS station of the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory with an array of four Clover HPGe detectors for γ-rays and two plastic scintillators for β detection. The γ rays were identified as belonging to Gd163 via mass selection and γ-γ-β, x-ray-γ, or γ-γ coincidences. Results: In total 107 new γ-ray transitions were observed in Gd163 from 53 newly identified levels. Conclusions: The structure of Gd163 has been identified for the first time. This structure has been evaluated in comparison to projected shell model, and potential energy surface calculations with good agreement.

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.

A novel method for stellar electron-capture rates of excited nuclear states

We propose a novel shell-model method to calculate stellar electron-capture (EC) rates of highly-excited nuclear states. This method is based on the Projected Shell Model that can incorporate high-order multi-quasiparticle configurations in a large model space. By taking the EC calculation from 59Co to 59Fe as the first example, we study the effects of nuclear excitations (including both single-particle and collective excitations) on the stellar EC rates. It is found that the predicted EC rates exhibit large variations as functions of excitations in both parent and daughter nuclei, which sensitively depend on the density and temperature in the stellar environment. We emphasize the importance of inclusion of multi-quasiparticle configurations constructed in a large model space for the calculation of EC rates used in astrophysical studies.