Nilsson Potential Research Articles

Parity-doublet bands in the odd- A isotones U237 and Pu239 investigated by a particle-number-conserving method based on the cranked shell model

Based on the reflection-asymmetric Nilsson potential, the parity-doublet rotational bands in odd-$A$ isotones \element{237}U and \element{239}Pu have been investigated by using the particle-number-conserving (PNC) method in the framework of the cranked shell model (CSM). The experimental kinematic moments of inertia (MOIs) and angular momentum alignments are reproduced very well by the PNC-CSM calculations. The significant differences of rotational properties between \element{237}U and \element{239}Pu are explained with the contribution of nucleons occupying proton octupole-correlation pairs of $\pi ^{2} i_{13/2}f_{7/2}$. The upbendings of moments of inertia of the parity-doublet bands in \element{237}U are due to the interference terms of alignments of protons occupying $\pi f_{7/2}$ (${1/2}$) and the high-$j$ intruder $\pi i_{13/2}$ $(1/2, 3/2)$ orbitals. The splittings between the simplex partner bands of the parity-doublet bands in both \element{237}U and \element{239}Pu result from the contribution of alignment of neutron occupying the $\nu d_{5/2}$ ($1/2$) orbital.

Investigation of Gamow–Teller strength of 186Hg within deformed pn-QRPA

Recently, the total absorption gamma spectroscopy technique was used to determine the Gamow–Teller (GT) distribution of β-decay of 186Hg. It was concluded that the best description of the measured data was obtained with dominantly prolate components for both parent 186Hg and daughter 186Au. Motivated by the recent findings, we investigate the effect of nuclear deformation on the energy distribution of the GT strength of the decay of 186Hg into 186Au within the framework of proton–neutron quasiparticle random phase approximation (pn-QRPA) based on the deformed Nilsson potential. To do the needful, we first calculate the energy levels and shape prediction of 186Hg within the interacting boson model. The computed GT strength distribution satisfied the model-independent Ikeda sum rule 100% (99.98%) for the prolate (oblate) case. Based on the strength distributions, the deformed pn-QRPA model with separable interaction prefers a prolate shape for the ground state of 186Hg and supports the shape coexistence for this nucleus.

Alternating-parity bands of U236,238 and Pu238,240 in a particle-number-conserving method based on the cranked shell model

The particle-number-conserving (PNC) method in the framework of cranked shell model (CSM) is developed to deal with the reflection-asymmetric nuclear system by applying the ${S}_{x}$ symmetry. Based on an octupole-deformed Nilsson potential, the alternating-parity bands in $^{236,238}\mathrm{U}$ and $^{238,240}\mathrm{Pu}$ are investigated. The experimental kinematic moments of inertia (MoI) and the angular momentum alignments of all studied bands are reproduced well in the PNC-CSM calculations. The striking difference of rotational behaviors between U and Pu isotopes can be linked to the strength of octupole correlations. The upbendings of the alternating-parity bands in $^{236,238}\mathrm{U}$ are due to the alignments of pairs of nucleons occupying $\ensuremath{\nu}{g}_{9/2}, \ensuremath{\pi}{f}_{7/2}$ orbitals and $\ensuremath{\nu}{j}_{15/2}, \ensuremath{\pi}{i}_{13/2}$ high-$j$ intruder orbitals. In particular, the interference terms of nucleon occupying the octupole-correlation pairs of ${\ensuremath{\nu}}^{2}{j}_{15/2}{g}_{9/2}$ and of ${\ensuremath{\pi}}^{2}{i}_{13/2}{f}_{7/2}$ give a very important contribution to the suddenly gained alignments.

Rotational excitations in rare-earth nuclei: A comparative study within three cranking models with different mean fields and treatments of pairing correlations

High-spin rotational bands in rare-earth Er ($Z=68$), Tm ($Z=69$) and Yb ($Z=70$) isotopes are investigated by three different nuclear models. These are (i) the cranked relativistic Hartree-Bogoliubov (CRHB) approach with approximate particle number projection by means of the Lipkin-Nogami (LN) method, (ii) the cranking covariant density functional theory (CDFT) with pairing correlations treated by a shell-model-like approach (SLAP) or the so called particle-number conserving (PNC) method, and (iii) cranked shell model (CSM) based on the Nilsson potential with pairing correlations treated by the PNC method. A detailed comparison between these three models in the description of the ground state rotational bands of even-even Er and Yb isotopes is performed. The similarities and differences between these models in the description of the moments of inertia, the features of band crossings, equilibrium deformations and pairing energies of even-even nuclei under study are discussed. These quantities are considered as a function of rotational frequency and proton and neutron numbers. The changes in the properties of the first band crossings with increasing neutron number in this mass region are investigated. On average, a comparable accuracy of the description of available experimental data is achieved in these models. However, the differences between model predictions become larger above the first band crossings. Because of time-consuming nature of numerical calculations in the CDFT-based models, a systematic study of the rotational properties of both ground state and excited state bands in odd-mass Tm nuclei is carried out only by the PNC-SCM. With few exceptions, the rotational properties of experimental 1-quasiparticle and 3-quasiparticle bands in $^{165,167,169,171}$Tm are reproduced reasonably well.

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.

Study of nuclear structure of odd mass 119–127I nuclei in a phenomenological approach

By using the phenomenological approach of Projected Shell Model (PSM), the positive and negative-parity band structures of odd mass neutron-rich 119–127I nuclei have been studied with the deformed single-particle states generated by the standard Nilsson potential. For these isotopes, the band structures have been analyzed in terms of quasi-particles configurations. The phenomenon of backbending in moment of inertia is also studied in the present work. Besides this, the reduced transition probabilities, i.e. B(E2) and B(M1), are obtained from the PSM wavefunction for the first time for yrast bands of these isotopes.

Studying thermal properties of 45Sc in static path approximation

We have extracted thermal quantities such as chemical potential and heat capacity of the nucleons system of 45Sc in the static path approximation. This method was used in order to take into account the pairing correlations between the nucleons and the fluctuations of the nucleus finite system. The single particle energies of the nucleons which were used in the calculations have been extracted by the use of the modified Nilsson potential. The results have been compared with the corresponding values calculated in the other microscopic models and the empirical values which were extracted by the use of the experimental data on nuclear level densities.

Excited quasiparticles and entropy in 161,162Dy

In this paper, the nuclear level densities of [Formula: see text]Dy is studied by the use of a microscopic theory which includes nuclear pairing interaction. It is based on the modified harmonic oscillator model according to the Nilsson potential. The entropy of even–odd and even–even nuclei as a function of nuclear temperature is obtained. The entropy excess of [Formula: see text]Dy is compared with that of [Formula: see text]Dy. It is concluded that the difference is related to the entropy carried by the neutron hole coupled to the even–even core. The numbers of excited quasiparticles are calculated. Good agreement was observed between calculated results and the experimental data.

Collective properties of neon isotopes investigated by projected shell model

Collective phenomenon in neon isotopes is an interesting topic. However, even the ground-state deformations cannot be well described by theories. Recently, QJ Zhi and ZZ Ren [Phys Lett B 638: 166 (2006)] have suggested an improved Nilsson potential, which can give a suitable description of ground-state properties in magnesium isotopes. In order to test the description of neon isotopes located around the “island of inversion”, we have used this potential to provide the deformed basis for the projected-shell-model calculations. The low-lying spectra and transition properties of neon isotopes can be reproduced reasonably. The gyromagnetic factors of neon isotopes have also been investigated. The structures of excited states along the yrast line are studied in the language of band diagrams.

Coexisting shapes with rapid transitions in odd-Zrare-earth proton emitters

The phenomenon of shape coexistence and rapid shape phase transitions expected in deformed odd-$Z$ proton emitters from $Z=51$ to 75 are investigated using the triaxially deformed Nilsson potential and Strutinsky's prescription for the evaluation of shell correction. Calculations suggest prolate and triaxial shapes with large deformations except for a few oblate deformations, along with the occurrence of some coexisting configurations with different intrinsic shapes. Shape coexistence is observed in ${}^{113}$Cs with two energy minima for different shapes at similar energies. Location of the first proton unbound nuclei for odd-$Z$ rare-earth region is predicted and compared with the available experimental data.

Projected shell model study of quasiparticle structure of arsenic isotopes

Odd-mass isotopic chain of 67–79As has been studied within the context of the projected shell model. Deformed single-particle states generated by the standard Nilsson potential are used to calculate various nuclear structure properties like yrast spectra, rotational frequencies and reduced transition probabilities. The study of band structures of these As nuclei based on the band diagrams indicates the presence of multi-quasiparticle structure in the high spin realm of these nuclei. Rotational alignment phenomenon has also been studied in terms of band crossing which is understood to occur due to the rotational alignment of g9/2 neutron pair. We also have compared the results of the present calculations with the available experimental as well as the other theoretical data and an overall good agreement has been achieved between the two.

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.

Prolate non-collective-A rare shape phase in high spin state proton emitters141–144Ho and131–135Eu

Structural transitions in high spin states of deformed odd - Z proton emitters 141–144 Ho and 131–135 Eu are studied in a theoretical framework using the deformed Nilsson potential and Strutinsky’s prescription combined with statistical theory of hot rotating nuclei. These proton emitters are found to exhibit shape transition to a rare prolate non-collective shape phase in excited high spin state which is caused directly by rotation at certain angular momentum values which creates a residual quantum shell effect. This phase exists only in a narrow domain bound by the two spin dependent very low critical temperatures. This unexpected prolate noncollective phase generated by rotation undergoes the expected transition to the oblate noncollective phase at higher angular momentum values. Phenomenon of shape coexistence with prolate and oblate non-collective shapes is also speculated in high spin state 131 Eu.

Nuclear prolate-shape dominance with the Woods-Saxon potential

We study the prolate-shape predominance of the nuclear ground-state deformation by calculating the masses of more than two thousand even-even nuclei using the Strutinsky method, modified by Kruppa, and improved by us. The influences of the surface thickness of the single-particle potentials, the strength of the spin-orbit potential, and the pairing correlations are investigated by varying the parameters of the Woods-Saxon potential and the pairing interaction. The strong interference between the effects of the surface thickness and the spin-orbit potential is confirmed to persist for six sets of the Woods-Saxon potential parameters. The observed behavior of the ratios of prolate, oblate, and spherical nuclei versus potential parameters are rather different in different mass regions. It is also found that the ratio of spherical nuclei increases for weakly bound unstable nuclei. Differences of the results from the calculations with the Nilsson potential are described in detail.

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.

Microscopic study of nuclear level densities and thermodynamical properties in 170,171,172Yb

The nuclear level density and entropy were extracted for 170,171,172Yb isotopes within microscopic theory, which includes nuclear pairing interaction. The calculations were based on the modified harmonic oscillator according the Nilsson potential for deformed nuclei. From the level densities, thermodynamical quantities such as temperature and entropy have been deduced. The entropies of the neutron hole and particle are estimated from the entropy difference between the odd-mass and even–even nuclei. The critical temperature of the pair-breaking process is found to be Tc ∼ 0.4–0.5 MeV. The results were compared with experimental data obtained by the Oslo group.

Microscopic insight into the structure of gallium isotopes

Abstract Projected Shell Model technique has been applied to odd- A 71–81 Ga nuclei with the deformed single-particle states generated by the standard Nilsson potential. Various nuclear structure quantities have been calculated with this technique and compared with the available experimental data in the present work. The known experimental data of the yrast bands in these nuclei are persuasively described and the band diagrams obtained for these nuclei show that the yrast bands in these odd- A Ga isotopes donʼt belong to the single intrinsic state only but also have multi-particle states. The back-bending in moment of inertia and the electric quadrupole transitions are also calculated.

Fingerprint states in 115,117,119I in the framework of the particle-rotor model

Odd-mass iodine nuclei with Z = 53 have low-lying ΔJ = 1 and ΔJ = 2 bands based on πg9/2 and πh11/2 orbitals. Using the particle-rotor model we have investigated the band structure of these states. In this model, the experimental excitation energies of the A + 1 core were fed directly as the input parameter. A standard axially symmetric Nilsson potential has been used with prolate deformation. The parameters of the model were chosen from earlier theoretical work and experimental odd–even mass difference. Only the Coriolis attenuation factor has been treated as the adjustable parameter. We have also investigated the alignment plot to study the alignments of these bands up to fairly high spin. The extracted B(M1)/B(E2) ratios for the band based on πg9/2 orbital have been utilized to obtain information about the deformation parameter. With the same deformation parameter excellent agreement has been achieved in the relative bandhead separation of the πg9/2 and πh11/2 bands. The band structure of the πg9/2 as well as πh11/2 band has been calculated with that deformation. The experimental transition probability and branching ratio were also compared with the calculated data.

The study of shape and shape-coexistence of neutron rich nuclei around N=28

With the isospin-dependent Nilsson potential, we calculate the properties of the N=28 nuclei in the framework of macroscopic-microscopic model. The shape and shape coexistence of these nuclei are calculated and discusses. It is shown that strong shape coexistences occur in the ground state of nuclei with N=28 in Na, Mg and Al isotopes. It is pointed out that, the ground state of 42Si is oblate shape and there is no obvious shape coexistence for 42Si.

Competition in rotation-alignment between high-jneutrons and protons in transfermium nuclei

The study of rotation-alignment of quasiparticles probes sensitively the properties of high-$j$ intruder orbits. The distribution of very-high-$j$ orbits, which are consequences of the fundamental spin-orbit interaction, links with the important question of single-particle levels in superheavy nuclei. With the deformed single-particle states generated by the standard Nilsson potential, we perform Projected Shell Model calculations for transfermium nuclei where detailed spectroscopy experiments are currently possible. Specifically, we study the systematical behavior of rotation-alignment and associated band-crossing phenomenon in Cf, Fm, and No isotopes. Neutrons and protons from the high-$j$ orbits are found to compete strongly in rotation-alignment, which gives rise to testable effects. Observation of these effects will provide direct information on the single-particle states in the heaviest nuclear mass region.