Triaxial 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.

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.

Observation of quasi-$ \gamma$ bands in Te nuclei

Excited states of 124Te have been studied via 122Sn(9Be,$ \alpha$3n)124Te reaction at 48MeV. The spin and parity of several states have been confirmed on the basis of results of angular correlation ( $ R_{DCO}$ and linear polarization asymmetry measurements. The positive parity band structures of 124Te and 126Te have been investigated and the quasi-$ \gamma$ bands have been proposed in these nuclei. The structures of these bands have also been discussed under the framework of triaxial projected shell model (TPSM) calculations. The TPSM calculations fairly supported the interpretation of quasi-$ \gamma$ bands in 124Te and 126Te. The staggering pattern of odd-even spin states of the quasi-$ \gamma$ band suggests the $ \gamma$-soft behaviour of 124Te and the typical values of staggering factors indicate the presence of the E(5)-critical point symmetry in 124Te. The potential energy surface calculations have also been carried out for 124Te and 126Te, which also supports the $ \gamma$-soft behaviour for these nuclei.

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.

Theoretical study of triaxial shapes of neutron-rich Mo and Ru nuclei

Background: Recently, transition quadrupole moments in rotational bands of even-mass neutron-rich isotopes of molybdenum and ruthenium nuclei have been measured. The new data have provided a challenge for theoretical descriptions invoking stable triaxial deformations. Purpose: To understand experimental data on rotational bands in the neutron-rich Mo-Ru region, we carried out theoretical analysis of moments of inertia, shapes, and transition quadrupole moments of neutron-rich even-even nuclei around $^{110}$Ru using self-consistent mean-field and shell model techniques. Methods: To describe yrast structures in Mo and Ru isotopes, we use nuclear Density Functional Theory (DFT) with the optimized energy density functional UNEDF0. We also apply Triaxial Projected Shell Model (TPSM) to describe yrast and positive-parity, near-yrast band structures. Results: Our self-consistent DFT calculations predict triaxial ground-state deformations in $^{106,108}$Mo and $^{108.110,112}$Ru and reproduce the observed low-frequency behavior of moments of inertia. As the rotational frequency increases, a negative-$\gamma$ structure, associated with the aligned $\nu(h_{11/2})^2$ pair, becomes energetically favored. The computed transition quadrupole moments vary with angular momentum, which reflects deformation changes with rotation; those variations are consistent with experiment. The TPSM calculations explain the observed band structures assuming stable triaxial shapes. Conclusions: The structure of neutron-rich even-even nuclei around $^{110}$Ru is consistent with triaxial shape deformations. Our DFT and TPSM frameworks provide a consistent and complementary description of experimental data.

Nature ofγdeformation in Ge and Se nuclei and the triaxial projected shell model description

Recent experimental data have demonstrated that ${}^{76}$Ge may be a rare example of a nucleus exhibiting rigid $\ensuremath{\gamma}$ deformation in the low-spin regime. In the present work, the experimental analysis is supported by microscopic calculations using the multi-quasiparticle triaxial projected shell model (TPSM) approach. It is shown that to best describe the data of both yrast and $\ensuremath{\gamma}$-vibrational bands in ${}^{76}$Ge, a rigid-triaxial deformation parameter $\ensuremath{\gamma}\ensuremath{\approx}{30}^{\ensuremath{\circ}}$ is required. TPSM calculations are discussed in conjunction with the experimental observations and also with the published results from the spherical shell model. The occurrence of a $\ensuremath{\gamma}\ensuremath{\gamma}$ band in ${}^{76}$Ge is predicted with the bandhead at an excitation energy of $\ensuremath{\sim}$2.5 MeV. We have also performed TPSM study for the neighboring Ge and Se isotopes and the distinct $\ensuremath{\gamma}$-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states.

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.

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.

Abnormal signature inversion and multiple alignments in doubly odd126I

High-spin states in ${}^{126}$I have been investigated by using in-beam $\ensuremath{\gamma}$-ray spectroscopy with the ${}^{124}$Sn(${}^{7}\text{Li},5n$)${}^{126}$I reaction at a beam energy of 48 MeV. The level scheme of ${}^{126}$I has been extended and modified considerably by adding about 80 new $\ensuremath{\gamma}$ rays and establishing five new bands. The configurations have been tentatively assigned for the yrast, yrare, and other excited bands with the help of triaxial projected shell-model (TPSM) and cranked shell-model calculations. The first band crossing in the yrast band is found due to alignments of a pair of ${({h}_{11/2})}^{2}$ neutrons. The first and the second band crossings in the yrare band are caused by the alignments of a pair of ${({d}_{5/2})}^{2}$ protons and a pair of ${({h}_{11/2})}^{2}$ neutrons, respectively. Due to the successive excitations of two, four, and six quasiparticles, the alignments in the yrare band present a gigantic rising feature. The yrast band exhibits a signature inversion at low spins and becomes normal after a reversion spin of ${I}_{\mathrm{rev}}=14$. The yrare band exhibits an abnormal signature inversion in which the signature inversion phase persists up to the highest spin. The signature inversions in ${}^{126}$I are well reproduced and successfully interpreted by the TPSM calculations. Some features of chirality are found for the four-quasiparticle (4qp) part of the yrast band and the 4qp excited band 2.

High-spin structure and multiphononγvibrations in very neutron-richRu114

High-spin levels of the neutron-rich $^{114}\mathrm{Ru}$ have been investigated by measuring the prompt $\ensuremath{\gamma}$ rays in the spontaneous fission of $^{252}\mathrm{Cf}$. The ground-state band and one-phonon $\ensuremath{\gamma}$-vibrational band have been extended up to 14${}^{+}$ and 9${}^{+}$, respectively. Two levels are proposed as the members of a two-phonon $\ensuremath{\gamma}$-vibrational band. A back bending (band crossing) has been observed in the ground-state band at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}$ 0.40 MeV. Using the triaxial deformation parameters, the cranked shell model calculations indicate that this back bending in $^{114}\mathrm{Ru}$ should originate from the alignment of a pair of ${h}_{11/2}$ neutrons. Triaxial projected shell model calculations for the $\ensuremath{\gamma}$-vibrational band structures of $^{114}\mathrm{Ru}$ are in good agreement with the experimental data. However, when using the oblate deformation parameters, both of the above-calculated results are not in agreement with the experimental data.

Study of the Multiphonon γ-Vibrational Bands in Even–Even176–190Pt Isotopes

We study multiphonon γ-vibrational bands in even–even 176–190 Pt isotopes in the framework of the triaxial projected shell model (TPSM), which is based on a fully quantum–mechanical and microscopic theory. The g -band moments of inertia have been calculated for a range of triaxial parameter ε' values, and the ε' value which correctly reproduces the experimental g -band moments of inertia is employed for all further TPSM calculations. The theoretical results, which agree with data on the g - and γ-band spectra in even–even 176–190 Pt isotopes, are discussed in terms of the K -mixing. In addition, the calculations lead to predictions for the 2 + γ-, 4 + 2γ-, and 6 + 3γ-bandhead energies where current experimental data are still sparse.