Three-quasiparticle Configuration Research Articles

Bandhead Energies of npp/pnn Three-Quasiparticle Quadruplets

Semi-empirical frameworks are widely used in calculating the bandhead energies of three-quasiparticle (3qp) configurations observed in well-deformed odd-A nuclei. In the present study, our aim is to improve the previous version of the semi-empirical model [Physical Review C. 1992, 45(6), 3013]. This is achieved by incorporating the ignored vital contributions owing to the irrotational motion of valance protons/neutrons, diagonal components of particle–particle coupling (ppc), and rotor–particle coupling (rpc) terms. We tested the validity of the improved version of the model by calculating the bandhead energies of twelve 3qp npp/pnn quadruplets observed in 163Er, 171,175,177Lu, 177Ta, and 183Re nuclides. Our new results show better agreement with the experimental data indicating the importance of newly added terms. We strongly expect that the present version of the model will provide support to future experimental campaigns for making configuration assignments to the newly observed 3qp bands and also in the identification of exact Nilsson’s configurations of 3qp quadruplets where experimental data that differentiate among the competing configuration are scarce.

Investigation of isomeric states in Rf255

Using the GABRIELA detector array, $\ensuremath{\gamma}$-ray and internal-conversion-electron decay spectroscopy has been performed on $^{255}\mathrm{Rf}$ nuclei that were produced via the $^{207}\mathrm{Pb}(^{50}\mathrm{Ti},2n)^{255}\mathrm{Rf}$ fusion-evaporation reaction using the SHELS velocity filter. Three isomers were identified in $^{255}\mathrm{Rf}$ with the aid of Geant4 simulations. The existence of two high-$K$ isomeric states in cascade has been confirmed. Possible three-quasiparticle configurations involving the coupling of the unpaired $9/{2}^{\ensuremath{-}}[734]$ neutron to two-quasiparticle states have been suggested and a likely decay scenario has been proposed on the basis of comparisons to Geant4 simulations. The simulations have also confirmed the existence of the $5/{2}^{+}[622]$ spin isomer at low excitation energy.

Systematic study of near-yrast band structures in odd-mass Pr125−137 and Pm127−139 isotopes

In the present work, the basis space in the triaxial projected shell model approach is expanded to include three and five quasiparticle configurations for odd-proton systems. This extension allows to investigate the high-spin band structures observed in odd-proton systems up to and including the second band crossing region, and as a first major application of this development, the high-spin properties are investigated for odd-mass $^{125-137}$Pr and $^{127-139}$Pm isotopes. It is shown that band crossings in the studied isotopes have mixed structures with first crossing dominated by one-proton coupled to two-neutron configuration for the lighter isotopes which then changes to three-proton configuration with increasing neutron number. Further, $\gamma$-bands based on quasiparticle states are also delineated in the present work, and it is predicted that these band structures built on three-quasiparticle configurations become favoured in energy for heavier systems in the high-spin region.

Possible ‘stapler’ band in 109Ag nucleus

High-spin states of 109Ag have been studied using the 7Li + 110Pd reaction at a beam energy of 46 MeV. A negative-parity band decaying to the ground-state band by several new linking transitions is established. Meanwhile, seven new E2 crossover transitions of this band are observed, thereby confirming the spin-parity assignment and ordering of the dipole transitions above the Iπ = 19/2− level. A low energy γ-ray transition of 88 keV is found and placed at the bottom of the negative-parity band, and thus the Iπ = 17/2− level is tentatively assigned as the lowest observed state of this band. Experimental excitation energies and total angular momenta of the negative-parity band are compared with the predictions of self-consistent titled axis cranking relativistic mean-field theory with a three-quasiparticle configuration of . Based on the theoretical description and the analyses of the angular momentum coupling, this negative-parity dipole band is suggested as a ‘stapler’ band. By investigating the angular momentum components, it is found that the valence nucleons in the low-j orbitals play an active role in the ‘stapler’ mechanism.

Evidence for pseudospin-chiral quartet bands in the presence of octupole correlations

Three nearly degenerate pairs of doublet bands are identified in 131Ba. Two of them, with positive-parity, are interpreted as pseudospin-chiral quartet bands. This is the first time that a complete set of chiral doublet bands built on the pseudospin partners π(d5/2,g7/2) is observed. The chiral bands with opposite parity built on 3-quasiparticle configurations are directly connected by many E1 transitions, without involving an intermediary non-chiral configuration. The observed band structures in 131Ba have been investigated by using the reflection-asymmetric particle rotor model. The energies and the electromagnetic transition ratios of the three pairs of doublet bands observed in 131Ba are reproduced and they are interpreted as chiral doublet bands with three-quasiparticle configurations. It is the first time that multiple chiral bands are observed in the presence of enhanced octupole correlations and pseudospin symmetry.

Systematic investigations of positive-parity doublet bands with three-quasiparticle configurations in Cs125,127,129,131

The experimental features of positive-parity doublet bands in the odd-\emph{A} cesium isotopes $^{125,127,129,131}$Cs, including angular momentum alignment, energy staggering, $B(M1)/B(E2)$ etc. are studied systematically and compared to those of the candidate chiral bands in the adjacent odd-odd Cs isotopes. The configuration assignments and the dynamics of these bands are discussed. The self-consistent tilted axis cranking relativistic mean-field calculations are performed with configuration reassigned to these bands. The experimental level schemes of four nuclei are well reproduced, and the calculations also show four nuclei have obvious triaxial deformations and thus support the candidate chiral doublet bands in $^{125,127,129,131}$Cs.

Negative parity three-quasiparticle band in 127I

The excited states of 127I were populated via 124Sn(7Li, 4n $\gamma$ ) fusion-evaporation reaction at $ E_{beam} = 33$ MeV. A strongly coupled $\Delta I = 1$ band has been established above 2423keV state with $J^{\pi} = 19/2^{-}$ as bandhead, likely to be associated with the three-quasiparticle configuration. Spin and parity of these multi-quasiparticle states have been confirmed from DCO ratio and linear polarization asymmetry of depopulating $\gamma$ -rays. The parity of these states have been found altered from their previous assignment.

A new high-spin isomer in 195Bi

A new high-spin isomer has been identified in 195Bi at the focal plane of the HYbrid Recoil mass Analyser (HYRA) used in the gas-filled mode. The fusion evaporation reactions 169Tm (30Si, x n) 193, 195Bi were used with the beam energies on targets of 168 and 146MeV for 6n and 4n channels, respectively. The evaporation residues, separated from the fission fragments, and their decays were detected at the focal plane of HYRA using MWPC, Si-Pad and clover HPGe detectors. The half-life of the new isomer in 195Bi has been measured to be 1.6(1)μs. The configuration of the new isomer has been proposed and compared with the other isomers in this region. The Total Routhian Surface (TRS) calculations for the three-quasiparticle configurations corresponding to the new isomer suggest an oblate deformation for this isomeric state. The same calculations for different configurations in 195Bi and for the even-even 194Pb core indicate that the proton i 13/2 orbital has a large shape driving effect towards oblate shape in these nuclei.

High spin band structure of3885Sr47

High spin states in the $^{85}\mathrm{Sr}$ nucleus were populated in the reaction $^{76}\mathrm{Ge}({}^{13}\text{C},4n)$ at a beam energy of 45 MeV. The $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ and $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidence measurements have been utilized to establish the level scheme of $^{85}\mathrm{Sr}$ up to ${I}^{\ensuremath{\pi}}=35/{2}^{\ensuremath{-}}$. Nearly 50 new $\ensuremath{\gamma}$ rays and about 25 new levels were identified and most of the previously known levels confirmed. The spin-parity assignment of the levels was made by using the directional correlations of the oriented nuclei ratios and polarization asymmetry measurements. The shell-model calculations have been performed by using two recent interactions, JUN45 and jj44b, for a detailed comparison between theoretical results and the experimental data obtained in the present work. The shell-model results are in good agreements with the experimental data and are able to explain the various features such as the odd-even staggering well. Tilted axis cranking calculations were also performed to understand the magnetic rotation (MR) phenomenon at higher spins. One of the positive-parity $\ensuremath{\Delta}I=1$ bands has been assigned a three-quasiparticle (3qp) configuration, which appears to behave like a MR band. A negative-parity band populated up to ${I}^{\ensuremath{\pi}}=35/{2}^{\ensuremath{-}}$ was also assigned a 3qp configuration at low spin and a five-quasiparticle configuration at high spin; however, it does not exhibit the expected MR features, in contrast to a similar band in the $^{83}\mathrm{Kr}$ nucleus.

High spin structure in 130,131Ba

High spin states of 130,131Ba have been investigated via fusion evaporation reactions 122Sn(13C,4n)131Ba and 122Sn(13C, 5n)130Ba at $ E_{beam}=65$ MeV. The level schemes of 130,131Ba have been extended by placing several new $ \gamma$ transitions. A few interband transitions connecting two negative-parity bands, which are the experimental fingerprints of signature partners, have been established in 130Ba. Spin and parity of a side band have been assigned in 131Ba and this dipole band is proposed to have a three-quasiparticle configuration, $ \nu h_{11/2}\otimes\pi h_{11/2}\otimes\pi g_{7/2}$ . The observed band structures and nuclear shape evolution as a function of the angular momentum have been discussed in the light of Total-Routhian-Surface calculations.

The Influence of Triaxiality Parameter γ on the Chiral Doublet Bands with (πg9/2)−1 (νh11/2)2 Configuration

The chiral doublet bands with three-quasiparticle configuration (πg9/2)−1 (νh11/2)2 are studied by the fully quantal triaxial particle rotor model. The energy spectra and B(M1)/B(E2) ratios of the doublet bands with different triaxiality parameter γ are systematically analyzed. It is found that γ is a sensitive parameter for the properties of these doublet bands.

High-spin states in127I

In-beam $\ensuremath{\gamma}$ spectroscopy of the stable nucleus ${}^{127}$I has been studied experimentally using the ${}^{124}$Sn(${}^{7}$Li, 4$n\ensuremath{\gamma}$)${}^{127}$I reaction at a beam energy of 32 MeV. The high-spin level scheme of ${}^{127}$I is extended significantly. Negative-parity levels built on the $11/{2}^{\ensuremath{-}}$, $\ensuremath{\pi}{h}_{11/2}$ particle state are observed up to $(35/{2}^{\ensuremath{-}})$ and described as a decoupled band, extending our knowledge of decoupled structures to the most neutron-rich stable iodine isotope. Two $\ensuremath{\Delta}I=2$ yrast positive-parity sequences are proposed to be associated with the $\ensuremath{\pi}{g}_{7/2}$ configuration due to observations of several strong interband transitions, and two weakly populated $\ensuremath{\Delta}I=2$ positive-parity bands are newly identified and interpreted as arising mainly from the $\ensuremath{\pi}{d}_{5/2}$ configuration. Three-quasiparticle configurations are assigned to the ${I}^{\ensuremath{\pi}}=15/{2}^{+}$ and $23/{2}^{+}$ states according to the existing knowledge in neighboring nuclei; irregular noncollective and regular collective excitations built on these two ($15/{2}^{+}$ and $23/{2}^{+}$) states are observed to coexist at similar energies. The observed three-quasiparticle band structures are further interpreted with the aid of configuration-constrained potential energy surface calculations.

Residual interactions and theK-mixing-induced fast decay of the three-quasiparticle isomer in171Tm

The anomalously fast decay of a $19/{2}^{+}$ three-quasiparticle isomer in ${}^{171}$Tm was interpreted recently as an example of $K$ mixing induced by a very small mixing matrix element but a (random) close proximity to a collective state. To understand the source of the residual interaction we have generalized the projected shell model by introducing two-body octupole and hexadecupole forces into the Hamiltonian and expanding the model space with inclusion of specific three-quasiparticle configurations. It is found that the $K$ mixing is built up from small interactions transferred through numerous highly excited configurations that contain high-$j$ orbitals. While the chance near-degeneracy enhances the transition strength, the octupole correlation and Coriolis coupling produce the mixing matrix element.

Band structures inCs129

The $^{122}\mathrm{Sn}(^{11}\mathrm{B},4n)$ fusion-evaporation reaction at ${E}_{\mathrm{lab}}=60$ MeV was used to populate excited states in $^{129}\mathrm{Cs}$, and the deexcitations were investigated using in-beam $\ensuremath{\gamma}$-ray spectroscopic techniques. The level scheme of $^{129}\mathrm{Cs}$ is established up to \ensuremath{\sim}8 MeV excitation energy and 47/2 \ensuremath{\Elzxh} spin. The observed band structures are interpreted for their configurations in the framework of cranking model calculations and systematic of the neighboring ${}_{55}$Cs isotopes. A negative-parity $\ensuremath{\Delta}I=1$ coupled band has been assigned the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}({h}_{11/2}){}^{2}$ configuration as solution of the tilted-axis cranking, which coexists with the $\ensuremath{\pi}{h}_{11/2}$ yrast band resulting from the principal-axis cranking. A new band has been identified as a $\ensuremath{\gamma}$-vibrational band built on the $\ensuremath{\pi}{h}_{11/2}$ orbital. A pair of strongly coupled positive-parity bands exhibiting similar features have been assigned different unpaired three-quasiparticle configurations involving the $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ component. The previously identified unfavored signature partners of the $\ensuremath{\pi}{d}_{5/2}$ and $\ensuremath{\pi}{g}_{7/2}$ bands are reassigned as $\ensuremath{\gamma}$ vibrations of the core coupled to the $\ensuremath{\pi}{g}_{7/2}$ single-particle configuration, and the favored signature of the $\ensuremath{\pi}{d}_{5/2}$ band, respectively.

Multiple band structures ofCs131

Excited states in $^{131}\mathrm{Cs}$ were investigated through in-beam $\ensuremath{\gamma}$-ray spectroscopic techniques following its population in the $^{124}\mathrm{Sn}$($^{11}\mathrm{B}$, $4n$) fusion-evaporation reaction at a beam energy of 46 MeV. The previously known level scheme has been substantially extended up to $\ensuremath{\sim}$9 MeV excitation energy and $49/2\ensuremath{\hbar}$ spin with the addition of seven new band structures. The present level scheme consisting of 15 bands exhibits a variety of collective features in this nucleus at intermediate spin. The excitation energies of the observed levels in different bands and the corresponding ratios of transition strengths, i.e., $B(M1)/B(E2)$, have been compared with the results of projected deformed Hartree-Fock calculations based on various quasiparticle configurations. A strongly coupled band has been reassigned a high-$K$ three-quasiparticle $\ensuremath{\pi}{h}_{11/2}\ensuremath{\bigotimes}\ensuremath{\nu}({h}_{11/2}{d}_{3/2})$ configuration based on the properties of this band and that of its new coupled side band. The configurations of these bands are also discussed in the framework of tilted-axis cranking model calculations and the systematics of the odd-$A$ Cs isotopes. Additional three energetically closely placed coupled bands have been assigned different unpaired three-quasiparticle configurations. $\ensuremath{\gamma}$-vibrational bands coupled to the $\ensuremath{\pi}{h}_{11/2}$ and $\ensuremath{\pi}{g}_{7/2}$ single-particle configurations have been reported in this nucleus. Observation of new $E1$ transitions linking the opposite-parity $\ensuremath{\pi}{h}_{11/2}$ and $\ensuremath{\pi}{d}_{5/2}$ bands provides fingerprints of possible octupole correlations.

Theoretical description of the fourth-forbidden non-unique β decays ofCd113andIn115

The half-lives and $\mathrm{log}\mathit{ft}$ values for the fourth-forbidden non-unique beta decays of the ground states of $^{113}\mathrm{Cd}$ and $^{115}\mathrm{In}$ were calculated using a transparent formulation for the ${\ensuremath{\beta}}^{\ensuremath{-}}$ transition amplitude. The microscopic quasiparticle-phonon model (MQPM) was used to calculate the initial and final states of the transitions. The corresponding wave functions were described as linear combinations of one- and three-quasiparticle configurations built in a realistic single-particle model space by using a realistic microscopic two-body interaction. The computed results for the $\mathrm{log}\mathit{ft}$ values and half-lives are reasonably close to the available experimental data.

Rotational structures in the 125Cs nucleus

The collective band structures of the 125Cs nucleus have been investigated by in-beam γ-ray spectroscopic techniques following the 110Pd ( 19F, 4n) reaction at 75MeV. The previously known level scheme, with rotational bands built on πg7/2, πg9/2 and πh11/2 orbitals, has been extended and evolves into bands involving rotationally aligned ν(h11/2)2 and π(h11/2)2 quasiparticles. A strongly coupled band has been reassigned a high-K πh11/2 ⊗ νg7/2 ⊗ νh11/2 three-quasiparticle configuration and a new side band likely to be its chiral partner has been identified. Configurations assigned to various bands are discussed in the framework of Principal/Tilted Axis Cranking (PAC/TAC) model calculations.

Evolution of the $\pi g_{9/2} \nu h_{11/2}^{2}$ multiplet in the neutron-rich 49 In isotopes: Evidence for the gradual filling of the neutron sub-shell

High-spin states from the three-quasiparticle (3qp) configuration $\pi$ g $_{9/2}\nu$ h11/2 2 in the neutron-rich 49In isotopes have been studied in the framework of shell model calculation. The two-body residual interactions needed for such calculations have been extracted from the level schemes of neighbouring nuclei. In particular, the evolution of the proton-neutron $\pi g_{9/2}\nu h_{11/2}$ interaction has been analyzed as a function of the neutron number. When the gradual filling of the $\nu h_{11/2}$ sub-shell is taken into account, the results of the 3qp configuration calculations are found to be very close to the experimental positive-parity yrast states located above 2 MeV excitation energy in $^{113\mbox{--}121}$ In. Moreover, several long-lived isomeric states with positive parity are predicted in 123,125,127In.

Magnetic and collective rotation in79Br

Excited states of the nucleus ${}^{79}\mathrm{Br}$ were investigated via the reaction ${}^{76}\mathrm{Ge}{(}^{7}\mathrm{Li},4n)$ at a beam energy of 35 MeV. Coincidence data of emitted \ensuremath{\gamma} rays were measured with an arrangement of six EUROBALL CLUSTER detectors. The $E2$ bands built on the ${9/2}^{+}$ and ${3/2}^{\ensuremath{-}}$ states were extended up to $J=37/2$ at $E\ensuremath{\approx}8.8 \mathrm{MeV}.$ The $M1$ band starting with a ${15/2}^{\ensuremath{-}}$ state at 2.6 MeV was observed up to $J=(29/2)$ at $E=6.4 \mathrm{MeV}.$ Crossover $E2$ transitions within this band were observed for the first time. Mean lifetimes of 17 levels were deduced using the Doppler-shift-attenuation method. The $M1$ band can be described within the tilted-axis-cranking model on the basis of the tilted three-quasiparticle configuration $\ensuremath{\pi}{(g}_{9/2}) \ensuremath{\nu}{(g}_{9/2}) \ensuremath{\nu}(\mathrm{fp})$ which has a triaxial shape. This band appears as a mixed case including contributions of both magnetic and collective rotation.

General properties of the πh9/2[541]1/2 − configuration and level scheme of 165Tm

165Tm has been studied through the reactions 150Nd( 19F, 4n), E beam=85 MeV and 154Sm ( 15N, 4n), E beam=70 MeV. The level scheme has been extended to spin 71/2 −ℏ, and four new bands have been added. Two are assigned to the K=17/2, three-quasiparticle configurations, π[523]7/2 −⊗ ν[642]5/2 +⊗ ν[523]5/2 − and π[404]7/2 +⊗ ν[642]5/2 +⊗ ν[523]5/2 −, and the remaining two are assigned to γ-vibrations coupled to an h 9/2 proton. Lifetimes of high-spin states in the [541]1/2 − and [411]1/2 + bands have been measured using DSAM techniques, allowing transition quadrupole moments to be deduced. Furthermore, crossings between the [541]1/2 − and [523]7/2 − bands and between the [411]1/2 + and [404]7/2 + bands are analysed with a band-mixing calculation to obtain the quadrupole moments of the [523]7/2 − and [404]7/2 + bands. While the [523]7/2 −, [411]1/2 + and [404]7/2 + bands all have similar deformations, the [541]1/2 − band has a quadrupole moment approximately 15% larger. The relative deformations are in good agreement with diabatic potential energy surface calculations performed using the code “Ultimate Cranker”. The experimental crossing frequency, due to the alignment of i 13/2 neutrons, is found to be delayed in the [541]1/2 − band compared to the other bands. This is a universal feature in the rare-earth region, and extensive systematic Cranked Shell Model calculations have been performed to predict deformations and crossing frequencies for nuclei in the region. The model is unable to reproduce the full delay in crossing frequency, confirming that deformation alone is not responsible for the shift.