Gamma rays emitted by fission fragments of Cf-252 and measured using the Gammasphere array continue to give insight into neutron rich nuclei. Using our high statistics data, we have reexamined high-spin states and linking transitions associated with octupole correlations in Ba-143,Ba-145,Ba-146. This has been a region of interest, when it was proposed that near Ba-145 there was a region of octupole deformation. In an even-A system, it is possible that rotational band structures are explainable by simplex quantum numbers, s = +1 and s = -1. The previous bands including octupole bands in Ba-143,Ba-145,Ba-146 have been extended. The new s = i octupole bands in Ba-145 and new s = -1 octupole bands in Ba-146 have been identified. In addition, collective model analysis of energy displacement, rotational frequency and B(E1)/B(E2) ratios have been carried out. Evidence of the rotational consequences of octupole deformation in even-even and even-odd isotopes is given. These nuclei have trends as rotation stabilizes the vibrational degrees of freedom. The experimental results are in agreement with theoretical calculations using the interacting boson and boson fermion models that are based on a universal nuclear energy density functional. (C) 2023 Elsevier B.V. All rights reserved.

Received 16 September 2022Revised 30 January 2023DOI:https://doi.org/10.1103/PhysRevC.107.029902©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic transitionsEnergy levels & level densitiesFissionNuclear structure & decaysProperties90 ≤ A ≤ 149Nuclear Physics

Gamma rays emitted by fission fragments of 252Cf and measured using the Gammasphere array continue to give insight into neutron rich nuclei. Using our high statistics data, we have reexamined high-spin states and linking transitions associated with octupole correlations in 143,145,146Ba. This has been a region of interest, when it was proposed that near 145Ba there was a region of octupole deformation. In an even-A system, it is possible that rotational band structures are explainable by simplex quantum numbers, s=+1 and s=−1. The previous bands including octupole bands in 143,145,146Ba have been extended. The new s=i octupole bands in 145Ba and new s=−1 octupole bands in 146Ba have been identified. In addition, collective model analysis of energy displacement, rotational frequency and B(E1)/B(E2) ratios have been carried out. Evidence of the rotational consequences of octupole deformation in even-even and even-odd isotopes is given. These nuclei have trends as rotation stabilizes the vibrational degrees of freedom. The experimental results are in agreement with theoretical calculations using the interacting boson and boson-fermion models that are based on a universal nuclear energy density functional.

Collective rotational bands were observed for the first time in neutron-rich odd–odd [Formula: see text]La by means of [Formula: see text]-[Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] coincidence measurements of prompt fission [Formula: see text] rays from [Formula: see text]Cf using multi-detector array Gammasphere. Similarity between the yrast band of [Formula: see text]La and those of neighboring [Formula: see text]La, [Formula: see text]Ce was found and interpreted as quasiparticle excitations. PES calculations suggested triaxial deformation for the ground state of 142La. Considerable triaxial and near zero octupole deformations were deduced for the yrast band of [Formula: see text]La by the TRS model calculations. The band-crossing observed in the yrast band of [Formula: see text]La was interpreted to be caused by alignment of the (h[Formula: see text]) 2 proton pair, and the crossing frequency was best reproduced by the TRS calculations taking into account triaxial deformations. In contrast to the interpretations for the band crossing of [Formula: see text]La, alignments of the (i[Formula: see text]) 2 neutron pair were found to be responsible for the band-crossing of the yrast band in the neighboring even-N [Formula: see text]La, and triaxial degree of freedom was found to play a more significant role than octupole deformations in the nucleus, although its [Formula: see text] values deduced are large.

This paper reviews the systematic investigations of the shape transitions and coexistence with regard to triaxial deformations in neutron-rich nuclei with A similar to 100-126, Z from Zr (Z = 40) to Cd (Z = 48). Shape changes with Z, N and spins are addressed. gamma vibrations, chiral symmetry breaking and wobbling motions identified in the region are discussed.

Gamma rays emitted by fission fragments of Cf-252 and measured using the Gammasphere array continue to give insight into neutron rich nuclei. Using our high statistics data, we have reexamined high-spin states and linking transitions associated with octupole correlations in Ba-144 and Ce-148. In an even-A system, it is possible that rotational band structures are explainable by simplex quantum numbers, s = +1 and s = -1. In Ba-144 and Ce-148 we have deduced spin values from angular correlations and assigned parities from mixing ratios for s = -1 characterized states. These are the first examples of both simplex bands in even even nuclei. Extensions to higher spins of bands in Ba-144 and in Ce-148 are also reported. In addition to collective model analysis of energy displacement and rotational frequency, the intrinsic dipole moment via B(E2)/B(E1) ratios are also analyzed.

Multipole mixing ratios have been measured, using Cf-252 spontaneous-fission, gamma-ray coincidence data, for transitions from states in the gamma-vibrational-bands to states in the ground state bands of deformed, neutron-rich isotopes, Mo-102,Mo-104,Mo-106,Mo-108, Ru-108,Ru-110,Ru-112, Pd-112,Pd-114,Pd-116. These mixing ratios have been found to be pure, or nearly pure, E2, in agreement with theory.

E2/M1 mixing ratios have been measured for transitions from states in the \(\gamma\) vibrational bands (\( I^{+}_{\gamma}\)) to states in the ground state bands (\(I^{+}\) or \( [I-1]^{+}\)) of the neutron rich, even-even, deformed isotopes, 102, 104, 106, 108Mo, 108, 110, 112Ru, and 112, 114, 116Pd, including from states as high as \( 9^{+}_{\gamma}\). These measurements were done using the GAMMASPHERE detector array, which, at the time of the experiment, had 101 working HPGe detectors, arranged at 64 different angles. A 62 \(\mu\)Ci source of 252Cf was placed inside GAMMASPHERE yielding \(5.7\times 10^{11}\) \(\gamma\)-\(\gamma\)-\(\gamma\) and higher coincidence events. The angular correlations between the transitions from the \(\gamma\)-bands to the ground bands, and the pure E2 transitions within the ground band were then measured. These angular correlations yielded the mixing ratios, demonstrating that these transitions are pure or nearly pure E2, in agreement with theory. In order to correct for possible attenuation due to the lifetime of the intermediate state in these correlations, the g-factors of the intermediate states needed to be known. Therefore, the g-factors of the 2+ states in the ground state band have been measured.

The level structures of Ru-108,Ru-110,Ru-112 (Z = 44) and Pd-112,Pd-114,Pd-115,Pd-116,Pd-117,Pd-118 (Z = 46) have been significantly expanded through studies of prompt gamma-gamma-gamma and gamma-gamma-gamma-gamma coincidences observed with Gammasphere following the spontaneous fission of Cf-252. Chiral doublet bands were observed in Ru-110,Ru-112. Softness to triaxiality perturbs the bands of Ru-108 and even-N Pd isotopes. In Ru-112, evidence for wobbling motion is found in the behavior of the gamma vibrational band. Similar evidence for wobbling motion is found in Pd-114, the N = 68 isotone of Ru-112. A transition from triaxial prolate to triaxial oblate was found in Pd112-116 with shape coexistent bands in Pd-115. New levels were observed in Gd-162,Gd-163.

This paper reviews the systematic investigations and understanding for the shape transitions and coexistence with regard to triaxial deformations in A ～100 to 126 neutron-rich Rh (Z=45), Pd (Z=46), Ag (Z=47), Cd (Z=48) and Zr (Z=40), Nb (Z=41), Mo (Z=42), Tc (Z=43) isotopes with Z beyond and below Ru (Z = 44), respectively, in Ru the maximal triaxial deformation having been predicted and deduced. The recent measurements and studies of prompt triple-and four-fold,γ-γ-γand γ-γ-γ-γ, coincidence data from the spontaneous fission of 252Cf using Gammasphere have yielded considerable expansion and extension or first observation of the bands in Ru, Pd, Cd, and Nb isotopes, which provided important data for the studies of nuclear shapes in this region. Combined with previous investigations, recent systematic studies of the new data well reproduced by PES, TRS, PSM, CCCSM and SCTAC model calculations have traced shape changes along the isotonic and isotopic chains, re-spectively, and with changing excitations/spins as well, significantly expanding our knowledge of shape transitions/coexistence in nuclei. For the neutron-rich Ru and beyond, Rh, Pd, Ag and Cd isotopes, triaxial deformations γ=?28°, slightly smaller than the maximal value, were deduced in Rh (Z =45) isotopes, with chiral symmetry breaking proposed in 103?106Rh;onset of wobbling motions were identified in 112Ru and 114Pd (N=68), and probably also in 114Ru (N=70);evolution from chiral symmetry breaking in 110,112Ru with maximal triaxial deformations to disturbed chirality in 112,114,116Pd with less pronounced triaxial deformations was proposed; rich nuclear structure was proposed in soft Ag isotopes with possible chiral doubling structure suggested in 104,105Ag, and softness towards triaxial deformation proposed in heavier 115,117Ag;quasi-particle couplings, quasi-rotations and soft triaxiality were suggested in Cd (Z=48) isotopes with small deformations;onset of collectivity was recently suggested in 122,124,126 Cd in the vicinity of Z=50 and N = 82 closed shells by studies of Coulomb excitations; shape evolutions from maximal triaxial deformations in Ru (γ=?30°, with triaxial minimum energy gain of 0.67 MeV), through Rh with large triaxial deformations (γ=?28°), to less pronounced triaxiality in Pd (with triaxial minimum energy gain of 0.32 MeV), then soft triaxiality in Ag, and finally to slightly deformed Cd isotopes but with emergence of collectivity and soft triaxiality were proposed. The systematic studies of the band crossings in Pd revealed up-rising γ drivings of the first band crossings caused by (νh11/2)2 and down-sloping γdrivings of the second band crossings by (πg9/2)2, explained the onset of wobbling motions in 114Pd, and showed a long-sought picture of shape evolution and coexistence in the Pd isotopic chain which is more complete but complex than earlier predictions. Based on the systematic studies in the mass region, maximal triaxial deformation is found to be reached in 112Ru and less-pronounced triaxiality centered at 114Pd, both for N=68, four neutrons more than predicted in earlier theoretical calculations. In the neutron-rich Zr (Z=40), Nb (Z=41), Mo (Z=42) and Tc (Z=43) isotopes with Z just below Ru, large quadrupole deformations of axially symmetric shapes were deduced in Y and Zr isotopes, with emergence of the γ degree of freedom having been suggested for heavier Zr isotopes; medium triaxial deformations were deduced for the ground states of heavier (A>104) Nb isotopes, and, with increasing excitations and spins, evolution from medium triaxial deformations with strong quadrupole deformations at ground states to nearly axially-symmetric shapes were deduced;light Nb isotopes (A 6 103) have near axially-symmetric shapes with strong quadrupole deformations;combining with the identification of onset of strong quadrupole deformation at 100Nb in the Nb isotopic chain, an increase of soft triaxiality with increasing neutron number was proposed in 100?106Nb. Shape coexistence with regard to soft triaxiality is also proposed in Nb isotopes;large triaxial deformations,γvibrations and chiral doublets were proposed in Mo isotopes; chiral doubling and large triaxial deformations (γ ～ ?26°) slightly smaller than the maximal triaxiality were suggested in Tc isotopes. The neutron-rich nuclei with Z ranging from 41 through 48 and A ～100 to 126, especially the Pd and Nb isotopes are thus found to be transitional nuclei with regard to triaxiality.

Analysis of high statistics triple coincidence fission gamma data from Cf-252 at Gammasphere including angular correlations yielded well-expanded high-spin level schemes with more complete and reliable spin/parity assignments for Ge-82, Cd-118,Cd-120,Cd-122 and Rh-114,Rh-115. Both the quasi-particle/hole couplings and quasi-rotational degrees of freedom are implied to play roles in these Cd isotopes. Evidence for triaxial shapes and octupole components in the Cd isotopes is presented. These Cd isotopes may have triaxial deformations. High-spin level schemes of Rh-114,Rh-115 have been established for the first time. The existence of a relatively large signature splitting and an yrare band shows typical features of a triaxially deformed nucleus. Possible excited deformed rotational bands are observed, for the first time, in Ge-82. From the multipole mixing ratio measurement, the ground state configurations of Ru-109,Ru-111, as well as excited states in Mo-103,Mo-107 and Ru-111 were determined.