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A systematic investigation of the wobbling band structures observed in odd-mass nuclei of $^{161,163,165,167}$Lu, $^{167}$Ta $^{131}$Cs, $^{135}$Pr, $^{151}$Eu, $^{183}$Au, $^{133}$Ba, $^{105}$Pd, $^{133}$La, $^{187}$Au and $^{127}$Xe is performed using the triaxial projected shell model (TPSM) approach. It is demonstrated that all the studied band structures have transverse wobbling mode, except for $^{133}$La, $^{187}$Au (negative parity), $^{183}$Au (positive parity) and $^{127}$Xe nuclei where the wobbling frequency increases with spin, indicating that the collective motion has a longitudinal character. To elucidate further the wobbling nature of the band structures, electromagnetic transition probabilities have been evaluated and it is observed that inter-band transitions are dominated by $E2$ rather than $M1$ as expected for a typical signature partner band. It is shown that TPSM approach provides a reasonable description of all the measured properties of the studied nuclei., Comment: Version of the submitted version on arxiv to be published as chapter 12 of the book titled "Chirality and wobbling in Nuclei" by Taylor & Francis

The importance of the isospin symmetry and its breaking in elucidating the properties of atomic nuclei is reviewed. The quark mass splitting and the electromagnetic origin of the isospin symmetry breaking (ISB) for nuclear many-body problem is discussed. The experimental data on isobaric analogue states cannot be described only with the Coulomb interaction, and ISB terms in the nucleon-nucleon interaction are needed to discern the observed properties. In the present work, the ISB terms are explicitly considered in nuclear energy density functional and spherical shell model approaches, and a detailed investigation of the analogue states and other properties of nuclei is performed. It is observed that isospin mixing is largest for the $N=Z$ system in the density functional approach., Comment: 44 pages, 19 figures

An experimental investigation of $^{105}$Pd has revealed, for the first time, the existence of two wobbling bands both having one phonon configuration and originating from the coupling of the wobbling phonon to the ground state band and to its signature partner. The doublet one-phonon wobbling bands are, in turn, found to be the signature partner bands. These observations have been drawn from the measured ratios of the inter-band and intra-band gamma transition rates. The model calculations based on the triaxial projected shell model (TPSM) approach have been performed and are found to be in good agreement with the experimental observations. These calculations provide an insight into the nature of the observed structures at a microscopic level.

The triaxial projected shell model (TPSM) approach is generalized to investigate the negative parity band structures in even-even systems. In the earlier version of the TPSM approach, the quasiparticle excitations were restricted to one major oscillator shell and it was possible to study only positive parity states in even-even systems. In the present extension, the excited quasiparticles are allowed to occupy two major oscillator shells, which makes it possible to generate the negative parity states. As a major application of this development, the extended approach is applied to elucidate the negative parity high-spin band structures in $^{102-112}$Ru and it is shown that energies obtained with neutron excitation are slightly lower than the energies calculated with proton excitation. However, the calculated aligned angular momentum ($i_x$) clearly separates the two spectra with neutron $i_x$ in reasonable agreement with the empirically evaluated $i_x$ from the experimental data, whereas proton $i_x$ shows large deviations. Furthermore, we have also deduced the transition quadrupole moments from the TPSM wavefunctions along the negative-parity yrast- and yrare- bands and it is shown that these quantities exhibit rapid changes in the bandcrossing region., Comment: 14 pages, 17 figures

The energies and $B(E2)$ transitions involving the states of the ground- and $\gamma$-bands in thirty transitional and deformed nuclei are calculated using the triaxial projected shell model (TPSM) approach. Systematic good agreement with the existing data substantiates the reliability of the model predictions. The Gamma-rotor version of the collective Bohr Hamiltonian is discussed in order to quantify the classification with respect to the triaxial shape degree of freedom. The pertaining criteria are applied to the TPSM results and the staggering of the energies of the $\gamma$-bands is analyzed in detail. An analog staggering of the intra-$\gamma$ $B(E2,I\rightarrow I-2)$ is introduced for the first time. The emergence of the staggering phenomena in the transitions is explained in the terms of interactions between the bands., Comment: 31 pages, 35 figures

The microscopic origin of the $\gamma$-softness (fluctuations in the triaxiality parameter $\gamma$ of the nuclear shape) observed in atomic nuclei is studied in the framework of the triaxial projected shell model approach, which is based on the deformed mean-field picture with multi-quasiparticle configuration space. It is demonstrated that the coupling to quasiparticle excitations drives the system from a $\gamma$-rigid to a $\gamma$-soft pattern. As an illustrative example for a $\gamma$-soft nucleus, a detailed study has been performed for the $^{104}$Ru nucleus. The experimental energies and a large sample of measured $E2$ matrix elements available for this nucleus are reproduced quite accurately. The shape invariant analysis of the calculated $E2$ matrix elements elucidates the $\gamma$-soft nature of $^{104}$Ru.

In an effort to elucidate the rich band structures observed in odd-neutron systems, triaxial projected shell model approach is extended to include three-quasineutron and five-quasiparticle configurations. This extension makes it possible to investigate the high-spin states up to and including the second band crossing. Detailed investigation has been performed for odd-mass Xe isotopes with the extended basis, and it is shown that character of the band crossing along the yrast line changes with shell filling of the 1h11/2 orbital. Further, it is observed that the three-quasiparticle state that crosses the ground-state configuration, leading to the normal band crossing phenomenon along the yrast line, first crosses the {\gamma} band based on the ground-state configuration at an earlier spin value. This crossing feature explains the occurrence of the signature inversion observed in the {\gamma} bands for some of the studied 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., Comment: 18 pages, 18 figures

A systematic study of $\gamma$-bands observed in atomic nuclei is performed using the triaxial projected shell model (TPSM) approach. The staggering phase between the even and odd spin members of the $\gamma$-band for most the nuclei investigated in the present work is found to have even-I-below-odd-I, which in the framework of the collective model is considered as a signature of $\gamma$-softness. It is observed that out of twenty-three systems studied, only four nuclei, namely, $^{76}$Ge, $^{112}$Ru, $^{170}$Er and $^{232}$Th depict staggering phase with odd-I-below-even-I, which is regarded as an indication of the static $\gamma$-deformation in the collective model picture. The inclusion of the quasiparticle excitations in the framework of configuration mixing is shown to reverse the staggering phase from odd-I-down to the even-I-down for all the studied nuclei, except for the aforementioned four nuclei. Furthermore, by fitting a collective Bohr Hamiltonian to the TPSM energies, the differences between the two models are delineated through a comparison of the transition probabilities., Comment: 12 pages, 15 figures

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., Comment: 11 pages, 17 figures, to appear in EPJA

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.

The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Some examples are strongly interacting medium and heavy mass atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. In this way, additional correlations are subsumed in the system. However, the mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group-theory techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries, where the latter corresponds to the restoration of the particle number. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. Applications of the projection methods are presented for simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted in the present work., Comment: 145 pages, 23 figures, 456 references, accepted for publication in Journal of Physics G

Aiming to understand the role of triaxiality and the evolution of the ground state nuclear shapes, we have carried out a microscopic study for a series of chains of Pd, Xe, Ba, Nd, Sm, Gd, and Dy isotopes. This is done within the self-consistent Relativistic-Hartree-Bogoliubov (RHB) formalism, and supported by the Triaxial Projected Shell Model (TPSM) approach. Pairing interaction separable in the momentum space with DD-ME2 force parameter is used to generate the potential energy surfaces(PESs) under the axial and triaxial symmetry. Shape evolution manifest themself in very clear manner in almost all the isotopic chains. Properties of the global mimima have been found to be in good agreement with the available experimental data. Relatively flat PESs, and $\gamma$-soft nature, have been suggested $^{108,110}$Pd, $^{132,134}$Xe and $^{134}$Ba as good candidates for E(5) symmetry, while $^{102}$Pd is not found suitable for E(5) symmetry. The PESs with a bump, and rigidity against triaxial variable($\gamma$) suggested $^{150}$Nd, $^{152}$Sm and $^{154}$Gd to be good candidates while $^{150}$Sm and $^{156}$Dy are poor candidates of X(5) critical-point symmetry. The findings of the present RHB calculations supported by TPSM are qualitatively in good agreement with the experimental and other theoretical calculations., Comment: accepted in Nucl. Phys. A

Low lying states of $^{198}$Hg have been investigated via $^{197}$Au($^{7}$Li, $ \alpha $2n$ \gamma $)$ ^{198} $Hg reaction at E$ _{\text{beam}} $ = 33 MeV and 38 MeV and the members of $ \gamma $-vibrational band have been identified. Results are compared with the systematic of this mass region and found in agreement. Observed band structures have been interpreted using the theoretical framework of microscopic triaxial projected shell model (TPSM) approach and it is shown that TPSM results are in fair agreement with the observed energies.

Excited band structures recently observed in $^{156}$Dy are investigated using the microscopic triaxial projected shell model (TPSM) approach and the quasiparticle random phase approximation (QRPA) based on the rotating mean-field. It is demonstrated that new observed excited bands, tracking the ground-state band, are the $\gamma$-bands based on the excited two-quasineutron configurations as conjectured in the experimental work., Comment: 12 pages, 12 figures

The band structures of $^{68,70}$Ge, $^{128,130,132,134}$Ce and $^{132,134,136,138}$Nd are investigated using the triaxial projected shell model (TPSM) approach. These nuclei depict forking of the ground-state band into several s-bands and in some cases, both the lowest two observed s-bands depict neutron or proton character. It was discussed in our earlier work that this anamoluos behaviour can be explained by considering $\gamma$-bands based on two-quasiparticle configurations. As the parent band and the $\gamma$-band built on it have the same intrinsic structure, g-factors of the two bands are expected to be similar. In the present work, we have undertaken a detailed investigation of g-factors for the excited band structures of the studied nuclei and the available data for a few high-spin states are shown to be in fair agreement with the predicted values., Comment: 29 pages, 20 figures. Nucl. Phys. A (2017)

Excited states of $^{133}$La have been investigated to search for the wobbling excitation mode in the low-spin regime. Wobbling bands with $n_\omega$ = 0 and 1 are identified along with the interconnecting $\Delta I$ = 1, $E2$ transitions, which are regarded as one of the characteristic features of the wobbling motion. An increase in wobbling frequency with spin implies longitudinal wobbling for $^{133}$La, in contrast with the case of transverse wobbling observed in $^{135}$Pr. This is the first observation of a longitudinal wobbling band in nuclei. The experimental observations are accounted for by calculations using the quasiparticle-triaxial-rotor (QTR) model, which attribute the appearance of longitudinal wobbling to the early alignment of a $\pi=+$ proton pair., Comment: 9 pages, 6 figures, 1 table

The structure of $^{70}$Ge has been studied through in-beam gamma ray spectroscopy. A new band structure is identified that leads to forking of the ground-state band into two excited bands. Band structures have been investigated using the microscopic triaxial projected shell model approach. The observed forking is demonstrated to result from almost simultaneous band crossing of the two neutron aligned and the \gamma-band built on this two-quasiparticle configuration with the ground-state band., Comment: 9 pages, 13 figures, Accepted for publication as a Regular Article in PRC. in Physical Review C, 24th Feb 2016

A systematic investigation of the nuclear observables related to the triaxial degree of freedom is presented using the multi-quasiparticle triaxial projected shell model (TPSM) approach. These properties correspond to the observation of $\gamma$-bands, chiral doublet bands and the wobbling mode. In the TPSM approach, $\gamma$-bands are built on each quasiparticle configuration and it is demonstrated that some observations in high-spin spectroscopy that have remained unresolved for quite some time could be explained by considering $\gamma$-bands based on two-quasiparticle configurations. It is shown in some Ce-, Nd- and Ge-isotopes that the two observed aligned or s-bands originate from the same intrinsic configuration with one of them as the $\gamma$-band based on a two-quasiparticle configuration. In the present work, we have also performed a detailed study of $\gamma$-bands observed up to the highest spin in Dysposium, Hafnium, Mercury and Uranium isotopes. Furthermore, several measurements related to chiral symmetry breaking and wobbling motion have been reported recently. These phenomena, which are possible only for triaxial nuclei, have been investigated using the TPSM approach. It is shown that doublet bands observed in lighter odd-odd Cs-isotopes can be considered as candidates for chiral symmetry breaking. Transverse wobbling motion recently observed in $^{135}$Pr has also been investigated and it is shown that TPSM approach provides a reasonable description of the measured properties., Comment: Submitted to special Physica Scripta edition "Focus Issue on Nuclear Structure: Celebrating the 75 Nobel Prize" in Physics

Band structures of the neutron-rich Mo- and Ru-isotopes around A $\sim $ 110 are investigated using the triaxial projected shell model (TPSM) approach employing multi-quasiparticle configuration space. The mass region under investigation depicts a rich variety of band structures with well developed $\gamma$- and $\gamma\gamma$-bands, and quasiparticle excitations based on them. It is demonstrated that TPSM provides a reasonable description of most of the observed properties, in particular, detailed structure variations observed in Mo-isotopes are well reproduced in the present work., Comment: 19 pages, 7 figures, to appear in Nucl. Phys. A

High spin states in 105Cd were studied using 16O beam on 92Mo reaction at an incident beam energy of 75 MeV. The level scheme of 105Cd has been observed up to an excitation energy of 10.8 MeV with the addition of 30 new gamma transitions to the previous work. Spin and parity for most of the reported levels are assigned from the DCO ratios and linear polarization measurements. The microscopic origin of the investigated band structures is discussed in the context of triaxial projected shell model. The energies of observed positive and negative parity bands agree with the predictions of the TPSM by considering triaxial deformation for the observed excited band structures. The shape evolution with increasing angular momentum is explained in the framework of Cranked Shell Model and the Total Routhian Surface calculations., Comment: 13 pages, 16 figures, Accepted in PRC on 29th January 2015

Collective inertia is strongly influenced at the level crossing at which quantum system changes diabatically its microscopic configuration. Pairing correlations tend to make the large-amplitude nuclear collective motion more adiabatic by reducing the effect of those configuration changes. Competition between pairing and level crossing is thus expected to have a profound impact on spontaneous fission lifetimes. To elucidate the role of nucleonic pairing on spontaneous fission, we study the dynamic fission trajectories of $^{264}$Fm and $^{240}$Pu using the state-of-the-art self-consistent framework. We employ the superfluid nuclear density functional theory with the Skyrme energy density functional SkM$^*$ and a density-dependent pairing interaction. Along with shape variables, proton and neutron pairing correlations are taken as collective coordinates. The collective inertia tensor is calculated within the nonperturbative cranking approximation. The fission paths are obtained by using the least action principle in a four-dimensional collective space of shape and pairing coordinates. Pairing correlations are enhanced along the minimum-action fission path. For the symmetric fission of $^{264}$Fm, where the effect of triaxiality on the fission barrier is large, the geometry of fission pathway in the space of shape degrees of freedom is weakly impacted by pairing. This is not the case for $^{240}$Pu where pairing fluctuations restore the axial symmetry of the dynamic fission trajectory. The minimum-action fission path is strongly impacted by nucleonic pairing. In some cases, the dynamical coupling between shape and pairing degrees of freedom can lead to a dramatic departure from the static picture. Consequently, in the dynamical description of nuclear fission, particle-particle correlations should be considered on the same footing as those associated with shape degrees of freedom., Comment: Submitted to PRC

Background: Recent experiments on beta-delayed fission reported an asymmetric mass yield in the neutron-deficient nucleus 180Hg. Earlier experiments in the mass region A=190-200 close to the beta-stability line, using the (p,f) and (\alpha,f) reactions, observed a more symmetric distribution of fission fragments. While the beta-delayed fission of 180Hg can be associated with relatively low excitation energy, this is not the case for light-ion reactions, which result in warm compound nuclei. Purpose: To elucidate the roles of proton and neutron numbers and excitation energy in determining symmetric and asymmetric fission yields, we compute and analyze the isentropic potential energy surfaces of 174,180,198Hg and 196,210Po. Methods: We use the finite-temperature superfluid nuclear density functional theory, for excitation energies up to E*=30MeV and zero angular momentum. For our theoretical framework, we consider the Skyrme energy density functional SkM* and a density-dependent pairing interaction. Results: For 174,180Hg, we predict fission pathways consistent with asymmetric fission at low excitation energies, with the symmetric fission pathway opening very gradually as excitation energy is increased. For 198Hg and 196Po, we expect the nearly-symmetric fission channel to dominate. 210Po shows a preference for a slightly asymmetric pathway at low energies, and a preference for a symmetric pathway at high energies. Conclusions: Our self-consistent theory suggests that excitation energy weakly affects the fission pattern of the nuclei considered. The transition from the asymmetric fission in the proton-rich nuclei to a more symmetric fission in the heavier isotopes is governed by the shell structure of pre-scission configurations., Comment: 6 pages, 6 figures

We develop the isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed has the most general form that depends quadratically on the isoscalar and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space. We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant EDF approach with all possible p-n mixing terms. Explicit expressions have been derived for all the densities and potentials that appear in the isospin representation. In practical tests, we consider the Skyrme EDF SkM* and, as a first application, concentrate on Hartree-Fock aspects of the problem, i.e., pairing has been disregarded. Calculations have been performed for the (A=78, T~11), (A=40, T~8), and (A=48, T~4) isobaric analog chains. Isospin structure of self-consistent p-n mixed solutions has been investigated with and without the Coulomb interaction, which is the sole source of isospin symmetry breaking in our approach. The extended axial HFBTHO solver has been benchmarked against the symmetry-unrestricted HFODD code for deformed and spherical states. We developed and tested a general isospin-invariant Skyrme-EDF framework. The new approach permits spin-isospin densities that may give rise to, hitherto, unexplored modes in the excitation spectrum. The new formalism has been tested in the Hartree-Fock limit. A systematic comparison between HFODD and HFBTHO results show a maximum deviation of about 10 keV on the total binding energy for deformed nuclei when the Coulomb term is included. Without this term, the results of both solvers agree down to a ~10 eV level., Comment: 13 pages, 10 figures, submitted to Phys. Rev. C

Recent experimental data have demonstrated that $^{76}$Ge may be a rare example of a nucleus exhibiting rigid $\gamma$-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 $\gamma$-vibrational bands in $^{76}$Ge, a rigid-triaxial deformation parameter $\gamma\approx 30^\circ$ 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 $\gamma\gamma$-band in $^{76}$Ge is predicted with the bandhead at an excitation energy of $ \sim$ 2.5 MeV. We have also performed TPSM study for the neighboring Ge- and Se-isotopes and the distinct $\gamma$-soft feature in these nuclei is shown to result from configuration mixing of the ground-state with multi-quasiparticle states., Comment: 12 pages, 15 figures, To appear in Phys. Rev. C

Doublet bands observed in $^{124,126,130,132}$Cs isotopes are studied using the recently developed multi-quasiparticle microscopic triaxial projected shell model (TPSM) approach. It is shown that TPSM results for energies and transition probabilities are in good agreement with known energies and the recently measured extensive data on transition probabilities for the bands in $^{126}$Cs. In particular, it is demonstrated that characteristics transition probabilities expected for the doublet bands to originate from the chiral symmetry breaking are well reproduced in the present work. The calculated energies for $^{124,130,132}$Cs are also shown to be in reasonable agreement with the available experimental data. Furthermore, a complete set of the calculated transition probabilities is provided for the doublet bands in $^{124,130,132}$Cs isotopes., Comment: 14 pages, 9 Figures, Accepted in Nuclear Physics A

A systematic study of the doublet bands observed in odd-odd mass $\sim$ 100 is performed using the microscopic triaxial projected shell model approach. This mass region has depicted some novel features which are not observed in other mass regions, for instance, it has been observed that two chiral bands cross diabatically in $^{106}$Ag. It is demonstrated that this unique feature is due to crossing of the two 2-quasiparticle configurations having different intrinsic structures. Further, we provide a complete set of transition probabilities for all the six-isotopes studied in this work and it is shown that the predicted transitions are in good agreement with the available experimental data., Comment: 7 pages, 10 figures

The electromagnetic transition probabilities of the excited levels for the two nearly degenerate bands of $^{106}$Ag have been measured using the Doppler Shift Attenuation Method. A comparison with the calculated values using triaxial projected shell model approach indicates that these bands originate from two different quasi-particle configurations but constructed from the same mean-field deformation.

The spontaneous fission lifetime of 264Fm has been studied within nuclear density functional theory by minimizing the collective action integral for fission in a two-dimensional quadrupole collective space representing elongation and triaxiality. The collective potential and inertia tensor are obtained self-consistently using the Skyrme energy density functional and density-dependent pairing interaction. The resulting spontaneous fission lifetimes are compared with the static result obtained with the minimum-energy pathway. We show that fission pathways strongly depend on assumptions underlying collective inertia. With the non-perturbative mass parameters, the dynamic fission pathway becomes strongly triaxial and it approaches the static fission valley. On the other hand, when the standard perturbative cranking inertia tensor is used, axial symmetry is restored along the path to fission; an effect that is an artifact of the approximation used., Comment: 5 pages, 5 figures

Background: Deep third minima have been predicted in some non-self-consistent models to impact fission pathways of thorium and uranium isotopes. These predictions have guided the interpretation of resonances seen experimentally. On the other hand, self-consistent calculations consistently predict very shallow potential-energy surfaces in the third minimum region. Purpose: We investigate the interpretation of third-minimum configurations in terms of dimolecular states. We study the isentropic potential-energy surfaces of selected even-even thorium and uranium isotopes at several excitation energies. In order to understand the driving effects behind the presence of third minima, we study the interplay between pairing and shell effects. Methods: We use the finite-temperature superfluid nuclear density functional theory. We consider a traditional functional, SkM*, and a recent functional, UNEDF1, optimized for fission studies. Results: We predict very shallow or no third minima in the potential-energy surfaces of 232Th and 232U. In Th and U isotopes with N=136 and 138, the third minima are deeper. We show that the reflection-asymmetric configurations around the third minimum can be associated with dimolecular states involving the spherical doubly magic 132Sn and a lighter deformed Zr or Mo fragment. The potential-energy surfaces for 228,232Th and 232U at several excitation energies are presented. Conclusions: We show that the neutron shell effect that governs the existence of the dimolecular states around the third minimum is consistent with the spherical-to-deformed shape transition in the Zr and Mo isotopes around N=58. We demonstrate that the thermal reduction of pairing and enhancement of shell effects at small excitation energies help to develop deeper third minima. At large excitation energies, shell effects are washed out and third minima disappear altogether., Comment: 9 pages, 10 figures; published in Physical Review C