Experimental data indicate that the mass tensor of collective Bohr Hamiltonian cannot be considered as a constant but should be considered as a function of the collective coordinates. In this work our purpose is to investigate the properties of low-lying collective states of the odd nuclei $^{173}$Yb and $^{163}$Dy by using a new generalized version of the collective quadrupole Bohr Hamiltonian with deformation-dependent mass coefficients. The proposed new version of the Bohr Hamiltonian is solved for Davidson potential in $β$ shape variable, while the $γ$ potential is taken to be equal to the harmonic oscillator. The obtained results of the excitation energies and B(E2) reduced transition probabilities show an overall agreement with the experimental data. Moreover, we investigate the effect of the deformation dependent mass parameter on energy spectra and transition rates in both cases, namely: when the mass coefficients are different and when they are equal. Besides, we will show the positive effect of the present formalism on the moment of inertia.
After identifying the nuclei in the regions near A =80 and A = 160 for which beta-decay rates have the greatest effect on weak and main r-process abundance patterns, we apply the finite-amplitude method (FAM) with Skyrme energy-density functionals (EDFs) to calculate beta-decay half-lives of those nuclei in the quasiparticle random-phase approximation (QRPA). We use the equal filling approximation to extend our implementation of the charge-changing FAM, which incorporates pairing correlations and allows axially symmetric deformation, to odd-A and odd-odd nuclei. Within this framework we find d…
We use the finite amplitude method (FAM), an efficient implementation of the quasiparticle random phase approximation, to compute beta-decay rates with Skyrme energy-density functionals for 3983 nuclei, essentially all the medium-mass and heavy isotopes on the neutron rich side of stability. We employ an extension of the FAM that treats odd-mass and odd-odd nuclear ground states in the equal filling approximation. Our rates are in reasonable agreement both with experimental data where available and with rates from other global calculations.
The nuclear shell model assumes an effective mean-field plus interaction Hamiltonian in a specific configuration space. We want to understand how various interaction matrix elements affect the observables, the collectivity in nuclei and the nuclear level density for odd-A and odd-odd nuclei. Using the sd and pf shells, we vary specific groups of matrix elements and study the evolution of energy levels, transition rates and the level density. In all cases studied, a transition between a "normal" and a collective phase is induced, accompanied by an enhancement of the level density in the collect…
Two types of average neutron-proton interaction formulas are compared: In the first type, neutron-proton interactions for even-even and odd-$A$ nuclei extracted from experimental binding energies show a smooth behavior as a function of mass number $A$ and are dominated by the contribution from the symmetry energy. Whereas in the second type large systematic staggering is seen between even-$A$ and odd-$A$ nuclei. This deviation is understood in term of the additional neutron-proton interaction in odd-odd nuclei relative to the neighboring even-even and odd-$A$ systems. We explore three possible…
The first excited 2+ energy states of nuclei give many substantial information related to the nuclear structure. Including these levels, all excited states of nuclei are shown regularities in spin, parity and energy. In the even-even nuclei, the first excited state is generally 2+ and the energy values of them increase as the closed shells are approached. The excited levels in nuclei can be investigated by using theoretical nuclear models such nuclear shell model. In the present study for the first time, we have used artificial neural networks for the determination of the energies of first 2+ …
The quartet condensation model (QCM) is extended for the treatment of isovector and isoscalar pairing in odd-odd N=Z nuclei. In the extended QCM approach the lowest states of isospin T=1 and T=0 in odd-odd nuclei are described variationally by trial functions composed by a proton-neutron pair appended to a condensate of 4-body operators. The latter are taken as a linear superposition of an isovector quartet, built by two isovector pairs coupled to the total isospin T=0, and two collective isoscalar pairs. In all pairs the nucleons are distributed in time-reversed single-particle states of axia…
We provide a description of odd-odd self-conjugate nuclei in the sd shell in a formalism of collective quartets and pairs. Quartets are four-body structures carrying isospin T=0 while pairs can have either T=0 or T=1. Both quartets and pairs are labeled by the angular momentum J and they are chosen so as to describe the lowest states of 20Ne (quartets) and the lowest T=0 and T=1 states of 18F (pairs). We carry out configuration interaction calculations in spaces built by one quartet and one pair for 22Na and by two quartets and one pair for 26Al. The spectra that are generated are in good agre…
We introduce a new Bose-Fermi framework for studying spectral properties and quantum phase transitions (QPTs) in odd-mass nuclei, in the presence of configuration mixing. A detailed analysis of odd-mass Nb isotopes discloses the effects of an abrupt crossing of states in normal and intruder configurations (Type II QPT), accompanied by a gradual evolution from spherical- to deformed-core shapes within the intruder configuration (Type I QPT). The pronounced presence of both types of QPTs demonstrates, for the first time, the occurrence of intertwined QPTs in odd-mass nuclei.
A statistical approach based on the Weisskopf evaporation theory has been developed to describe the de-excitation process of highly excited heavy and superheavy nuclei, in particular for the proton-rich nuclei. The excited nucleus is cooled by evaporating $γ$-ray, light particles (neutrons, protons, $α$ etc) in competition with the binary fission, in which the structure effects (shell correction, fission barrier, particle separation energy) contribute to the processes. The formation of residual nuclei is evaluated via sequential emission of possible particles above the separation energies. The…
Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbo…
Accurate estimates of the binding energy of nuclei far from stability that cannot be produced in the laboratory are crucial to our understanding of nuclear processes in astrophysical scenarios. Models based on energy density functionals have shown that they are capable of reproducing all known masses with root-mean-square error better than 800 keV, while retaining a firm microscopic foundation. However, it was recently pointed out in [M. Hukkanen et al., arXiv:2210.10674] that the recent BSkG1 model fails to account for a contribution to the binding energy that is specific to odd-odd nuclei, a…
After shortly analyzing data relevant to fission hindrance of odd-A nuclei and high-$K$ isomers in superheavy (SH) region we point out the inconsistency of current fission theory and propose an approach based on the instanton formalism. A few results of this method, simplified by replacing selfconsistency by elements of the macro-micro model, are given to illustrate its features.
We study the ground and the first excited $0^{+}$ states of two mirror nuclei $^{14}$C and $^{14}$O within a five-cluster model (three alpha-particles and two extra nucleons) with the use of high accuracy variational approach with Gaussian bases. The first excited $0^{+}$ state of these nuclei is shown to be connected with a change of the structure of the two-nucleon subsystem moving in the field of the $^{12}$C cluster. The density distributions, electric form factors (both the elastic and transition ones), pair correlation functions, and the momentum distributions of the constituent particle…
$α$ decay is usually associated with both ground and low-lying isomeric states of heavy and superheavy nuclei, and the unpaired nucleon plays a key role on $α$ decay. In this work, we systematically studied the $α$ decay half-lives of odd-$A$ nuclei, including both favored and unfavored $α$ decay within the two-potential approach based on the isospin dependent nuclear potential. The $α$ preformation probabilities are estimated by using an analytic formula taking into account the shell structure and proton-neutron correlation, and the parameters are obtained through the $α$ decay half-lives dat…
We present an approach for the calculation of odd-nuclei with exact self-consistent blocking and particle number and angular momentum projection with the finite range density dependent Gogny force. As an application we calculate the nucleus $^{31}$Mg at the border of the $N=20$ inversion island. We evaluate the ground state properties, the excited states and the transition probabilities. In general we obtain a good description of the measured observables.
Solvababe supersymmetric algebraic model for descriptions of transitional even and odd mass nuclei near the critical point of the spherical to unstable shapes
