The study of highly charged electronic and muonic hydrogen-like ions, provides an intriguing way to probe the internal structure of their atomic nuclei. In this work, we use nuclear structure calculations to accurately calculate the hyperfine splitting of electronic and muonic hydrogen-like ions, focusing in particular on the incorporation of finite-volume corrections, such as Bohr-Weisskopf and Breit-Rosenthal, due to the penetration of the electron and muon wavefunction into the nuclear electric charge and magnetic dipole densities. These corrections are essential for refining our understanding of the nuclear magnetic dipole and electric quadrupole moments. Our simulations use a Skyrme-Hartree-Fock-BCS model known for its effectiveness in modeling well-deformed nuclei such as ^159Tb^64+ and ^165Ho^66+, with particular emphasis on ^161,163Dy^65+ isotopes. It can also be generalised to multi-electron ions by studying the hyperfine anomaly between two isotopes.

Spontaneous fission of 252Cf and fusion-induced fission of 250Cf are investigated within a multidimensional Langevin model. The potential-energy surface is calculated in the macroscopic-microscopic Lublin-Strasbourg drop (LSD) + Yukawa-folded approach using the four-dimensional (4D) Fourier-overspheroid shape parametrization. The dynamical evolution described by the Langevin equation is coupled to neutron evaporation, thereby allowing for the possibility of multichance fission. Charge equilibration and excitation-energy sharing between the fragments emerging at scission are evaluated, and their deexcitation is finally computed. The correlation between various observables, particularly the isotopic properties of the fragments, is discussed and compared with the experiment whenever available. The theoretical predictions are generally in good agreement with the data.

Low-lying bandhead states in axially prolate deformed odd-odd nuclei have long been described essentially within the rotor+two-quasiparticle picture. This approach allows one to explain the appearance of so-called Gallagher-Moszkowski doublets of bandheads with $K = \Omega_n \pm \Omega_p$, sum and difference of neutron and proton angular momentum projections on the symmetry axis. According to an empirical rule stated by Gallagher and Moszkowski the spin-aligned configuration lies lower in energy than the spin-anti-aligned configuration. A recent study by Robledo, Bernard and Bertsch in Phys. Rev. C 89, 021303(R) (2014) within the Gogny energy-density functional with selfconsistent blocking of the unpaired nucleons showed that calculations fail to reproduce this rule in about half of the cases and points to the density-dependent term of the functional as responsible of this failure. In this paper we aim at pushing further this analysis to exhibit the mechanism underlying the energy splitting in a Gallagher-Moszkowski doublet. We work in the framework of the Skyrme energy-density functional approach, including BCS pairing correlations with selfconsistent blocking. We use the SIII parametrization with time-odd terms and seniority pairing matrix elements extending a previous study of K-isomeric states in even-even nuclei [Phys. Rev. C 105, 044329 (2022)]. We find that the energy splitting results from a competition between the spin-spin, density-dependent and current-current terms of the Skyrme energy-density functional. In doublets where the larger K value is lower in energy the Gallagher-Moszkowski rule is always satisfied by the SIII Skyrme energy-density functional. In doublets, on the contrary, where the smaller K value lies lower, the energy splittings are calculated to be rather small and often a disagreement with the Gallagher-Moszkowski rule occurs.

We study the evolution of K pi = 6+ and 8- two-quasiparticle (q.p.) configurations in the isotopic and isotonic chains of even-even deformed nuclei around 178Hf and their ability to describe series of observed K-isomer excitations within the framework of a Skyrme Hartree-Fock-BCS (SHFBCS) approach using SIII interaction and seniority pairing strengths with self-consistent blocking. We apply the approach along the prescription of Minkov et al. [Phys. Rev. C 105, 044329 (2022)] used to describe K isomers in the actinide and transfermium mass regions. The calculations allow us to identify the regions where proton or neutron configurations or their mixture may be responsible for the K-isomer formation. The obtained results provide a detailed test for the Skyrme SIII interaction used and outline the limits of applicability of the overall SHFBCS approach in the regions of well deformed nuclei. The study suggests that similar systematic analysis can be implemented in the heavier mass regions whenever enough data are available.

A rapidly converging 4-dimensional Fourier shape parametrization is used to model the fission process of heavy nuclei. Potential energy landscapes are computed within the macroscopic-microscopic approach, on top of which the multi-dimensional Langevin equation is solved to describe the fission dynamics. Charge equilibration at scission and de-excitation by neutron evaporation of the primary fragments after scission is investigated. The model describes various observables, including fission-fragment mass, charge, and kinetic energy yields, as well as post-scission neutron multiplicities and, most importantly, their correlations, which are crucial to unravel the complexity of the fission process. The parameters of the dynamical model were tuned to reproduce experimental data obtained from thermal neutron-induced fission of $^{235}$U, which allows us to discuss the transition from asymmetric to symmetric fission along the Fm isotopic chain.

Spontaneous fission half-lives of actinide and super-heavy nuclei are calculated, using the least-action integral, through the WKB tunneling probability of the barrier that appears in the deformation landscape obtained in the macroscopic-microscopic potential-energy surface. This deformation-energy landscape is obtained using a Fourier shape parametrization with 4 deformation parameters, taking into account the nuclear elongation, left-right asymmetry, neck formation and non-axiality degrees of freedom. The collective inertia tensor entering the WKB half-life expression is given through the so-called irrotational flow approach, successfully used in nuclear fission to reproduce observables that characterize the nuclear system in the vicinity of the scission configurations, such as fragment mass or charge distributions. For a comparisons, we have also used the so-called phenomenological mass parameter depending only on the center-of-mass difference of the forming fission fragments. Our approach is shown to be able to reproduce empirical fission half-lives of all here considered nuclei to within 3 orders of magnitude.

We study excited states of two-quasiparticle (2qp) character in well-deformed even-even actinide and heavier nuclei exhibiting K isomerism within the framework of the Skyrme energy-density functional (SEDF) approach, including BCS pairing correlations with self-consistent blocking. We use the SIII SEDF parametrization with time-odd terms and seniority pairing residual interaction as in a previous study of magnetic moments in odd-mass nuclei [Phys. Rev. C 91, 054307 (2015)]. The strength of the seniority interaction is determined through an overall fit on the 2(1)(+) excitation energies along the lines of Phys. Rev. C 99, 064306 (2019). Our calculations confirm the 2qp configurations reported in the literature providing an overall good agreement with the available data on isomeric energies. One notes, however, a few significant deviations such as in the N = 142 uranium and N = 152 nobelium isotopes, which are explained through known single-particle features of the SEDF used. Given the good predictive capability of the approach, we expect it to serve as a reliable tool in the search for similar kinds of qp excitations and to suggest additional or alternative qp configurations.

Potential energy surfaces of even-even superheavy nuclei are evaluated within the macroscopic-microscopic approximation. A very rapidly converging analytical Fourier-type shape parametrization is used to describe nuclear shapes throughout the periodic table, including those of fissioning nuclei. The Lublin Strasbourg Drop and another effective liquid-drop type mass formula are used to determine the macroscopic part of nuclear energy. The Yukawa-folded single-particle potential, the Strutinsky shell-correction method, and the BCS approximation for including pairing correlations are used to obtain microscopic energy corrections. The evaluated nuclear binding energies, fission-barrier heights, and Q-alpha energies show a relatively good agreement with the experimental data. A simple one-dimensional WKB model a la Swiatecki is used to estimate spontaneous fission lifetimes, while alpha-decay probabilities are obtained within a Gamow-type model.

Shell corrections to the moment of inertia (MI) are calculated for a Woods–Saxon potential of spheroidal shape and at different deformations. This model potential is chosen to have a large depth and a small surface diffuseness which makes it resemble the analytically solved spheroidal cavity in the semiclassical approximation. For the consistent statistical-equilibrium collective rotations under consideration here, the MI is obtained within the cranking model in an approach which goes beyond the quantum perturbation approximation based on the nonperturbative energy spectrum, and is therefore applicable to much higher angular momenta. For the calculation of the MI shell corrections [Formula: see text], the Strutinsky smoothing procedure is used to obtain the average occupation numbers of the particle density generated by the resolution of the Woods–Saxon eigenvalue problem. One finds that the major-shell structure of [Formula: see text], as determined in the adiabatic approximation, is rooted, for large as well as for small surface deformations, in the same inhomogenuity of the distribution of single-particle states near the Fermi surface as the energy shell corrections [Formula: see text]. This fundamental property is in agreement with the semiclassical results [Formula: see text] obtained analytically within the non perturbative periodic orbit theory for any potential well, in particular for the spheroidal cavity, and for any deformation, even for large deformations where bifurcations of the equatorial orbits play a substantial role. Since the adiabatic approximation, [Formula: see text], with [Formula: see text] the distance between major nuclear shells, is easily obeyed even for large angular momenta typical for high-spin physics at large particle numbers, our model approach seems to represent a tool that could, indeed, be very useful for the description of such nuclear systems.

Deformation-energy surfaces of 54 even-even isotopes of Pt, Hg and Pb nuclei with neutron numbers up to 126 are investigated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop macroscopic energy and shell plus pairing-energy corrections obtained from a Yukawa-folded mean-field potential at the desired deformation. A new, rapidly converging Fourier shape parametrization is used to describe nuclear shapes. The stability of shape isomeric states with respect to non-axial and higher-order deformations is investigated.

In a macroscopic-microscopic approach, the Fourier parametrization of deformed shapes is used to describe the deformation-energy landscapes of nuclei in a 6-dimensional deformation space. A special attention is hereby paid to the convergence of this expansion, in particular for nuclear shapes in the vicinity of the scission configuration. It is shown that the Fourier expansion converges very rapidly and that contributions of multipolarity higher that 4 can be safely neglected, even for extreme deformations as they occur close to the scission configuration.

We show that semiclassical methods that are traditionally used to describe many-body sytems in physics can also be used to describe partitions that are studied in the number theory within pure mathematics. For the partitions P(n) of a number n into sums of distinct squares, we show that the smooth asymptotic part P-as(n) can be well-reproduced by quantum statistical methods, and that its oscillating part delta P(n) = P(n) - P-as(n) is well-reproduced by the periodic orbit theory in terms of a few "orbits" that can be related to Pythagorean triples (m, p, q) of integers with m(2) +p(2) = q(2).

A simple model to study the collective coupling between pairing and rotational degrees of freedom in well-deformed even-even nuclei is proposed. It relies on the description of the effects of pairing correlations on the rotational motion in terms of intrinsic vortical currents. As a result, an expression of the rotational energy within a band is provided as a polynomial of order three in the square of the angular velocity. The coefficients of this polynomial have a well-defined analytical form and their values are determined from merely three experimental pieces of data: the energy of the first 2(+) state, the ground-state charge quadrupole moment as deduced from B(E2, 2(+) -> 0(+)) measurements, and a quantity deduced from the odd-even mass differences in neighboring odd nuclei. This model is tested in 24 deformed nuclei chosen across the rare-earth and actinide regions. In spite of the very restricted input of data, and moreover which is limited to nuclear properties at zero or very low excitation energies, the agreement with the data within the yrast line is in many cases, especially in actinide nuclei, excellent up to angular momenta of the order of 30h or more. Of course, such an approach is by construction unable to reproduce physical effects which do not result from this Coriolis antipairing (CAP) type of collective quenching of pairing correlations. This is especially the case in the rare-earth region, where a backbending effect is often observed. In such cases our model may be considered as a baseline in order to disentangle the effect of the CAP collective mode from those of other existing spectroscopic phenomena.

Using the Fourier shape parametrisation of deformed nuclei developed by us recently, potential-energy landscapes for isotopes of nuclei between platinium (Z = 78) and lead (Z = 82) are analysed in a 4-dimensional deformation space, searching for local extrema, ridges and valleys. A certain number of yet unknown super- and hyper-deformed shape isomers in even-even Pt, Hg and Pb isotopes are predicted. Quadrupole moments in the relevant minima are evaluated. A nice agreement of the theoretical predictions with the experimental ground-state data for these quantities gives strong confidence on the quality of our results for the corresponding isomeric states.

The potential-energy surfaces of even-even super-heavy nuclei are evaluated within the LSD macroscopic-microscopic approach with a Yukawa-folded mean-field potential using the Fourier shape parametrization. The calculations are performed in a four-dimensional deformation space, defined by quadrupole, octupole, hexadecapole and nonaxiality degrees of freedom. It is shown that the both pear-like and nonaxial deformation modes are important when evaluating fission barrier heights.

In this work we report on recent microscopic calculations of K-isomeric states of two-quasiparticle character in well-deformed rare-earth nuclei and actinide nuclei. In these calculations we employ a Skyrme energy-density functional together with a seniority residual interaction in the Hartree-Fock-BCS approximation with selfconsistent blocking (SCB). The strength of the seniority interaction is calibrated in a consistent way: as some of us showed in Ref. [1] for rare-earth nuclei, the same strength can be obtained in a fit on moments of inertia of eveneven nuclei and in a fit on odd-even mass staggering. The former fitting protocol is used for the actinide nuclei studied here. Once the seniority force was adjusted we calculated properties of variousK-isomeric states without additional parameters. Overall we have obtained a rather good agreement with available data around Nd and in the U-Pu region. We also found that an octupole deformation lowers the excitation energy of the K = 6− isomer in U.

An innovative parametrization of nuclear shapes, based on a Fourier expansion of the square distance from the surface of the nucleus to the symmetry axis is introduced. Surface, curvature and Coulomb energy coefficients of a charged liquid drop, that determine the semiclassical nuclear energy, are evaluated within this shape parametrization, together with the wall-friction and the irrotational-flow mass tensors. These transport coefficients are important ingredients of many nuclear models describing nuclear structure and dynamics. A numerical code allowing for the determination of all these quantities for a huge variety of nuclear shapes is made available to the interested user. Program summary Program title: inerfric Program Files doi: http://dx.doi.org/10.17632/gtvbc8b7sw.1 Licensing provisions: GPLv3 Programming language: Fortran Nature of problem: The inertia tensor evaluated in the hydrodynamical model using the Werner Wheeler approximation generalized to nonaxial shapes is evaluated, together with the friction tensor using the wall formula, and the shape functions that define the liquid-drop energy in terms of surface, curvature, Coulomb and congruence energy. For the description of the fission process, the mass ratio of the nascent fission fragments and their centre-of-mass distance is also evaluated together with the quadrupole moment and the moments of inertia for rotation of the deformed shape. Solution method: All these quantities are evaluated in our new rapidly converging Fourier shape parametrization, able to describe a huge variety of nuclear shapes, simply by reading in the (up to 7) shape parameters determining in an unambiguous way the nuclear deformation and corresponding for the (4) principal parameters to the nuclear elongation, left-right asymmetry, non axiality and neck degree of freedom, the remaining 3 allowing, if necessary, to optimize the evaluation of the asymmetry and neck degrees of freedom. (C) 2019 Elsevier B.V. All rights reserved.

Collective moments of inertia as well as quadrupole and octupole mass parameters are calculated in the perturbative cranking approximation using the folded-Yukawa mean-field potential written in Cartesian coordinates. The resulting single-particle Hamiltonian is required, as a minimal symmetry, to be invariant under z-signature and time-reversal transformations. The deformation of the nucleus is defined through a shape parametrization in cylindrical coordinates, with the so-called Funny-Hills and Trentalange-Koonin-Sierk shapes as typical and performant examples. To take pairing correlations into account, the standard set of BCS equations is solved with an approximation of constant pairing strength. The numerical program determining the quadrupole-octupole mass tensor and the moments of inertia, written in Fortran, is constructed according to the here presented study as an extension and application of the "yukawa" code for the diagonalization of the folded-Yukawa mean-field potential in the basis of a harmonic-oscillator in Cartesian coordinates, published in this journal in 2016. Program summary Program Title: yukmoms Program Files doi: http://dx.doi.org/10.17632/9ygk4bgkfr.1 Licensing provisions: GPLv3 Programming language: Fortran Nature of problem: The moments of inertia and the quadrupole and octupole mass parameters are calculated within the perturbative cranking approximation. As an input, the folded-Yukawa mean-field is diagonalized in the harmonic-oscillator deformed basis to generate the single-particle energies and wave functions. Nuclear shapes are given by means of well known Funny-Hills or Trentalange-Koonin-Sierk parametrizations able to describe the elongation, mass asymmetry, non-axiality and neck of the deformed nucleus. Solution method: Having diagonalized the matrix corresponding to the folded-Yukawa single-nucleon Hamiltonian expressed in the basis of the anisotropic harmonic oscillator basis, one then calculates the matrix elements of the one-body angular-momentum as well as the quadrupole and octupole-moments operators. These matrix elements together with the solutions of the coupled BCS equations are essential input to calculate the desired collective masses and moments of inertia of atomic nuclei. (C) 2018 Elsevier B.V. All rights reserved.