Spherical Single-particle Energies Research Articles

β decay of odd- A nuclei with the interacting boson-fermion model based on the Gogny energy density functional

The low-energy excitations and $\beta$ decays of odd-A nuclei are studied within the interacting boson-fermion model (IBFM), based on the Gogny-D1M nuclear energy density functional (EDF). The constrained Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential energy surfaces in terms of triaxial quadrupole degrees of freedom for even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field approximation also provides spherical single-particle energies and occupation probabilities for the neighboring odd-A nuclei. Those quantities represent a microscopic input for spectroscopic calculations in odd-A Xe and Ba, Cs and La isotopes. The Gamow-Teller (GT) and Fermi (F) transition matrix elements, needed to compute $\beta$-decay $\log{ft}$ values are obtained without any phenomenological fitting. It is shown that both the low-lying states and $\beta$ decays of the studied odd-A systems are described reasonably well within the employed theoretical framework.

Spectroscopy of odd-odd nuclei within the interacting boson-fermion-fermion model based on the Gogny energy-density functional

We present a method to calculate spectroscopic properties of odd-odd nuclei within the framework of the Interacting Boson-Fermion-Fermion Model based on the Gogny energy density functional. The $(\beta,\gamma)$-deformation energy surface of the even-even (boson-)core nucleus, spherical single-particle energies and occupation probabilities of the odd neutron and odd proton, are provided by the constrained self-consistent mean-field calculation within the Hartree-Fock-Bogoliubov method with the Gogny-D1M functional. These quantities are used as a microscopic input to fix most of the parameters of the IBFFM Hamiltonian. Only a few coupling constants for the boson-fermion Hamiltonian and the residual neutron-proton interaction are specifically adjusted to reproduce experimental low-energy spectra in odd-mass and odd-odd nuclei, respectively. In this way, the number of free parameters involved in the IBFFM framework is reduced significantly. The method is successfully applied to the description of the low-energy spectra and electromagnetic transition rates in the odd-odd $^{194,196,198}$Au nuclei.

Description of neutron-rich odd-mass krypton isotopes within the interacting boson-fermion model based on the Gogny energy density functional

The low-lying structure of neutron-rich odd-mass Kr isotopes is studied within the interacting boson-fermion model (IBFM) based on the Gogny-D1M energy density functional (EDF). The $(\beta,\gamma)$-deformation energy surfaces, spherical single-particle energies and occupation probabilities of the odd-mass systems are obtained using the constrained Hartree-Fock-Bogoliubov (HFB) approximation. Those quantities are used as a microscopic input to determine most of the parameters of the IBFM Hamiltonian. The remaining parameters are specifically tailored to the experimental spectrum for each of the studied odd-mass nuclei. A gradual structural evolution is predicted for the odd-mass isotopes $^{87-95}$Kr as a function of the nucleon number which, agrees well with the gradual growth of collectivity observed experimentally in the neighboring even-even isotopes.

Shape-phase transitions in odd-mass γ -soft nuclei with mass A≈130

Quantum phase transitions between competing equilibrium shapes of nuclei with an odd number of nucleons are explored using a microscopic framework of nuclear energy density functionals and a particle-boson core coupling model. The boson Hamiltonian for the even-even core nucleus, as well as the spherical single-particle energies and occupation probabilities of unpaired nucleons, are completely determined by a constrained self-consistent mean-field calculation for a specific choice of the energy density functional and pairing interaction. Only the strength parameters of the particle-core coupling have to be adjusted to reproduce a few empirical low-energy spectroscopic properties of the corresponding odd-mass system. The model is applied to the odd-A Ba, Xe, La and Cs isotopes with mass $A\approx 130$, for which the corresponding even-even Ba and Xe nuclei present a typical case of $\gamma$-soft nuclear potential. The theoretical results reproduce the experimental low-energy excitation spectra and electromagnetic properties, and confirm that a phase transition between nearly spherical and $\gamma$-soft nuclear shapes occurs also in the odd-A systems.

Beyond-mean-field boson-fermion model for odd-mass nuclei

A novel method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is introduced, based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the even-even core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained in a self-consistent mean-field calculation determined by the choice of the energy density functional and pairing interaction. This method uniquely determines the parameters of the Hamiltonian of the boson core, and only the strength of the particle-core coupling is specifically adjusted to selected data for a particular nucleus. The approach is illustrated in a systematic study of low-energy excitation spectra and transition rates of axially deformed odd-mass Eu isotopes.

Effects of Spin-Isospin-Interactions on Nuclear Collective Motion

The effects of the tensor force, the most prominent spin-isospin interaction, will be discussed from the viewpoints of the spherical single-particle energies and the correlation beyond single-particle motions. The former point will be started with basic properties of the tensor force, and a new mean-field model will be introduced. It will be shown that single-particle properties, including (sub-)magic gaps and spin-orbit splittings, are varied rather strongly by the tensor force. The effects are not weaker than the effects of the diffuse surface due to neutron skin. An example is presented for the so-called island of inversion, for which the boundary is being modified significantly. The latter point, correlations beyond single-particle motion, leads us to a special importance of the N = Z nuclei such as 56 Ni.

Mean field properties of exotic nuclei and the tensor force

The effects of the tensor force, the most prominent spin–isospin interaction, will be discussed from the viewpoint of the spherical single-particle energies. The discussion will be started with basic properties of the tensor force, and then a new mean-field model will be introduced. It will be shown that single-particle properties, including (sub-)magic gaps and spin–orbit splittings, are varied rather strongly by the tensor force. The effects are not weaker than the effects of the diffuse surface due to the neutron skin. An example is presented for the so-called island of inversion, for which the boundary is modified significantly. The structure of heavier nuclei, including Sb isotopes, are mentioned.

Evolution of Nuclear Shells due to the Tensor Force

The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the pi + rho meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments.

Shell model description of normal parity bands in even-even heavy deformed nuclei

The pseudo-SU(3) model is used to describe the low-energy spectra and electromagnetic transition strengths in ${}^{156}\mathrm{Gd},$ ${}^{158}\mathrm{Gd},$ and ${}^{160}\mathrm{Gd}.$ The Hamiltonian includes spherical single-particle energies, the quadrupole-quadrupole interaction, proton and neutron pairing interactions, plus four rotorlike terms. The quadrupole-quadrupole and pairing interaction strengths are assigned the values $\ensuremath{\chi}{=23A}^{\ensuremath{-}5/3}$ and ${G}_{\ensuremath{\pi}}=21/A,$ ${G}_{\ensuremath{\nu}}=17/A,$ respectively. The single-particle energies were taken from experiment but scaled to yield an overall best fit. For the other four rotorlike terms, which do not mix SU(3) representations and induce only small changes in the spectra, a consistent set of parameters is given. The basis states are built as linear combinations of SU(3) states which are the direct product of SU(3) proton and neutron states with pseudospin zero. The results are in good agreement with experimental data, demonstrating the suitability of the model to describe heavy deformed nuclei.

Single-particle dynamical symmetry breaking in fermion SU(3) theories of collective motion

The SU 3 symmetry of the fermion dynamical symmetry model is shown to be essentially unbroken, even by highly nondegenerate spherical single-particle energies. Thus, it is expected that symmetry-limit results obtained in the FDSM will survive the inclusion of realistic single-particle energies for both normal and superdeformation.

Single-particle nondegeneracy and SU(3) fermion dynamical symmetry.

It is shown that the SU(3) symmetry for low-lying states of the fermion dynamical symmetry model is essentially preserved even for highly nondegenerate spherical single-particle energies. The breaking of SU(3) symmetry by single-particle energy terms in heritage-0 configurations for either normal deformation or superdeformation occurs only through an indirect Pauli effect and is significant only when the spherical single-particle splitting within shells is artificially large relative to that observed experimentally.

Magnetic moments of even rare-earth nuclei in the cranked HFB approach

Magnetic moments of yrast levels of a large number of even-even rare-earth nuclei have been calculated using a simple version of the cranked Hartree-Fock-Bogoliubov (CHFB) model. In order to study the sensitivity of the calculated results to the input values of spherical single-particle energies, the calculation has been performed with two different sets of these energies, which are widely used in the literature. It is found that with proper choice of spherical single-particle energies, the CHFB formalism, in its simple version, is quite capable of reproducing the observed spin dependence of g-factors from Sm to Os nuclei.

Electromagnetic moments of isomers in 144, 146, 147, 148Gd in the deformed independent particle model

Recently measured gyromagnetic ratios and quadrupole moments of isomers in 144, 146, 147, 148Gd are well reproduced by the deformed independent particle model, provided that the spherical single particle energies are chosen in accordance with the empirical evidence from single particle stripping and pick-up data.

The [formula omitted] “intruder” state in odd mass Au and Tl isotopes

In the odd mass Au and Tl isotopes the h 9 2 proton level falls to the next lowest shell as the neutron number N decreases, thereby destroying the Z = 82 magic gap for these nuclei. With further reduction in N the h 9 2 . level rises in T1, tending to restore the gap. A self-consistent determination of the neutron dependence of the proton spherical single-particle energies reproduces these characteristics of the h 9 2 proton level.