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Register a new userBeta - and gamma-decay transition rates in the two-group shell model
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V.I. Isakov
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In the framework of the two-group configuration model we obtain formulas for the reduced transition rates for beta- and gamma-transitions in even-even, odd-odd, even-odd, and odd-even nuclei. We explored dependencies of the transition rates on the occupancies of the involved subshells, as well as on the spin values of the initial and final states. The obtained formulas are useful for the qualitative spectroscopic analysis of experimental data, particulary in the regions of magicity, including the regions of the remote nuclei.
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The nuclear matrix elements of neutrinoless double-$beta$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $gamma$ from $0^circ$ to $60^circ$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.
We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the neutrinoless double-beta decay detection, in a mass interval ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay properties we have studied in previous works. Our results will be finally compared with shell-model calculations for the same set of nuclei.
We investigate the radial-overlap part of the isospin-symmetry breaking correction to superallowed $0^+to 0^+$-decay using the shell-model approach similar to that of Refs. [1, 2]. The 8 sd-shell emitters with masses between $A=22$ and $A=38$ have been re-examined. The Fermi matrix element is evaluated with realistic spherical single-particle wave functions, obtained from spherical Woods-Saxon (WS) or Hartree-Fock (HF) potentials, fine-tuned to reproduce the experimental data on charge radii and separation energies for nuclei of interest. The elaborated adjustment procedure removes any sensitivity of the correction to a specific parametrisation of the WS potential or to vario
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.
The effects of the phonon-phonon coupling on the beta-decay rates of neutron-rich nuclei are studied in a microscopic model based on Skyrme-type interactions. The approach uses a finite-rank separable approximation of the Skyrme-type particle-hole (p-h) residual interaction. Very large two-quasiparticle spaces can thus be treated. A redistribution of the Gamow-Teller (G-T) strength is found due to the tensor correlations and the 2p-2h fragmentation of G-T states. As a result, the beta-decay half-lives are decreased significantly. Using the Skyrme interaction SGII together with a volume-type pairing interaction we illustrate this reduction effect by comparing with available experimental data for the Ni isotopes and neutron-rich N=50 isotones. We give predictions for 76Fe and 80Ni in comparison with the case of the doubly-magic nucleus 78Ni which is an important waiting point in the r-process.
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