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Title: Calculation of {beta}-decay rates in a relativistic model with momentum-dependent self-energies

Abstract

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of {beta}-decay half-lives of neutron-rich nuclei in the Z{approx_equal}28 and Z{approx_equal}50 regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the {pi}+{rho} exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of {beta}{sup -}-decay rates.

Authors:
; ;  [1];  [2]
  1. Physics Department, Faculty of Science, University of Zagreb, Croatia, and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching (Germany)
  2. (Germany)
Publication Date:
OSTI Identifier:
20991005
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevC.75.024304; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BETA DECAY; DENSITY; GROUND STATES; LAGRANGIAN FUNCTION; MEAN-FIELD THEORY; MESONS; NEUTRON-RICH ISOTOPES; NEUTRONS; PARTICLE INTERACTIONS; PROTONS; RANDOM PHASE APPROXIMATION; RELATIVISTIC RANGE; SELF-ENERGY

Citation Formats

Marketin, T., Vretenar, D., Ring, P., and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Calculation of {beta}-decay rates in a relativistic model with momentum-dependent self-energies. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.024304.
Marketin, T., Vretenar, D., Ring, P., & Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Calculation of {beta}-decay rates in a relativistic model with momentum-dependent self-energies. United States. doi:10.1103/PHYSREVC.75.024304.
Marketin, T., Vretenar, D., Ring, P., and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching. Thu . "Calculation of {beta}-decay rates in a relativistic model with momentum-dependent self-energies". United States. doi:10.1103/PHYSREVC.75.024304.
@article{osti_20991005,
title = {Calculation of {beta}-decay rates in a relativistic model with momentum-dependent self-energies},
author = {Marketin, T. and Vretenar, D. and Ring, P. and Physik-Department der Technischen Universitaet Muenchen, D-85748 Garching},
abstractNote = {The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of {beta}-decay half-lives of neutron-rich nuclei in the Z{approx_equal}28 and Z{approx_equal}50 regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the {pi}+{rho} exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of {beta}{sup -}-decay rates.},
doi = {10.1103/PHYSREVC.75.024304},
journal = {Physical Review. C, Nuclear Physics},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}
  • The Lagrangian density of standard relativistic mean-field models with density-dependent meson-nucleon coupling vertices is modified by introducing couplings of the meson fields to derivative nucleon densities. As a consequence, the nucleon self-energies that describe the effective in-medium interaction become momentum dependent. In this approach it is possible to increase the effective (Landau) mass of the nucleons, that is related to the density of states at the Fermi energy, as compared to conventional relativistic models. At the same time the relativistic effective (Dirac) mass is kept small to obtain a realistic strength of the spin-orbit interaction. Additionally, the empirical Schroedinger-equivalent centralmore » optical potential from Dirac phenomenology is reasonably well described. A parametrization of the model is obtained by a fit to properties of doubly magic atomic nuclei. Results for symmetric nuclear matter, neutron matter, and finite nuclei are discussed.« less
  • A systematic, fully self-consistent calculation of {beta}-decay rates is presented, based on a microscopic theoretical framework. Analysis is performed on a large number of nuclei from the valley of {beta} stability towards the neutron drip-line. Nuclear ground state is determined using the Relativistic Hartree-Bogoliubov (RHB) model with density-dependent meson-nucleon coupling constants. Transition rates are calculated within the proton-neutron relativistic quasiparticle RPA (pn-RQRPA) using the same interaction that was used in the RHB equations.
  • Conventional relativistic mean-field theory is extended with the introduction of higher-order derivative couplings of nucleons with the meson fields. The Euler-Lagrange equations follow from the principle of stationary action. From invariance principles of the Lagrangian density the most general expressions for the conserved current and energy-momentum tensor are derived. The nucleon self-energies show the explicit dependence on the meson fields. They contain additional regulator functions which describe the energy dependence. The density dependence of meson-nucleon couplings causes the apperance of additional rearrangement contributions in the self-energies. The equation of state of infinite nuclear matter is obtained and the thermodynamical consistencymore » of the model is demonstrated. This model is applied to the description of spherical, non-rotating stars in ╬▓-equilibrium. Stellar structure is calculated by solving the Tolman-Oppenheimer-Volkov (TOV) equations. The results for neutron stars are shown in terms of mass-radius relations.« less
  • We have performed quasiparticle-random-phase-approximation (QRPA) calculations of the {nu}{nu} transition matrix for {sup 76}Ge, {sup 82}Se, and {sup 100}Mo, using effective interactions derived from the Paris and the Bonn {ital NN} potentials. Unlike earlier QRPA calculations where the self-energy corrections to the single-particle spectra were suppressed, we have retained these corrections as given by our interactions. In this way our calculations are able to avoid the commonly encountered difficulty of QRPA instability near {ital g}{sub pp}=1. The {ital M}{sup 2{nu}} matrix elements of {sup 76}Ge, {sup 82}Se, and {sup 100}Mo given by our calculation, with no adjustable parameters, are inmore » reasonably good agreement with recent direct counter experiments.« less