The Energy-Weighted and Non Energy-Weighted Gamow-Teller Sum Rules in Relativistic Random Phase Approximation

Abstract

The non energy-weighted Gamow-Teller(GT) sum rule is satisfied in relativistic models, when all nuclear density-dependent terms, including Pauli blocking terms from nucleon-antinucleon excitations, are taken into account in the RPA correlation function. The no-sea approximation is equivalent to this approximation for the giant GT resonance state and satisfies the sum rule, but each of the total ${\beta }_{-}$ and ${\beta }_{+}$ strengths is different in the two approximations. It is also shown that the energy-weighted sum of the GT strengths for the ${\beta }_{-}$ and ${\beta }_{+}$ transitions in RPA is equal to the expectation value of the double commutator of the nuclear Hamiltonian with the GT operator, when the expectation value is calculated with the ground state in the mean field approximation. Since the present RPA neglects renormalization of the divergence, however, the energy-weighted strengths outside of the giant GT resonance region become negative. These facts are shown by calculating in an analytic way the GT strengths of nuclear matter.

REVTeX4, no figures

References in corpus (5)

• Distorted wave impulse approximation analysis for spin observables in nucleon quasi-elastic scattering and enhancement of the spin-longitudinal response
• Delta-Hole Interaction in Nuclei and the Gamow-Teller Strength in ^90Nb
• The role of the Dirac sea in the quenching of Gamow-Teller strength
• Effects of the Dirac Sea on the Giant Monopole States
• The Gamow-Teller States in Relativistic Nuclear Models

Cited by in corpus (5)

• Exotic modes of excitation in atomic nuclei far from stability
• Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model II: Nuclear spin and isospin excitations
• Nuclear charge-exchange excitations based on relativistic density-dependent point-coupling model
• Gamow-Teller sum rule in relativistic nuclear models
• Roles of Antinucleon Degrees of Freedom in the Relativistic Random Phase Approximation