Gamow-Teller Strength distributions in $^{76}\textrm{Ge}$, $^{76,82}\textrm{Se}$, and $^{90,92}\textrm{Zr}$ by the Deformed Proton-neutron QRPA

Abstract

We developed the deformed proton-neutron quasiparticle random phase approximation (QRPA) and applied to the evaluation of the Gamow-Teller (GT) transition strength distributions including high-lying excited states, which data becomes recently available beyond one or two nucleon threshold by charge exchange reactions using hundreds of MeV projectiles. Our calculations started with single-particle states calculated by a deformed axially symmetric Woods-Saxon potential. Neutron-neutron and proton-proton pairing correlations are explicitly taken into account at the deformed Bardeen Cooper Schriffer theory. Ground state correlations, and two-particle and two-hole mixing states are included in the deformed QRPA. In this work, we use a realistic two-body interaction given by the Brueckner $G$-matrix based on the CD Bonn potential to reduce the ambiguity on the nucleon-nucleon interactions inside nuclei. We applied our formalism to the GT transition strengths for $^{76}$Ge, $^{76,82}$Se, and $^{90,92}\textrm{Zr}$, and compared to available experimental data. The GT strength distributions were sensitive on the deformation parameter as well as its sign, {\it i.e.}, oblate or prolate. The Ikeda sum rule, which is usually thought to be satisfied under the one-body current approximation irrespective of nucleon models, is used to test our numerical calculations and shown to be satisfied without introducing the quenching factor, if high-lying GT excited states are properly taken into account. Most of the GT strength distributions of the nuclei considered in this work turn out to have the high-lying GT excited states beyond one nucleon threshold, which are shown to be consistent with available experimental data.