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Gamow-Teller strength of $^{12,14,16}$C within deformed quasiparticle random-phase approximation

Eunja Ha, Myung-Ki Cheoun, H. Sagawa, Gianluca Colò

Abstract

We investigate the Gamow-Teller (GT) transition strength distributions in the light carbon isotopes $^{12,14,16}$C within the framework of the deformed quasiparticle random-phase approximation (DQRPA). Nuclear deformation is explicitly incorporated through Skyrme Hartree-Fock mean-field calculations combined with the QRPA formalism. The residual particle-hole $(p-h)$ and particle-particle $(p-p)$ interactions are derived from Brückner $G$-matrix calculations based on the CD-Bonn potential, and their impact on the low-lying GT strengths is systematically examined by varying the corresponding interaction strengths. We find that nuclear deformation, associated with a reduced spin-orbit strength, plays a significant role in interpreting the GT strength distribution of $^{12}$C. In contrast, the calculated GT$^{(-)}$ strength distribution of $^{14}$C in the spherical limit reproduces the essential features of the experimental $(p,n)$ charge-exchange data. The case of $^{16}$C reveals additional high-lying GT strength associated with deformation-induced configuration mixing.

Gamow-Teller strength of $^{12,14,16}$C within deformed quasiparticle random-phase approximation

Abstract

We investigate the Gamow-Teller (GT) transition strength distributions in the light carbon isotopes C within the framework of the deformed quasiparticle random-phase approximation (DQRPA). Nuclear deformation is explicitly incorporated through Skyrme Hartree-Fock mean-field calculations combined with the QRPA formalism. The residual particle-hole and particle-particle interactions are derived from Brückner -matrix calculations based on the CD-Bonn potential, and their impact on the low-lying GT strengths is systematically examined by varying the corresponding interaction strengths. We find that nuclear deformation, associated with a reduced spin-orbit strength, plays a significant role in interpreting the GT strength distribution of C. In contrast, the calculated GT strength distribution of C in the spherical limit reproduces the essential features of the experimental charge-exchange data. The case of C reveals additional high-lying GT strength associated with deformation-induced configuration mixing.
Paper Structure (7 sections, 10 equations, 13 figures, 5 tables)

This paper contains 7 sections, 10 equations, 13 figures, 5 tables.

Table of Contents

  1. Introduction
  2. formalism
  3. Results and discussions
  4. GT strength distributions for $^{12}$C
  5. $^{14}$C
  6. $^{16}$C
  7. Summary and Discussions

Figures (13)

  • Figure 1: (Color online) Neutron pairing gaps of $^{16}$C vs the pairing strength, when the mean-field is obtained using the SGII set, for standard and reduced spin-orbit strength ($W_0$ and $0.6 \times W_0$). They are compared with the empirical pairing gaps obtained by the five-point formula. Relevant potential energy curves for each case are presented, respectively, in Figs. 2 and 7.
  • Figure 2: (Color online) Potential energy curves (PECs) of $^{12, 14,16}$C with SLy4, Skp, and SGII, respectively.
  • Figure 3: (Color online) SPSE (single particle state energy) of protons (a) and neutrons (b) of carbon isotopes with SGII.
  • Figure 4: (Color online) The B(GT$^{(-)}$) transition strength distributions from $^{12}$C with SkP, SLy4, and SGII are displayed, respectively. Experimental data are taken from Ref. Anderson96.
  • Figure 5: (Color online) Occupation probabilities of protons (red circles) and neutrons (black squares) in $^{12}$C. The red (black) dashed line is the Fermi energy of protons (neutrons). Occupation probabilities of SPSs of $0p_{3/2}$ and $0p_{3/2}$ of proton and neutron around Fermi energy are not smeared by the pairing interaction.
  • ...and 8 more figures