Estimation of a 2p2h effect on Gamow-Teller transitions within the second Tamm-Dancoff approximation

Two-particle two-hole (2p2h) effect on the Gamow-Teller (GT) transition for neutron-rich nuclei is studied by the second Tamm-Dancoff approximation (STDA) with the Skyrme interaction. Unstable ${}^{24}\mathrm{O}$ and ${}^{34}\mathrm{Si}$ and stable ${}^{48}\mathrm{Ca}$ nuclei are chosen to study the quenching and fragmentation of the GT strengths. Correlation of the 2p2h configurations causes about $20\%$ quenching and downward shift of GT giant resonances (GTGRs). The residual interaction changing relative angular momentum that appeared in the tensor force part gives a meaningful effect to the GT strength distributions. In this work, $17–26\%$ of the total GT strengths are brought to high-energy region above GTGRs. In particular, the tensor force brings strengths to high energy more than 50 MeV. STDA calculation within a small model space for 2p2h configuration is also performed and experimental data of ${}^{48}\mathrm{Ca}$ is reproduced reasonably.

Figure 1

GT strength distribution of ${}^{24}\mathrm{O}$ calculated by STDA(D) with various box boundary conditions from $r_{\text{box}}=8$ to 14 fm. The upper and lower panels show the result for (a) $N=8$ and (b) $N=13$, respectively. The strengths are smeared by the Lorentzian function with a width 1 MeV. $E_{\text{cut}}^{1\mathrm{p}1\mathrm{h}}$ is set to be 100 MeV.

Figure 2

Same as described in the caption of Fig. 1, but for ${}^{48}\mathrm{Ca}$. The upper and lower panels show the result for (a) $N=8$ and (b) $N=12$, respectively.

Figure 3

GT strength distributions of ${}^{24}\mathrm{O}$ and ${}^{48}\mathrm{Ca}$ calculated by STDA(D) with different cutoff energies of unperturbed 2p2h states denoted by $E_{\text{cut}}^{\text{2p2h}}$ from 80 to 120 MeV.

Figure 4

GT strength distribution of ${}^{24}\mathrm{O}$ as a function of excitation energy with respect to its daughter nucleus. The upper, middle, and bottom panels are the results for (a) TDA, (b) STDA, and (c) STDA(D), respectively. The solid and dashed lines indicate the results calculated with SGII and SGII+Te1 parameter sets, respectively. The arrow indicates the experimentally observed $1^{+}$ state [46]. The strengths are smeared by the Lorentzian function with a width 1 MeV.

Figure 5

B(GT) of ${}^{24}\mathrm{O}$ for (a)SGII and (b)SGII+Te1. The solid and dashed spikes indicate the results of STDA and TDA, respectively.

Figure 6

Same as described in the caption of Fig. 4, but for ${}^{34}\mathrm{Si}$.

Figure 7

GT-strength distribution of ${}^{48}\mathrm{Ca}$ as a function of excitation energy with respect to its daughter nucleus. The upper, middle, and bottom panels are the results for (a) TDA, (b) STDA, and (c) STDA(D), respectively. The solid and dashed lines indicate the results calculated with SGII and SGII+Te1 parameter sets, respectively. The experimental data is taken from Ref. [47]. The strengths are smeared by the Lorentzian function with a width 2 MeV for comparison with the experimental data as adopted in Ref. [48], which is the order of the experimental resolution.

Figure 8

GT strength distribution of ${}^{24}\mathrm{O}$ calculated various conditions of the central part of the residual interaction for (a) TDA and (b) STDA(D). The thin solid line indicates the HF solution. The dashed and bold lines are cases A and B, respectively (see the text).

Figure 9

Same as Fig. 8, but for the tensor part of the residual interaction. The thin solid line indicates the HF solution. The dashed and bold lines are case C and D, respectively.

Figure 10

GT strength distribution of ${}^{24}\mathrm{O}$ as a function of excitation energy with respect to its daughter nucleus. In contrast to Fig. 4, the horizontal axis is extended up to 100 MeV. The upper panel and lower panels are (a) TDA and (b) STDA(D) results, respectively. The resonances are smoothed by a Lorentzian function with 1 MeV width.

Figure 11

Same as described in the caption of Fig. 10, but for ${}^{34}\mathrm{Si}$ in the energy region from 20 to 85 MeV.

Figure 12

Same as described in the caption of Fig. 10, but for ${}^{48}\mathrm{Ca}$ in the energy region from 20 to 80 MeV.

Figure 13

Same as described in the caption of Fig. 7 in the case of the restricted model space (see the text for the detail).