Nuclear structure studies of double-charge-exchange Gamow-Teller strength

The double Gamow-Teller strength distributions in even-$A$ calcium isotopes were calculated using the nuclear shell model by applying the single Gamow-Teller operator two times sequentially on the ground state of the parent nucleus. The number of intermediate states actually contributing to the results was determined. The sum rules for the double Gamow-Teller operator in the full calculation were approximately fulfilled. In the case that the symmetry is restored approximately by introducing degeneracies of the $f$ levels, and the $p$ levels in the $fp$-model space, the agreement with the sum rules was very close.

Figure 1

Illustration of the method of calculation described in the text. The notations $1_{\text{max}}^{+}$ and $0_{\text{max}}^{+}$ are the corresponding cutoffs.

Figure 2

The cumulative sum of the single Gamow-Teller strength $B\left({\text{GT}}_{-}\right)$ as a function of the number of $1^{+}$ states (a) and excitation energies (b) of the intermediate nucleus ${}^{48}\mathrm{Sc}$. The calculation used FPD6 and KB3G interactions in the $fp$-model space.

Figure 3

The cumulative sum of the $B(\text{DGT};0^{+}\to 0^{+})$ (a) and $B(\text{DGT};0^{+}\to 2^{+})$ (b) in ${}^{44}\mathrm{Ca}$.

Figure 4

The same as Fig. 3, but for ${}^{46}\mathrm{Ca}$.

Figure 5

The cumulative sum of the $B(\text{DGT};0^{+}\to 0^{+})$ in ${}^{48}\mathrm{Ca}$.

Figure 6

$B(\text{DGT};0^{+}\to 0^{+})$ for ${}^{44}\mathrm{Ca}$ as the function of the excitation energy of the final nucleus ${}^{44}\mathrm{Ti}$ (a). The DGT transitions to low-lying states are shown in (b). The strengths were spread by using Lorentzian averaging with the width of 1 MeV.

Figure 7

The same as Fig. 6, but for $B(\text{DGT};0^{+}\to 2^{+})$.

Figure 8

$B(\text{DGT};0^{+}\to 0^{+})$ in ${}^{46}\mathrm{Ca}$ (a). The DGT transitions to low-lying states are shown in (b).

Figure 9

The same as Fig. 8, but for $B(\text{DGT};0^{+}\to 2^{+})$.

Figure 10

The same as Fig. 8, but for ${}^{48}\mathrm{Ca}$.

Figure 11

The dependence on the number of intermediate states of $B(\text{DGT};0^{+}\to 0^{+})$ in ${}^{44}\mathrm{Ca}$. The numbers in parentheses are the corresponding total strengths.

Figure 12

The same as Fig. 11, but for $B(\text{DGT};0^{+}\to 2^{+})$.

Figure 13

The same as Fig. 11, but for $B(\text{DGT};0^{+}\to 0^{+})$ in ${}^{48}\mathrm{Ca}$.

Figure 14

$B(\text{DGT};0^{+}\to 0^{+},2^{+})$ in ${}^{44}\mathrm{Ca}$ (a) and ${}^{46}\mathrm{Ca}$ (b).

Figure 15

$B(\text{DGT};0^{+}\to 0^{+})$ (a) and $B(\text{DGT};0^{+}\to 2^{+})$ (b) in ${}^{44}\mathrm{Ca}$ using FPD6 and KB3G interactions.

Figure 16

The same as Fig. 15, but for ${}^{46}\mathrm{Ca}$.

Figure 17

$B(\text{DGT};0^{+}\to 0^{+})$ in ${}^{48}\mathrm{Ca}$ using FPD6 and KB3G interactions. The strengths are spread with the width of 1 MeV. For comparison to Ref. [25] that also calculated the DGT distribution in ${}^{48}\mathrm{Ca}$ using the KB3G interaction, the strengths in our calculation shown in this figure are divided by the factor of 3 (see text).

Figure 18

The DGT distributions in the $f$-model space (including the $f_{7/2}$ and the $f_{5/2}$ orbits only) in even-$A$ calcium isotopes using the FPD6 interaction.