Gamow-Teller transitions in magic nuclei calculated by the charge-exchange subtracted second random-phase approximation

The Gamow-Teller (GT) transitions in four magic nuclei, ${}^{48}\mathrm{Ca}, {}^{90}\mathrm{Zr}, {}^{132}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$, are studied using a self-consistent Hartree-Fock (HF) plus charge-exchange subtracted second random-phase approximation (SSRPA) model with several Skyrme energy density functions (EDFs). These calculations show that SSRPA improves systematically the description of main GT strength distributions in terms of the excitation energy and the peak height. The quenching factors are evaluated to be 13–20% of the Ikeda sum rule for ${}^{48}\mathrm{Ca}, {}^{90}\mathrm{Zr}$, and ${}^{132}\mathrm{Sn}$, due to the couplings to two-particle–two-hole (2p-2h) configurations. Also examined are the effects of tensor interactions on the excitation energies and the quenching factors of GT strength distributions.

Figure 1

The strength distributions and corresponding cumulative sums of ${}^{208}\mathrm{Pb}$ calculated by SSRPA with SGII for 2p-2h energy cutofsf 30 and 32 MeV. The red line represents cutoff = 30 MeV and the blue dashed line represents cutoff = 32 MeV.

Figure 2

The strength distributions and corresponding cumulative sums of ${}^{90}\mathrm{Zr}$ calculated by SSRPA with SGII for the full calculation and the diagonal approximation used in the subtraction procedure one. The red line represent the result obtained with the diagonal approximation used in the subtraction procedure, labeled ${\mathrm{SSRPA}}_D$, and the blue dashed line represents the full calculation, labeled ${\mathrm{SSRPA}}_F$.

Figure 3

${\mathrm{GT}}_{-}$ strength distributions of ${}^{48}\mathrm{Ca}$ [panel (a)], ${}^{90}\mathrm{Zr}$ [panel (b)], ${}^{132}\mathrm{Sn}$ [panel (c)], and ${}^{208}\mathrm{Pb}$ [panel (d)] calculated with the SGII and SAMi EDFs by RPA (dashed lines) and SSRPA (solid lines). The results obtained by SGII and SAMi are shown by the red and blue lines, respectively. The experimental data of ${}^{48}\mathrm{Ca}$ [41],${}^{90}\mathrm{Zr}$ [42], ${}^{132}\mathrm{Sn}$ [43], and ${}^{208}\mathrm{Pb}$ [44] are shown by the black filled circles. The calculated discrete strength distributions are smoothed by a Lorentzian weighting function of 1 MeV width. See the text for more details.

Figure 4

Cumulative ${\mathrm{GT}}_{-}$ strengths up to 25 MeV for ${}^{48}\mathrm{Ca}$ [panel (a)] and ${}^{90}\mathrm{Zr}$ [panel (b)], 23 MeV for ${}^{132}\mathrm{Sn}$ [panel (c)], and 25 MeV for ${}^{208}\mathrm{Pb}$ [panel (d)] calculated with SGII and SAMi by RPA (dashed lines) and SSRPA (solid lines). The results obtained by SGII and SAMi are shown by the red and blue lines, respectively. The experimental data of ${}^{48}\mathrm{Ca}$ [41],${}^{90}\mathrm{Zr}$ [42], ${}^{132}\mathrm{Sn}$ [43], and ${}^{208}\mathrm{Pb}$ [44] are shown by the black filled circles.

Figure 5

The same as Fig 3, but for the SAMi-T EDF with or without tensor terms. Red lines represent SAMi-T without tensor terms, labeled w/o, and blue lines represent the SAMi-T EDF with tensor terms, labeled w/i.

Figure 6

The same as Fig 4, but for the SAMi-T EDF with or without tensor terms. Red lines represent SAMi-T without tensor terms, labeled w/o, blue lines represent SAMi-T with tensor terms, labeled w/i.

Figure 7

Strength distributions (upper panels) and corresponding cumulative sums (lower panels) of ${}^{48}\mathrm{Ca}$ [panels (a), (b)], ${}^{90}\mathrm{Zr}$ [panels (c), (d)], ${}^{132}\mathrm{Sn}$ [panels (e), (f)], and ${}^{208}\mathrm{Pb}$ [panels (g), (h)] calculated with the T21, T44, and T55 EDFs by SSRPA. The results obtained by T21, T44, and T55 are labeled by red solid lines, blue solid lines, and green dash-dot-dot lines, respectively. The experimental data are shown by the black filled circles.

Figure 8

Strength distributions (upper panels) and corresponding cumulative sums (lower panels) of ${}^{48}\mathrm{Ca}$ [panels (a), (b)], ${}^{90}\mathrm{Zr}$ [panels (c), (d)], ${}^{132}\mathrm{Sn}$ [panels (e), (f)], and ${}^{208}\mathrm{Pb}$ [panels (g), (h)] calculated with the SGII, SGII$+$Te1, SGII$+$Te2, and SGII$+$Te3 EDFs by SSRPA. The results obtained by SGII, SGII$+$Te1, SGII$+$Te2, and SGII$+$Te3 are shown by red solid lines, blue solid lines, green dash-dot-dot lines, and violet dashed lines, respectively. The experimental data are shown by the black filled circles.

Figure 9

Same as Fig. 8 but calculated without $J^2$ terms both in HF and SSRPA, and the results are labeled by ${\mathrm{SGII}}^{\mathrm{O}}, {\mathrm{SGII}}^{\mathrm{O}}+$Te1, ${\mathrm{SGII}}^{\mathrm{O}}+$Te2, and ${\mathrm{SGII}}^{\mathrm{O}}+$Te3, respectively.