Spin-triplet proton-neutron pair in spin-dipole excitations

Background: Spin-triplet $(S=1)$ proton-neutron $\left(pn\right)$ pairing in nuclei has been under debate. It is well known that the dynamical pairing affects the nuclear matrix element of the Gamow-Teller (GT) transition and the double $\beta$ decay.

Purpose: We investigate the effect of the $pn$-pair interaction in the $T=0,S=1$ channel on the low-lying spin-dipole (SD) transition. We then aim at clarifying the distinction of the role in between the SD and GT transitions.

Method: We perform a three-body model calculation for the transition ${}^{80}\mathrm{Ni}\to {}^{80}\mathrm{Cu}$, where ${}^{78}\mathrm{Ni}$ is taken as a core. The strength of the pair interaction is varied to see the effect on the SD transition-strength distribution. To fortify the finding obtained by the three-body model, we employ the nuclear energy-density functional method for the SD transitions in several nuclei, where one can expect a strong effect.

Results: The effect of the $S=1pn$-pair interaction depends on the spatial overlap of the $pn$ pair and the angular momentum of the valence nucleons; the higher the angular momentum of the orbitals, the more significant the effect.

Conclusions: The dynamical $S=1$ pairing is effective even for SD states, although the spatial overlap of the $pn$ pair can be smaller than GT states. The SD transition involving high-$\ell$ orbitals with the same principal quantum number is strongly affected by the dynamical $S=1$ pairing.

Figure 1

Single-particle energies of the valence nucleons relative to the Fermi levels of the ${}^{78}\mathrm{Ni}$ core. Shown are the proton single-particle states with the (a) original and (b) shifted ($-40$ MeV) Woods-Saxon potentials, respectively, while the neutron single-particle states are depicted in (c) and (d). The shaded area represents the continuum region of neutron states. Notice that the $2d_{3/2}$ and $3s_{1/2}$ states in case (d) are almost degenerate, which are located at 8.315 and 8.317 MeV, respectively.

Figure 2

(a) Calculated distributions for the SD $1^{-}$ transition as functions of the excitation energy with respect to the target nucleus. The smearing parameter $\gamma =0.1$ MeV is used. The result obtained with $f_{NN}=0,1.0$, and 1.7 is depicted by the dotted, dashed, and solid lines, respectively. (b) Results obtained by changing the depth of the WS potential by $-40$ MeV.

Figure 3

Similar to Fig. 2 but obtained by employing the $\mathrm{Skyrme-KSB}+pn\mathrm{QRPA}$ with the SGII functional for the SD $0^{-}$ transition in ${}^{132,134}\mathrm{Zr}\to {}^{132,134}\mathrm{Nb}$. The results obtained with $f_{NN}=0$ and 1.0 are depicted by the dashed and solid lines, respectively. Shown is also the unperturbed strengths by the dotted line.

Figure 4

Same as Fig. 3 but for the SD $2^{-}$ transition in ${}^{120,122}\mathrm{Sn}\to {}^{120,122}\mathrm{Sb}$ and ${}^{68,70}\mathrm{Ni}\to {}^{68,70}\mathrm{Cu}$.