Effects of quasiparticle-vibration coupling on Gamow-Teller strength and $\beta$ decay with the Skyrme proton-neutron finite-amplitude method

We adapt the proton-neutron finite-amplitude method, which in its original form is an efficient implementation of the Skyrme quasiparticle random phase approximation, to include the coupling of quasiparticles to like-particle phonons. The approach allows us to add beyond-quasiparticle random-phase approximation correlations to computations of Gamow-Teller strength and $\beta$-decay rates in deformed nuclei for the first time. We test the approach in several deformed isotopes for which measured strength distributions are available. The additional correlations dramatically improve agreement with the data, and will lead to improved global $\beta$-decay rates.

Figure 1

Diagrams illustrating the four contributions to the “spreading matrix” $W$ in Eq. (12). Blue lines represent protons and red lines neutrons. Black squiggly lines represent phonons, either emitted and reabsorbed by a single nucleon or exchanged between nucleons.

Figure 2

(a) Gamow-Teller strength distributions for the nucleus ${}^{82}\mathrm{Se}$. The red dashed and solid blue curves, representing results calculated with the pnFAM and pnFAM* (see text), have been scaled by 0.62. The black curve, from Ref. [41] is experimental data. In obtaining each curve, we chose the imaginary part $\mathrm{\Delta }$ of the perturbing frequency to be 0.5 MeV. (b) Integrated Gamow-Teller strength.

Figure 3

Same as Fig. 2, but restricted to strength below 8 MeV.

Figure 4

Same as in Fig. 2 but for ${}^{76}\mathrm{Ge}$.

Figure 5

Same as in Fig. 2 but for ${}^{150}\mathrm{Nd}$, with the experimental data from Ref. [43].

Figure 6

Gamow-Teller strength distribution in ${}^{82}\mathrm{Se}$ obtained in the pnFAM* with several values for the cutoff parameter $v_{\text{min}}$. The lower that quantity, the more phonons the calculation includes. As before, we include all natural-parity multipoles with $L\le 6$.

Figure 7

Gamow-Teller strength distribution in ${}^{82}\mathrm{Se}$ obtained in the pnFAM* with several values for the maximum angular momentum $L_{\text{max}}$ in states excited by the like-particle operators in Eq. (18). No other cutoffs are imposed, i.e., $v_{\text{min}}=0$.