Proton-neutron versus $\alpha$-like correlations above ${}^{100}\mathbf{Sn}$

It is known that the $\alpha$ particle reduced width has the largest values in the region above ${}^{100}\mathrm{Sn}$, and this behavior is usually attributed to the proton-neutron correlations. To reproduce the reduced $\alpha$-decay width we use an additional pocket-like surface potential in the single-particle mean field that simulates four-body correlations. We show that the strength of this interaction has a universal linear dependence on the experimental reduced width above the double magic nuclei ${}^{100}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$. Moreover, we demonstrate that proton-neutron pairing correlations have a small influence on this dependence and therefore cannot explain the larger reduced decay widths above ${}^{100}\mathrm{Sn}$. We give an indication of the possibility of detecting $\mathrm{Sn}+n\alpha$ structures as dipole Pigmy-like resonances.

Figure 1

Experimental reduced width versus $N/Z$ ratio.

Figure 2

Comparison between neutron densities obtained by BCS calculations and by diagonalization.

Figure 3

Formation amplitude in the BCS approach.

Figure 4

Formation amplitude in the $pn$-BCS approach.

Figure 5

Comparison of formation amplitudes in various approaches. The proton spectrum is considered identical to the neutron spectrum.

Figure 6

The strength of the $\alpha$-clustering additional part of the mean-field potential $V_{\alpha }$ versus the reduced width.

Figure 7

Exact (dark squares) and fitted expansion coefficients (open squares) given by Eq. (A4).