Isospin mixing from $\beta$-delayed proton emission

We present a general scheme of a shell-model analysis of a $\beta$-delayed proton emission. We show that the experimental proton to $\gamma$-ray branching ratio for the isobaric analog state (IAS) populated in $\beta$ decay of a precursor, supplemented by theoretical proton and $\gamma$-ray widths, can be used to extract spectroscopic factors for isospin-forbidden proton emission. In the case of a well-justified two-level mixing approximation and a relatively well known spectroscopic factor of the admixed state, the proposed scheme provides a new way to determine the amount of the isospin mixing in the IAS. This conjecture is illustrated by the theoretical analysis of ${}^{44}\mathrm{Cr}$ and ${}^{48}\mathrm{Fe}$ decay.

Figure 1

Experimental and theoretical partial decay schemes of ${}^{44}\mathrm{Cr}$. The intensity $I_{\beta }$ is the theoretically calculated feeding of the IAS via a superallowed $\beta$ decay; the proton intensity $I_p$ is the experimentally observed proton-emission branching ratio tentatively assigned to be from the IAS. The experimental data are from Refs. [18, 19, 20]. The theoretical calculations have been performed with two different effective interactions, cdGX1A and cdKB3G.

Figure 2

Experimental and theoretical partial decay schemes of ${}^{48}\mathrm{Fe}$. The experimental data are from Refs. [18, 19, 21]. See caption to Fig. 1 for other details.

Figure 3

Experimental (in the center) and theoretical (on the right and on the left) level schemes of mirror nuclei ${}^{44}\mathrm{V}$ and ${}^{44}\mathrm{Sc}$. The experimental data are from Refs. [19, 22, 23]. The theoretical calculations have been performed with two different effective interactions, cdGX1A and cdKB3G.

Figure 4

Experimental (in the center) and theoretical (on the right and on the left) level schemes of mirror nuclei ${}^{48}\mathrm{Mn}$ and ${}^{48}\mathrm{V}$. The experimental data are from Refs. [19, 21, 22]. See caption to Fig. 3 for other details.