Isospin-breaking interactions studied through mirror energy differences

Background: Information on charge-dependent (i.e., isospin-non-conserving) interactions is extracted from excited states of mirror nuclei.

Purpose: Specifically, the purpose of the study is to extract effective isovector ($V_{pp}-V_{nn}$) interactions which, in general, can either be of Coulomb or nuclear origin.

Methods: A comprehensive shell-model description of isospin-breaking effects is used to fit data on mirror energy differences in the A = 42–54 region. The angular-momentum dependence of isospin-breaking interactions was determined from a systematic study of mirror energy differences.

Results: The results reveal a significant isovector term, with a very strong spin dependence, beyond that expected of a two-body Coulomb interaction.

Conclusions: The isospin-breaking terms that are extracted have a $J$ dependence that is not consistent with the known CSB properties of the bare nucleon-nucleon interaction.

Figure 1

(a) The centroid-subtracted $V_B^J$ coefficients in the $f_{7/2}$ shell derived from the fits presented in this paper; see text for details. Fits across three mass ranges are shown: $A$ = 42–54 (red circles), $A$ = 47–54 (blue triangles), and $A$ = 51–54 (green squares). (b) The results of the fit across the whole shell, $A$ = 42–54 [red circles, same data as (a)], compared with (blue dot-dashed line) the results of Ref. [11] based on a CDE analysis.

Figure 2

The extracted value of $V_B^0$ from a single-parameter fit for (a) each mirror pair individually, with different symbols and colors corresponding to the isospin (T) of the analog states, and (b) for sets of mirror pairs grouped according to the isospin $T=|T_z|=\mathrm{\Delta }Z/2$. The best-fit value of $V_B^0=-79\left(6\right)$ keV, from a single-parameter fit across the whole shell, is indicated in (a) and (b), and ${\sigma }_{\mathrm{th}}=23$ keV was assumed. In (a), the data point of −440(210) for $T=1$, $A=44$, for which there are only two data points, is not included in the plot for clarity.

Figure 3

The experimental and predicted mirror energy differences for four mirror pairs in the $f_{7/2}$ shell of various masses and isospins as a function of total angular momentum $I$. The dashed line shows the result of the first term of Eq. (1) and the solid line shows the full calculation including the best-fit $V_B^J$ parameters shown in bold in Table 2.