*3.4. Isospin Non-Conserving (INC) Interaction: VB*

Zuker et al. [16] recognised that an additional multipole component is required, in the model, to account for the experimental MED and TED observed in the region (the inclusion of the HO Coulomb matrix elements were shown to be insufficient). Zuker et al. [16] extracted an additional effective INC interaction through comparing the HO Coulomb matrix elements with the MED and TED for the *A* = 42 isospin triplet. An isovector matrix element, *V*(1) *<sup>B</sup>* was derived for *f* <sup>7</sup> 2 orbital the from the *A* = 42, *T* = 1 mirror nuclei and an isotensor *f* <sup>7</sup> 2 matrix element *V*(2) *<sup>B</sup>* extracted from the TED for *T* = 1 triplet. These matrix elements were derived as a function of angular-momentum coupling *J*, and it was observed that the dominant components appeared to be at *J* = 2 for *V*(1) *<sup>B</sup>* and *<sup>J</sup>* <sup>=</sup> 0 for *<sup>V</sup>*(2) *<sup>B</sup>* and both of the order of +100 keV. It was observed [16] that these additional interactions, when included in the shell-model calculations, along with the first and third terms above, allowed for a very good description of the data available at the time. It was later noted [17], once more data became available, that an isovector INC matrix element of the order of −100 keV at *J* = 0 gives essentially very similar results to the original value of +100 keV at *J* = 2.

Whatever the origin of this effect, the inclusion of these additional effective isovector and isotensor interactions appeared to be an essential inclusion in the modelling of MED and TED, respectively, at least in the *f* <sup>7</sup> 2 region. The importance of inclusion of such INC isovector and/or isotensor interactions has also been investigated in the *sd* shell [11,52] and in the upper *p f* shell (e.g., [18,21]).
