*3.3. Radial Contribution: VCr*

A major innovation, introduced by Lenzi et al. [51], and included in the prescription of Ref. [16], is the recognition that the nuclear radius may change along the yrast line with increasing excitation energy, resulting in a change in the bulk Coulomb energy. This, in turn, will contribute to the MED through the difference in *Z* between the mirror pair. It was recognised [16,51] that orbital radii depend on *l* and that, in the *f* <sup>7</sup> 2 region, it was the changing occupancy of the low-*l* orbitals *p* <sup>3</sup> and *p* <sup>1</sup> which would drive the nucleus to larger radii.

2 2 Unlike the *Vll* and *Vls* terms above, for which the MED will depend on the difference between proton and neutron orbital occupancies, the *VCr* term will depend on the average (proton plus neutron) occupancy of the two *p* orbits. The MED contribution due to the *VCr* term is then calculated using

$$\text{MED}\_{V\_{\text{Gr}}}(f) = n\pi \left[ \left( \frac{m\_{\pi}(\text{gs}) + m\_{\nu}(\text{gs})}{2} \right) - \left( \frac{m\_{\pi}(f) + m\_{\nu}(f)}{2} \right) \right] \tag{3}$$

where *m*(*J*) is the total occupancy of the *p* <sup>3</sup> 2 and *p* <sup>1</sup> 2 orbitals for neutrons (*ν*) and protons (*π*), and *n* = 2|*Tz*| accounts for the difference in *Z* between the mirror nuclei. The coefficient *α* was estimated in Ref. [3] as 200 keV, based on the *A* = 41 mirror nuclei, and this number has been used extensively in the region. In the *f* <sup>7</sup> 2 region, the occupancy of *p* <sup>1</sup> 2 is often negligibly small, and so is neglected in the MED calculation. However, above *Z*, *N* ∼ 28 it should be included (e.g., [9]). In the *sd*-shell the same formalism has been used (e.g., [11,52,53]), but instead tracking the occupancy of the *s* <sup>1</sup> orbital.

2 Again, as with the previous term, this effect cancels in the calculation of TED.
