The one- plus two-body isospin non-conserving nuclear interactions, namely the isovector and isotensor ones, are included in the prediction of the energies of the ground state and the low-lying states of the $fp$ shell nuclei using spectral distribution theory. This in turn is used to calculate the linear term in the isobaric mass-multiplet equation and the predictions are then compared with experimental values after the addition of the Coulomb contribution. The agreement is found to be good as observed for $sd$ shell nuclei earlier. One also sees that in this method the contribution to the linear term comes almost completely from the one-body isovector Hamiltonian, resulting in a huge simpliﬁcation of the problem.
Volume 96, 2022
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