A shell model analysis of the isobaric mass multiplets in the $1p$ shell shows that the isotensor charge dependent contribution (the coefficient of $T_z^2$ in the multiplet relationship) is, in all cases save one, underestimated when only electromagnetic interactions [including ${\left(\frac{v}{c}\right)}^2$ corrections, vacuum polarization, the effect of short range correlations, and finite neutron and proton size] are considered. Furthermore, the discrepancy is nearly twice as large for the seniority zero levels as for the higher seniority states, indicative of the omission of a short range charge dependent interaction. Since the free nucleon-nucleon scattering data indicate that the ($\mathrm{np}$) interaction is ∼2% more attractive than the ($\mathrm{nn}$), the effect of including such a charge dependent nuclear interaction on this coefficient is examined. When a Yukawa potential with range given by the $\pi$-meson Compton wavelength is taken for this potential it is found that theory and experiment can be brought into much better agreement.

NUCLEAR STRUCTURE Shell model calculation of isotensor coefficient in mass-multiplet relationship. $1p$ shell studied; need for isotensor nucleon-nucleon interaction demonstrated.

• Received 5 June 1978

DOI:https://doi.org/10.1103/PhysRevC.19.2359