The quartic isobaric multiplet mass equation

Abstract

The quadratic isobaric multiplet mass equation must be replaced by an expression which is quartic in Tz if the electrostatic interaction is treated in second-order perturbation theory. The coefficients of the cubic and quartic terms as well as the corrections to the constant, linear and quadratic terms are related to the off-diagonal reduced Coulomb matrix elements. A numerical analysis of the experimental Coulomb displacement energies in the 1p and 1d2s shell in terms of Hecht's (first-order) Coulomb energy equations showed systematic deviations for the multiplets, which were attributed to higher-order perturbations. For the A = 9 quadruplet the major perturbations appear to result from a lower-lying state (or states) which increases the excitation energies of the states in 9B and 9Be by about 105 and 93 keV, respectively, while the energies of 9C and 9Li are essentially unaffected. The constant and linear terms are changed very little, but the quadratic term is decreased by about 15%. Small cubic and quartic terms are generated. It is concluded that the quadratic isobaric multiplet mass equation often works well, not because first-order perturbation theory is a good approximation, but because higher-order perturbations are mostly absorbed by the three coefficients. Particularly the coefficient of the quadratic term may be affected considerably.