New Tests of the Isobaric Multiplet Mass Equation

Abstract

The isobaric multiplet mass equation (IMME), first propounded by Wigner1 in 1957, states that the masses M of members of an analog multiplet should be related by an equation quadratic in Tz $$ M = a + b{T_z} + cT_z^2. $$ A non-trivial test of the equation requires a multiplet of at least 4 states (i.e. TZ=3/2), and in 1964 Cerny and his collaborators completed the first isobaric quartet.2 Since that time, some 18 quartets have been measured, a few with extreme precision, and in only one case, the lowest mass 9 quartet, is there a significant disagreement with the IMME. The present status of isobaric quartets is summarized in this conference by Benenson and Kashy. There is considerable incentive to make new tests of the equation by considering multiplets other than quartets, but only very recently has it become experimentally feasible to test the IMME even in quintets. A number of features make such tests interesting. If one represents deviations from the IMME by additional terms dT Z 3 , eT Z 4 , etc., only one such term can be determined in a quartet, but two in a quintet. Thus one can test the IMME more rigorously, and, in the event of a violation, gain better insight into the possible mechanisms causing it. Furthermore, many quintets include both particle-stable and unbound nuclei, and if changes in the spatial wave functions across a multiplet can cause deviations from the IMME, then quintets may be rather sensitive to that influence. Finally, if there exists a many-body charge-dependent force, the presence of two determined parameters (d and e) makes quintets an attractive testing ground.