On the validity of the O ( 18 ) coupling scheme in N ∼ Z nuclei

Wave-functions from the newly proposed O(18) coupling scheme in IBM-3 are compared with those from a numerical calculation fitted to some Zn, Ge and Se nuclei. The interacting boson model [1], in which nucleon pairs are approximated by sand d-bosons has enjoyed some success in describing nuclear systematics and, in lighter nuclei, a version incorporating isospin symmetry, IBM-3 [2], has been used. Each boson in IBM-3 has isospin T = 1 giving it a total of 18 states so that the states of N bosons belong, trivially, to the totally symmetric representation [N ] of the group U(18). The existence of any chain of subgroups of U(18) which contains the group O(3) × SU(2), corresponding to the exact symmetries of angular momentum and isospin, provides a coupling scheme with analytic properties. The most natural chain below U(18) starts with U(6) × SU c (3) which separates the three charge states M T = 1, 0, −1 of the boson from the six " orbital " states of s and d. The isospin group SU(2) is then a subgroup of SU c (3) and, below U(6) are the three alternative chains via U(5), O(6) or SU(3) which are familiar from the earliest days of the IBM [1] and describe vibrational, γ-unstable and rotational nuclei respectively. It is found that the U(6) × SU c (3) chain has validity, with the low states in numerical IBM-3 calculations [3,4] containing large amounts of the totally symmetric states [N ] of each of the two factors SU c (3) and U(6). For each value of T = N , N − 2, .. 1 or 0 allowed from SU c (3) the set of orbital states is then identical to those in IBM-1. Recently two new chains starting with the subgroup O(18) of U(18) have been discovered [5]. One of them proceeds via O(6) × SU(2) followed by the familiar reduction from the γ-unstable group O(6). The other goes first to O(15) × SU s (2), in which O(15) belongs entirely to the d-boson and SU s (2) is the isospin of the s-bosons. Then O(15) is reduced to O(5) × SU d (2) and finally SU(2) is reached from the product SU s (2) × SU d (2), a vector-coupling of the separate isospins of sand d-bosons. Since the new O(18) classifications generally break the U(6) symmetry, which is known to be reasonably …