Spin-aligned neutron-proton pairs inN=Znuclei

Abstract

A study is carried out of the role of the aligned neutron-proton pair with angular momentum J = 9 and isospin T = 0 in the low-energy spectroscopy of the N = Z nuclei 96 Cd, 94 Ag, and 92 Pd. Shell-model wave functions resulting from realistic interactions are analyzed in terms of a variety of two-nucleon pairs corresponding to different choices of their coupled angular momentum J and isospin T . The analysis is performed exactly for four holes ( 96 Cd) and carried further for six and eight holes ( 94 Ag and 92 Pd) by means of a mapping to an appropriate version of the interacting boson model. The study allows the identification of the strengths and deficiencies of the aligned-pair approximation.PACS numbers: 21.60.Cs, 21.60.Ev 92 Pd. We consider several realistic two-body interactions for the 1g 9/2 orbit and analyze the shell-model wave functions, obtained with these interactions, of the four-nucleon-hole system ( 96 Cd), in terms of a variety two-pair states. For the six-and eight-hole nuclei ( 94 Ag and 92 Pd) a direct shell-model analysis in terms of pair states is more difficult, and we prefer therefore to carry out an indirect check by means of a mapping to a corresponding boson model. In these cases our approach is intermediate between that of Blomqvist [4] and of Danos and Gillet [5]. The boson mapping takes care of antisymmetry effects in an exact manner on the level of four nucleons but becomes approximate for more. This paper is organized as follows. First, some necessary concepts and techniques are introduced: the formulas needed to carry out a shell-model calculation in a pair basis are given in Sect. II and two mapping techniques from an interacting fermion to an interacting boson model are reviewed in Sect. III. The results of our analysis of N = Z nuclei are presented and discussed in Sect IV. The conclusions and outlook of this work are summarized in Sect. V. II. FOUR-PARTICLE MATRIX ELEMENTSThis section summarizes the necessary ingredients to carry out calculations in an isospin formalism. The formulas given are valid for fermions as well as for bosons. Four-particle states are described by grouping the particles in two pairs. These two-pair states can be used, for example, as a basis in a shell-model calculation, facilitating the subsequent analysis of the pair structure of the eigenstates. Furthermore, the two-pair representation of fourparticle states is the natural basis to map the shell model onto a corresponding model in terms of bosons. Once this mapping is carried out, the original interacting fermion problem is reduced to one of interacting bosons, which can also be solved with the results summarized in this section.In the pair representation of four particles with angular momentum j and isospin t (both integer for bosons and half-odd-integer for fermions), a state can be written as |(jt) 2 (J 1 T 1 )(jt) 2 (J 2 T 2 ); JT where particles 1 and 2 are coupled to angular momentum and isospin J 1 T 1 , particles 3 and 4 to J 2 T 2 , and the intermediate quantum numbers J 1 T 1 and J 2 T 2...

Symmetries in theg9/2shell

“…With regards to the works of Refs. [12][13][14][15], this suggests the J = J max pairing is a better approximation in the upper half of a j shell rather than the lower half.…”

“…An interesting observation in Ref. [13] is that, although the spectrum looks vibrational, the B(E2)s might obey a rotational formula rather than vibrational. It would be of interest to have experimental verification.…”

“…One obvious distinction of our work relative to that of Refs. [12][13][14][15] is that we are dealing with higher spins than the ones that they consider. In the Nature article [12], they measure J = 0, 2, 4, and 6 and also discuss J = 8, whereas the PDS that we consider occur for J = 11 + and beyond.…”

“…[12][13][14][15]). In the Nature article [12], an experiment is presented in which an almost equal-spaced spectrum is found in N = Z 92 Pd for J = 0 + , 2 + , 4 + , and 6 + .…”

N=Znuclei: a laboratory for neutron–proton collective mode

“…There are quite many recent publications following the same direction or re-interpret the results in slight different ways (see, Refs. [70,71,72,73,74,75] and references contained therein). A detailed investigation on the applications of the nucleon-pair approximation of the shell model on this subject is presented in Ref.…”