Quartet structure of N = Z nuclei in a boson formalism: The case of 28Si

Abstract

The structure of the N = Z nucleus 28 Si is studied by resorting to an IBM-type formalism with s and d bosons representing isospin T = 0 and angular momentum J = 0 and J = 2 quartets, respectively. T = 0 quartets are four-body correlated structures formed by two protons and two neutrons. The microscopic nature of the quartet bosons, meant as images of the fermionic quartets, is investigated by making use of a mapping procedure and is supported by the close resemblance between the phenomenological and microscopically derived Hamiltonians. The ground state band and two low-lying side bands, a β and a γ band, together with all known E2 transitions and quadrupole moments associated with these states are well reproduced by the model. An analysis of the potential energy surface places 28 Si, only known case so far, at the critical point of the U(5)-SU(3) transition of the IBM structural diagram.

Band-like structures and quartets in deformed N=Z nuclei

“…Altogether, then, the choice of generating the quartets from the second minimum has revealed to be the most effective one. The occurrence of this double minimum confirms a certain degree of "instability" of the ground intrinsic state of 28 Si which had already emerged in a previous semi-phenomenological study of this nucleus [48].…”

“…The last case under investigation, 48 Cr, shares some analogies with the corresponding one of 24 Mg. Indeed one observes in Fig.…”

“…1,2,3) depends almost entirely on the low-J quartets of the intrinsic ground state. Indeed, by performing configuration-interaction calculations which include only the quartets (q + g ) J with J = 0, 2 these errors remain confined within 0.7% for 24 Mg and 28 Si while, for 48 Cr, one finds 1.6%. In the latter case, however, it is sufficient to add the J=4 quartet to reduce this error to 0.6%.…”

“…1,2 and 3, columns (A) and (B), we show what changes occur in the low-lying spectra of the nuclei under study when a set of dynamical quartets replace the analogous set of static quartets. These static quartets are those describing the lowest states of 20 Ne for the sd shell nuclei and those of 44 Ti for 48 Cr. In the columns (A) we plot all the positive parity states up to the 6 1 obtained using a set of static J=0,2,4 (plus J=6 in the case of 48 Cr) quartets.…”

“…Also intriguing has been observing that these structures interfere little with each other in the sense that once one structure has been generated by means of a set of quartets, enlarging the configuration space with a new set of quartets moves down the states associated with the new structure without, however, strongly affecting the previous structure. The procedure has been applied to 24 Mg, 28 Si and 48 Cr nuclei and it has provided a good description of the low-lying spectra in all three cases. A merit of this description is that of relying on only a few degrees of freedom.…”