M1transitions between low-lying levels inXe128and the proton-neutron interacting boson model

Abstract

The branching ratios of the collective levels in ' Xe were discussed in the frame&work of the proton-neutron interacting boson model . It is shown that the experiment is only consistent with rather small M1 admixtures among the low-lying collective levels. These small Ml matrix elements imply strong constraints on the proton-neutron interacting boson model Hamiltonian.The various collective models have focused hitherto mostly on the excitation energies and E2 transitions.With the discovery of the 3.08 MeV isovector (1+) excitation in ' Gd and of similar excitations in neighboring nuclei by the Darmstadt group, ' there has been a surge of interest in a theoretical description of the magnetic properties of collective nuclei, viz. , g factors and Ml transitions.Clearly, besides the experimental evidence on the isovector excitations there exists in the literature a large body of information on Ml transitions in the form of intensity branching ratios and less accurately in the form of E2jM1 mixing ratios of transitions. These data clearly involve both E2 and Ml matrix elements, and in order to obtain reliable information on the Ml matrix elements one should consider only those transitions which have strong E2 matrix elements in the collective model considered. In the following we will consider as an example the nucleus ' Xe, because there exist particularly detailed data for this nucleus from recent experiments at Koln and Jyvaskyla, and also because this nucleus belongs to a large class of nuclei in the Xe-Ba region which have been shown to belong to the O(6) limit in the interacting boson model (IBM-1). Thus we have a rather good understanding of the energies and of the E2 transitions of the collective levels of ' Xe. In order to describe Ml transitions we will use the IBM-2 version of the interacting boson model which comprises both proton and neutron bosons, which has been introduced by Arima et al. 3 In the IBM-2 model one can describe Ml transitions with the operator T (Ml), T(M1 ) =g pL p+g"L" =(Np+N") '[(N~p+N"g")(L p+L") +(gp -gn)(NBLp -NpLn)l in nuclear Bohr magneton units, where gp and g"are the g factors for the proton and neutron bosons. The values of these g factors of the bosons are not completely known at the moment. The experimental evidence comes from the M1 transitions to the mixed symmetry 1+ state usually called the isovector state' which leads to 0.6 &gp -g"&1. ' Similar values are also found from systematic fits to the g factors of the 2+ states which have been performed by Wolf et al. which yield gp M =(spd"-s"dp)(spd"-s"dp)

General projection from IBA-2 to IBA-1

“…A completely symmetric IBA-2 state has F = F,,, = by F = F,,, -1. The low states have typically F,,, amplitudes of some 98% (Harter et al 1986(Harter et al , 1987. De Coster and Heyde (1989a, b) have recently made an extensive study of F spin.…”