General projection from IBA-2 to IBA-1

Abstract

We present general formulae for projecting operators of the protonneutron interacting-boson approximation (IBA-P) into operators of the basic IBA ( I B A -I ) , which ignores the proton-neutron difference. The formulae are valid for bosons of any spatial character (s, p, d, f, g, . . . ) and they are given for general o n e and two-body tensor operators. The IBA-P Hamiltonian with single-boson energies and quadrupole and dipole interactions for s, d and g bosons is considered as an example. The dependence of M1 and E2 matrix elements on the proton and neutron boson numbers is studied.

Simple model for derivingsdginteracting boson model Hamiltonians:Nd150example

“…Note that (j,j ) take the values (31/2, 43/2) and (43/2, 57/2) for rare earths and actinides respectively. Now, carrying out an IBM-2 to IBM-1 projection [16] by assuming that the low-lying levels belong to the F spin [17] F =F"""=(N+N )/2, and using the simple In (3), ::denotes normal ordering. Assuming sd and E to be free parameters (instead of deriving them from pp and nn interactions) the Hamiltonian Ho~, ", is used to study the spectroscopy of ' Nd; the boson number N =9 with N =5 and N, =4.…”

Modified one nucleon transfer operator in IBA

“…For IBA-1 and IBFA-1 projection techniques must be used [5].The existing IBA-2 and IBFA-2 code for one particle transfer [6] has been modified in order to include this new term and is available under request [7].…”

Quadratic M1 operator in the IBA

“…Below we pursue two avenues t o the same end. First, in section 2, we propose in IBA-2 an effective quadratic M1 operator which yields by projection (Harter et a1 1985, Frank andLipas 1990) the desired IBA-1 operator. Then, in section 3, we follow up the scheme of Sambataro et al We carry out all explicit calculations in or near the U(5) limit.…”