Electromagnetic properties of theK=1band in the rotational limit of the neutron-proton interacting boson model

Abstract

Within the framework of the SU͑3͒ limit of the neutron-proton interacting boson model the matrix elements of the angular momentum and the quadrupole operator between states belonging to the Kϭ1 band are given in closed forms. To obtain the matrix elements analytically, we first derive the extended U(6)ʛSU(3) isoscalar factors associated with low-lying bands by using the intrinsic SU͑3͒ states. The extended U(6)ʛSU(3) isoscalar factor is defined as the product of the ordinary U(6)ʛSU(3) isoscalar factor and the U͑6͒-reduced matrix element of the one-body boson operator. Using these results, M 1 and E2 intraband transition probabilities and the electromagnetic moments in the Kϭ1 band are derived in closed forms.

M1 transitions between low-lying states in the SU(3) limit of the IBM-2

“…To derive the M1 matrix elements between perturbed wavefunctions, we first have to determine the matrix elements of the angular momentum and the quadrupole operators which are given by the generators of SU(3) between SU(3) bases. These matrix elements can be calculated by using the tensorial properties of the SU(3) generators [15,17,22] and by applying the generalized Wigner-Eckart theorem [23]. Although this method leads to closed forms for individual matrix elements of the SU(3) generators, the process in calculating the matrix elements of Q π • Q ν with them is tedious because of the SU(3) ⊃ O(3) isoscalar factors.…”

“…In the process of our calculation knowledge of matrix elements of the SU(3) generators is necessary. Although these matrix elements between the SU(3) Vergados bases [21] can be determined directly by using tensorial properties of the SU(3) generators [15,17,22] and applying the generalized Wigner-Eckart theorem [23], the process for calculating the matrix elements of Q π • Q ν is very tedious and complex because of the SU(3) ⊃ O(3) isoscalar factors. Therefore, for simplicity we use the matrix elements of the SU(3) generators determined from the expansion method whose results are similar to the ones of the intrinsic state formalism used in the standard collective model [19,24].…”