Transformation from a U(3) to a pseudo U(3) basis of the matrix representation of a deformed Nilsson Hamiltonian

In recent publications Castanos, Moshinsky and Quesne obtained explicitly the operator U that transforms us from a U(3) to pseudo U(3) basis. They then applied it to a spherical Nilsson Hamiltonian to show that it transforms into a similar one in which the coefficient of the spin orbit term changes and, in fact, becomes very small for the parameters of the Nilsson Hamiltonian taken for experimental results in the spectra of heavy nuclei. In this paper we consider the deformed Nilsson Hamiltonian H. We show how we can obtain its matrix elements in an oscillator basis with spin and we then obtain the