A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U
2-
. For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to
24
Mg in
L-S
coupling shows very little mixing of the quantum number
K
but an appreciable (10 to 20 %) mixing of
U
3
representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 <
A
< 40.
Matrix Elements for the one-dimensional Harmonic Oscillator
