Effective electromagnetic operators in light nuclei

The effective operator method is used to calculate matrix elements of the magnetic dipole and electric quadrupole operator in the nuclear 1p shell. The calculational obstacles involved in obtaining the many-body model wavefunctions from an exact application of the effective interaction approach are bypassed by using eigenfunctions determined by a shell model phenomenological fit. The effective operators are assumed to be at most two-body. Realistic two-body (correlated) wavefunctions, which are generated by solving the Bethe-Goldstone equation using a modern nuclear potential, are used to determine the matrix elements of the operators. These are then combined with the appropriate angular momentum coefficients and the many-body wavefunctions, and the results compared with the experimental transition rates and moments throughout the shell. The absence of improvement over the results using the bare operators indicates that the effects of channel coupling and core exclusion are insufficient. A detailed analysis of the M1 data is carried out for the low-lying states in ¹⁴N. Using an unmodified operator, the many-body wavefunctions are phenomenologically adjusted to reproduce the experimental results. In addition, an effective interaction is extracted from these wavefunctions. The definite inconsistencies between this analysis and previous shell model results of other authors indicate unequivocally that some alteration of the M1 operator is necessary. A two parameter phenomenological operator is constructed using the sum of the orbital g-factors as one of the adjustable parameters. The operator is fit to two pieces of data in ¹⁴N. The moments and transition widths are recalculated, resulting in improved agreement with experiment throughout the shell. (author)