Multipole moments and spin-dependent sum rules and their applications to f72 and s-d shell nuclei

Matrix elements of multipole operators, defined separately for neutrons and protons, are related to spin-dependent sums of spectroscopic factors. A clarification of their relation to the matrix elements of single-particle operators enables the overlap representation to be formally extended to a stripping form for J ≠ 0 operators. Multipole moments obtained from $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ transfer data are found to be dominated by the quadrupole moments when the final nucleus is odd-odd.A previously found (2J + 1) rule for spectroscopic sums, which arises when the odd-J multipole moments vanish, is shown to lead to approximate sum rules which apply separately to stripping and pickup data. The sum rules are generally well satisfied for transfers leading to odd-odd nuclei in the s-d shell.