Center-of-mass corrections to overlap factors for two-nucleon transfer

The following simple recipe is presented for making c.m. corrections to the overlap factors involved in two-nucleon transfer: Expand the shell-model overlap in products of harmonic oscillator wave functions of the relative and c.m. coordinates of the two nucleons. Change the oscillator ν-value to $\text{Aν}\text{(A + 2)}$ in the c.m. functions, and multiply each term in the sum by [$\text{(A + 2)}\text{A}\text{]}\text{1}\text{2}{}^{\mathrm{N}}$, where N is the energy quantum number associated with the c.m. state of that term. The recipe depends on the value of ν used in the expansion. The proper choice of ν is discussed, and numerical examples are presented which indicate the magnitude of the correction. The zero-range form factor for two-neutron stripping on ¹⁶O is increased by a factor of about two, or more, in the surface region, resulting in a factor of about five in the cross section. The correction is greater at larger distances, implying that heavy-ion reactions will be effected more than light ion reactions.