Exact Treatment of Pure Coulomb Distortions in (X, n) Stripping Reactions

We obtain simple analytic formulas to express the amplitudes for stripping a particle into an orbit of arbitrary $L$ value, using a Coulomb wave to describe the relative motion of the incident particles and a plane wave to describe the relative motion of the products. This approximation may be appropriate for the description of ($X, n$) reactions, where $X$ is any charged projectile, and $n$ is a neutron, particularly when the incident energy is well below the Coulomb barrier. Initially, the neutron is assumed to be bound to a particle which is later captured by the target; the wave function of this initial bound state is taken to be asymptotic and of zero orbital angular momentum, of the form $\frac{e^{-\alpha r}}{r}$. The resulting nucleus is described as a bound state of two particles moving with arbitrary relative orbital angular momentum $L$; the radial wave function of this bound state may be taken to be of the form $r^{L-1\mathrm{}}(e^{-\beta r}-e^{-{\beta }^{\prime }r})$. The cross sections predicted by these amplitudes are compared to the cross sections predicted by the analogous plane-wave Born approximation, and graphs are shown for a representative case. The qualitative appearance of the angular distribution is found to be much the same in both cases; however, the Coulomb-wave calculation predicts cross sections of smaller magnitude with previously assigned values of the reduced widths.