Theory of the Effective Range in Nuclear Scattering

The scattering of neutrons up to about 10 or 20 Mev by protons can be described by two parameters, the scattering length at zero energy, $a$, and the effective range, $r_0$. A formula (16), expressing the phase shift in terms of $a$ and $r_0$ is derived; it is identical with one previously derived by Schwinger but the derivation is very much simpler. Reasons are given why the deviations from the simple formula are very small, as shown by the explicit calculations by Blatt and Jackson.