Optical Model Analysis of the Scattering of Alpha Particles from Helium

An optical model analysis using a complex potential $\frac{V+iW}{1+\exp \left[\frac{(r-r_0)}{d}\right]}$ has been made of the elastic scattering of alpha particles from helium. In the data which are analyzed the bombarding energy ranges from 23.1 Mev to 47.1 Mev. The best agreement with the angular distributions taken at eight different bombarding energies was obtained when the parameters $V$, $W$, $r_0$, and $d$ were -112 Mev, -1 Mev (for bombarding energies near 40 Mev), 1.8×${10}^{-13\mathrm{}}$ cm, and 0.6±0.1×${10}^{-13\mathrm{}}$ cm, respectively. The value -112 Mev for $V$ is an average value; $V$ decreases by 15% when the bombarding energy is increased from 23 Mev to 47.1 Mev. Since $W$ is small, the central depth of the real part of the potential $V$ has significance. This is in contrast to the scattering of alpha particles from heavier elements where the absorption is so large that the central part of the potential is not easily determined. No lower limit was placed on $r_0$, however, $r_0$ must be less than 2.7×${10}^{13}$ cm. The phase shifts obtained from this analysis are in good agreement with the preliminary results of Snyder below 42 Mev. Above 42 Mev they continue to vary slowly with no new states of ${\mathrm{Be}}^8$ appearing up to 47.1 Mev.