Alpha-Alpha Scattering at Low Energies

We have measured the differential cross section for the scattering of alpha particles in helium between laboratory angles of 10 and 80 degrees and in the energy range 150 kev to 3 Mev, using ${\mathrm{He}}^{+}$ ions from our electrostatic generators. Below 400 kev no nuclear interaction occurs within the accuracy of the experiments (±1%), and Mott's formula for the Coulomb scattering of identical zero-spin particles is verified in detail. Above 400 kev the nuclear $s$-wave interaction begins to contribute, starting at a phase shift $K_0$ near $\pi$, and smoothly decreasing with increasing energy to about 128 degrees at 3 Mev. Starting at 2.5 Mev, a small $d$-wave phase shift, $K_2$ is found necessary to account for the observed angular distributions, reaching a value of 2.5 degrees at 3 Mev. Absolute values of the cross sections were determined by fitting the relative angular distributions with the single parameter $K_0$ below 2 Mev, and by comparison with Rutherford scattering in argon above 2 Mev. The phase shift analysis was facilitated by a simple mechanical monograph described in Appendix III. A careful survey of the low-energy region containing the ground state of ${\mathrm{Be}}^8$, and the absence of any measurable effect leads to a lower limit for the mean life of the ground state of ${\mathrm{Be}}^8$ of 2×${10}^{-16\mathrm{}}$ sec. Combined with a recently established upper limit of 4×${10}^{-15\mathrm{}}$ sec, this locates the lifetime to within a factor of twenty.