Alpha-Alpha Scattering at Low Energies

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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 (\ifmmode\pm\else\textpm\fi{}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 $\ensuremath{\pi}$, 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\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ sec. Combined with a recently established upper limit of 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$ sec, this locates the lifetime to within a factor of twenty.