Theory of the Lithium Two-Alpha-Reactions. II. Angular Distribution ofLi6(d,α)α

An analysis is presented of the variation of the intensity of alphas from ${\mathrm{Li}}^6(d,\alpha )\alpha$ with angle and energy. This variation has been observed to have the form $1+A\left(E\right)\mathrm{}{cos}^2\theta +B\left(E\right)\mathrm{}{cos}^4\theta$, just as in the case of ${\mathrm{Li}}^7(p,\alpha )\alpha$ for which an analysis has already been given. For ${\mathrm{Li}}^6(d,\alpha )\alpha$ it is again the Bose statistics and consequent even parity of the alphas that makes analysis possible. It is assumed that ${\mathrm{Li}}^6$ has even parity so that only $s,d,\cdots$ deuterons are relevant here, in contrast to ${\mathrm{Li}}^7(p,\alpha )\alpha$ in which $p,f,\cdots$ protons are involved. The two analyses differ also in the spin combinations, but are similar in the assumption of only two contributing states of the compound nucleus, with angular momentum quantum numbers 0 and 2. An expression for the energy variation of the angular distribution in ${\mathrm{Li}}^6(d,\alpha )\alpha$ is derived from the dispersion formula and the treatment with two sharp levels is compared with that for one sharp and one broad level. The latter is found simpler and adequate for obtaining agreement with the experimental $A\left(E\right)\mathrm{}$ and $B\left(E\right)\mathrm{}$. After recognizing limitations on the parameters consistent with order-of-magnitude estimates of the matrix elements involved, it is found that the theoretical formulas rather naturally give the general form of the experimental results, including the feature that both $A\left(E\right)\mathrm{}$ and $B\left(E\right)\mathrm{}$ rise more slowly in the ${\mathrm{Li}}^6(d,\alpha )\alpha$ reaction than in the ${\mathrm{Li}}^7(p,\alpha )\alpha$ reaction as the bombarding energy is increased from zero, a consequence of the spherical symmetry of the entering $s$ waves which participate in the ${\mathrm{Li}}^6$ reaction only.