Angular correlations in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:mrow></mml:math> decay of excited states in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>8</mml:mn></mml:mmultiscripts></mml:math>
A. C. Hayes, J. L. Friar, G. M. Hale, G. T. Garvey
Abstract
Motivated by the recent observation of anomalous electron-positron angular correlations in the decay of the 18.15-MeV ${1}^{+}$ excited states in $^{8}\mathrm{Be}$, we reexamine in detail the standard model expectations for these angular correlations. The 18.15-MeV state is above particle threshold, and several multipoles can contribute to its ${e}^{+}{e}^{\ensuremath{-}}$ decay. We present the general theoretical expressions for ${e}^{+}{e}^{\ensuremath{-}}$ angular distributions for nuclear decay by $C0,C1,C2,M1,E1$, and $E2$ multipoles, and we examine their relative contribution to the ${e}^{+}{e}^{\ensuremath{-}}$ decay of $^{8}\mathrm{Be}$ at 18.15 MeV. We find that this resonance is dominated by $M1$ and $E1$ decay, and that the ratio of $M1$ to $E1$ strength is a strong function of energy. This is in contrast to the original analysis of the ${e}^{+}{e}^{\ensuremath{-}}$ angular distributions, where the $M1/E1$ ratio was assumed to be a constant over the energy region ${E}_{p}=0.8--1.2$ MeV. We find that the existence of a ``bump'' in the measured angular distribution is strongly dependent on the assumed $M1/E1$ ratio, with the present analysis finding the measured large-angle contributions to the ${e}^{+}{e}^{\ensuremath{-}}$ angular distribution to be lower than expectation. Thus, in the current analysis we find no evidence for axion decay in the 18.15-MeV resonance region of $^{8}\mathrm{Be}$.