Capture of medium-energy positrons in deuterium.

Abstract

A formalism for investigating the positron-capture reaction ${\mathrm{e}}^{+}$+d\ensuremath{\rightarrow}\ensuremath{\nu}${\ifmmode\bar\else\textasciimacron\fi{}}_{\mathrm{e}+\mathrm{p}+\mathrm{p}}$ at medium positron energy (i.e., 0.5--2.0 GeV) and small p-p excitation energies (i.e., ${E}_{\mathrm{rel}\mathrm{\ensuremath{\le}}10}$ MeV) is described. In view of the small p-p excitation energy ${E}_{\mathrm{rel}}$ being considered, we take into account only the $^{1}\mathrm{S}_{0}$ and $^{3}\mathrm{P}_{\mathrm{J}}$ p-p final states (J=0, 1, 2). For the polar vector current, an impulse approximation, modified to incorporate current conservation, is employed and additional meson-exchange currents are included in the dominant channel. For the axial vector current, the nucleon-only impulse approximation is used. Numerical results are presented to highlight the prospect of measuring the ${q}^{2}$ dependence of the nucleon axial form factor ${f}_{A}$(${q}^{2}$). The proposed precision measurement of the nucleon axial form factor may be feasible at the upcoming Continuous Electron Beam Accelerator Facility if the proposed positron ring can actually be constructed.