Direct determination of the doublet and quartetM1cross sections inp-dradiative capture at near-thermal energies

Data obtained from studies of the $p(d\to ,\gamma {)}^3\mathrm{He}$ and the $d(p\to ,\gamma {)}^3\mathrm{He}$ reactions have been used to extract the transition amplitudes corresponding to $S=1/2\mathrm{}$ (doublet) and $S=3/2\mathrm{}$ (quartet) $M1\mathrm{}$ radiative capture. Protons (deuterons) of 40 keV (80 keV) were stopped in ${\mathrm{D}}_2\mathrm{O}$ $\left({\mathrm{H}}_2\mathrm{O}\right)$ ice targets. Angular distributions of $\sigma$, $A_y,$ $T_{20},$ $P_{\gamma }$, and ${\mathrm{iT}}_{11}$ were fit simultaneously in terms of the four possible $E1\mathrm{}$ $p$-wave capture amplitudes and the two $(S=1/2\mathrm{}$ and $3/2)$ possible $M1\mathrm{}$ $s$-wave capture amplitudes. The results obtained at $E_{\mathrm{cm}}=23.3\mathrm{}$ keV indicate that the $S=1/2\mathrm{}$ $M1\mathrm{}$ capture cross section is 13.77 $\pm$ 0.66 nb, while the $S=3/2\mathrm{}$ $M1\mathrm{}$ capture cross section is 6.74 $\pm$ 0.44 nb. These results agree with the predictions of a recent three-body theoretical calculation which includes two-body currents [e.g., meson-exchange currents (MEC’s)]. They also agree with the previous experimental determination of the doublet and quartet fusion rates obtained using the Wolfenstein-Gerstein effect to vary the relative population of $S=1/2\mathrm{}$ and $3/2$ nuclear spins in the $\mu$-$p$-$d$ molecule prior to fusion.