Magnetic dipole contribution to the $\gamma$-spectrum from $d$-$t$ collisions

One in about a few hundred thousand sub-Coulomb $d$-$t$ collisions is accompanied by the emission of a $\gamma$-photon. The $\gamma$-spectrum from these collisions is dominated by a 16.7 MeV peak, corresponding to the population of the $p$-wave $3/2^-$ $\alpha$-$n$ ground-state resonance in the E1 transition from an intermediate $d$-wave $\alpha$-$n$ state, corresponding to the $^5$He excited state around 16.7 MeV. The strength of this spectrum at the large $\gamma$-energy endpoint decreases fast both due to kinematic factors and due to centrifugal repulsion between neutron and $\alpha$-particle at near-zero relative energies. However, no centrifugal repulsion would occur if $s$-wave $\alpha$-$n$ states were populated in magnetic dipole transition. Therefore, one can expect that close to the $\gamma$-spectrum endpoint around 17.5 MeV the M1 transition could dominate, leading to additional counts in experimental spectra which could be easily misinterpreted as a background. This work presents calculations of the M1 contribution to the $d+t\rightarrow \alpha+n+\gamma$ cross section caused both by convection and magnetization currents. While the first contribution was found to be negligible, the one from magnetization depends strongly on the choice of the model for the $d$-$t$ channel scattering wave function. Using $d$-$t$ interaction models from the literature, represented either by a gaussian of by a square well, resulted in unrealistically strong M1 contribution. With constructed in the present work optical folding potential, correctly representing the sizes of deuteron and triton, the M1 contribution near the endpoint is reduced to about 2$\%$ of the 16.7-MeV E1 peak. Arguments in favor of more detailed calculations, that could potentially change this number, are put forward.