General formalism for pion production in nuclei: Application topd→tπ

Abstract

Motivated by the recent interest in ($p, \ensuremath{\pi}$) reactions which leave the nucleus in a definite final state, we have obtained a general formalism for such reactions and applied it to the reaction $pd\ensuremath{\rightarrow}t\ensuremath{\pi}$, for which there is recent medium energy data. The approach is essentially impulse approximation based on the assumption, originally used by Ruderman, that the reaction mechanism is the same as in $pp\ensuremath{\rightarrow}d\ensuremath{\pi}$. It differs from previous such calculations in that we have included distortion effects and have derived and used an expression for the form factor which does not require the crude approximations for the wave functions used before. We apply this formula to $pd\ensuremath{\rightarrow}t\ensuremath{\pi}$ and obtain zero parameter fits which are a significant improvement over previous calculations and which reproduce the shape and normalization of the data quite well at 470 and 590 MeV and qualitatively at 340 MeV, except that as in other calculations the backward peak at 470 MeV is not reproduced. Distortion effects are important but purely absorptive and serve, as do most other theoretical uncertainties, simply to adjust the normalization.NUCLEAR REACTIONS ($p, \ensuremath{\pi}$) derived general formalism $\ensuremath{\sigma}(\ensuremath{\theta})$ at medium energies; distorted-wave impulse approx. Applied $d(p, \ensuremath{\pi})t$; $E=340, 470, 590$ MeV.