Three-body formalism for deuteron stripping reactions on 40Ca

A three-body formalism for deuteron stripping reactions has been developed. This is applied to Ca-40 for incident deuteron energies of 10 MeV and 5 MeV. The equations of Alt Grassberger and Sandhas for the three particles (target A,n,p) are reduced to a set of one dimensional coupled integral equation with the use of (i) angular momentum basis for representation and (ii) separable approximation for the two-body t-matrices., when the coulomb interactions between particles pairs are included. While working out the connection between the matrix element of AGS operator between the initial and final asymptotic states and one-dimensional coupled integral equation, a hypothesis emerged which we call Conservation of Channel Spin in Transfer Reactions'. Using this formalism preliminary calculations for the (d,p) and (d,n) reaction cross-sections on Ca-40 have been carried out and they seem to have considerable semblance with the observed cross-sections.