Non-orthogonality effects in heavy-ion transfer reactions

Calculations are made of the effects arising from the non-orthogonality of channel states in heavy-ion neutron transfer reactions, as well as the associated elastic-scattering processes. A single iteration is performed upon the integral equations associated with the coupled-channel treatment of the transfer process. The reactions considered are ¹³C(¹⁶O, ¹⁷O)¹²C leading to the ground state and first excited state of ¹⁷O and the ²⁹Si(¹⁶O, ¹⁷O)²⁸Si reaction leading to the first excited state of ¹⁷O. Corrections are found to be as large as 10 % at angles where the cross sections are sizeable. Similar results are obtained for the elastic-scattering processes. The choice of reactions was made so as to emphasise the importance of these corrections.Consideration of the errors associated with the depiction of bound states in terms of a sum of Hankel functions and the use of a local-momentum approximation for the channel motion suggests that the figure for the correction represents an upper bound.