Four-Body Model of Two-Nucleon Transfer Reactions

Abstract

An exact four-body model of heavy-ion two-nucleon transfer reactions is described that includes all orders of interaction between the exchanged nucleons. The relative importance of the Q value of the reaction and of the nature of the nucleon-nucleon interaction in governing the magnitude of the transfer cross section is studied.In the distorted-wave treatment of two-nucleon transfer reactions initiated by both light and heavy ions, there are persistent discrepancies (factor of ~ 5) in the predicted magnitude of the cross sections when compared with experimental results. 1 It has also been observed 2 that a large suppression (factor of ~ 50) of nn-and ^-exchange heavy-ion reactions exists relative to those involving np exchange. Some current attempts to understand these problems have centered on multistep contributions to the two-nucleon-exchange process, 3 and on damping due to Qmismatch effects as well. 4 A possible alternative source of concern is that the conventional reaction theories do not include rescattering corrections among the nucleons being exchanged and, since the nucleon-nucleon interaction cannot be considered weak, the proper inclusion of the higher-order terms of that interaction could be a significant factor in a proper theoretical description of these processes. In this Letter, we study a simplified but exact four-body model of two-nucleon transfer reactions in order to assess the importance of higher-order terms of the nucleonnucleon interaction.Our four-body model is based on the extended Lee model of which a detailed description has been given elsewhere. 5 The spinless version to be used here involves a pair of nucleons («) as well as two "heavy nuclei" a and b. Two-body n-n scattering proceeds as in the Amado model 6 by a coupling to a d quasiparticle so that the allowed process is d~n + n. The nature of this interaction 7 may be altered considerably by adjusting the wave-function renormalization constant Z d of the d particle, subject to the constraint 0 ^ Z d ^ 1. If we take Z d~ 1, the d is an elementary particle with no coupling to n + n, while if we choose Z d =0, a separable-potential model with a single bound state may be obtained that is appropriate to the spin-triplet nucleon-nucleon interaction. We may also have n-n attraction with no bound state present, as would be required for the spin-singlet two-nucleon state. In the following we will make use of this freedom in the choice of the n-n interaction.The three-body nuclei of the model, a and /3, are generated by the additional couplings 8 d + a -a and d + ft -/3; and thus elastic da and db scattering are mediated by the spinless quasiparticles a and /3. In the four-body sector of the model, the two-to-two reactions of interest are the elastic process ba-*bot as well as the rearrangement collision ba-^afi. Both of these processes are driven by successive d exchange; an odd number of exchanges are required for ba^ap, while ba •~ba involves an even number. The dynamical integral equations that govern these processes are similar to t...