The Deuteron Break-Up Effect in the Two-Step Process

Abstract

An extended coupled method for the multistep processes is given. In this method, the intermediate state is described by the quasi-particle state. In actual calculations, the so-called two-step approximation is made and the virtual break-up effect of the deuteron in the two-step (p-d-t) process is investigated for the Ca (p, t) Ca (0+, g.s.) transition. §I. Introduction The multistep transfer processes hm~e been studied by many authors and the importance of the effect has been recognized. In such a sequential multistep trans­ fer process, the proper choice of the intermediate states is the important subject. A criterion of the choice for the intermediate states is, up to the present, based mainly on the physical consideration. The (P-d-t) process in the (p, t) reaction which has been analyzed by several authorsD~sl is an example of the choice based on such a physical consider­ ation. We have no assurance that we may choose only the deuteron ground state for the intermediate state since a deuteron is loo:3ely bound. It might be necessary to take into account the p~n continuum state in the intermediate In this paper, vve propose the new coupled method for the multi,;tep processes including such a continuum state approximately. In this method, the integral over the continuum state is approximated by the sum oYer the qLlasi-partide states. This method is similar to the treatment of Johnson ancl Tandy for the (d, jJ) reaction. 4l The difference between our method and conventional coupled method is that we assume the quasi-particle states to form the quasi­ which differs from the concept of the channel. However, it is assumed that the initial and final states are physically meaningful states, i.e., the channel in a conventional sense. Our treatment vvould be a reasonable approximation meth­ od within the range of the interaction, but it is not clear whether this approximate treatment is better than the other treatment. 5l Conventional coupled theory prevents one from directly calculating the wave function in the continuum states. In the distorted wave perturbation theory, 6l we could roughly estimate the contribution of the continuum state in the intermediate under the two~step approximation. However, the calculation needs a great deal of work and mathematical difficulty arises clue to the divergence