By Daphne F. Jackson (auth.), Michel Baranger, Erich Vogt (eds.)

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The parameters of such cluster-model wave functions are determined by a variational calculation on the ground-state energy (TWP 61, Kop+ 61, STW 63); unfortunately, this variational method is not sensitive to the long-range behavior of the wave function. A number of calculations on the (p, pd) and (e, ed) reactions have been carried out (Ruh+ 62, Ruh+ 63, Ber+ 65, JE 65, GOS 66, and Dwi 68) using a single term in the cluster-model expansion and wave functions of Gaussian form. The corresponding overlap integrals have incorrect asymptotic behavior and the calculations are in principle no more realistic than those of the simple shell model although in practice the relative motion of the clusters is often described by a Gaussian function of longer range than would arise in the oscillator shell model.

1 Comparison of Knockout and Pickup Reactions In order to make a simple comparison of the pickup and knockout reactions we examine the cross sections for the (p, 2p) and (p, d) reactions given by PWBA. For the (p,2p) reaction we take the momentum of the incident proton to be Po and the momenta of the two outgoing protons to be PI and P2 respectively. The matrix element can then be written as (31) where Q = Po - PI - P2 is the recoil momentum of the residual nucleus, q = Po - PI is the momentum transfer, s is the proton-proton separation distance, V(s) is the proton-proton interaction, and 1jJp is the proton overlap integral.

In the (p, 2p) calculations, the additional low momentum components introduced by the distortion have an important effect on the angular distribution, whereas in the (p, d) calculations it is the additional high momentum components, introduced particularly by the distortion of the deuteron, which have the most significant effects. 2. Special Features of Knockout Reactions The symmetric coplanar case of the (p, 2p) reaction has a rather special symmetry, since a rotation of kn, where k is any integer, about the direction of the incident beam transforms the system into one which is physically indistinguishable, provided that polarizations are not measured.