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MESON PA I R THEOR Y with respect to g. The real difhculty in treating (C.24) is that of extracting the self-energy and Green's function renormalization from the last factor, without expanding the log in a Taylor series. We have checked that the first few terms are in agreement with the corresponding expressions obtained by expanding our previous results for the renormalization constants. We can recognize the Green's function renormalization as a multiplicative constant and the self-energy from its form exp [sly(tt') ].It appears that the meson scattering can be obtained in closed form from the p dependent terms, but we shall omit any further discussion of this matter.High-energy nuclear reactions which depend strongly on nucleon position correlations in the nuclear ground state are analyzed and shown to give evidence for the existence of marked correlation effects. The following high-energy experiments are considered: nuclear photoeffect, meson absorption in nuclei, deuteron pickup, proton-proton scattering in a nucleus, and meson production in proton-nucleus collisions. The corresponding cross sections depend on a nucleon momentum distribution which can be represented at high energies by a single function giving reasonable agreement with all the experiments considered. This momomentum distribution differs substantially from that for the shell model of the nucleus and thus provides strong evidence for correlation in the nuclear ground-state wave function.The transformation methods developed in previous papers are used to provide a uni6ed theory of the above 6ve processes. The momentum distribution predicted by this theory is estimated by two methods each of which gives close agreement with the experimentally determined function in the relevant energy ranges.

A theory of the interaction of low-energy neutrons with nuclei has been developed using methods previously applied to the study of the nuclear ground state. It is show that an average potential is predicted by the theory which very closely resembles that used by Feshbach, Porter, and Weisskopf in their studies of the neutron cross sections. The calculated parameters for scattering at a few Mev are a real depth of 41 Mev and an imaginary part somewhat less than 1 Mev. The theory also predicts the appearance of characteristic narrow compound-state resonances in the cross section; these are the result of sharp fluctuations in the real and imaginary part of the equivalent potential acting on a neutron which are the result of appreciable coupling between the single-particle and compound-nucleus states. An estimate of the level width is given for a simple class of compound-state levels and is of the order of typical widths observed experimentally.A comparison of these results is made with a theory of Wigner, Lane, and Thomas; the principal difference is in the much smaller imaginary part of the potential determined by this theory. NEUTRON REACTIONSWITH NUCLEI AT LOW ENERGY 895

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