By G. Breit, M. H. Hull Jr., J. S. McIntosh, R. L. Gluckstern (auth.)

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Extra resources for Nuclear Reactions II: Theory / Kernreaktionen II: Theorie

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The imaginary part of E is taken to be negative as in the case of the simpler one-body problem. The square of the absolute value of the wave function thus decays exponentially with t. The channel velocities also contain negative imaginary parts. The channel functions thus contain a factor increasing exponentially with channel distance similarly to Eq. 22). A special type of complex eigenvalue solution will be considered for which the behaviour of "p in each channel is similar to that of G in the one-body problem.

It may be inferred from the above general summary that there is considerable promise in the development reported on. The minimum in accomplishments that may be claimed is the satisfactory account of the presence of high momenta of individual nucleons in the nucleus. A very probable accomplishment is the consistent treatment of effective potentials for the nuclear shell model and the potentials used in nuclear reaction and scattering theories. The development will probably be fruitful in providing an improved basis for the shell theory of nuclear structure.

This is accomplished in the combination n) 1 iL"'. , sm k r - L _. --;2 1 2 2~ 22 + z. , " . " Here L is the orbital angular momentum of the channel. Y-. 6) 48 G. BREIT: Theory of Resonance Reactions and Allied Topics. Sect. 7. The scattering cross section has accordingly the value + (2L -1) nj. 7) 4 It will be noted that as is not necessarily (2L + 1) A2J:77: for K =:77:/2 but may be as = (2L + 1) _A~n sin2[K - {} appreciably smaller than this upper bound for as at prescribed A. On the other hand, K and therefore K' vary most rapidly with energy at the resonance energy (Ec+E'Z) Eo=----- .

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