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
The quantities A, B depend on E in a more complicated manner, the simple entrance of E being in the differential equation. The latter can be solved for complex values of E, the solution being arrived at by the same procedures as for real values. For real E the function F can be made real by making C real. Since the values of F for r > 0 are obtained from the values of F and iFldr by operations involving only real numbers, F will be real for any r and consequently A*=B, (E =E*), (C =C*). (3·2) It is thus impossible for real E to have a solution which does not vanish identically and for which either A or B is identically zero.
28 G. BREIT: Theory of Resonance Reactions and Allied Topics. Sect. 3. The derivation of this relation has not made use of a time dependent treatment. 22) R fl\hl2dr o It is obviously convenient to relate the time i to properties of a state the function for which is f5L and which does not extend beyond r = R. 19) in comparison with the first. Changing R affects the first part only through compensating changes of the second and the choice of R is thus immaterial within the validity of the assumptions made.
In the vicinity of such a root one can expand A(E) = (E -Eo + iA~) (~) 2 dE A~O + .... (3·7) For sufficiently small An,12 the important range of real values of E occupies a band of approximate width An, which is then sufficiently small to make it sufficient 1 2 3 4 G. GAMOW: Z. Physik 51,204 (1928). T. SEXL: Z. Physik 81, 163 (1933). G. BREIT: Phys. Rev. 40, 127 (1932). - Ref. [6J. H. CASIMIR: Physica, Haag 1, 193 (1934). 30 G. BREIT: Theory of Resonance Reactions and Allied Topics. Sect. 3. 7) in the expansion of A(E).