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High‐Energy Phase Shifts Produced by Repulsive Singular Potentials
1.R. Serber, Phys. Rev. Letters 10, 357 (1963);
1.R. Serber, Rev. Mod. Phys. 36, 649 (1964).
2.A. D. Krisch, Lectures in Theoretical Physics (University of Colorado, Boulder, Colorado, 1965), Vol. VII B.
3.H. H. Aly, D. Lurié, and S. Rosendorff, Phys. Letters 7, 198 (1963).
4.G. Tiktopoulos, Phys. Rev. 138, B1550 (1965).
5.S. Rosendorff and S. Tani, Phys. Rev. 128, 457 (1962).
6.F. Calogero, Phys. Rev. 135, B693 (1964).
7.L. Bertocchi, S. Fubini, and G. Furlan, Nuovo Cimento 35, 633 (1965).
8.Y. Nambu and M. Sugawara, Phys. Rev. Letters 10, 304 (1963).
9.The case may also be considered as a Schrödinger model with an energy‐independent potential in which the relativistic dependence of the mass has been taken care of.
10.F. Calogero and M. B. De Stefano, Phys. Rev. 146, 1196 (1966). In this paper many references to the problem of scattering on singular potentials are to be found.
11.In general, we get a power series in
12.For the relativistic wave equation.
13.It should be noted that the power series which represents the function at is absolutely covergent at all boundary points of the circle of convergence. See, e.g., K. Knopp, Infinite Sequences and Series (Dover Publications, Inc., New York, 1956), p. 140. Hence the above series is uniformly convergent, and interchange of summation and integration is permissible. Obviously, the series of Eq. (20) converges absolutely.
14.According to Eq. (3) and Footnote 11, the ρ representation becomes meaningless for
15.There is a slight discrepancy between our value of and the corresponding one in Ref. 7. This is probably due to the fact that we use the WKB approximation, whereas in Ref. 7 an improved WKB approximation has been used.
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