β Scribed by M Bawin
No coin nor oath required. For personal study only.
The analytic properties of the partial-wave S-matrix S(I, E) in the framework of the radial quasipotential equation in relativistic space given by Freeman and coworkers are studied. As in the nonrelativistic case, this is done by defining regular and irregular solutions to the equation, and analyzing the properties of S(I, E) by means of the corresponding properties of these solutions. For reasons connected with the uniqueness of the solution to the quasipotential equation, we have only considered analytic solutions. Our main result is that for 2 particles of mass m and center of mass energy E interacting through an analytic potential V(z) such that 1 V(z)1 < Xe-Pi"I, S(I, E) is a meromorphic function of x (cash x = E/m) in that region of the complex x plane where 1 x I < p/2, I x j > E > 0. Poles in the upper x plane in the region of analyticity correspond to bound states and must lie on the imaginary axis. Difficulties connected with a similar analysis in the complex I plane are briefly considered.
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