Intro
Separable Expansions When solving any integral equation
there are several properties one would really love the kernel to
have in order to a easier solving of the problem. One of this
nice properties is the separability of the kernel.A kernel
is said to be separable when :
when the kernel is separable a straigh forward solution of the integral equation can be found easily. In the problem of two- and three-body scattering one several integral equations appear, the first being the Lippmann-Schwinger equation which can be written for the t matrix as:
where Go is the free propagator of the system.
Similar kind of equations, much more complicated of course, are to be found when dealing with three body problems. There is where separable expansions of the potentials, as funcions of p and p' are interesting to be obtained as they can reduce the calculation time by several factors.
One method of finding such a expansion is the EST method which does not expand the potential itself but the t matrix. So that the original and the separable expanded potentials will have the same half-off-shell behavior for a certain set of chosen enegies.
Bibliography
- D. J. Ernst, C. M. Shakin, and R. M. Thaler, Phys. Rev. C 8 ,507 (1973)