Monte Carlo Calculation of ThreeBody Scattering.
Abstract
We construct an eigenvalue problem by confining manybody system to a bounded domain with the boundary condition that the wave function vanishes. By changing the boundary, however, the eigenvalues of the energy can be varied continuously. The Dmatrix is defined for a series of bounded problems with the same value for the ground state energy. The Dmatrix is related to the S matrix, enabling us to calculate the Smatrix at a given energy. The Schrodinger equation for the system is transformed to a diffusion equation by regarding time as imaginary. Initial ensemble, representing an approximate wave function, is evolved, through Monte Carlo simulation of random walks and branching, to the ground state ensemble. The limitations of investigation are: (1) Ingoing and outgoing channels have two fragments. (2) The interaction between the fragments is negligible outside the boundary mentioned above. (3) The particles are bosons or we know the zeros of the wave function. First we consider the scattering of a particle by a potential, which is equivalent to the twobody problem, in one dimension. Here we use the PoschlTeller potential for which the exact solution is known. We use this case to investigate a new sampling method and study of various parameters. Next we consider three particles in one dimension. Here we take interaction to be a potential well, where at least one of the interactions is attractive so that a twobody bound state is possible.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT........85M
 Keywords:

 Physics: Nuclear