A NUMERICAL INVESTIGATION OF THE DEUTERON GROUND STATE.
Abstract
Schrodinger's equation is used to compute the energy depth and range parameters used in various forms for the potential experienced by the two nucleons of the deuteron in its ground state. Analytic expressions for the wave function, effective range, scattering length, and root-mean-square radius for that system under the influence of a spherical square well are determined. For the more complex cases of potentials with exponential forms in them (excluding the cut-off exponential), analytic solutions are not so readily attainable; accordingly, a numerical scheme involving the Numerov iteration technique, a Runge-Kutta method particularly useful for second-order differential equations lacking first order terms and suggested by Raynal, was set up and programmed for use on the COMNET computer system using BASIC as the primary language. Parameters for various potentials were calculated and, as a result a new picture of the nucleus developed. While a complete search scheme for these parameters could not be formed, three programs were written which can, with a minimum of assistance from the programmer, determine the parameters for potential forms involving four arbitrary constants. Among the criteria they use are the values of the binding energy, scattering length, effective range, and root-mean-square radius. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 15, 1970
- Accession Number
- AD0711285
Entities
People
- Philip T. Cahill
Organizations
- United States Naval Academy