An Analytical Solution Of The Time-Independent Schr?dinger Equation For The Woods-Saxon Potential For Arbitrary Angular Momentum l States

摘要

The Woods-Saxon potential is probably the most studied and widely used short range potential in all of nuclear physics. For the angular momentum l= 0 case, Flügge had devised a method to obtain an analytical expression for the bound state energies of the radial time-independent Schr?dinger equation for a neutron confined in a Woods-Saxon potential well. In this study, we extend Flügge's method to solve the radial Schr?dinger equation for a neutron within the Woods-Saxon potential and the centrifugal potential for arbitrary values of I. Here, the Pekeris method is used to deal with the centrifugal term. We obtain an analytical expression for the bound states, valid for arbitrary angular momentum, and show that our expression reduces to that of Flügge, which applies to the l= 0 case. The numerical computations performed also show very good agreement with our analytical expression.