Natural boundary condition methods for nuclear reactions

Two methods for calculating cross sections are discussed. Method I is that due to Barrett and Delsanto; method II is the R-matrix method with energy-dependent basis states. Both methods are characterized by their use of natural boundary conditions at the surfaces separating internal and external regions of configuration space. The methods are compared with both standard and generalized R-matrix calculations with energy-independent basis states for the reaction ¹²C(n,n)¹²C at incident energies below the inelastic threshold using a weak vibrational model. The convergence of the natural boundary condition methods was found to be substantially better than for the other cases.