Response matrix solution to discrete ordinates approximation of the ID monoenergetic neutron transport equation

For nearly 70 years, the solution to the discrete ordinates approximation of the ID monoenergetic neutron transport equation has been an effective approximation. During that time, the method has experienced numerous improvements as numerical and computational techniques have advanced. Here, we propose a new, consistent expression of the analytical solution to the ID, monoenergetic discrete ordinates (DOM) equations, called the Response Matrix DOM (RM/DOM), which is an improvement over past forms. The approach takes advantage of the second order form of the discrete ordinates approximation to express the solution as hyperbolic functions rather than ordinary exponentials. By comparison, a highly anisotropic radiative transfer benchmark will demonstrate the precision of the solution. We then establish a new high order benchmark for scattering in a purely hydrogenous medium and apply RM/DOM to general monoenergetic elastic scattering.