Consider a one-dimensional variable geometry reactor composed of an inner core of multiplying medium of radius R surrounded by an outer reflector (water) of thickness ?R. Using two-group diffusion theory, write a computer program that solves the numerical finite-difference diffusion equation to determine the critical core radius as well as the optimal thickness of the reflector. Once a reflector reaches a maximum thickness, it no longer provides "reflector savings.

TABLE 7-2 Few-Group Diffusion Theory Constants for a Typical PWR Reactor Core Two-Group Four-Group Group Constant 1 of 2 2 of 2 1 of 4 3 of 4 3 of 4 4 of 4 .008476 .18514 009572 .001193 01768 . 18514 Ef 003320 .07537 .003378 0004850 006970 07527 Ea .01207 .1210 .004946 002840 03053 .1210 1.2627 .3543 2.1623 1.0867 .6318 .3543 ER 02619 .1210 08795 06124 09506 1210