Deriving the critical radius of Uranium using diffusion equation

Homework Statement

I have solved the equation for the neutron density as a function of position and time. I need the boundary conditions to change my infinite number of solutions (the varying seperation constant) into one value so that my answer for the critical radius does not contain a sum!

Homework Equations

del squared (n) - A(dn/dt) = -Bn (which i have solved)

The Attempt at a Solution

i assumed spherically symmetric solutions so using spherical polar coordinates n varies only (spatially) from the distance to the centre of the sphere. The r dependence is of form cos(kr)/r + sin(kr)/r. So the coefficients of cos term must all be 0 (as the density at the centre of any given sphere cannot be infinite). I thought that at the surface, the density is 0 as neutrons do not diffuse back into the sphere once they are out. Is this right?