  In this paper, we present an accurate and robust scaling operator based on
material optical thickness (OT) for the least-squares spherical harmonics
(LSP$_N$) method for solving neutron transport problems. LSP$_N$ without proper
scaling is known to be erroneous in highly scattering medium, if the optical
thickness of the material is large. A previously presented scaling developed by
Manteuffel, et al.\ does improve the accuracy of LSP$_N$, in problems where the
material is optically thick. With the method, however, essentially no scaling
is applied in optically thin materials, which can lead to an erroneous solution
with presence of highly scattering medium. Another scaling approach, called the
reciprocal-removal (RR) scaled LSP$_N$, which is equivalent to the self-adjoint
angular flux (SAAF) equation, has numerical issues in highly-scattering
materials due to a singular weighting. We propose a scaling based on optical
thickness that improves the solution in optically thick media while avoiding
the singularity in the SAAF formulation.
