  It is shown that the Constant Temperature (CT) model of nuclear level density
is a direct consequence of a symmetrized Poisson distribution of nuclear level
spacings. The standard CT model describing the total level density is shown to
be fatally flawed due to discontinuities at the Yrast energies, the onset of
new $J^{\pi}$ sequences, that disrupt the exponential formula and cause the
back shift parameter to become nonphysically negative. A new CT-JPI level
density model is proposed with a constant temperature and separate back shift
parameters for each $J^{\pi}$ sequence. The CT-JPI model is also constrained to
reproduce the spin distribution predicted by Ericson's spin distribution
function at the neutron separation energy. A fitting procedure is described for
determining the temperature $T$, back shifts $E_0(J^{\pi})$, and spin cutoff
parameters $\sigma_c$ from nuclear structure and resonance data. The CT-JPI
model is demonstrated to successfully predict the level densities for a wide
range of spins and parities for 46 nuclear with Z=7-92. In variance with
earlier predictions the spin cut-off parameters show no mass dependence and
instead substantial variation at all mass regions.
