  Using an exactly solvable pairing model Hamiltonian in the static path
approximation together with small-amplitude quantal fluctuation corrections in
random phase approximation (SPA+RPA), we have analyzed the behaviour of
canonical (number projected) and grandcanonical treatments of nuclear level
densities as a function of temperature and number of particles. For small
particle numbers at a low temperature, we find that though the grandcanonical
partition function in SPA+RPA approach is quite close to its exact value, the
small errors in its estimation causes significant suppression of level density
obtained using number projected partition function. The results are also
compared with the smoothed out exact values of level density. Within this model
study, it appears that due to saddle point approximation to multiple
Laplace-back transform, the grandcanonical treatment of level density at low
temperature may be reliable only for relatively large number of particles.
