CANONICAL NUMBER PROJECTION IN A SIMPLE NUCLEAR-MODEL

The heat capacity for a system of nucleons as a function of temperatur e is determined from the canonical partition function, which is projec ted from an approximation to the grand canonical partition function. T his approximation is obtained from a functional integral representatio n of the partition function, including both thermodynamic fluctuations and first-order quantum corrections. The number projection methods in clude a simple contour integration or ''Wick rotation,'' and a Chebysc hev polynomial expansion, both of which are formally exact. The above procedure is tested in a simple i13/2 pairing model for which the exac t canonical and grand canonical results can be obtained. It is found t hat both number projection methods fail to predict the position or the height of the peak in the heat capacity due to errors in the approxim ation to the grand partition function, even though the path integral a pproximation is very good.