Numerical study of the density of states for the bag model

The density of states for an extended MIT bag model is numerically studied using a parameterized smooth representation which provides the best fit to the numerical data. It is found that the mass dependence of the surface term in the density of states agrees with that derived from the multi-reflection theory calculation. The mass dependence of the curvature term in the density of states is extracted for finite values of the quark mass. The scaling properties of the data, assumed in the parameterization, are studied. The difference between the parameterized smooth representation determined by a best fit and the results derived from direct smoothing, of the numerical data is discussed. The fluctuations in the density of states are also discussed. We provide a smooth representation of the density of states of a spherical cavity for non-relativistic particles.