  We study a dilute and ultracold Bose gas of interacting atoms by using an
effective field theory which takes account finite-range effects of the
inter-atomic potential. Within the formalism of functional integration from the
grand canonical partition function we derive beyond-mean-field analytical
results which depend on both scattering length and effective range of the
interaction. In particular, we calculate the equation of state of the bosonic
system as a function of these interaction parameters both at zero and finite
temperature including one-loop Gaussian fluctuation. In the case of zero-range
effective interaction we explicitly show that, due to quantum fluctuations, the
bosonic system is thermodynamically stable only for very small values of the
gas parameter. We find that a positive effective range above a critical
threshold is necessary to remove the thermodynamical instability of the uniform
configuration. Remarkably, also for relatively large values of the gas
parameter, our finite-range results are in quite good agreement with recent
zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.
