  The Lieb-Liniger equation of state accurately describes the zero-temperature
universal properties of a dilute one-dimensional Bose gas in terms of the
s-wave scattering length. For weakly-interacting bosons we derive non-universal
corrections to this equation of state taking into account finite-range effects
of the inter-atomic potential. Within the finite-temperature formalism of
functional integration we find a beyond-mean-field equation of state which
depends on scattering length and effective range of the interaction potential.
Our analytical results, which are obtained performing dimensional
regularization of divergent zero-point quantum fluctuations, show that for the
one-dimensional Bose gas thermodynamic quantities like pressure and sound
velocity are modified by changing the ratio between the effective range and the
scattering length.
