  This work extends the seminal work of Gottfried on the two-body quantum
physics of particles interacting through a delta-shell potential to many-body
physics by studying a system of non-relativistic particles when the thermal
De-Broglie wavelength of a particle is smaller than the range of the potential
and the density is such that average distance between particles is smaller than
the range. The ability of the delta-shell potential to reproduce some basic
properties of the deuteron are examined. Relations for moments of bound states
are derived. The virial expansion is used to calculate the first quantum
correction to the ideal gas pressure in the form of the second virial
coefficient. Additionally, all thermodynamic functions are calculated up to the
first order quantum corrections. For small departures from equilibrium, the net
flows of mass, energy and momentum, characterized by the coefficients of
diffusion, thermal conductivity and shear viscosity, respectively, are
calculated. Properties of the gas are examined for various values of physical
parameters including the case of infinite scattering length when the unitary
limit is achieved.
