A gas of elongated objects; an analytical approach

We calculate a collective number of thermodynamic quantities in a one-dimensional gas of hard elongated objects (such as needles) whose centers mobile on a line. Our formalism uses an approximation for the probabilities of contact between the objects. We show that in moderate pressures the quantities extracted from the noncentral potential do not rely on its noncentrality, instead we can extract them analytically from a central potential. Our formalism reproduces the nontrivial features of a gas of elongated objects. Finally, we show below a crossover pressure $p_o$ the rotational couplings causes quantities proportional to inverse distance (such as density) are on average deviated from the inverse of average distance.