A theoretical model of the equation of state for a two-component fluid with the $\text{exp}$-$6$ potential based on the perturbation theory

A theoretical model of the equation of state of a two-component fluid with the exp-$6$ interaction potential has been developed. The model was created based on an improved version of perturbation theory. A technique for calculating the excessive Helmholtz energy of the two-component fluid is proposed. The technique is based on applying the Laplace transform for hard sphere distribution functions $g_{ij}(r)$ it considerably reduces time expenditures and increases the accuracy of calculations as compared to the technique that uses the functions $g_{ij}(r)$ directly. Based on the model proposed, the thermodynamic parameters of the two-component mixture of helium and hydrogen are calculated. To eliminate the problem of nonadditivity of hard sphere diameters and to obtain the best agreement of the calculated thermodynamic parameters with data of a computer experiment according to the Monte Carlo method, different schemes for separating the potential of interaction between helium atoms and hydrogen molecules into the reference and perturbing components were investigated.