Study of dense helium plasma in the optimal hypernetted chain approximation

We have studied the helium plasma in the hypernetted chain approximation considering both short-ranged internuclear and long-ranged Coulomb interactions. The optimal two-particle wave function has been determined in fourth order; fifth-order corrections have been considered in the calculation of the two-body and three-body correlation functions. The latter has been used to determine the pycnonuclear triple-alpha-fusion rate in the density regime ${10}^8$ g/${\mathrm{cm}}^3$≤ρ≤${10}^{10}$ g/${\mathrm{cm}}^3$, which is of importance for the crust evolution of an accreting old neutron star. The influence of three-particle terms in the many-body wave function on the rate is estimated within an additional variational hypernetted chain calculation. Our results support the idea that the helium liquid undergoes a phase transition to stable ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ matter at densities ρ≊3×${10}^9$ g/${\mathrm{cm}}^3$ as the plasma induced screening potential then becomes strong enough to bind the ${}_{}{}^8{}_{}{}^{}\mathrm{Be}$ ground state.