Thermodynamic Properties and Critical Behavior of Spin-Polarized Atomic Hydrogen (H↓) Using the Quantum Second-Virial Coefficient

Abstract

The quantum–mechanical formulations for the second-virial, and the acoustic virial, coefficients are derived for spin-polarized atomic hydrogen (H↓). The dependence of these coefficients on the temperature T as well as the nuclear polarization $\zeta \;$ is analyzed. This is done for the first time. The main inputs in these computations are the scattering phase shifts, which are obtained using the Lippmann–Schwinger equation, with the Silvera triplet-state potential. Starting with these phase shifts, comprehensive calculations of the thermophysical properties for this system are performed for T ranging from 1 µK to 100 K, and $\zeta \;$ varying from 0 to 1. These properties include, in addition to the quantum second-virial coefficient and the acoustic virial coefficient: the pressure–polarization–temperature $\left( {P {-} \zeta {-} T} \right)$ behavior, the entropy (per atom), the speed of sound, the second-virial correction (to the total internal energy per atom and unit density), and the specific heat capacity (per atom and unit density). The Boyle temperature and the Joule inversion temperature are determined. The T-dependence of these thermophysical properties, and related quantities, is explored. As expected, this dependence is most evident in the low-T limit, where quantum effects predominate. The corresponding $\zeta$-dependence becomes noticeable at 80 K and below. It is observed that the virial coefficients tend to decrease with increasing $\zeta$. Comparison of the present results to previous results are included whenever possible. The overall agreement is very good. As T is lowered, the disruptive effects of thermal energy are weakened relative to the attractive interactions between the atoms. Consequently, the H↓ gas makes a transition to a state of higher order and lower entropy—Bose–Einstein condensation (BEC). This is explored carefully.