Transition temperature to the Bose-Einstein condensation of spin polarized tritium, hydrogen, and 4He gases using the second virial coefficient

In this study, the transition temperature to the Bose-Einstein condensation of spin-polarized tritium (T↓), hydrogen (H↓), and ⁴He gases is obtained based on the second virial coefficient. The computations are performed using the Silvera triplet-state potential and HFDHE2 potential for spin-polarized atomic hydrogen isotopes and ⁴He gas, respectively. The thermophysical properties of these Bose systems are computed, including the Helmholtz free energy, entropy, the acoustic virial coefficient, and the second virial coefficient. Large negative values of the second virial coefficient and the acoustic virial coefficient are obtained, reflecting the strong overall attraction of inter-bosonic potential, which gives an indication of the onset of condensation at very low temperatures. At the transition temperature, the stable minimum of the Helmholtz free energy is an indicator of the sort of Bose-Einstein condensation (BEC). As a consequence, the system made a transition to a higher-order state, which is recognized with BEC and explored. The transition temperature is shifted towards a lower value than for the ideal Bose gas.