Theory of Intermolecular Potential and Second Virial Coefficient of Hydrogen at Low Temperature

The intermolecular potential between hydrogen molecules is calculated taking into account its dependence on the relative orientation of the molecules. Assuming that the rotational quantum number of each molecule is a good quantum number throughout collision at low temperature, the matrix elements of the repulsive short-range intermolecular potential and the London potential are calculated. If the intermolecular potential depends on the relative orientation of colliding molecules, the resulting matrix element depends on the rotational quantum number. Thus it is pointed out that the second virial coefficient of ordinary hydrogen (which is, at low temperature, a mixture of 75 percent of J = 1 molecule and 25 percent of J = 0 molecules, where J is the rotational quantum number), and pure para hydrogen (which consists of only J = 0 molecules at low temperature) must be different, even if there were no statistical effect. The virial coefficient is calculated for very low temperature by solving the Schrödinger equation numerically.