On the theory of the catalysis of the ortho-para transformation by paramagnetic gases

Abstract

According to quantum statistics, there exists for a diatomic molecule containing similar atoms an important difference between states with even and uneven rotational quantum numbers j . These two kinds of states have different statistical weights in the ratio of (S + 1)/S or S/(S + 1) where S is the nuclear spin. Whether the states of larger statistical weight possess even or uneven values of j depends on the symmetry properties of the electronic configuration and on the nuclear statistics. The states with the larger weight are called the ortho-states, those with the smaller weight the para-states. Under normal conditions, the transition probability between ortho-and para-states is zero. There are, however, two ways of inducing an ortho-para transformation. The one consists in dissociating the molecules, after which the atoms will recombine at random. The other possibility is to introduce a perturbation which depends both on the spins and on the positions of the nuclei. Under such conditions a transition may take place for the following reason: the unperturbed eigenfunction can be written as a product of two factors Ψ = ψ ( q 1 , q 2 ) ψ (s 1 , s 2 ) depending respectively on the space-co-ordinates q and the spin-vectors s of the two nuclei. Now, in order that an ortho-para transition may take place, it is necessary that the symmetry properties with respect to a permutation of the nuclei shall be changed in both factors. A simultaneous transition in ψ( q 1 , q 2 ) and ψ(s 1 , s 2 ) can, however, only occur if the perturbation contains a term depending both on q and s. It is due to a perturbation of this kind that the ortho-para hydrogen transformation is catalysed by paramagnetic gases as was found by Farkas and Sachsse. The interaction between the magnetic field of the paramagnetic molecules and the magnetic moment of the H-nuclei depends on the nuclear spin and, as the field is inhomogeneous, it also involves the nuclear positions. The theory of this catalysis was given by Wigner.