The Scattering of Neutrons by Ortho- and Parahydrogen

Calculations have been performed which indicate that experiments on the scattering of neutrons by ortho- and parahydrogen would enable one to determine the sign of the singlet state binding energy and the range of the neutron-proton interaction, in addition to providing direct information concerning the spin dependence of the neutron-proton interaction. A dependence of the neutron-proton interaction upon the relative spin orientation of the particles will manifest itself in a marked difference between the slow neutron scattering cross sections of orthohydrogen (parallel proton spins) and parahydrogen (anti-parallel proton spins). Neutrons with energy less than 0. 068 ev, incident upon para-H₂ in its ground state (J=0, v=0, S=0), may be either elastically scattered, or inelastically scattered with excitation of the molecule to the ground state of the ortho system (J=1, v=0, S=1). This latter process, requiring 0. 023 ev, occurs only if the neutron-proton interaction is spin dependent. When the neutron energy is less than 0. 045 ev, the cross section for the scattering of neutrons by ortho-H₂ in its ground state will be the sum of the elastic scattering cross section and the cross section for the inelastic process in which the molecule is converted to a para-H₂ molecule in its ground state, with the neutron taking up the excess energy. The cross sections of these four processes have been calculated, assuming an interaction range of 210^-13 cm and a virtual singlet state of the deuteron. For liquid-air temperature neutrons (3kT2=0. 012 ev), ₏₀ₑ₀ (0. 012) =0. 2110^-24 cm^2, while ₎ₑₓ₇₎ (0. 012) =6510^-24 cm^2. The cross sections for neutrons at ordinary temperatures (3kT2=0. 037 ev), however, are ₏₀ₑ₀ (0. 037) =1910^-24 cm^2, and ₎ₑₓ₇₎ (0. 037) =5010^-24 cm^2. Therefore, if the present concept of the neutron-proton interaction is valid, one would expect the following results: (a) The ortho-scattering cross section for liquid air neutrons should be about 300 times the corresponding para-scattering cross section. (b) The para-scattering cross section for ordinary thermal neutrons should be roughly 100 times the para-scattering cross section for liquid air neutrons. For a real singlet state, however, these ratios are of the order of one. The elastic para-scattering cross section is quite sensitive to the value of the range of interaction if the singlet state is virtual. For example, the value of this cross section at liquid air neutron temperatures with zero range of interaction is 1. 7510^-24 cm^2, as compared with 0. 2610^-24 cm^2 for an interaction range of 210^-13 cm. Hence, from a measurement of the para elastic scattering cross section for homogeneous neutrons at some energy less than 0. 023 ev, the range of interaction in the triplet state may be inferred with some degree of accuracy. A discussion of the influence of intermolecular forces on the previous results is given.