Theoretical analysis of inelastic neutron scattering in solid hydrogen

The inelastic-neutron-scattering cross section of ( J=1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement ⟨u2⟩1/2 is deduced from the data via different methods and mutually consistent values of order 0.65 A are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both one-and two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libron-phonon crossovers is found to be about 1 cm−1, somewhat smaller than found by Mertens and Biem. A sum rule for the J=1 to J=0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J=1 to J=0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments. Disciplines Physics | Quantum Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/398 PHYSICAL REVIEW B VOLUME 16, NUMBER 8 15 OCTOBER 1977 Theoretical analysis of inelastic neutron scattering in solid hydrogen* A. Brooks Harris Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19174 A. John Berlinsky Department of Physics, University of British Columbia, Vancouver 8, British Columbia, Canada (Received 11 August 1975) The inelastic-neutron-scattering cross section of (J = 1) solid hydrogen is studied and the experimental data of Stein and co-workers analyzed. The rms displacement (u )'" is deduced from the data via diA'erent methods and mutually consistent values of order 0.65 A are obtained. The enhancement of the cross section at the libron energy due to libron-phonon interactions is found to be the same, about 40% each for both oneand two-libron processes, in agreement with the neutron scattering data. The rms splitting at the libronphonon crossovers is found to be about 1 cm ', somewhat smaller than found by Mertens and Biem. A sum rule for the J = 1 to J = 0 cross section is given which relates the average energy of this transition to the orientational internal energy. Using high-temperature expansions and experimental data for the specific heat, we obtain a qualitative fit to the neutron scattering data in the orientationally disordered phase. In the ordered phase both the sum rule and a direct calculation indicate the existence of a libron sideband above the main J = 1 to J = 0 line having an intensity of 10% of the main line. The energy of the main line at zero temperature is calculated including (a) tipping corrections, (b) virtual excitations with J not conserved, and (c) modified zero-point energy. The value of the electrostatic quadrupole-quadrupole coupling constant deduced from the data of Stein and co-workers using this calculation is in agreement with that obtained from other experiments.