The total neutron scattering cross section of solid methane in phase II

Abstract

The total neutron scattering cross section per molecule σtot of solid methane in phase II was measured for incident neutron energies 0.5 meV⩽En⩽10 eV in the temperature range 0.3 K⩽T⩽19.5 K. The σtot depends on the rotational, translational and vibrational dynamics of the CH4 molecule and shows significant dependence both on En and T. For En above 165 meV, which corresponds to the first vibrational excitation level of CH4, the σtot is equal to 4σp(A/(A+1))2=80 b with proton mass A=1 and a bound cross section σp=80 b of a single proton. For En≈6.5 meV, which is approximately the librational energy of the CH4 rotor, σtot approaches 205 b at all temperatures. This is the cross section of a rigid H4 tetrahedron rotating freely about its fixed center; the effective mass is A=4. For En<6.5 meV, the interference effects of scattering from different protons within the same molecule, sensitive to nuclear spin symmetry, are observed. σtot∼〈I(I+1)〉T with total nuclear spin of the ortho, meta, para molecules I=2, 1 or 0, respectively. For En→0, two limiting cases can be distinguished. At high temperatures, the lower limit of σtot is given by the bound (incoherent) cross section of four protons 4σp=320 b. At low temperature, where only the ground state with I=2 is occupied, σtot=8σp=640 b. The experimental data compare well with a quantum-mechanical model and the mass-tensor approximation. Multiple rotational-translational-vibrational scattering contributions are discussed also.