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An approach is presented for theoretical calculations of the Debye-Waller factors in x-ray absorption spectra. These factors are represented in terms of the cumulant expansion up to third order. They account respectively for the net thermal expansion σ(1) (T ), the mean-square relative displacements σ 2 (T ), and the asymmetry of the pair distribution function σ (3) (T ). Similarly, we obtain Debye-Waller factors for x-ray and neutron scattering in terms of the mean-square vibrational amplitudes u 2 (T ). Our method is based on density functional theory calculations of the dynamical matrix, together with an efficient Lanczos algorithm for projected phonon spectra within the quasiharmonic approximation. Due to anharmonicity in the interatomic forces, the results are highly sensitive to variations in the equilibrium lattice constants, and hence to the choice of exchangecorrelation potential. In order to treat this sensitivity, we introduce two prescriptions: one based on the local density approximation, and a second based on a modified generalized gradient approximation. Illustrative results for the leading cumulants are presented for several materials and compared with experiment and with correlated Einstein and Debye models. We also obtain Born-von Karman parameters and corrections due to perpendicular vibrations.

The neutron emission from fusionlike reactions leading to evaporation residues and fission fragments was measured in the reaction ' 'Ho+ Ne at 220, 292, and 402 MeV 2 Ne bombarding energies. Preequilibrium high-energy neutrons having up to twice the beam velocity were observed. The multiplicity of these neutrons increases with the bombarding energy from 0.4 to 2.3. This corresponds to 5 to 15% of the total number of neutrons emitted per fusionlike event. The measured energy spectra of the highly energetic neutrons cannot be described with the Fermi-jet mechanism (one body promptly emitted particles), especially at angles larger than 35'. Reasonable agreement with the modified Harp-Miller-Berne model can be obtained. In that case, however, it is necessary to treat the initial degree of freedom as a parameter which increases with bombarding energy from 20 to 28. The evaporative component in the energy spectra of fusion-fission events was used to deduce that the number of prefission neutrons is 5.6+0.5, 5.8+0.5, and 5.3+1.0 at bombarding energies of 220, 292, and 402 MeV, respectively, whereas the statistical model predicts a maximum number of 1.6 to 2.0 prefission neutrons. Although no conclusive explanation can be given for the unexpectedly large multiple chance fission probability, it is suggested that most of the additional prefission neutrons are emitted during the transition from saddle to scission.

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