Prog. Theor. Phys. Vol. 56 No. 5 (1976) pp. 1383-1395
The Inadequacy of the Impulse Approximation for a Hard Core Potential
Department of Physics, University of California, Berkeley, California 94720
(Received April 30, 1976)
Microscopic evidence is found based on the derivation and study of the Bethe-Salpeter differential wave equation whose solutions determine dynamic structure factor S(k, ω) which suggests that the impulse approximation to S(k, ω) may not yield the correct excitation intensities of the high-energy neutron scattering from a liquid with a hard core potential, even though it should indeed yield the correct excitation energies. This is because S(k, ω) involves as the excitation intensities the square |φ(0)|2 of the relative wave functions at zero distance and hence well inside the negative (infinite attractive) core, where the free-particle or incoming solutions should be appreciably distorted even in the infinite kinetic energy limit. This definitely explains why a sharp peak representing the condensate expected from the impulse approximation has never been experimentally observed in the high-energy neutron scattering from liquid He4.
DOI : 10.1143/PTP.56.1383
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