Quantum momentum distribution and kinetic energy in solid 4He.
We present measurements of neutron scattering from solid 4He at high momentum transfer. The solid is held close to the melting line at molar volume 20.87 cm3/mol and temperature T=1.6 K. From the data, we determine the shape of the momentum distribution, n(k), of atoms in the solid and the leading final state contribution to the scattering. We show that n(k) in this highly anharmonic, quantum solid differs significantly from a Gaussian. The n(k) is more sharply peaked with larger occupation of low momentum states than in a Maxwell-Boltzmann distribution, as found in liquid 4He and predicted qualitatively by path integral Monte Carlo calculations. The atomic kinetic energy is =(24.25+/-0.30) K. If n(k) is assumed to be Gaussian, as is usually the practice, a 10% smaller is obtained.
Elementary Excitations in Liquid Helium
An analysis of some recent experimental and theoretical investigations of the elementary excitation spectrum of liquid He II is carried out. The spectrum of density fluctuations, which is measured in an inelastic neutron scattering experiment, is shown to consist of two distinct parts: direct excitation of single quasi-particles from the condensed zero-momentum state; and excitation of more complex configurations arising from the interaction of two, three, or more quasi-particles. With the aid of general sum-rule arguments it is demonstrated that: (1) in the long-wavelength limit, a single quasi-particle excitation exhausts the $f$-sum rule; the resulting excitation spectrum is identical to the phonon spectrum proposed by Feynman and found experimentally by Henshaw and Woods; (2) this asymptotic behavior of the density fluctuation spectrum may be used to normalize the experimental results of Henshaw and Woods; one thereby obtains a somewhat altered liquid structure-factor curve, detailed information on the efficiency of quasi-particle excitation from the condensed state of an incident slow neutron, and an estimate of the depletion of the zero-momentum state as a consequence of particle interaction; (3) the backflow introduced by Feynman and Cohen corresponds to taking into account the coupling between a Feynman excitation and higher configurations involving several elementary excitations.
The Legacy of Art in Plastic Surgery
Summary The consistent relationship between surgery and art has been very well documented since 2000 BC. The close relationship between plastic surgery and art is historical and is still expected by the public and our patients. This article emphasizes the many links plastic surgery has with art, and presents a few practical examples of its reverberation in aesthetic and reconstructive plastic surgery procedures. Based on his surgical and actual sculpting activities in the realm of contemporary art, the author elaborates on 7 contributions art education affords the plastic surgery praxis, as an incentive and a reflection of its value to the plastic surgeon’s life.