Formation of Nonlocalized Vacancies in bcc<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Several experiments have indicated the formation of some defect in body-centered cubic solid ${\mathrm{He}}^{3}$ at relatively low energies. A few alternative hypotheses are discussed which could explain this effect, but vacancy formation is singled out for study. The wave function and formation energy of vacancies in solid ${\mathrm{He}}^{3}$ are then calculated variationally, and it is found that such a vacancy would be highly nonlocalized and would propagate as a wave in the crystal. The calculation of the energy of formation, actually an energy band, uses the Nosanow cluster expansion. The energy so calculated is compared with the experimental formation energies, and it has the correct dependence on density although it is higher than the experimental values.

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