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https://hdl.handle.net/2142/22742
Description
Title
Deep inelastic scattering by quantum liquids
Author(s)
Belic, Aleksandar
Issue Date
1992
Doctoral Committee Chair(s)
Pandharipande, V.R.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Fluid and Plasma
Language
eng
Abstract
The impulse approximation and the related concept of the scaling of the dynamic structure function S(k,$\omega$) at large k and $\omega$ have played a dominant role in the analysis of the deep inelastic neutron scattering by quantum liquids. These concepts are reviewed along with the prevalent approximations to treat final state interactions neglected in the impulse approximation.
At large momentum transfers it is convenient to express the dynamic structure function S(k,$\omega$) as the sum of a part symmetric about $\omega$ = k$\sp2$/2m and an antisymmetric part. The latter is zero in the impulse approximation, and its leading contribution is given by (m/k)$\sp2$J$\sb1$(y), where y $\equiv$ (m/k)($\omega$ $-$ k$\sp2$/2m) is the usual scaling variable. The integrals of J$\sb1$(y), weighted with y, y$\sp3$ and y$\sp5$ in liquid $\sp4$He are calculated using sum-rules. Polynomial expansions are used to construct models of J$\sb1$(y) which appear to be in qualitative agreement with the observed antisymmetric part at large values of k.
Next, we study the dynamic structure function S(k,$\omega$) of Bose liquids in the asymptotic limit k,$\omega$ $\to \infty$ at constant y, using the orthogonal correlated basis of Feynman phonon states. This approach has been traditionally and successfully used to study S(k,$\omega$) at small k,$\omega$, and it appears possible to develop it further to obtain a unified theory of S(k,$\omega$) at all k and $\omega$. In this thesis, we prove within this approach that S(k,$\omega$) scales exactly in the k$\omega \to \infty$ limit, as is well known. It is also shown that, within a very good approximation, the scaling function J(y) is determined solely by the static structure function S(q) of the liquid. In contrast, the traditional approach to determining S(k,$\omega$) at large k,$\omega$ is based on the impulse approximation; J$\sb{IA}$(y) is solely determined by the momentum distribution n(q) of the particles in the liquid. In weakly interacting systems, where the impulse approximation is exact, the J(y) calculated from the Feynman phonon basis is identical to J$\sb{IA}$(y). The J(y) of liquid $\sp4$He is calculated using this theory and the experimental S(q). It is quite similar to the J$\sb{IA}$(y) obtained from the theoretical n(q) of liquid $\sp4$He. A number of technical developments in orthogonal correlated basis theories are also reported.
Finally, we develop the orthogonal correlated basis formalism that is suitable for studying the dynamic structure function S(k,$\omega$) of Fermi liquids in the asymptotic limit k,$\omega\to\infty$ at constant y.
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