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https://hdl.handle.net/2142/18907
Description
Title
Deep inelastic scattering by quantum liquids
Author(s)
Belic, Aleksandar
Issue Date
1992
Director of Research (if dissertation) or Advisor (if thesis)
Pandharipande, V.R.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
deep inelastic scattering
quantum liquids
neutron scattering
impulse approximation
dynamic structure function
Language
en
Abstract
The impulse approximation and the related concept of the scaling of the dynamic
structure function S(k, w) at large k and w 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, w) as the sum of a part symmetric about w = k2 /2m and an antisymmetric part.
The latter is zero in the impulse approximation, and its leading contribution is given by
(mjk)2J1(y), where y = (mfk)(w- P /2m) is the usual scaling variable. The integrals of
Jt(y), weighted withy, y3 and y5 in liquid 4He are calculated using sum-rules. Polynomial
expansions are used to construct models of Jt(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,w) of Bose liquids in the asymptotic
limit k,w -+ oo at constant y, using the orthogonal correlated basis of Feynman phonon
states. This approach has been traditionally and successfully used to study S(k,w) at small
k,w, and it appears possible to develop it further to obtain a unified theory of S(k,w) at all k
and w. In this thesis, we prove within this approach that S(k,w) scales exactly in the k,w-+
oo 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, w) at large k, w is based on the
impulse approximation; hA(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 hA(y). The
J(y) of liquid 4He is calculated using this theory and the experimental S(q). It is quite
similar to the hA(Y) obtained from the theoretical n(q) ofliquid 4He. A number oftechnical
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, w) of Fermi liquids in the asymptotic limit k, w --+ oo
at constant y.
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