439 research outputs found
Coherent and Incoherent Dynamic Structure Function of the Free Fermi Gas
A detailed calculation of the coherent and incoherent dynamic structure
functions of the free Fermi gas, starting from their expressions in terms of
the one- and semi-diagonal two-body density matrices, is derived and discussed.
Their behavior and evolution with the momentum transfer is analyzed, and
particular attention is devoted to the contributions that both functions
present at negative energies. Finally, an analysis of the energy weighted sum
rules satisfied by both responses is also performed. Despite of the simplicity
of the model, some of the conclusions can be extended to realistic systems.Comment: LaTeX, 3 figure
A Droplet within the Spherical Model
Various substances in the liquid state tend to form droplets. In this paper
the shape of such droplets is investigated within the spherical model of a
lattice gas. We show that in this case the droplet boundary is always
diffusive, as opposed to sharp, and find the corresponding density profiles
(droplet shapes). Translation-invariant versions of the spherical model do not
fix the spatial location of the droplet, hence lead to mixed phases. To obtain
pure macroscopic states (which describe localized droplets) we use generalized
quasi-averaging. Conventional quasi-averaging deforms droplets and, hence, can
not be used for this purpose. On the contrary, application of the generalized
method of quasi-averages yields droplet shapes which do not depend on the
magnitude of the applied external field.Comment: 22 pages, 2 figure
Final state effects on superfluid He in the deep inelastic regime
A study of Final State Effects (FSE) on the dynamic structure function of
superfluid He in the Gersch--Rodriguez formalism is presented. The main
ingredients needed in the calculation are the momentum distribution and the
semidiagonal two--body density matrix. The influence of these ground state
quantities on the FSE is analyzed. A variational form of is used, even
though simpler forms turn out to give accurate results if properly chosen.
Comparison to the experimental response at high momentum transfer is performed.
The predicted response is quite sensitive to slight variations on the value of
the condensate fraction, the best agreement with experiment being obtained with
. Sum rules of the FSE broadening function are also derived and
commented. Finally, it is shown that Gersch--Rodriguez theory produces results
as accurate as those coming from other more recent FSE theories.Comment: 20 pages, RevTex 3.0, 11 figures available upon request, to be appear
in Phys. Rev.
Theoretical aspects of the CEBAF 89-009 experiment on inclusive scattering of 4.05 GeV electrons from nuclei
We compare recent CEBAF data on inclusive electron scattering on nuclei with
predictions, based on a relation between structure functions (SF) of a nucleus,
a nucleon and a nucleus of point-nucleons. The latter contains nuclear
dynamics, e.g. binary collision contributions in addition to the asymptotic
limit. The agreement with the data is good, except in low-intensity regions.
Computed ternary collsion contributions appear too small for an explanation. We
perform scaling analyses in Gurvitz's scaling variable and found that for
, ratios of scaling functions for pairs of nuclei differ by less
than 15-20% from 1. Scaling functions for are, for increasing ,
shown to approach a plateau from above. We observe only weak -dependence
in FSI, which in the relevant kinematic region is ascribed to the diffractive
nature of the NN amplitudes appearing in FSI. This renders it difficult to
separate asymptotic from FSI parts and seriously hampers the extraction of
from scaling analyses in a model-independnent fashion.Comment: 11 p. Latex file, 2 ps fig
Description of recent large- neutron inclusive scattering data from liquid He
We report dynamical calculations for large- structure functions of liquid
He at =1.6 and 2.3 K and compare those with recent MARI data. We extend
those calculations far beyond the experimental range q\le 29\Ain in order to
study the approach of the response to its asymptotic limit for a system with
interactions having a strong short-range repulsion. We find only small
deviations from theoretical behavior, valid for smooth . We repeat an
extraction by Glyde et al of cumulant coefficients from data. We argue that
fits determine the single atom momentum distribution, but express doubt as to
the extraction of meaningful Final State Interaction parameters.Comment: 37 pages, 13 postscript fig
Beyond the binary collision approximation for the large- response of liquid He
We discuss corrections to the linear response of a many-body system beyond
the binary collision approximation. We first derive for smooth pair
interactions an exact expression of the response , considerably
simplifying existing forms and present also the generalization for interactions
with a strong, short-range repulsion. We then apply the latter to the case of
liquid He. We display the numerical influence of the correction
around the quasi-elastic peak and in the low-intensity wings of the response,
far from that peak. Finally we resolve an apparent contradiction in previous
discussions around the fourth order cumulant expansion coefficient. Our results
prove that the large- response of liquid He can be accurately understood
on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques
Relativistic approaches to structure functions of nuclei
We employ a propagator technique to derive a new relativistic 1/\qq
expansion of the structure function of a nucleus, composed of point-nucleons.
We exploit non-relativistic features of low-momentum nucleons in the target and
only treat relativistically the nucleon after absorption of a high-momentum
virtual photon. The new series permits a 3-dimensional reduction of each term
and a formal summation of all Final State Interaction terms. We then show that
a relativistic structure function can be obtained from its non-relativistic
analog by a mere change of a scaling variable and an addition of an energy
shift. We compare the obtained result with an ad hoc generalized
Gersch-Rodriguez-Smith theory, previously used in computations of nuclear
structure functions.Comment: Comparison with data is included, to be published in PRC, Feb. 200
Bose-Einstein condensation in the presence of a uniform field and a point-like impurity
The behavior of an ideal -dimensional boson gas in the presence of a
uniform gravitational field is analyzed. It is explicitly shown that,
contrarily to an old standing folklore, the three-dimensional gas does not
undergo Bose-Einstein condensation at finite temperature. On the other hand,
Bose-Einstein condensation occurs at for if there is a
point-like impurity at the bottom of the vessel containing the gas.Comment: 14 pages, REVTEX. Revised version, accepted for publication in Phys.
Rev.
Confinement and scaling in deep inelastic scattering
We show that parton confinement in the final state generates large
corrections to Bjorken scaling, thus leaving less room for the logarithmic
corrections. In particular, the -scaling violations at large are
entirely described in terms of power corrections. For treatment of these
non-perturbative effects, we derive a new expansion in powers of for
the structure function that is free of infra-red singularities and which
reduces corrections to the leading term. The leading term represents scattering
from an off-mass-shell parton, which keeps the same virtual mass in the final
state. It is found that this quasi-free term is a function of a new variable
, which coincides with the Bjorken variable for . The
two variables are very different, however, at finite . In particular, the
variable depends on the invariant mass of the spectator particles.
Analysis of the data at large shows excellent scaling in the variable , and determines the value of the diquark mass to be close to zero. -scaling allows us to extract the structure function near the elastic
threshold. It is found to behave as . Predictions for the
structure functions based on -scaling are made.Comment: Discussion of target mass corrections is added. Accepted for
publication in Phys. Rev.
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