959 research outputs found
Electric polarizability of nuclei and a longitudinal sum rule
Recently, a longitudinal sum rule for the electric polarizability of nuclei
was used to revise a relativistic correction in a dipole sum rule for the
polarizability (nucl-th/9802011). This revision is shown to be wrong because of
neglecting an asymptotic contribution in the underlying dispersion relation.
The status and correct use of the longitudinal sum rule is clarified.Comment: 9 pages, revtex, minor clarifications added. To appear in Nucl. Phys.
Towards a Nonperturbative Theory of Hydrodynamic Turbulence:Fusion Rules, Exact Bridge Relations and Anomalous Viscous Scaling Functions
In this paper we derive here, on the basis of the NS eqs. a set of fusion
rules for correlations of velocity differences when all the separation are in
the inertial interval. Using this we consider the standard hierarchy of
equations relating the -th order correlations (originating from the viscous
term in the NS eq.) to 'th order (originating from the nonlinear term) and
demonstrate that for fully unfused correlations the viscous term is negligible.
Consequently the hierarchic chain is decoupled in the sense that the
correlations of 'th order satisfy a homogeneous equation that may exhibit
anomalous scaling solutions. Using the same hierarchy of eqs. when some
separations go to zero we derive a second set of fusion rules for correlations
with differences in the viscous range. The latter includes gradient fields. We
demonstrate that every n'th order correlation function of velocity differences
{\cal F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length
to dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . When all these
separations are of the same order this length scales like with ,
with being the scaling exponent of the 'th order structure
function. We derive a class of exact scaling relations bridging the exponents
of correlations of gradient fields to the exponents of the 'th
order structure functions. One of these relations is the well known ``bridge
relation" for the scaling exponent of dissipation fluctuations .Comment: PRE, Submitted. REVTeX, 18 pages, 7 figures (not included) PS Source
of the paper with figures avalable at
http://lvov.weizmann.ac.il/onlinelist.htm
Anomalous Scaling in a Model of Passive Scalar Advection: Exact Results
Kraichnan's model of passive scalar advection in which the driving velocity
field has fast temporal decorrelation is studied as a case model for
understanding the appearance of anomalous scaling in turbulent systems. We
demonstrate how the techniques of renormalized perturbation theory lead (after
exact resummations) to equations for the statistical quantities that reveal
also non perturbative effects. It is shown that ultraviolet divergences in the
diagrammatic expansion translate into anomalous scaling with the inner length
acting as the renormalization scale. In this paper we compute analytically the
infinite set of anomalous exponents that stem from the ultraviolet divergences.
Notwithstanding, non-perturbative effects furnish a possibility of anomalous
scaling based on the outer renormalization scale. The mechanism for this
intricate behavior is examined and explained in detail. We show that in the
language of L'vov, Procaccia and Fairhall [Phys. Rev. E {\bf 50}, 4684 (1994)]
the problem is ``critical" i.e. the anomalous exponent of the scalar primary
field . This is precisely the condition that allows for
anomalous scaling in the structure functions as well, and we prove that this
anomaly must be based on the outer renormalization scale. Finally, we derive
the scaling laws that were proposed by Kraichnan for this problem, and show
that his scaling exponents are consistent with our theory.Comment: 43 pages, revtex
Spin structure of the Delta(1232) and inelastic Compton scattering
Radiative transitions gamma + Delta(1232) -> N^* are discussed in the
nonrelativistic quark model with spin-orbit corrections for the 70-plet L^P=1^-
nucleon resonances N^*. The reaction gamma + N -> gamma + Delta is considered
as a tool to measure some of these transitions. A particular sensitivity to
photoexcitations of S_{11}(1535), D_{13}(1700), and D_{15}(1675) is predicted.Comment: 4 pages, 1 figure. Talk given at NSTAR01, Mainz, German
The GDH sum rule for the Delta isobar: A possible anomaly?
The GDH sum rule is discussed for the Delta(1232) resonance. It is shown that
apart from ordinary excitations to higher-energy states, the sum rule contains
a large negative contribution due to de-excitation into the nucleon state.
Therefore, a fulfillment of the sum rule assumes a strong coupling of Delta^+
and Delta^0 to resonances of spin 5/2 and higher. Calculations performed in
quark models suggest that D15(1675) may be such a resonance. However, its
strength is found to be not sufficient for bringing the GDH sum rule to a
theoretically expected positive magnitude.Comment: 5 pages, no figures. Extended talk at the GDH2000 Symposium, Mainz,
June 14-17, 2000. To appear in proceeding
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