18 research outputs found
Low energy universality and scaling of Van der Waals forces
At long distances interactions between neutral ground state atoms can be
described by the Van der Waals potential V(r) =-C6/r^6-C8/r^8 - ... . In the
ultra-cold regime atom-atom scattering is dominated by s-waves phase shifts
given by an effective range expansion p cot d0 (p) = -1/a0 + r0 p^2/2 + ... in
terms of the scattering length a0 and the effective range r0. We show that
while for these potentials the scattering length cannot be predicted, the
effective range is given by the universal low energy theorem r0 = A + B/a0+
C/a0^2 where A,B and C depend on the dispersion coefficients Cn and the reduced
di-atom mass. We confront this formula to about a hundred determinations of r0
and a0 and show why the result is dominated by the leading dispersion
coefficient C6. Universality and scaling extends much beyond naive dimensional
analysis estimates.Comment: 4 pages, 3 figure
Nucleon-Nucleon interaction, charge symmetry breaking and renormalization
We study the interplay between charge symmetry breaking and renormalization
in the NN system for s-waves. We find a set of universality relations which
disentangle explicitly the known long distance dynamics from low energy
parameters and extend them to the Coulomb case. We analyze within such an
approach the One-Boson-Exchange potential and the theoretical conditions which
allow to relate the proton-neutron, proton-proton and neutron-neutron
scattering observables without the introduction of extra new parameters and
providing good phenomenological success.Comment: 15 pages, 6 figure
Renormalization vs Strong Form Factors for One Boson Exchange Potentials
We analyze the One Boson Exchange Potential from the point of view of
Renormalization theory. We show that the nucleon-meson Lagrangean while
predicting the NN force does not predict the NN scattering matrix nor the
deuteron properties unambiguously due to the appearance of short distance
singularities. While the problem has traditionally been circumvented by
introducing vertex functions via phenomenological strong form factors, we
propose to impose physical renormalization conditions on the scattering
amplitude at low energies. Working in the large Nc approximation with
pi,sigma,rho and omega mesons, we show that, once these conditions are applied,
results for low energy phases of proton-neutron scattering as well as deuteron
properties become largely insensitive to the form factors and to the vector
mesons and yield a reasonable agreement with the data, for realistic values of
the coupling constants.Comment: 30 pages, 17 fig
Causality bounds for neutron-proton scattering
We consider the constraints of causality and unitarity for the low-energy
interactions of protons and neutrons. We derive a general theorem that
non-vanishing partial-wave mixing cannot be reproduced with zero-range
interactions without violating causality or unitarity. We define and calculate
interaction length scales which we call the causal range and the Cauchy-Schwarz
range for all spin channels up to J = 3. For some channels we find that these
length scales are as large as 5 fm. We investigate the origin of these large
lengths and discuss their significance for the choice of momentum cutoff scales
in effective field theory and universality in many-body Fermi systems.Comment: 36 pages, 10 figures, 7 tables, version to appear in Eur. Phys. J.
Ab initio alpha-alpha scattering
Processes involving alpha particles and alpha-like nuclei comprise a major
part of stellar nucleosynthesis and hypothesized mechanisms for thermonuclear
supernovae. In an effort towards understanding alpha processes from first
principles, we describe in this letter the first ab initio calculation of
alpha-alpha scattering. We use lattice effective field theory to describe the
low-energy interactions of nucleons and apply a technique called the adiabatic
projection method to reduce the eight-body system to an effective two-cluster
system. We find good agreement between lattice results and experimental phase
shifts for S-wave and D-wave scattering. The computational scaling with
particle number suggests that alpha processes involving heavier nuclei are also
within reach in the near future.Comment: 6 pages, 6 figure
A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)
Meeting abstrac