1,467 research outputs found
Weinberg Eigenvalues and Pairing with Low-Momentum Potentials
The nonperturbative nature of nucleon-nucleon interactions evolved to low
momentum has recently been investigated in free space and at finite density
using Weinberg eigenvalues as a diagnostic. This analysis is extended here to
the in-medium eigenvalues near the Fermi surface to study pairing. For a fixed
value of density and cutoff Lambda, the eigenvalues increase arbitrarily in
magnitude close to the Fermi surface, signaling the pairing instability. When
using normal-phase propagators, the Weinberg analysis with complex energies
becomes a form of stability analysis and the pairing gap can be estimated from
the largest attractive eigenvalue. With Nambu-Gorkov Green's functions, the
largest attractive eigenvalue goes to unity close to the Fermi surface,
indicating the presence of bound states (Cooper pairs), and the corresponding
eigenvector leads to the self-consistent gap function.Comment: 16 pages, 9 figure
Low-momentum interactions with smooth cutoffs
Nucleon-nucleon potentials evolved to low momentum, which show great promise
in few- and many-body calculations, have generally been formulated with a sharp
cutoff on relative momenta. However, a sharp cutoff has technical disadvantages
and can cause convergence problems at the 10-100 keV level in the deuteron and
triton. This motivates using smooth momentum-space regulators as an
alternative. We generate low-momentum interactions with smooth cutoffs both
through energy-independent renormalization group methods and using a multi-step
process based on the Bloch-Horowitz approach. We find greatly improved
convergence for calculations of the deuteron and triton binding energies in a
harmonic oscillator basis compared to results with a sharp cutoff. Even a
slight evolution of chiral effective field theory interactions to lower momenta
is beneficial. The renormalization group preserves the long-range part of the
interaction, and consequently the renormalization of long-range operators, such
as the quadrupole moment, the radius and 1/r, is small. This demonstrates that
low-energy observables in the deuteron are reproduced without short-range
correlations in the wave function.Comment: 29 pages, 19 figure
Convergence of the Born Series with Low-Momentum Interactions
The nonperturbative nature of nucleon-nucleon interactions as a function of a
momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This
investigation extends an earlier study of the perturbative convergence of the
Born series to partial waves beyond the 3S1-3D1 channel and to positive
energies. As the cutoff is lowered using renormalization-group or model-space
techniques, the evolution of nonperturbative features at large cutoffs from
strong short-range repulsion and the iterated tensor interaction are monitored
via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit
circle, the expansion of the scattering amplitude in terms of the interaction
is perturbative, with the magnitude of the largest eigenvalue setting the rate
of convergence. Major decreases in the magnitudes of repulsive eigenvalues are
observed as the Argonne v18, CD-Bonn or Nijmegen potentials are evolved to low
momentum, even though two-body observables are unchanged. For chiral EFT
potentials, running the cutoff lower tames the impact of the tensor force and
of new nonperturbative features entering at N3LO. The efficacy of separable
approximations to nuclear interactions derived from the Weinberg analysis is
studied as a function of cutoff, and the connection to inverse scattering is
demonstrated.Comment: 21 pages, 15 figures, minor additions, to appear in Nucl. Phys.
The Shell Model, the Renormalization Group and the Two-Body Interaction
The no-core shell model and the effective interaction can
both be derived using the Lee-Suzuki projection operator formalism. The main
difference between the two is the choice of basis states that define the model
space. The effective interaction can also be derived using
the renormalization group. That renormalization group derivation can be
extended in a straight forward manner to also include the no-core shell model.
In the nuclear matter limit the no-core shell model effective interaction in
the two-body approximation reduces identically to . The same
considerations apply to the Bloch-Horowitz version of the shell model and the
renormalization group treatment of two-body scattering by Birse, McGovern and
Richardson
Shelf and cycle life evaluation of silver-zinc cells
Silver-zinc cells having a separator system of cross-linked high-density polyethylene with a methacrylic acid graft withstand corrosion when subjected to thermal sterilization treatments
Storage battery comprising negative plates of a wedge shaped configuration
An improved silver-zinc battery particularly suited for use in an environment where battery operation is subjected to multiple charge/discharge cycling over extended periods is described. The battery seperator system, containing a highly absorbent material continguous with the surfaces of the plates and multiple semi-permeable membranes interposed between the plates, is also characterized
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