131 research outputs found
Weakly bound states with spin-isospin symmetry
We discuss weakly bound states of a few-fermion system having spin-isospin
symmetry. This corresponds to the nuclear physics case in which the singlet,
, and triplet, , scattering lengths are large with respect to
the range of the nuclear interaction. The ratio of the two is about
. This value defines a plane in which and can
be varied up to the unitary limit, and , maintaining its
ratio fixed. Using a spin dependant potential model we estimate the
three-nucleon binding energy along that plane. This analysis can be considered
an extension of the Efimov plot for three bosons to the case of three
-spin-isospin fermions.Comment: Proceedings of the 21st International Conference on Few-Body Problems
in Physics. May 18-22, 2015. Chicago, Illinois, US
Recombination rates from potential models close to the unitary limit
We investigate universal behavior in the recombination rate of three bosons
close to threshold. Using the He-He system as a reference, we solve the
three-body Schr\"odinger equation above the dimer threshold for different
potentials having large values of the two-body scattering length . To this
aim we use the hyperspherical adiabatic expansion and we extract the -matrix
through the integral relations recently derived. The results are compared to
the universal form, , for
different values of and selected values of the three-body parameter
. A good agreement with the universal formula is obtained after
introducing a particular type of finite-range corrections, which have been
recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the
validity of the above formula in the description of a very different system:
neutron-neutron-proton recombination. Our analysis confirms the universal
character of the process in systems of very different scales having a large
two-body scattering length
The harmonic hyperspherical basis for identical particles without permutational symmetry
The hyperspherical harmonic basis is used to describe bound states in an
--body system. The approach presented here is based on the representation of
the potential energy in terms of hyperspherical harmonic functions. Using this
representation, the matrix elements between the basis elements are simple, and
the potential energy is presented in a compact form, well suited for numerical
implementation. The basis is neither symmetrized nor antisymmetrized, as
required in the case of identical particles; however, after the diagonalization
of the Hamiltonian matrix, the eigenvectors reflect the symmetries present in
it, and the identification of the physical states is possible, as it will be
shown in specific cases. We have in mind applications to atomic, molecular, and
nuclear few-body systems in which symmetry breaking terms are present in the
Hamiltonian; their inclusion is straightforward in the present method. As an
example we solve the case of three and four particles interacting through a
short-range central interaction and Coulomb potential
Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
In chiral effective field theory the leading order (LO) nucleon-nucleon
potential includes two contact terms, in the two spin channels , and the
one-pion-exchange potential. When the pion degrees of freedom are integrated
out, as in the pionless effective field theory, the LO potential includes two
contact terms only. In the three-nucleon system, the pionless theory includes a
three-nucleon contact term interaction at LO whereas the chiral effective
theory does not. Accordingly arbitrary differences could be observed in the LO
description of three- and four-nucleon binding energies. We analyze the two
theories at LO and conclude that a three-nucleon contact term is necessary at
this order in both theories. In turn this implies that subleading three-nucleon
contact terms should be promoted to lower orders. Furthermore this analysis
shows that one single low energy constant might be sufficient to explain the
large values of the singlet and triplet scattering lengths.Comment: 5 pages, 3 figure
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