2,960 research outputs found
Subleading contributions to the three-nucleon contact interaction
We obtain a minimal form of the two-derivative three-nucleon contact
Lagrangian, by imposing all constraints deriving from discrete symmetries,
Fierz identities and Poincare' covariance. The resulting interaction, depending
on 13 unknown low-energy constants, leads to a three-nucleon potential which we
give in a local form in configuration space. We also consider the leading
(no-derivative) four-nucleon interaction and show that there exists only one
independent operator.Comment: 11 pages. Three more operators found after correcting some mistaken
Fierz relation
Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
For the first time, the inhomogeneous Bethe-Salpeter Equation for an
interacting system, composed by two massive scalars exchanging a massive
scalar, is numerically investigated in ladder approximation, directly in
Minkowski space, by using an approach based on the Nakanishi integral
representation. In this paper, the limiting case of zero-energy states is
considered, extending the approach successfully applied to bound states. The
numerical values of scattering lengths, are calculated for several values of
the Yukawa coupling constant, by using two different integral equations that
stem within the Nakanishi framework. Those low-energy observables are compared
with (i) the analogous quantities recently obtained in literature, within a
totally different framework and (ii) the non relativistic evaluations, for
illustrating the relevance of a non perturbative, genuine field theoretical
treatment in Minkowski space, even in the low-energy regime. Moreover,
dynamical functions, like the Nakanishi weight functions and the distorted part
of the zero-energy Light-front wave functions are also presented.
Interestingly, a highly non trivial issue related to the abrupt change in the
width of the support of the Nakanishi weight function, when the zero-energy
limit is approached, is elucidated, ensuring a sound basis to the forthcoming
evaluation of phase-shifts.Comment: 23 pages and 4 figures. Minor changes in the abstract, typos fixed
and added a figure. Submitted for publicatio
Breakup of three particles within the adiabatic expansion method
General expressions for the breakup cross sections in the lab frame for
reactions are given in terms of the hyperspherical adiabatic basis. The
three-body wave function is expanded in this basis and the corresponding
hyperradial functions are obtained by solving a set of second order
differential equations. The -matrix is computed by using two recently
derived integral relations. Even though the method is shown to be well suited
to describe processes, there are nevertheless particular configurations
in the breakup channel (for example those in which two particles move away
close to each other in a relative zero-energy state) that need a huge number of
basis states. This pathology manifests itself in the extremely slow convergence
of the breakup amplitude in terms of the hyperspherical harmonic basis used to
construct the adiabatic channels. To overcome this difficulty the breakup
amplitude is extracted from an integral relation as well. For the sake of
illustration, we consider neutron-deuteron scattering. The results are compared
to the available benchmark calculations
Coulomb effects in nucleon-deuteron polarization-transfer coefficients
Coulomb effects in the neutron-deuteron and proton-deuteron
polarization-transfer coefficients , ,
and are studied at energies above the deuteron breakup threshold.
Theoretical predictions for these observables are evaluated in the framework of
the Kohn Variational Principle using correlated basis functions to expand the
three-nucleon scattering wave function. The two-nucleon Argonne and
the three-nucleon Urbana IX potentials are considered. In the proton-deuteron
case, the Coulomb interaction between the two protons is included explicitly
and the results are compared to the experimental data available at
MeV. In the neutron-deuteron case, a comparison to a
recent measurement of by Hempen {\sl et al.} at MeV
evidences a contribution of the calculated Coulomb effects opposite to those
extracted from the experiment.Comment: 7 pages, 3 figure
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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