1,880 research outputs found
Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials
The integral relations formalism introduced in \cite{bar09,rom11}, and
designed to describe 1+ reactions, is extended here to collision energies
above the threshold for the target breakup. These two relations are completely
general, and in this work they are used together with the adiabatic expansion
method for the description of 1+2 reactions. The neutron-deuteron breakup, for
which benchmark calculations are available, is taken as a test of the method.
The s-wave collision between the He atom and He dimer above the
breakup threshold and the possibility of using soft-core two-body potentials
plus a short-range three-body force will be investigated. Comparisons to
previous calculations for the three-body recombination and collision
dissociation rates will be shown.Comment: To be published in Physical Review
General integral relations for the description of scattering states using the hyperspherical adiabatic basis
In this work we investigate 1+2 reactions within the framework of the
hyperspherical adiabatic expansion method. To this aim two integral relations,
derived from the Kohn variational principle, are used. A detailed derivation of
these relations is shown. The expressions derived are general, not restricted
to relative partial waves, and with applicability in multichannel
reactions. The convergence of the -matrix in terms of the adiabatic
potentials is investigated. Together with a simple model case used as a test
for the method, we show results for the collision of a He atom on a \dimer
dimer (only the elastic channel open), and for collisions involving a Li
and two He atoms (two channels open).Comment: Accepted for publication in Physical Review
Variational description of continuum states in terms of integral relations
Two integral relations derived from the Kohn Variational Principle (KVP) are
used for describing scattering states. In usual applications the KVP requires
the explicit form of the asymptotic behavior of the scattering wave function.
This is not the case when the integral relations are applied since, due to
their short range nature, the only condition for the scattering wave function
is that it be the solution of in the internal region.
Several examples are analyzed for the computation of phase-shifts from bound
state type wave functions or, in the case of the scattering of charged
particles, it is possible to obtain phase-shifts using free asymptotic
conditions. As a final example we discuss the use of the integral relations in
the case of the Hyperspherical Adiabatic method.Comment: 34 pages, 7 figures, accepted in Phys. Rev.
Bethe-Salpeter bound-state structure in Minkowski space
The quantitative investigation of the scalar Bethe-Salpeter equation in
Minkowski space, within the ladder-approximation framework, is extended to
include the excited states. This study has been carried out for an interacting
system composed by two massive bosons exchanging a massive scalar, by adopting
(i) the Nakanishi integral representation of the Bethe-Salpeter amplitude, and
(ii) the formally exact projection onto the null plane. Our analysis, on one
hand, confirms the reliability of the method already applied to the ground
state and, on the other one, extends the investigation from the valence
distribution in momentum space to the corresponding quantity in the
impact-parameter space, pointing out some relevant features, like (i) the
equivalence between Minkowski and Euclidean transverse-momentum amplitudes, and
(ii) the leading exponential fall-off of the valence wave function in the
impact-parameter space.Comment: 15 pages, 7 figure
Benchmark calculation of p-3H and n-3He scattering
p-3H and n-3He scattering in the energy range above the n-3He but below the
d-d thresholds is studied by solving the 4-nucleon problem with a realistic
nucleon-nucleon interaction. Three different methods -- Alt, Grassberger and
Sandhas, Hyperspherical Harmonics, and Faddeev-Yakubovsky -- have been employed
and their results for both elastic and charge-exchange processes are compared.
We observe a good agreement between the three different methods, thus the
obtained results may serve as a benchmark. A comparison with the available
experimental data is also reported and discussed.Comment: 13 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1109.362
Total cross section for p-d breakup below 30 MeV
The total cross section for p-d breakup is studied in terms of the elastic S-matrix through the unitary condition. Calculations using the complex Kohn variational method along with the Pair Correlated Hyperspherical Harmonic basis are presented. The results have been restricted to energies below Ep=30 MeV where Coulomb effects are expected to be sizable and are compared to the existing data. Two different measurements have been found in the literature: 40 years ago, Gibbons and Macklin (1959); and 26 years ago, Carlosn et al. (1973). The calculations are found to be in reasonable agreement with these old data, though a discrepancy is observed near the deuteron breakup threshold. Moreover, a detailed analysis of the contributions to the observable from different partial waves has been presented. Unexpectedly, the main contribution for a wide range of energies has been detected in the J=3/2- state
Restricted infinitesimal deformations of restricted simple Lie algebras
We compute the restricted infinitesimal deformations of the restricted simple
Lie algebras over an algebraically closed field of characteristic different
from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its
Application
Realistic Calculation of the hep Astrophysical Factor
The astrophysical factor for the proton weak capture on 3He is calculated
with correlated-hyperspherical-harmonics bound and continuum wave functions
corresponding to a realistic Hamiltonian consisting of the Argonne v18
two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak charge
and current operators have vector and axial-vector components, that include
one- and many-body terms. All possible multipole transitions connecting any of
the p-3He S- and P-wave channels to the 4He bound state are considered. The
S-factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak
energy, is predicted to be 10.1 10^{-20} keV b, a factor of five larger than
the standard-solar-model value. The P-wave transitions are found to be
important, contributing about 40 % of the calculated S-factor.Comment: 8 pages RevTex file, submitted to Phys. Rev. Let
The Three-Nucleon System Near the N-d Threshold
The three-nucleon system is studied at energies a few hundred keV above the
N-d threshold. Measurements of the tensor analyzing powers and
for p-d elastic scattering at keV are presented
together with the corresponding theoretical predictions. The calculations are
extended to very low energies since they are useful for extracting the p-d
scattering lengths from the experimental data. The interaction considered here
is the Argonne V18 potential plus the Urbana three-nucleon potential. The
calculation of the asymptotic D- to S-state ratio for H and He, for
which recent experimental results are available, is also presented.Comment: Latex, 11 pages, 2 figures, to be published in Phy.Lett.
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