36 research outputs found
Generalized Faddeev equations in the AGS form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
Theoretical description of reactions in general, and the theory for
reactions, in particular, needs to advance into the new century. Here deuteron
stripping processes off a target nucleus consisting of nucleons are
treated within the framework of the few-body integral equations theory. The
generalized Faddeev equations in the AGS form, which take into account the
target excitations, with realistic optical potentials provide the most advanced
and complete description of the deuteron stripping. The main problem in
practical application of such equations is the screening of the Coulomb
potential, which works only for light nuclei. In this paper we present a new
formulation of the Faddeev equations in the AGS form taking into account the
target excitations with explicit inclusion of the Coulomb interaction. By
projecting the -body operators onto target states, matrix three-body
integral equations are derived which allow for the incorporation of the excited
states of the target nucleons. Using the explicit equations for the partial
Coulomb scattering wave functions in the momentum space we present the AGS
equations in the Coulomb distorted wave representation without screening
procedure. We also use the explicit expression for the off-shell two-body
Coulomb scattering -matrix which is needed to calculate the effective
potentials in the AGS equations. The integrals containing the off-shell Coulomb
T-matrix are regularized to make the obtained equations suitable for
calculations. For and nucleon-target nuclear interactions we assume the
separable potentials what significantly simplifies solution of the AGS
equations.Comment: 34 pages, 13 figure
Momentum Space Integral Equations for Three Charged Particles: Diagonal Kernels
It has been a long-standing question whether momentum space integral
equations of the Faddeev type are applicable to reactions of three charged
particles, in particular above the three-body threshold. For, the presence of
long-range Coulomb forces has been thought to give rise to such severe
singularities in their kernels that the latter may lack the compactness
property known to exist in the case of purely short-range interactions.
Employing the rigorously equivalent formulation in terms of an
effective-two-body theory we have proved in a preceding paper [Phys. Rev. C
{\bf 61}, 064006 (2000)] that, for all energies, the nondiagonal kernels
occurring in the integral equations which determine the transition amplitudes
for all binary collision processes, possess on and off the energy shell only
integrable singularities, provided all three particles have charges of the same
sign, i.e., all Coulomb interactions are repulsive. In the present paper we
prove that, for particles with charges of equal sign, the diagonal kernels, in
contrast, possess one, but only one, nonintegrable singularity. The latter can,
however, be isolated explicitly and dealt with in a well-defined manner. Taken
together these results imply that modified integral equations can be
formulated, with kernels that become compact after a few iterations. This
concludes the proof that standard solution methods can be used for the
calculation of all binary (i.e., (in-)elastic and rearrangement) amplitudes by
means of momentum space integral equations of the effective-two-body type.Comment: 36 pages, 2 figures, accepted for publication in Phys. Rev.
Concept for the Antiproton Production Target at FAIR
This report summarizes the status of the antiproton (pbar) production area at the future FAIR (Facility for Antiproton and Ion Research) complex at GSI, Darmstadt [1]. This area is composed of the pbar production target, a magnetic horn for the collection of the pbars, and the pbar separator between target and Collector Ring (CR). The emphasis is on the optimization of the accumulation rate of antiprotons to maximize the expected peak and average luminosity for the experiment. As the doses in the target area will be very high, also radiation protection issues will be addressed