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Register a new userThree-Body Scattering Below Breakup Threshold: An Approach without using Partial Waves
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The Faddeev equation for three-body scattering below the three-body breakup threshold is directly solved without employing a partial wave decomposition. In the simplest form it is a three-dimensional integral equation in four variables. From its solution the scattering amplitude is obtained as function of vector Jacobi momenta. Based on Malfliet-Tjon type potentials differential and total cross sections are calculated. The numerical stability of the algorithm is demonstrated and the properties of the scattering amplitude discussed.
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We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A,(a,b),X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80s by Ichimura, Autern and Vincent (IAV) cite{IAV1985}, Udagawa and Tamura (UT) cite{UT1981} and Hussein and McVoy (HM) cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.
Deuteron-deuteron elastic scattering and transfer reactions in the energy regime above four-nucleon breakup threshold are described by solving exact four-particle equations for transition operators. Several realistic nuclear interaction models are used, including the one with effective many-nucleon forces generated by the explicit $Delta$-isobar excitation; the Coulomb force between protons is taken into account as well. Differential cross sections, deuteron analyzing powers, outgoing nucleon polarization, and deuteron-to-neutron polarization transfer coefficients are calculated at 10 MeV deuteron energy. Overall good agreement with the experimental data is found. The importance of breakup channels is demonstrated.
We report on the first calculation of the scattering length A_{K^-d} based on a relativistic three-body approach where the two-body input amplitudes coupled to the Kbar N channels have been obtained with the chiral SU(3) constraint, but with isospin symmetry breaking effects taken into account. Results are compared with a recent calculation applying a similar set of two-body amplitudes,based on the fixed center approximation, considered as a good approximation for a loosely bound target, and for which we find significant deviations from the exact three-body results. Effects of the hyperon-nucleon interaction, and deuteron $D$-wave component are also evaluated.
Coulomb breakup strengths of 11Li into a three-body 9Li+n+n system are studied in the complex scaling method. We decompose the transition strengths into the contributions from three-body resonances, two-body ``10Li+n and three-body ``9Li+n+n continuum states. In the calculated results, we cannot find the dipole resonances with a sharp decay width in 11Li. There is a low energy enhancement in the breakup strength, which is produced by both the two- and three-body continuum states. The enhancement given by the three-body continuum states is found to have a strong connection to the halo structure of 11Li. The calculated breakup strength distribution is compared with the experimental data from MSU, RIKEN and GSI.
The Faddeev equations for the three body bound state are solved directly as three dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three body binding energy is calculated for Malfliet-Tjon type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schrodinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects.
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