Some applications of the Faddeev-Yakubovsky equations to the cold-atom physics

We present some recent applications of the Faddeev--Yakubovsky equations in describing atomic bound and scattering problems. We consider the scattering of a charged particle $X$ by atomic hydrogen with special interest in $X=p,e^{\pm}$, systems of cold bosonic molecules and the bound and scattering properties of N=3 and N=4 atomic $^4$He multimers

Three-nucleon hadronic and electromagnetic reactions with [Delta]-isobar excitations

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Recombination in the universal four-fermion system

In the systems of spin 1 2 fermions with resonant S-wave interactions supporting only weakly bound dimers the antisymmetry forbids recombination of three (or more) fermions at zero energy. However, the fermion-fermion-dimer recombination is only partially suppressed. It is studied in the framework of momentum-space integral equations for the four-particle transition operators. In the vicinity of the unitary limit the fermion-fermion-dimer recombination rate, rescaled to build dimensionless quantity, is found to be linear in the effective range parameter, enabling a simple and accurate parametrization as well as evaluation of finite-range effects for any potential model. This feature makes the present results very useful in benchmarking different methods for three-cluster breakup and recombination calculations in four-particle systems. The interplay of the three-fermion and fermion-fermion-dimer recombination processes and their consequences for ultracold mixtures of fermions and dimers is discussed

Reactions in the four-nucleon system above breakup threshold

Microscopic calculations of four-body scattering become very challenging in the energy regime above the threshold for four free particles. We consider mixed-isospin four-nucleon reactions initiated by the proton-3H, neutron-3He, or deuteron-deuteron collisions. We solve the Alt, Grassberger, and Sandhas equations for the four-nucleon transition operators in the momentum-space framework. The complex-energy method with special integration weights is applied to deal with the complicated singularities in the kernel of AGS equations. Results for the differential cross section and spin observables in elastic, charge-exchange, transfer, and breakup reactions using realistic potentials are presented

Merging first principle structure studies and few-body reaction formalism

Calculations for nucleon knockout from a 7Li beam due to the collision with a proton target at 400 MeV/u are shown based on ab initio Quantum Monte Carlo (QMC) and conventional shell-model nuclear structure approaches to describe the relative motion between the knockout particle and the heavy fragment of the projectile. Structure effects on the total cross section are shown

Many-body effects in (p,pN) reactions within a unified approach

We study knockout reactions with proton probes within a theoretical framework where ab initio Quantum Monte Carlo (QMC) wave functions are combined with the Faddeev/Alt-Grassberger-Sandhas few-body reaction formalism. QMC wave functions are used to describe 12C, yielding, for the first time, results consistent with the experimental root mean square (rms) point proton radii, (p,2p) total cross section data, as well as momentum distributions compatible with electron scattering data analysis. In our results for A≤12 and (N−Z)≤3 nuclei the ratios between the (i) theoretical cross sections evaluated using QMC and simple Shell Model structure inputs, and (ii) the corresponding ratios between the spectroscopic factors, summed over states below particle emission, are smaller than unity, pointing to the shortcomings of the simple Shell Model. This quenching is more significant for the knockout of the more correlated nucleon of the deficient species. These ratios can be represented reasonably well by a linear combination of the separation energy and the difference between the removed nucleon rms radius in the parent and residual nuclei, showing a mild dependence on these physical quantities

A comprehensive study of analyzing powers in the proton–deuteron break-up channel at 135 MeV

A measurement of the analyzing powers for the 2H (p→ , pp) n break-up reaction was carried out at KVI exploiting a polarized-proton beam at an energy of 135MeV. The scattering angles and energies of the final-state protons were measured using the Big Instrument for Nuclear-polarization Analysis (BINA) with a nearly 4 π geometrical acceptance. In this work, we analyzed a large number of kinematical geometries including forward–forward configurations in which both the final-state particles scatter to small polar angles and backward–forward configurations in which one of the final-state particles scatters to large polar angles. The results are compared with Faddeev calculations based on modern nucleon–nucleon (NN) and three-nucleon (3N) potentials. Discrepancies between polarization data and theoretical predictions are observed for configurations corresponding to small relative azimuthal angles between the two final-state protons. These configurations show a large sensitivity to 3N force effects