Bound state techniques to solve the multiparticle scattering problem

Abstract

Solution of the scattering problem turns to be very difficult task both from the formal as well as from the computational point of view. If the last two decades have witnessed decisive progress in ab initio bound state calculations, rigorous solution of the scattering problem remains limited to A$\le$4 case. Therefore there is a rising interest to apply bound-state-like methods to handle non-relativistic scattering problems. In this article the latest theoretical developments in this field are reviewed. Five fully rigorous methods will be discussed, which address the problem of nuclear collisions in full extent (including the break-up problem) at the same time avoiding treatment of the complicate boundary conditions or integral kernel singularities. These new developments allows to use modern bound-state techniques to advance significantly rigorous solution of the scattering problem.

To appear in Progress in Particle and Nuclear Physics

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• Probing the resonance of Dirac particle by the application of complex momentum representation
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• The quest for light multineutron systems
• Description of Four- and Five-Nucleon Systems by Solving Faddeev-Yakubovsky Equations in Configuration Space
• Probing the resonance in the Dirac equation with quadruple-deformed potentials by complex momentum representation method
• Four-body calculation of ${}^2\mathrm{H}(d,p){}^3\mathrm{H}$ and ${}^2\mathrm{H}(d,n){}^3\mathrm{He}$ reactions above breakup threshold
• Four-body calculation of elastic deuteron-deuteron scattering
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• Virtual states in the coupled-channel problems with an improved complex scaling method
• Proton-${}^3$H scattering calculation: Elastic and charge-exchange reactions up to 30 MeV
• Neutron-deuteron scattering cross-sections with chiral $NN$ interactions using wave-packet continuum discretization
• Energy Resolution with the Lorentz integral transform
• Nucleon-nucleon scattering with the Complex Scaling Method and realistic interactions
• New general approach in few-body scattering calculations: Solving discretized Faddeev equations on a graphics processing unit
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• Broad resonances and beta-decay
• Spectral function for ${}^4$He using the Chebyshev expansion in coupled-cluster theory
• Fast GPU-based calculations in few-body quantum scattering
• Perspectives on few-body cluster structures in exotic nuclei
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• Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-Like Calculations
• Calculation of the astrophysical S-factor S_12 with the Lorentz integral transform
• Posterior predictive distributions of neutron-deuteron cross sections
• Application of the complex scaling method in solving three-body Coulomb scattering problem
• Complex-scaled no-core shell model calculations of bound and unbound nuclear states in light nuclei
• Physics of many-body resonances with complex scaling and applications to light unstable nuclei