Ch. Elster, L. Hlophe TORUS collaboration Supported by: U.S. DOE

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Presentation transcript:

Towards a Faddeev Description of (d,p) Reactions: Separabilizaton of Optical Potentials Ch. Elster, L. Hlophe TORUS collaboration Supported by: U.S. DOE 9/18/2018

Reduce many-body to few-body problem Reactions of Interest: 3He (d,p) 4He  140Sn (d,p)141Sn  ? Ansatz: Reduce many-body to few-body problem Isolate important degrees of freedom in a reaction Keeping track of all relevant channels Connect back to the many-body problem Multiple scattering expansion d+A to be developed

Faddeev AGS (d,p) Reaction as three-body problem: p n A Elastic, breakup, rearrangement channels are included and fully coupled. Hamiltonian: H = H0 + Vnp + VnA + VpA Issues: Traditional Faddeev eqs do not consider target exitations Coulomb force for heavy nuclei: current calculations to not converge for Z ≥ 20

Including target excitations: Suggestion to extend Faddeev equations: Inclusion of target excitations Novel treatment of Coulomb in momentum space A.M. Mukhamedzhanov, V.Eremenko and A.I. Sattarov, arXiv:1206.3791 [nucl-th] Including target excitations: Formulation natural when transition amplitudes in sub-systems are separable. Reminder: t-matrices (= interactions summed up to all orders) from two-body subsystems are input to Faddeev amplitudes

Wood-Saxon functions in coordinate space Optical Potentials (phenomenological) for proton and neutron elastic scattering from nuclei: Wood-Saxon functions in coordinate space Example: Central part of CH89 optical potential Not a form that can be used in a Faddeev calculation in momentum space

n+48Ca CH89 cenral optical potential Our test case: n+48Ca CH89 cenral optical potential Steps for creating a separable t-matrix: 1. Fourier Transform Analytic in form of a series – lowest terms sufficient. 2. Separabilization via EST scheme Use in momentum space Use half-shell t-matrices as form factors at EST support points

EST Scheme: i,j give the rank Calculate matrix for given j,k and solve algebraic system of eqs. v|j := half-shell t-matrices at fixed energies Ek t-matrix exact those Ek =: EST support points EST separable t-matrix interpolates between the support points

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