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Potential Approach to Scattering of Exotic Nuclei Goncharov S.A.
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Optical Model Potential approach: effective potential conception P→ single elastic channel
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Potential approach: effective potential conception Mean Field Potential (“MFP”) Dynamic Polarization Potential (“DPP”) Dispersive Relation
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Phenomenological (Woods-Saxon) Optical Model Potential f (x) = ( e x + 1 ) -1, x i = ( r – R i ) / a i (i=V,W,D)
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Semi-microscopic (or semi-phenomenological) approach Folding Model Microscopic calculation of the mean field potential, + Phenomenological construction of DPP Microscopic calculation of the mean field potential +
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“SNKE” – single nucleon knock-out exchange approximation Exchange effects – Khoa-Knyazkov SNKE Procedure Semi-microscopic approach Microscopic calculation of the mean field potential,
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Effective nucleon-nucleon interaction s = r p - r t + r “M3Y” z c =z so =1, z ten =s 2 (m=c,so,ten, n =D,E) Semi-microscopic approach Microscopic calculation of the mean field potential
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Imaginary part of DPP (“absorptive potential”) Semi-microscopic approach W(E), W D (E), α(Е), β(Е ) – free for all energies C onstruction of DPP Real part of DPP (“dispersive correction”) r W, a W, r D, a D – free but the same for all energies Microscopic calculations → rather qualitative information about different processes contributions in particular energy regions Phenomenological construction of DPP is still topical
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Since wide-used version of the semi-microscopic approach Semi-microscopic approach Semi-microscopic Dispersive Optical Model Potential More flexible form but less number of parameters, less ambiguity Explicit account for the dispersive relations Explicit energy and radial dependences of DPP, the role of the DPP contribution
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6 Li Density: by Zhukov et al.(“DZ”) 12 C Density from: Sorensen & Winter (“SW”) Semi-microscopic Dispersive Optical Model Potential As Applied To 6 Li+ 12 C Elastic Scattering Experimental data set: E lab = 30, 60, 90, 99, 156, 210 and 318 Mev J V (E)=J fold (E)+J P (E)
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6 He Density: by Zhukov et al.(“DZ”) 12 C Density from: Sorensen&Winter (“SW”) Semi-microscopic Dispersive Optical Model Potential As Applied To Evaluations of 6 He+ 12 C Elastic Scattering
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6 Li & 6 He Density: by Zhukov et al.(“DZ”) 4 He Density : gaussian Semi-microscopic Dispersive Optical Model Potential As Applied To 4 He+ 6 Li & 6 He+ 4 He Elastic Scattering Experimental data set: E 4He = 36.6, 50.4, 59.2, 104 & 166 Mev E 6He = 151 Mev (Ter-Akopyan et al.)
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Semi-microscopic Dispersive Optical Model Potential As Applied To 4 He+ 6 Li & 6 He+ 4 He Elastic Scattering Analysis of experimental data: E 4He = 104 Mev & E 6He = 151 Mev
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3 He, 3 H Density: by Efros et al. Comparative Analysis of Data Sets: 3 He+ 14 C at E lab = 72 MeV (E cm =59 MeV) & 14 C+ 3 H at E lab = 334MeV Semi-microscopic Dispersive Optical Model Potential As Applied To Isospin Effects in Elastic Scattering V i 3He – V i 3H
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Semi-microscopic Dispersive Optical Model Potential As Applied To Density Model Effects Comparative Evaluations of 6 He+ 3 He & 6 He+ 3 H Elastic Scattering “DZ” – solid “2pF” - dush 1– 3 He 2 – 3 H
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1– 3 He 2 – 3 H Semi-microscopic Dispersive Optical Model Potential As Applied To Density Model Effects Comparative Evaluations of 8 He+ 3 He & 8 He+ 3 H Elastic Scattering
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1 – 3 He 2 – 3 H Semi-microscopic Dispersive Optical Model Potential As Applied To Density Model Effects Comparative Evaluations of 8 B+ 3 He & 8 B+ 3 H Elastic Scattering
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