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Arturo Gómez Camacho Instituto Nacional de Investigaciones Nucleares, México

Fusion radial potential barriers for 8 B+ 58 Ni from a simultaneous optical model analysis of elastic scattering and fusion data. Arturo Gómez Camacho Instituto Nacional de Investigaciones Nucleares, México. Reduced reaction cross section. Reduced energy E Red = E / γ where

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Arturo Gómez Camacho Instituto Nacional de Investigaciones Nucleares, México

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  1. Fusion radial potential barriers for 8B+58Ni from asimultaneous optical model analysis of elastic scattering and fusion data Arturo Gómez Camacho Instituto Nacional de Investigaciones Nucleares, México

  2. Reduced reaction cross section Reduced energy ERed = E / γ where γ = ZpZT / RpT with RpT =A11/3+A21/3 Wong Reduced cross section σRed =σ / R2pT V0 = γ VRed , R0 = RpTrob , ℏω0 = ε0γ

  3. Contents. Fusion potential barriers are determined from a simultaneous analysis of the elastic scattering and fusion cross section data for 8B+58Ni. The analysis uses fusion and direct reaction Woods-Saxon polarization potentials, UF = VF + iWF and UDR = VDR + iWDR, that respectively account for fusion and direct reaction couplings. VF and WF , as well as , VDR and WDR are linked by the dispersion relation. The potential parameters of VF , WF and VDR , WDR are calculated during the simultaneous fitting of the data. It is found that the calculated fusion polarization potential VF “pushes” the barriers to larger distances respect to the Coulomb barrier. 8B-Halo structure VDR results a repulsive potential that hinders fusion, particularly at the lowest energies. The net effect of break-up couplings on the fusion cross section is studied by analyzing the separate effect of VDR and WDR.

  4. Polarization Potential [ T + V ( E ) ] χ(+) = E χ(+) Dynamic Polarization potential ΔU ( E ) = ΔV ( E ) + iW( E ) Represents the effects on elastic scattering of couplings between the elastic and non-elastic channels. V (E) = V0 + ΔU (E) V0 ( r ) Static average nuclear potential ΔV ( E ) arises from virtual excitations to these non- elastic channels W describes the actual loss of flux into them

  5. Energy dependence of polarization potential. Threshold Anomaly ( Tightly bound systems ) 16O+208Pb Polarization potential ΔU (E) = ΔV(E) + iW(E) attractive with V (E) = V0 + ΔV (E) ΔV(E) Dispersion relation W(E) ←closing of reaction channels VB

  6. Fusion and direct reaction polarization potentials Polarization potential Upol ( r, E ) = UF ( r, E ) + UDR ( r, E ) Fusion polarization potential UF ( r,E ) = ΔVF ( r,E ) + i WF ( r,E ) Direct reaction polarization potential UDR ( r,E ) = ΔVDR ( r,E ) + i WDR ( r,E ) [ T + V ] χ(+) = E χ(+) V ( r, E ) = Vcoul ( r ) - Vbare ( r ) - Upol (r, E)

  7. Polarization potentials for 8B+58Ni from simultaneous χ2-analysis to elastic and fusion data E.F. Aguilera et al., Phys. Rev. C79, 021601 (2009)E.F. Aguilera et al., Phys. Rev. Lett, 107, 092701 (2011)

  8. Fusion and direct reaction polarization potentials Fusion polarization potential UF ( r,E ) = ΔVF ( r,E ) + i WF ( r,E ) Woods-Saxon volume shape Δ Ri = ri (A11/3+A21/3) DR polarization potential UDR (r,E) = ΔVDR (r,E) + iWDR (r,E) Woods-Saxon surface shape Δ

  9. Fusion and direct reaction cross sections Fusion and direct reaction cross sections σi (E) = 2 / ( ℏv ) < χ (+) | Wi ( E ) | χ(+)> ; i = F, DR Total reaction cross section σR ( E ) = 2 / ( ℏv ) < χ(+) | WF ( E )+WDR ( E ) | χ (+) >

  10. Potential parameters

  11. Fusion potential barriers (l = 0) V( r, E ) = Vcoul ( r ) – Vbare ( r ) - VF ( r, E ) - VDR ( r, E ) Barrier position { d V / dr }RB = 0 barrier height VB = V ( RB ) Nominal barrier → RB = 9.3 fm VB ≈ 20.8 MeV Parabolic approx. V( r )=VB - ( ½ ) μω2 ( r – RB ) 2 ℏω0 = ( ℏ / μ ) [ d 2V ( r ) / dr 2 ]1/2R0 = 5.3 MeV

  12. Effect of breakup on fusion cross section Effects of barrier lowering and rising due to VF and VDR real polarization potentials →VDR = 0, ≠ 0 → Nominal barrier

  13. Effect of breakup on fusion cross section Effects of barrier rising ( VDR ) and loss of flux ( WDR ) into DR reactions Blanco →VDR = 0, WDR≠ 0 VDR ≠ 0, WDR = 0 VDR ≠ 0, WDR ≠ 0

  14. Summary Fusion potential barriers for 8B+58Ni have been obtained from fusion and direct reaction polarization potentials. The parameters of the Wodds-Saxon fusion and direct reaction polarization potentials are determined from a simultaneous analysis of elastic scattering and fusion data Mainly by the action of the fusion polarization potential, the barrier is displaced to larger distances from the nominal barrier. The effect on the barrier from the attractive fusion and repulsive direct reaction polarization potentials has been studied The net effect of breakup reactions on fusion cross sections is obtained from the individual effects from barrier raising produced by VDR and the loss of flux into direct reactions accounted for by WDR

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