Arturo g mez camacho instituto nacional de investigaciones nucleares m xico
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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 g mez camacho instituto nacional de investigaciones nucleares m xico

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


Reduced reaction cross section

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


Arturo g mez camacho instituto nacional de investigaciones nucleares m xico

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.


Polarization potential

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


Arturo g mez camacho instituto nacional de investigaciones nucleares m xico

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


Fusion and direct reaction polarization potentials

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)


E f aguilera et al phys rev c79 021601 2009 e f aguilera et al phys rev lett 107 092701 2011

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)


Fusion and direct reaction polarization potentials1

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


Fusion and direct reaction cross sections

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 (+) >


Potential parameters

Potential parameters


Fusion potential barriers l 0

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


Effect of breakup on fusion cross section

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


Effect of breakup on fusion cross section1

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


Arturo g mez camacho instituto nacional de investigaciones nucleares m xico

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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