Extended optical model analyses of elastic scattering and fusion cross sections
description
Transcript of Extended optical model analyses of elastic scattering and fusion cross sections
Extended optical model analyses of elastic scattering and fusion cross sections
for 6, 7 Li + 208Pb systems at near-Coulomb-barrier energies
by using a folding potential
W. Y. So, T. Udagawa (University of Texas at Austin)K. S. Kim (Hankuk Aviation University)B. T. Kim, S.W.H (Sung Kyun Kwan University)
International Nuclear Physics ConferenceJune 6, 2007
Normalization of folding potential for elastic scattering
G. R. Satchler and W. G. Love, Phys. Lett. B76, 23 (1978).
7Li6Li
G. R. Satchler and W. G. Love, Phys. Rep. 55, 183 (1979).
Normalization of Double Folding Potential
Breakup threshold energies- 1.48 MeV for 6Li- 2.47 MeV for 7Li
Breakup effect in elastic scattering
Coupled Discretized Continuum Channel (CDCC) By including breakup channel (6Li + d) and using folding potential, it was shown1. Normalization of folding potential is no longer needed.2. Breakup coupling is repulsive at the surface causing N ~ 0.5.
6Li + 208Pb EB = 30 MeV
Sakuragi, Phys. Rev. C35, 2161 (1987)
Normalization of folding potential and threshold anomaly
• An experiment done at near-barrier energies.
6Li + 208Pb7Li + 208Pb
N. Keeley et al, Nucl. Phys. A571, 326 (1994)
Threshold anomaly No threshold anomaly
Simultaneous χ2 analyses using extended optical model
Simultaneous:- elastic scattering, - semi-experimental direct reaction, - fusion cross section data
Extended optical model: two types of complex polarization potentials;DR and fusion potentials
Folding potential will not be adjusted. (N=1)
el/ R
F
DR
Search 4 parameters VF , WF , VD, and WD (in UF and UD)
χ2-fitting
Extended optical model
U = Vc – [V0 + UF + UDR ]Ui = Vi + iWi (i = F or DR)
F= 2/(h v) < (+) | WF | (+) >DR= 2/(h v) < (+) | WDR | (+) >
Search 2 parametersVF , WF
χ2-fitting
Dispersion relation
rF=1.4 fm, rD=1.47 fm
Semi-experimental DR is obtained by a preliminary OM calculation
Energy dependency of DR and fusion potentials separately
(1) VF, WF, VD, WD: Dispersion relation is satisfied for DR and fusion potentials.
15 20 25 30 35 40 450
2
4
-2
0
2
4
6
Ec.m.
(MeV)
Wi (
i =
F,
D )
(M
eV
) i = F (Extracted) i = F (Th) i = D (Extracted) i = D (Th)
Vi (
i =
F,
D )
(M
eV
) 6Li + 208Pb
15 20 25 30 35 40 45 500
2
4
-2
0
2
4
Ec.m.
(MeV)
Wi (
i =
F,
D )
(M
eV
)
7Li + 208Pb
i = F (Extracted) i = F (Th) i = D (Extracted) i = D (Th)
Vi (
i =
F,
D )
(M
eV
)
Results
Repulsive DR potential
1
10
1
1
1
1
0 30 60 90 120 150 180
1
28.1MeV
30.0MeV
33.9MeV
31.9MeV
PE
c.m.
(deg)
37.7MeV
42.6MeV
1
10
1
1
1
0 30 60 90 120 150 1801E-3
0.01
0.1
1
28. 2MeV
30.1MeV
34.0MeV
32.1MeV
PE
37.9MeV
c.m.
(2) Elastic cross sections 6Li + 208Pb 7Li + 208Pb
Data: Keely et al, Nucl Phys A571, 326 (1994)
(3) Reaction and fusion cross sections
Experimental Fexp taken from
6Li + 208Pb: Wu et al, PRC68, 44605 (2003)7Li + 209Bi : Dasgupta et al, PRC66, 41602 (2002), PRC70, 24606 (2004)
Real potential for 6Li + 208Pb
-Reduction of folding potential-
Disappearance of threshold anomaly(T.A.)?
• Weak T.A. in (dominating) DR potential
• Strong T.A. in (small) fusion potential
• Apparent disappearance of T.A. in total potential with loosely bound projectile.
• Separation of potential to DR and fusion parts shows T.A. (particularly in fusion).
Imaginary potentials at strong absorption radii
• The physical origin of the normalization factor for the folding potential is the repulsive DR dynamic polarization potential.
• The repulsive DR potential is consistent with CDCC calculations.
• Separation of the potential is needed to see the weak T.A. of dominating DR potential and strong T.A. of small fusion potential.
• Dispersion relation is satisfied for both DR and fusion potentials.
Summary