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