Breakup effects of weakly bound nuclei on the

fusion reactions

C.J. Lin, H.Q. Zhang, F. Yang, Z.H. Liu, X.K. Wu, P. Zhou, C.L. Zhang, G.L. Zhang, G.P. An, H.M. Jia, and X.X. Xu

(China Institute of Atomic Energy)

§Dynamics of both fusion and elastic scattering are influenced by coupling to direct-reaction channels (including breakup if the projectile and/or target nuclei are weakly bounded);

§These couplings generate a distribution of potential barriers;

§Barrier distributions can derived from the excitation functions of fusion and elastic (or quasielastic) scattering.

Barrier distributions extracted from fusion excitation functions

N. Rowley et al., Phys. Lett. B254, 25(1991)

2 2

1fus fus

f

dD E E E

R dE

48Ca+90,96Zr fusion

◆The experiment was carried out at the XTU Tandem accelerator of Legnaro National Laboratory, Legnaro Italy;◆ The evaporation residues (ER) were s

eparated from the background of beam and beam-like particles by means of an electrostatic deflector;

• The energy ranges are :

for 48Ca+90Zr

for 48Ca+96Zr

in 0.5 MeV energy steps.

. .

. .

90.7 98.5

88.6 97.6c m

c m

MeV E MeV

MeV E MeV

Barrier distribution deduced from quasielastic scatering

※ is the transmission coefficient for angular momentum ;

•

※ the reflection coefficient of .

0 01T R

0T

0R

0l

0l

※ is the quasielastic differential cross section at back angles.

• H. Timmer et al., Nucl. Phys. A584,

190(1995)

qel

qelR

d dD E E

dE d

qel

Barrier distributions from elastic scattering

• N. Rowley et al., Phys. Lett. B373, 23 (1995)

1/ 2el

elR

d dD E

dE d

Barrier distributions for tightly-bound projectiles

• The results of tightly bound projectile can be taken as a reference for probing the break-up effects of weakly bound-projectiles on fusion

Barrier distributions for 16O+152Sm quasielastic scattering

※ The experiment was carried out with 16O beam from the HI-13 tandem accelerator at CIAE, Beijing;

※ Three gas-ionization chambers set at 1560,1600,1640 were used to measure scattering particles.

45 50 55 60 65 70

0.00

0.04

0.08

0.12

0.16

Dqe

l (M

eV-1)

Ec.m.

(MeV)

fusion

1560

1600

1640

1700

16O+152Sm

quasi-elastic

50 55 60 65 70

0.00

0.05

0.10

0.15

0.20

Del (

MeV

-1)

Ec.m.

(MeV)

fusion

1560

1600

1640

1700

16O+152Sm

elastic

32S+90,96Zr experiment

※ The excitation functions of quasielastic scattering were measured at back angles.

※ The barrier distributions for these two systems are compared.

※ The influence of neutron transfer on the barrier of 32S+96Zr are observed. This system have positive Q-values for 1n, 2n, and 4n neutron transfer.

Structures are very similar at high energies.

• Comparison of the barrier height distributions obtained from excitation functions of fusion and elastic scattering for more systems. (N. Rowley et al., Phys. Lett. B 373(1996)23)

-0.2 -0.1 0.0 0.10.0

0.1

0.2

Del

,fus

(E)

(MeV

-1)

(E-B0)/B

0

fusion data elastic data

16O+154Sm

-0.2 -0.1 0.0 0.10.00

0.05

0.10

0.15

Del

,fus

(E)

(MeV

-1)

(E-B0)/B

0

fusion data elastic data

16O+186W

-0.10 -0.05 0.00 0.05 0.10 0.150.00

0.05

0.10

0.15

0.20

0.25

Del

,fus

(E)

(MeV

-1)

(E-B0)/B

0

fusion data elastic data

16O+144Sm

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.150.00

0.04

0.08

0.12

0.16

0.20

Del

,fus

(E)

(MeV

-1)

(E-B0)/B

0

elastic data fusion data

18O+208Pb

• Conclusion 1:

Except some details, the barrier distributions derived from the data of fusion and elastic/quasielastic scattering are almost the same.

• Barrier distributions for weakly bound projectiles

• The experiments were carried out at the HI-13 tandem accelerator at CIAE, Beijing;

6,7Li are weakly bound stable light nuclei.

6

7

( ) 1.474

2.467

S Li MeV

S Li MeV

6Li+208Pb fusion

• The compound nucleus 214At formed following complete fusion de-excites dominantly through 1n, 2n, 3n, 4n evaporation resulting residue 213-210At. These Nuclei are particle emitters. Their half-life time and energies are known.

On-line measurements

0 2 4 6 8 10 12 14 160

50

100

150

200

211At+210At

212At+211At

213At

C

ou

nts

Ec.m.

(MeV)

Off-line measurements

0 2 4 6 8 10 12 14 160

5

10

15

20

25

210At

211At

Cou

nts

Ec.m.

(MeV)

24 26 28 30 32 34 36 38 40 42

10-1

100

101

102

103

fusion+fission fission

3-,5- in 208Pb,3+ in 6Li

3-,5- in 208Pb no coupling

fus(m

b)

Ec.m.

(MeV)

Elastic and breakup experiment

The experiments were carried out at the HI-13 tandem accelerator at CIAE, Beijing with 6,7Li beams bombarding 208Pb target. The detector system arrangement is similar to 16O+152Sm experiment.

E=33MeV

• Conclusion 2: For the weakly bound projectiles, the

Barrier distributions extracted from the data of (complete) fusion and scattering are different, but nearly the same if the contributions of breakup are added into the differential cross sections of quasielastic scattering.

Possible Reason

Barrier distribution is a good probe for the breakup effects on fusion and elastic scattering.

'0 0 01 1 ( )rT R R B

Complete fusion of weakly bound nuclei at above barrier energies

Fusion cross section of tightly-bound nuclei can be satisfactory described with the semi-classical approach formula at above barrier energies:

2 1 Bfus B

VE R

E

• The tightly bound system 16O+208Pb can be taken as a reference for study of breakup effects.

2

fusB

B

E EE V

R

0

2

4

6

8

10

12

14

16

18

(a)

fu

sE/(R

B

2 )/M

eV

16O+208Pb

6Li+208Pb

9Be+208Pb

0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

14

16

18

fusE

c.m

./R

B

2 (M

eV)

E-VB/MeV

16O+208Pb

9Be+209Bi

6Li+209Bi

24 26 28 30 32 34 36 38 40 42

10-1

100

101

102

103

fusion+fission fission

3-,5- in 208Pb,3+ in 6Li

3-,5- in 208Pb no coupling

fus(m

b)

Ec.m.

(MeV)

Complete fusion and total fusion

※ For weakly bound-projectile, the total fusion cross section is the sum of the complete fusion and partial fusion cross sections, .

※ The fusion of weakly bound nuclei is suppressed at the above barrier energies.

CF INF

0 5 10 15 200

5

10

15

20

fusE

/(R

B

2 )/M

eV

E-VB/MeV

16O+208Pb

6Li+209Bi

6Li+209Bi total

9Be+208Pb

9Be+208Pb total

• Conclusion 3:◆ The complete fusion of weakly bound

projectile with heavy target is suppressed, whereas in most cases breakup has very little effects on the total fusion at the above barrier energies;

◆ This result indicates that partial fusion of weakly bound nuclei most likely takes place near the absorption region.

Thanks!