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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)
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§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.
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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
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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;
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• 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
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Barrier distribution deduced from quasielastic scatering
※ is the transmission coefficient for angular momentum ;
•
※ the reflection coefficient of .
0 01T R
0T
0R
0l
0l
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※ 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
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Barrier distributions from elastic scattering
• N. Rowley et al., Phys. Lett. B373, 23 (1995)
1/ 2el
elR
d dD E
dE d
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Barrier distributions for tightly-bound projectiles
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• The results of tightly bound projectile can be taken as a reference for probing the break-up effects of weakly bound-projectiles on fusion
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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.
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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
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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
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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.
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Structures are very similar at high energies.
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• 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)
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-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
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-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
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-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
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-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
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• Conclusion 1:
Except some details, the barrier distributions derived from the data of fusion and elastic/quasielastic scattering are almost the same.
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• Barrier distributions for weakly bound projectiles
• The experiments were carried out at the HI-13 tandem accelerator at CIAE, Beijing;
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6,7Li are weakly bound stable light nuclei.
6
7
( ) 1.474
2.467
S Li MeV
S Li MeV
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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.
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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)
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Off-line measurements
0 2 4 6 8 10 12 14 160
5
10
15
20
25
210At
211At
Cou
nts
Ec.m.
(MeV)
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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)
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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.
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E=33MeV
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• 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.
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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
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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
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• The tightly bound system 16O+208Pb can be taken as a reference for study of breakup effects.
2
fusB
B
E EE V
R
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0
2
4
6
8
10
12
14
16
18
(a)
fu
sE/(R
B
2 )/M
eV
16O+208Pb
6Li+208Pb
9Be+208Pb
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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
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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)
![Page 47: 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](https://reader035.vdocuments.mx/reader035/viewer/2022062321/56649f155503460f94c2a6c4/html5/thumbnails/47.jpg)
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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
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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
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• 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.
![Page 51: 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](https://reader035.vdocuments.mx/reader035/viewer/2022062321/56649f155503460f94c2a6c4/html5/thumbnails/51.jpg)
Thanks!