systematic study of fusion reactions leading to super-heavy nuclei ning wang ( ) guangxi normal...
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Systematic study of fusion reactions leading to super-heavy nuclei
Ning Wang ( 王宁 )
Guangxi Normal University
www.ImQMD.com/wangning/
Workshop on Synthesis of Super-heavy nuclei, August 10-13, 2012, Lanzhou
1. Introduction
2. Capture cross section
3. Survival probablity Wsur
4. Fusion probabilty PCN
5. Summary
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1) to study the three parts individually; 2) to estimate the model uncertainty
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I. Capture
II. Decay
III. Formation
# Coulomb Barrier (Skyrme EDF)
# Barrier Distribution
# Deformation & Dynamics … (ImQMD)
# Fission Barrier
# Masses & Shell corrections (mass formula)
# Fission Fragment Yields … (DNS)
# Quasi-Fission Barrier
# Potential Energy Surface
# Dynamics …
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I. Capture cross sections with the Skyrme energy-density functional
Density distributions of the reaction partners
Entrance-channel Coulomb barrier
Capture cross sections
Skyrme energy-density functional
Barrier penetration & empirical fusion barrier distribution D(B)
M. Liu, N. Wang, Z. Li, X. Wu and E. Zhao, Nucl. Phys. A 768 (2006) 80
Ning Wang, et al., Phys. Rev. C 74 (2006) 044604
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Woods-Saxon form for densities
Search for the minimum of energy by varying densities (R0p, R0n, ap, an)
according to Hohenberg-Kohn theorem
0 2 4 6 8 10 120.00
0.02
0.04
0.06
0.08
0.10
(f
m-3
)
r (fm)
p n
208Pb
1. Determination of density distributions
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E1E2
Sudden approximation for density
R
V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002).
2. Entrance-channel inter-nucleus potential
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8 12 1630
40
50
60
70
80
Vb (
MeV
)
R (fm)
28Si+92ZrB0
R0
3. Fusion (capture) cross section
with
D(B) considers the coupling between the relative motion and other degrees of freedom such as dyn. deform. etc.壳效应,形变效应,动力学效应
16O+208Pb, E=80MeV, ImQMD
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for reactions with nuclei near the beta-stability line but the neutron-shell is not closed
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The fusion excitation functions for a series of reactions with 16O bombarding on medium mass targets.
Wang et al. Sci China G 52, 1554 (2009)
suppression
enhancement
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50 55 60 65 70 75
0.0
0.1
0.2
0.3
50 60 70
0.0
0.1
0.2
70 80 90 100 110
0.0
0.1
0.2
24 28 32 36 40
0.0
0.2
0.4
D (
MeV
-1)
B (MeV)
Dder
Deff
16O+144Sm
(b)
D (
MeV
-1)
B (MeV)
Dder
Deff
16O+154Sm
(d)
D (
MeV
-1)
B (MeV)
Dder
with E=2.5
Dder
with E=4.0
Deff
19F+208Pb
(c)
D (
MeV
-1)
B (MeV)
Dder
Deff
12C+92Zr
(a)
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24 30 36 42 480.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
12C+92Zr
(a)40 50 60 70
0.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
16O+92Zr
(b)75 80 85 90 95 100
0.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
35Cl+92Zr
(d)70 80 90 100
0.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
33S+92Zr
(c)
40 48 56 640.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
16O+112Cd
(e)50 60 70 80 90
0.01
0.1
1
10
100
1000
fus
(mb)
Ec.m.
(MeV)
exp. calc.
16O+144Nd
(f)50 60 70 80 90 100
0.01
0.1
1
10
100
1000
exp. calc.
fus
(mb)
Ec.m.
(MeV)
16O+166Er
(g)
60 80 100 120 140 1600.01
0.1
1
10
100
1000
10000
fus
(mb)
Ec.m.
(MeV)
exp. B.B.Back exp. H.Q.Zhang calc.
16O+232Th
(h)
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75 90 105 1200.01
0.1
1
10
100
1000
10000
20 30 40 50 601
10
100
1000
100 110 120 130 140 1500.01
0.1
1
10
100
1000
100 120 140 160 1800.01
0.1
1
10
100
1000
10000
100 110 120 130 140 1500.01
0.1
1
10
100
1000
105 120 135 150 1650.01
0.1
1
10
100
1000
110 120 130 140 1500.01
0.1
1
10
100
1000
120 140 160 180 2000.1
1
10
100
1000
120 140 160 180 2000.01
0.1
1
10
100
1000
fus (m
b)
Ec.m.
(MeV)
exp. calc.
19F+197Au
(a)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
28Si+28Si
(b)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
28Si+178Hf
(c)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
28Si+198Pt
(d)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
29Si+178Hf
(e)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
30Si+186W
(f)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
31P+175Lu
(g)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
32S+181Ta
(h)
fus (m
b)
Ec.m.
(MeV)
exp. calc.
32S+182W
(i)
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60 70 80 900.01
0.1
1
10
100
1000
fus (
mb)
Ec.m.
(MeV)
exp. calc.
16O+186WDeviations from exp. data for 120 reactions
For about 70% systems, the deviations are smaller than 0.005, estimated systematic error 18%.
N. Wang et al., J. Phys. G: 34 (2007) 1935
rms deviation for (E>B0)
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II. Survival probability Wsur with HIVAP
The sensitive parameters:
1. fission barriers (Liquid-drop barriers, Sierk’s barriers…)
2. level density parameters (Fermi gas model, angular-momentum and shape-dependent)
3. masses shell corrections and particle separation energies
In the standard HIVAP code: ra=1.153fm
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Wang, Zhao, Scheid, Wu, PRC 77 (2008) 014603
Fusion-fission : EDF + HIVAP
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For 68% reactions, the deviations are smaller than 0.0714,
Estimated systematic errors of the HIVAP code: 1.85Wsur and Wsur /1.85
Deviations of calculated evaporation (and fission) cross sections from exp. data for 51 fusion-fission reactions
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A reliable nuclear mass formula is crucial for a description of the properties and production cross sections of super-heavy nuclei
WS : PRC 81 (2010) 044322
WS*: PRC 82 (2010) 044304
WS3: PRC 84 (2011) 014333
3). Masses of super-heavy nuclei
An improved nuclear mass formula
WS*
152
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Alpha-decay energies of super-heavy nuclei have been predicted
rms ~ 248 keV to 46 Qa of SHN
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H.F. Zhang, et al., Phys. Rev. C 85, 014325 (2012)
N=178
WS*
N=178
WS*
N=162 N=178
WS*
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B0
BfBqf
III. Fusion probability
E* also influences the results
水坝
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1) quasi-fission barrier
Wang, Tian, Scheid, PRC84, 061601(R) (2011)
Yu. Oganessian
Wang, et al, PRC77, 014603 (2008)
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Fusion probability
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2) Evaporation residual cross sections
Mean barrier height PRC84, 061601(R) (2011)
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Uncertainty at E>Bm : 1.18 (capture) x 1.85 (Wsur) x 2 (PCN) = 4.4
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Opt. 50Ti+249Bk 50Ti+249Cf 54Cr+248Cm 58Fe+244Pu
ZagrebaevPRC(2008) ~ 50 fb ~ 40 fb ~ 20 fb ~ 5 fb
Liu-BaoPRC(2011) ~ 600 fb ~ 100 fb
NasirovPRC(2011) ~ 100 fb ~ 70 fb
Ning Wang(王宁)PRC(2011)
~ 35 fb ~ 20 fb ~ 5 fb ~ 3 fb
Nan Wang (王楠)PRC(2012)
~ 110 fb ~ 50 fb ~ 6 fb ~ 4 fb
Siwek-WilczynskaPRC(2012)
~ 30 fb ~ 6 fb ~ 1 fb ~ 0.1 fb
exp. (GSI) < 70 fb < 200 fb (from talk of D. Ackermann)
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Summary
Models for calculations of capture cross sections, survival probability of compound nucleus and the fusion probability in fusion reactions leading to SHN have been tested step by step.
Coulomb barrier, fission barrier and quasi-fission barrier play important roles for the calculations of three parts.
More precise calculations for masses, fission barriers, fission fragment yields and the study of fusion dynamics are still required.
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China Institute of Atomic energy :Zhu-Xia Li 、 Xi-Zhen Wu 、 Kai Zhao (李祝霞) (吴锡真) (赵凯)
Institute of Theoretical Physics (CAS) : En-Guang Zhao (赵恩广)
Justus-Liebig-Univ. Giessen : Werner Scheid
Guangxi Normal Univ. Min Liu (刘敏)
Anyang Normal Univ. Jun-Long Tian (田俊龙)
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Fission fragment yields with driving potentialDNS:
En-Guang ZhaoShan-Gui ZhouJun-Qing LiNan Wang
Nuclear engineering
Nuclear structure
Fission cycle in nuclearastrophysics
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Thanks for your attention
Some codes and data are available at : www.ImQMD.com
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Kinetic Nuclear Coulomb
Skyrme energy-density functional
M. Brack, C. Guet, H.-B. Hakanson, Phys. Rep. 123, 275 (1985).
Skyrme force SkM*
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1). Fission barrier
Nuclei Cohen-Swiatecki Sierk Dahlinger MWS 244Pu 4.16 5.17 3.95 4.13 256No 1.74 1.44 1.02 1.19
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2). Level density parameters
In the standard HIVAP code: Ed=18.5MeV, ra=1.153fm
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Large-angle quasi-elastic scattering
PRC78, 014607 (2008)
Tail of the barrier distribution influences the large-angle quasi-elastic cross sections
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S. G. ZhouTail of barrier distribution influences the large-angle quasi-elastic cross sections