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
Guangxi Normal University
www.ImQMD.com/wangning/
BLTP/JINR-KLFTP/CAS Joint Workshop on Nuclear Physics, Aug. 2-6, 2012, Dubna
1. Introduction
2. capture cross sections
3. Survival probablity Wsur
4. Fusion probabilty PCN
5. Conclusion
I. Capture cross sections with the Skyrme energy-density functional
Density distributions of the reaction partners
Entrance-channel fusion barrier
Fusion 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
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
E1E2
Sudden approximation for density
R
V.Yu. Denisov and W. Noerenberg, Eur. Phys. J. A15, 375 (2002).
2. Entrance-channel fusion barrier
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.
16O+208Pb, E=80MeV, ImQMD
for reactions with nuclei near the beta-stability line but the neutron-shell is not closed
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)
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)
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)
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)
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
About 70% systems are less than 0.005, which gives the system error 18%.
N. Wang et al., J. Phys. G: 34 (2007) 1935
rms deviation for (E>B)
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
Wang, Zhao, Scheid, Wu, PRC 77 (2008) 014603
Fusion-fission : EDF + HIVAP
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
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
WS*3). Masses of super-heavy nuclei
Alpha decay energies of super-heavy nuclei have been predicted
rms ~ 248 keV to 46 Qa of SHN
Zhang, et al., Phys. Rev. C 85, 014325 (2012)
N=178
WS*
N=178
WS*
N=162 N=178
WS*
1) quasi-fission barrier
Wang, Tian, Scheid, PRC84, 061601(R) (2011)
III. Fusion probability
Yu. Oganessian
Fusion probability
2) Evaporation residual cross sections
Mean barrier height PRC84, 061601(R) (2011)
Uncertainty at E>Bm : 1.18 (capture) x 1.85 (Wsur) x 2 (PCN) = 4.4
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 WangPRC(2011) ~ 35 fb ~ 20 fb ~ 5 fb ~ 3 fb
Nan WangPRC(2012) ~ 110 fb ~ 50 fb ~ 6 fb ~ 4 fb
Siwek-WilczynskaPRC(2012)
~ 30 fb ~ 6 fb ~ 1 fb ~ 0.1 fb
Conclusion and discussion
Methods for calculations of capture cross sections, survival probability of compound nucleus and the fusion probability in fusion reactions leading to super-heavy nuclei have been established and checked 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.
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)
Thanks for your attention
Codes and data are available at : www.ImQMD.com
Kinetic Nuclear Coulomb
Skyrme energy-density functional
M. Brack, C. Guet, H.-B. Hakanson, Phys. Rep. 123, 275 (1985).
Skyrme force SkM*
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 …
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
2). Level density parameters
In the standard HIVAP code: Ed=18.5MeV, ra=1.153fm
Large-angle quasi-elastic scattering
PRC78, 014607 (2008)
Tail of the barrier distribution influences the large-angle quasi-elastic cross sections
S. G. ZhouTail of barrier distribution influences the large-angle quasi-elastic cross sections