Systematics of fusion probability in reactions leading to super-heavy nuclei Ning Wang ( ) Guangxi Normal University 2011 Dec., Beijing.

Systematics of fusion probability in reactions leading to super-heavy nuclei

Ning Wang ( 王宁 )

Guangxi Normal University

www.imqmd.com 2011 Dec., Beijing

N. Wang www.Im（王宁）QMD.com

Introduction

Calcualtions of capture cross sections

Survival probablity Wsur

Fusion probabilty PCN


2010

6 new superheavy elements

48 new isotopes

Yu.

Oga

nes

sian

20

10118

116

115

114

113

112

111

110

109

108

107

106

105

104

T1/2= 320d

249Bk +48Ca

117

Yu. Oganessian “SHE in JINR” 109-th Session of the SC of JINR, Feb. 17-18, 2011, Dubna

???


S.Hofmann, GSI

2003-2008, 7477hours / 312days, 2 events

Theoretical support for these very time-consuming and extremely-expensive experimentsis vital in choosing the optimum target-projectile-energy combinations, and for the estimation of cross sections.

50Ti, 54Cr, 58Fe, 64Ni, 70Zn

+ 208Pb

48Ca ： 1 克 20 万美金 Cf ： 1 克 10 亿美元



I. Capture

II. Decay

III. Formation

# Coulomb barrier

# Barrier distribution (~2005 -- 2007)

# Deformation & dynamics … (~2000 -- present)

# Fission barrier

# Masses & shell corrections (~2009 -- present)

# Mass distributions …

# Quasi-fission barrier

# Potential energy surface (~2005 、 2011…)

# Dynamics …


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


Kinetic Nuclear Coulomb

Skyrme energy-density functional

M. Brack, C. Guet, H.-B. Hakanson, Phys. Rep. 123, 275 (1985).

Skyrme force SkM*


Spherical symmetric Fermi functions

Search for the minimum of energy by varying densities (R0p, R0n, ap, an)

according to Hohenburg-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


withDetermination of D(B) is the key of this approach

8 12 1630

40

50

60

70

80

Vb (

MeV

)

R (fm)

28Si+92ZrB0

R0

D(B) to empirically take into account the coupling between the relative motion and other degrees of freedom such as deformation etc.

3. Fusion (capture) cross section

Min Liu, Ning Wang, et al., Nucl. Phys. A 768 (2006) 80


for reactions with nuclei near the beta-stability line but the neutron-shell is not closed


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)


60 70 80 900.01

0.1

1

10

100

1000

fus (

mb)

Ec.m.

(MeV)

exp. calc.

16O+186WDeviations from experimental 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 偏差


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)


The fusion excitation functions of a series of reactions with 16O bombarding on medium mass targets.


Large-angle quasi-elastic scattering

PRC 78, 014607 (2008)


S. G. ZhouTail of barrier distribution influences the large-angle quasi-elastic cross sections


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


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


Obtained deviations with different models for 51 fusion-fission reactions

N. Wang, M. Liu and Y. Yang, Sci. China G 52, 1554 (2009)


2). Level density parameters

In the standard HIVAP code: Ed=18.5MeV, ra=1.153fm


Radius parameter ra in the level density parameter


Optimal value of the radius parameter ra

68% reactions have a value smaller than 0.0714,

Estimated systematic errors of the HIVAP code: 1.85Wsur and Wsur /1.85


A reliable nuclear mass model is needed for studies on synthesis of super-heavy, nuclear astrophysics and nuclear symmetry energy, etc.

“Mass Olympics” Trento 2008

WS : PRC 81 (2010) 044322

WS*: PRC 82 (2010) 044304

WS3: PRC 84 (2011) 014333

WS*3). Masses of super-heavy nuclei


Ning Wang, et al., Phys. Rev. C 77 (2008) 014603

Fusion-fission ： EDF ＋ HIVAP ER cap CN surP W








M. Itkis ， Dubna

1) Driving potential

2) Quasi-fission

3) Calculations of evaporation residual cross sections

III. Fusion probability PCN (preliminary)


Y. Oganessian, 109th Session of the JINR Scientific Council, 2010, Dubna.

2) quasi-fission barrier

Bqf

Esh



Mean barrier height

3) Evaporation residual cross sections



Uncertainty at E>Bm : 1.18 (capture) x 1.85 (Wsur) x 2 (PCN) = 4.4


Collected by Junlong Tian


A. K. Nasirov, et al., Phys. Rev. C 84, 044612 (2011)



Results fromNan Wang ( 王楠 )

http://www.phys-hutc.net/conference/2011-09-trans/pdf/ 王楠 .pdf



Zagrebaev, et al., arXiv:1105.1659v1

For 4n channel


Opt. 50Ti+249Bk 50Ti+249Cf 54Cr+248Cm 58Fe+244Pu

Nasirov(2009)(2011)

~ 100 fb

~ 10 pb ~ 70 fb

~ 6 fb

Liu & Bao(2011)

~ 600 fb ~ 100 fb

Nan Wang(2011)

~1000 fb ~ 200 fb ~ 40 fb ~ 30 fb

Zagrebaev(2008)

~ 50 fb ~ 40 fb ~ 20 fb ~ 5 fb

This work(2011)

~ 35 fb ~ 20 fb ~ 5 fb ~ 3 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 are established step by step.

Coulomb barrier, fission barrier and quasi-fission barrier play important role for the calculations of three parts.

More precise calculations for masses, fission barrier and the study on dynamics of fusion and fission processes 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

I am very grateful to Prof. Shan-Gui Zhou ( 周善贵 ) for many discussions and valuable suggestions

This work was supported by Alexander von Humboldt Foundation and National Natural Science Foundation of China

Systematics of fusion probability in reactions leading to super-heavy nuclei Ning Wang ( ) Guangxi Normal University 2011 Dec., Beijing.

Documents

dynamics slide

beijing slide

fm slide

rms slide

level density parameter

fusionfission edf hivap

quasifission barrier

fusionfission reactions