采用热熔合方法合成超重核的理论研究

王楠 深圳大学 合作者

:

赵恩广 周善贵 李君清 ( 中科院 理论物理所 ) ( 中科院 理论物理所 ) ( 中科院 近代物理所 ) W. Scheid (Giessen University, Giessen) 兰州 2012 年 8 月 10 日 1

Outline



Introduction



Theoretical Models



Results and discussions



Summary

2

Experimental achievements

Super-heavy elements up to Z=118 have been synthesized experimentally.

Z=107-113: cold fusion, 208 Pb/ 209 Bi based reactions by evaporating 1 or 2 neutrons (

Rev.Mod.Phys.72(2000)733, Rep.Prog.Phys.61(1998)639)

Z=112-118: 48 Ca induced fusion reactions, 48 Ca bombarding actinide targets by evaporating 3-5 neutrons (

J.Phys.G34(2007)R165, NPA787(2007)343c, PRC 83, 054315 (2011))

IMP in Lanzhou: 259 Db, 265 Bh, 271 Ds

3

Theoretical models for SHN production

Macroscopic dynamical model

S. Bjornholm and W.J. Swiatecki

Fusion by diffusion model

Y. Abe, Y. Aritomo , Z.H. Liu, J.D. Bao , C.W. Shen, K. Siwek-Wilczynska et al

Nucleon collectivization model

V.I. Zagrebaev

Dinuclear system model

V.V Volkov, G.G. Adamian, N.V. Antonenko, A.K. Nasirov , W. Scheid, et al J.Q.Li, E.G. Zhao, S.G. Zhou, Z.Q. Feng, M.H.Huang, Nan Wang et al

Other model

Ning Wang 4

Schematic picture of the formation of SHN

capture

T

P CF CN fusion

EN

evaporation

Evaporation residue cross section:



ER

(

E c

.

m

.

)    2 2 

E c

.

m

.



J

( 2

J

 1 )

T

(

E c

.

m

.

,

J

)

P CN

(

E c

.

m

.

,

J

)

W sur

(

E c

.

m

.

,

J

) 5

Capture of two colliding nuclei



c

(

E c

.

m

.

)    2 2 

E c

.

m

.



J

( 2

J

 1 )

T

(

E c

.

m

.

,

J

)

Transmission probability calculated from barrier distribution:

T

(

E c

.

m

.

,

J

)   1

f

(

B

) 1  exp      2   (

J

)   

E c

.

m

.



B

  2 2 

R B

2 (

J

)

J

(

J

 1 )      

dB f

(

B

)        1

N

1

N

exp      

B

  1

B m

  2    ,

B



B m

exp      

B

  2

B m

  2    ,

B



B m

V.I. Zagrebaev, Phys.Rev.C 64 (2001) 034606

B m

 2   ( (

B

0

B

0 

B s

) / 2 

B s

) / 2 The value of  1 is 2-4 MeV than the one of  2 less 6

Di-nuclear system concept

Dinuclear system concept (from the investigation of deep inelastic collisions) V.V. Volkov, Phys. Rep. 44(1978) 93

The formation of compound nuclei is the fusion along the mass asymmetry degree of freedom.

7

Formation of compound nucleus - Master equation

dP

(

A

1 ,

E

1 ,

t

)

dt

 

A

1 '

W A

1

A

1 ' (

t

)[

d A

1

P

(

A

1 ' ,

t

) 

d A

1 '

P

(

A

1 ,

t

)]  

qf A

1 (

t

)

P

(

A

1 ,

t

)

P CN



A BG i

  0

P

(

A i

)

Hamiltonian

H



H

0

H

0

V t

 

   

K

 

K K

,   '

K



K



K

'

u



K



K

'

     

K K a

 

K



K

' 

K

,  '

V KK K

'

t

 

8

Effects of nuclear static deformation and dynamical deformation

development of dynamical deformation Li, Wang ， Li et al., J.Phys. G 32(2006) 1143 G. Wolschin, Phys.Lett.B 88 (1979) 35 C. Riedel, G.Wolschin, and W. Noerenberg, Z. Phys. A 290, 47(1979).

9

Potential energy surface

Excitation energy of DNS *

E DNS



E E total total

  0

E DNS E c

.

m

.



rot E DNS

 (

M T



M P

)

c

2 0

E DNS



V C



V N

 (

M

1 

M

2 )

c

2 Potential Energy Surface(PES)

V PES



V C



V N

 (

M

1 

M

2 

M T



M P

)

c

2 Deformation dependent Intrinsic energy

E

int (

A

1 ,  ) 

V C

(

r

,  1 ,  2 ) 

V N

(

r

,  1 ,  2 ) 

i

  1 , 2 1 2

C i



i

2    max ( 1 

e



t

/  )

C

1 (

C

2 (   1 2     1 2 0 0 ) ) 2 2 

A A

2 1 G. Wolschin, Phys.Lett.B 88 (1979) 35 C. Riedel, G.Wolschin, and W. Noerenberg, Z. Phys. A 290, 47(1979).

V.I. Zagrebaev, Phys.Rev.C 64 (2001) 034606 10

Driving potential

Intrinsic energy and PES for 50 Ti+ 249 Cf Nan Wang, En-guang Zhao, Werner Scheid and Shan-gui Zhou, Phys.Rev.C 85 (2012) 041601(R) 11

Driving potential

12

Survival probability of excited compound nucleus The thermal compound nucleus will decay by evaporating



-ray, light particles and fission. The survival probabilities can be written as

W sur

(

E

*

CN

,

x

,

J

) 

P

(

E

*

CN

,

x

,

J

)

x



i



n

(

E

 ,

J

)  ( 2

s

 1 )   2

m

  (

R

2

E

 ,

J

)

E

* 

B

 

n

(

E i

* , 

J n

( )

E i

*  , 

f J

) (

E i

* ,

J

)  

i

 0

E



rot

    

E

1

a

 

B

 

f E

1 (  )

E rot

   , 4 1  

J

3  

d



mc

2

e

2 

c NZ A

 

G

2  

G

 

E G

2 4   2 2  

inv



f

(  ( )

E

    , 

J R

 ) 2  1 

V

  2 

f

/  1  (

E

 ,

for J for

)

E

   

f V



E rot

   

V

  0 

a V

1 

f

1    

Z

  exp 

f Z

 

E



Z

  

K



B

 /

f

 2  

E

   

R



E



rot

1 .

6  

B f



E rot

,

J

 

d

   /    13

Results and discussions

Capture cross sections for 48 Ca + 238 U, 237 Np, 242 Pu, 244 Pu, 243 Am, 248 Cm, 249 Bk, 249 Cf Exp. W.Q. Shen et al, PRC 88(1979) 35 M. G. Itkis, et al , Proceedings of International Workshop on Fusion Dynamics at the Extremes, Dubna, Russia, 2000 , (2001).

14

Potential energy surface and Pcn for 48 Ca+ 238 U, 48 Ca+ 248 Cm 15

Fusion probabilities for some hot fusion reactions 16

Survival probabilities for some compound nuclei produced in hot fusion reactions 17

Excitation functions for 48 Ca+ 238 U, 237 Np Exp. Yu.Ts. Oganessian, et al., PRC 70 (2004) 064609 18

Evaporation residue cross sections for 48 Ca + 242, 244 Pu Exp. Yu.Ts. Oganessian et al., PRC 70 (2004) 064609 P. A. Ellison, et al, PRL 105 (2010) 182701 19

Evaporation residue cross sections for 48 Ca+ 243 Am, 248 Cm Exp. Yu.Ts. Oganessian et al., PRC 69 (2004) 021601(R) , PRC 70 (2004) 064609 S. Hofmann, S. Heinz, R. Mann,

et al.

, Euro. Phys. J. A 48, (2012) 1 20

Evaporation residue cross sections for 48 Ca + 249 Bk, 249 Cf Exp. Yu.Ts. Oganessian et al., PRC 74.044602(2006) PRC 83, 054315 (2011) 21

Evaporation residue cross sections for the SHN 112-120 22

Experiment about synthesis of elements 120

58 Fe + 244 Pu Yu.Ts. Oganessian, et al., PRC 79 (2009) 024603 50 Ti + 249 Cf C. E. Dullmann, “News from TASCA”, talk given at the 10thWorkshop on Recoil Separator for Superheavy Element Chemistry, October 14, 2011, GSI Darmstadt, Germany (unpublished) 23

Theoretical investigations of the production of SHN 119 and 120 DNS Model

A.K.Nasirov et al. PRC 79(2009) 024606 A.K.Nasirov et al. PRC 84(2011) 044612 G.G.Adamian, G.A. Antonenko, W. Scheid. EJPA 41(2009) 235 Z.-G. Gan, et al , Sci. China-Phys. Mech. Astron.54 (Suppl. 1), s61 (2011)

FBD model

Z.H.Liu, J.D.Bao. PRC 84(2011) 031602(R) K. Siwek-Wilczynska, T. Cap, M. Kowal, A. Sobiczewski, and J. Wilczynski, PRC 78(2008) 034610 V. Zagrebaev, W. Greiner PRC 78(2008) 034610

Other model

Ning Wang, J.L.Tian, W.Scheid PRC 84(2011) 061601(R) 24

25

Excitation functions for producing nuclei Z=120 Fusion probabilities as a function of excitation energy for producing nuclei Z=120 E* (MeV) 26

Evp. Cross sections for 50 Ti+ 249 Bk, 54 Cr+ 243 Am and 58 Fe+ 237 Np reactions leading to nuclei with Z=119 Fusion probabilities for 50 Ti+ 249 Bk, 54 Cr+ 243 Am and 58 Fe+ 237 Np reactions leading to nuclei with Z=119 E* (MeV) 27

Excitation functions for some Ti+ Bk, Cf isotope reactions 28

Summary

 By using a newly developed dinuclear system model with a dynamical potential energy surface for synthesizing superheavy nuclei (SHN) with charge numbers 120 are studied. —the DNS-DyPES model, hot fusion reactions Z = 112 –  Several combinations producing elements Z=119, 120 with Fe, Cr and Ti as projectile are calculated and analyzed.  The maximum ER cross section for reaction 50 Ti + 249 Bk is about 0.11pb in the 4n emission channel.  The maximum ER cross sections for reactions 50 Ti + 249 Cf and 50 Ti + 251 Cf are about 0.05pb and 0.2pb in the 3n emission channels. 29

Thanks 谢谢

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