Study the properties of fissionable heavy nuclei within the Generalized Liquid Drop Model 郭树青指导老师：张鸿飞兰州大学 2010.7.25 The 13th National Nuclear Structure

Study the properties of fissionable heavy nuclei within the Generalized Liquid Dr

op Model

郭树青

指导老师：张鸿飞

兰州大学

2010.7.25

The 13th National Nuclear Structure Conference of China, Chifeng

Quasi-molecular shape Generalized Liquid Drop Model(GLDM) The most probable exit channals and cor

responding half-lives; Ellipsoid shape Spontaneous fission barriers and half-liv

es

Contents

School of Nuclear Science and Technology,Lanzhou University


Quasi-molecular deformation



The one-body shape sequence is described within quasi-molecular shape sequence which allow to simulate the development of a deep neck in compact and little enlongated shapes with almost spherical ends.

Quasi-molecular defaormation

2cossin

20cossin

)(22

222

221

22

2

ca

ca

R


21

2222

122

2 )(R

RaCaC


21

222

121

212

2

)1(R

Rss

ss

22 c

as

11 c

as

G.Royer and B.Remaud Nuclear Physics A444 (1985)477.

EGLDM=Evol+Esurface+ECoulomb +Eproximity +Eshell+Epairing


elTFpairing

sphereshellshell

Coul

sssurf

vvvol

EE

eEE

rr

dd

R

ZeE

R

SurfAIkaE

AIkaE

mod

2

60

2

22

20

3/22

2

2

)6.21(

'

'

16

9

4)1(

)1(

3/13/10

s

v

s

v

A8.076.0A28.1R

spherethefromdeviation:

6.2k

8.1k

MeV9439.17a

MeV494.15a

A/)ZN(I

Generalized Liquid Drop Model(GLDM)


G.Royer and B.Remaud Nuclear Physics A444 (1985)477.


Proximity Energy

max

min

h

hproximity hdh2b/)h,r(D2)r(E


But the surface energy takes only into account the effects of the surface tension forces in a half space and does not include the contribution due to the attractive nuclear forces between the surfaces in regard in a neck or a gap between two separated fragments. Thus, an additional term called proximity energy must be added to take into account the nuclear interaction between opposite nucleons in a neck or a gap between fragments (~ - 40 MeV for heavy nuclei)

Shell Correction

;)21(22 eEE sphere

shellshell

];26.05.0())()(([8.5 3132 AAZFNFE sphereshell

);(6.0)()( 351

35 iii MXMXqXF

);)(6.0 1351

35 iiiii MMMMq （

Deformed:

Sphere:

Deviation: ;)(

2

2

2

a

dRr

.34.0 0ra



Myers W D.Droplet modelof atomic nuclei. Plenum,New-York,1977

Potential Barrier


-15

-10

-5

0

5

10

15

5 6 7 8 9 10 11 12 13 14

r (fm)

E (

MeV

)


-15

-10

-5

0

5

10

15

5 6 7 8 9 10 11 12 13 14

r (fm)

E (

MeV

)

MoSnU 10642

13050

23692

WKB method

]))()((22

exp[ . drErEruh

Pout

in

r

rsg

PT

021

2ln

])(25.3exp(241[)( 0RRrr sph

1200 10 s



Exit channals

n

ii

1

n

i iTT1

11

U236

Half-lives

230 232 234 236 238 240 242 244 246 248 250100

105

1010

1015

1020

1025

1030

Filled: Theo.Not filled: Exp.

Ha

lf-lif

e(s

)

A

Th

U

Pu

Cm

Ellipsoid shape

c

as



When one fragment is close to a magic spherical nucleus while the other one varies from spherical to prolate shapes.

S>1:oblate S=1:spherical S<1:prolate

Ellipsoid shape

])1(

arcsin1[

2

1212

312

ee

eeBs

e

e

e

eBc

1

1ln

2

)1( 312

]1)([212

int, sr

ZZeEc

2

222

r

ac

23 2

3)

1

1ln()

11(

4

3)(

s

Surface enrgy:

Columb energy:

Interaction energy:



Potential Barrier



Red:fragments are spherical

Green:heavy(sphere)+light (ellipsoid) without shell correction(Royer)

Black:heavy(sphere)+light (ellipsoid) with shell correction

6 7 8 9 10 11 12 13 14 15-20

-15

-10

-5

0

5

10

15

E(M

eV)

r(fm)

Inner barrier



Outer barrier



230 232 234 236 238 2400

2

4

6

8

10

12

14

234 236 238 240 242 2440

2

4

6

8

10

12

14

240 242 244 246 248 2500

2

4

6

8

10

12

E (

Me

V)

A

Our result Shpere Exp.

A

A

Spontaneous fission half-lives



230 232 234 236 238 240 242 244 246 248 2501E8

1E10

1E12

1E14

1E16

1E18

1E20

1E22

1E24

1E26

Hal

f-liv

es(s

)

A

Z=92

Z=94

Z=96

Summary The half-lives corresponding to the supposed most

probable exit channals vary regularly for the expermental half-lives

Elliposoid shape introduced after the complement of the quasi-molecular deformation is resonable because of the proximity energy;

The GLDM taking into the ellipsoidal shape explains the inner and outer barriers very well.

310(< )



Problems Shell correction is semiempirical,In large deformati

on around the two touching spherical fragments,new shell closures are formed.We add the shell correction simply;

The choice of the most probable fission path is difficult.They should be descrbed by the multi-dimensional potential surfaces.



Thank you

for your attention!



Documents

Study the properties of fissionable heavy nuclei within the Generalized Liquid Drop Model 郭树青 指导老师：张鸿飞 兰州大学 2010.7.25 The 13th National Nuclear Structure

Study the properties of fissionable heavy nuclei within the Generalized Liquid Drop Model 郭树青指导老师：张鸿飞兰州大学 2010.7.25 The 13th National Nuclear Structure