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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
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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
The 13th National Nuclear Structure Conference of China, Chifeng
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Quasi-molecular deformation
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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.
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Quasi-molecular defaormation
2cossin
20cossin
)(22
222
221
22
2
ca
ca
R
School of Nuclear Science and Technology,Lanzhou University
21
2222
122
2 )(R
RaCaC
The 13th National Nuclear Structure Conference of China, Chifeng
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.
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EGLDM=Evol+Esurface+ECoulomb +Eproximity +Eshell+Epairing
School of Nuclear Science and Technology,Lanzhou University
elTFpairing
sphereshellshell
Coul
sssurf
vvvol
EE
eEE
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dd
R
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A8.076.0A28.1R
spherethefromdeviation:
6.2k
8.1k
MeV9439.17a
MeV494.15a
A/)ZN(I
Generalized Liquid Drop Model(GLDM)
The 13th National Nuclear Structure Conference of China, Chifeng
G.Royer and B.Remaud Nuclear Physics A444 (1985)477.
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School of Nuclear Science and Technology,Lanzhou University
Proximity Energy
max
min
h
hproximity hdh2b/)h,r(D2)r(E
The 13th National Nuclear Structure Conference of China, Chifeng
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)
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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
School of Nuclear Science and Technology,Lanzhou University
The 13th National Nuclear Structure Conference of China, Chifeng
Myers W D.Droplet modelof atomic nuclei. Plenum,New-York,1977
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Potential Barrier
School of Nuclear Science and Technology,Lanzhou University
-15
-10
-5
0
5
10
15
5 6 7 8 9 10 11 12 13 14
r (fm)
E (
MeV
)
The 13th National Nuclear Structure Conference of China, Chifeng
-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
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WKB method
]))()((22
exp[ . drErEruh
Pout
in
r
rsg
PT
021
2ln
])(25.3exp(241[)( 0RRrr sph
1200 10 s
School of Nuclear Science and Technology,Lanzhou University
The 13th National Nuclear Structure Conference of China, Chifeng
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Exit channals
n
ii
1
n
i iTT1
11
U236
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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
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Ellipsoid shape
c
as
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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
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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:
School of Nuclear Science and Technology,Lanzhou University
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Potential Barrier
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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)
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Inner barrier
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Outer barrier
The 13th National Nuclear Structure Conference of China, Chifeng
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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
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Spontaneous fission half-lives
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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
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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(< )
School of Nuclear Science and Technology,Lanzhou University
The 13th National Nuclear Structure Conference of China, Chifeng
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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.
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Thank you
for your attention!
The 13th National Nuclear Structure Conference of China, Chifeng
School of Nuclear Science and Technology,Lanzhou University