HT 2005 T8: Fission 1

Nuclear Fission• Historic Dates

• Fission Mechanism

• Binding Energy

• Liquid-Drop Model

• Classification of Heavy Nuclides

• Prompt Neutrons

• Delayed Neutrons

HT 2005 T8: Fission 2

Historic Introduction

• 1932: The neutron is discovered byJ.Chadwick → experiments with neutrons.

• 1939: Bombardment of U gives medium-heavy atoms (Ba), O.Hahn and F.Strassman; L.Meitner explains; E.Fermi and co-workers did not recognize fission.

• 1940: Spontaneous Fission (SF) is discovered by G.N.Flerov and K.A.Petrzhak.

• 1947: Ternary fission is discovered by Qian Sabqiang and He Zehui.

HT 2005 T8: Fission 3

Basic Notation

• Z is the number of protons, charge number or atomic number

• N is the number of neutrons

• A = Z + N is the number of nucleons,A is called the mass number

• is a specific nucleus, X – chem. sym.

• is in an excited state

XAZ

*XAZ

HT 2005 T8: Fission 4

Nuclides and Isotopes

• Isotope ≡ atoms with same Z and A

• Nuclide = atoms/nuclei with same Z and A and being in a specific energy state

• Isomer = long-lived excited states, 113

49 Inm

238 238 * 113 11392 92 49 49U U In Inm

Isotope Isotope

HT 2005 T8: Fission 5

Nuclear Energy Production

( ) ( )

1) 0

2)

A A

tot totb b

Q X X Q

E EQ

A AQ Q

HT 2005 T8: Fission 6

Fission Process1710 s 1710 s 1410 s

1 min

Ternary: 1/400

32

60

5.2 0.00650.7%

MeVE

MeVE

util

tot

200180

210190

fission

MeVf 200

( , ) ( , )th ffV

P E vn E dV r r

HT 2005 T8: Fission 7

Compound Nucleus

1 2

A+1A A+1 *

A A

XX X

Y

En

Z Q

A A+1 * A+1

A+1 A+1 * A

X X X

X X X : Photoelectric liberation

Detailed balance theorem: b

b

E

n E

E

E

n

HT 2005 T8: Fission 8

Binding Energy

2

2 2

2

totb n p

n p p n

totb

b n

E c Nm A N m M

c N m m Am M c Am M

E ME c m

A A

1MeV 9MeV

A 70: 8.6MeV(A=70) 7.5MeV(A=238)b

b

E

E

HT 2005 T8: Fission 9

Energy Release

1 2A AA A+1 *

21 2

2

2 1 21 1 2

X X Y

( 1) 1

f

f c

ib

i i n

cf b b b b c

n Z E

E c M M M

EM A m

c

E A E E A E E A A A A

HT 2005 T8: Fission 10

Fission Energy

0 50 100 150 200 250 3000

50

100

150

200

250

300

Mass number A

Ene

rgy

[Me

V]

fE

85

fE

1 2r r0

maxpE

r

THE

maxpE

THE

HT 2005 T8: Fission 11

Liquid-Drop Model

2

2 3 3 41 3

1 2

AZ p nM X Zm A Z m M

Z Z A ZM A A A

A A

Nuclear force

Surface force

Coulomb repulsion

Stability maximum

Spin factor

: 15.8; 17.8; 0.71; 23.7MeV 34,

0, or

34

Even Even

O E E O

Odd Odd

HT 2005 T8: Fission 12

Fissionable Ratio

2 1 3 2

2 3

2

223592

223994

Fissionable ratio:

50 does not exist

U: 35.9

Pu: 36.8

Coulomb

Surface

AZ

E Z A ZE A A

ZX

AZAZA

HT 2005 T8: Fission 13

Excitation Energy

2 2( ) 2 3

1 3 1 2

23.2( 2 ) 0.72 11.215.8 18.3

tot

b

A Z ZE A A D

A A A

kEAX A+1X* 1 ( ) ( )A tot A tot

ex Z b Z b kE E E E

2

2 3Fission: 0.17 5.2 0.117 MeVex TH

ZE E A

A

1 ( ) ( )

1 ( ) ( )

1 ( ) ( )

0

A tot A totex Z b Z b k TH

A tot A totk Z b Z b TH

A tot A totk TH Z b Z b

E E E E E

E E E E

E E E E

HT 2005 T8: Fission 14

Classification of Heavy Nuclides

233 235 239 24192 92 94 94

232 238 240 24290 92 94 94

232 23390 92

238 239 24192 94 94

241 2

Fertile

5294 98

Fissionable

Fissile

Fertil

0 U, U, Pu, Pu:

1MeV Th, U, Pu, Pu:

Th U

U Pu,

e:

Pu

Pu, CfSF:

k

k

E

E

HT 2005 T8: Fission 15

Examples of Fission

235 236 * 144 9192 55 37

235 236 * 140 9492 54 38

235 236 * 136 9992 53 38

U U Cs Rb 1

U U Xe Sr 2

U U I Y

n n

n n

n n

HT 2005 T8: Fission 16

Fission Product Yield

1 2

1 2

A AA

A A

X Y

1 Y

n Z

A M M Z

HT 2005 T8: Fission 17

Kinetic Energy Distribution1 2A AA

2 21 1 2 2

1 2

2 11 1 2 2

1 2

1 2 2 1

2

1

X Y

;2 2

95

140

n Z

M v M vE E

E MM v M v

E M

M M E E

EE

HT 2005 T8: Fission 18

Energy Released in FissionFission

fragmentsReleased energy

[MeV]Range [m]

235U 239PuLighter fragment 99.81 101.82 < 110-4

Heavier fragment 68 73.2 < 110-4

Prompt neutrons 4.8 5.8 *Prompt (t < 1 µs) 7.5 7.0 1.0

Decay products:

-particles 7.8 8.0 < 110-2

– rays (t > 1 s)

6.8 6.2 1.0

neutrino 12.0 12.0

210 215

HT 2005 T8: Fission 19

Prompt Neutrons239Pu

235U

233U

235

239

233

2.432 0.066

2.349 0.1

2.482 0.

50

075

2.41

2.8

2 0.136

44 0.138 E

E

E

E

E

E = 1

HT 2005 T8: Fission 20

Prompt Neutron Energy

1.036

3

0.1 10MeV

( ) 0.453 sinh 2.29

2( ) ; 1.29MeV

E

EkT

E

N E e E

EN E e T

T

HT 2005 T8: Fission 21

Delayed Neutron Precursors87Br

T½s

87Kr* 86Kr + n

β–

β–

87Kr

87Rb

87Sr

6 groups of precursors

decay constant of the -th group

fraction of all (prompt+delayed)

neutrons from the -th group

i

i

i

i

HT 2005 T8: Fission 22

Delayed Neutron Groups

HT 2005 T8: Fission 23

Delayed Neutron Spectra

23592

Delayed neutron fraction:

U 0.0065 0.7%

d

HT 2005 T8: Fission 24

Microscopic Cross Section

θ

x

Δx

cross section σ

Monoenergeticbeam of neutrons

I = n/(sm2 sec)

Reaction rate R = #/(sm2 sec)

detector

detector

Microscopic cross section σ is defined by

R = σ × I × NB

[#/(sm2 sec)] = [sm2] ×[#/(sm2 sec)]×[#/sm2]

Background material

σ/A = Probability per nucleus that a neutron in the beam will interact with it

2[ ]BR Nsm

I

HT 2005 T8: Fission 25

Fission Cross Section

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Energy (eV)

10-2

10-1

100

101

102

103

104

(b

arns

)

235 U

capture

fission

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Energy (eV)

10-2

10-1

100

101

102

103

104

(b

arns

)

239 Pu

capture

fission

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Energy (eV)

10-2

10-1

100

101

102

103

104

(b

arns

)

233 U

capture

fission

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Energy (eV)

10-2

10-1

100

101

102

103

104

(b

arns

)

241 Pu

fission

HT 2005 T8: Fission 26

Resonances

238 239 * 23992 92 92U U Un

2 238 2nm c Mc

( )a E

E

Incident n

23992 U

6.67kE eV

HT 2005 T8: Fission 27

235U vs. 238U

10-3 10-2 10-1 100 101 102 103 104 105 106 107

Energy (eV)

10-2

10-1

100

101

102

103

104

(b

arns

)

235 U

capture

fission

HT 2005 T8: Fission 28

The END