Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

1

Neutron Attenuation

X

X

t

t

eXP

eXP

1)(

)(

ninteractio

ninteractiono

Recall t = N t

Probability per unit path length.

X

I0 I

Probability

mfp for scattering s = 1/s

mfp for absorption a = 1/a

…………. total mfp t = 1/t

XteIXI 0)(

Show that, after elasticelastic scattering the ratio between the final neutron energy E\ and its initial energy E is given by:

For a head-on collision:

After n ss-wave-wave collisions:where the average change in lethargy lethargy is

HW 6HW 6

2

222

2

2\

)1(

sincos

)1(

cos21

A

A

A

AA

E

E CM

2

min

\

1

1

A

A

E

E

nEEn lnln \

1

1ln

2

)1(1ln

2

\

A

A

A

A

E

Eu

av

2Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Neutron Moderation (revisited)

)ln( EEu M

Reference

Average decrease in ln(E) after one collision.

11H ?H ?

Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

3

Neutron Moderation HW 6 HW 6 (continued)(continued)

• Reproduce the plot.• Discuss the effect of the thermal motion of the moderator atoms.

On 12C.

Most Most probable probable

and average and average energies?energies?

Neutron Moderation HW 6 HW 6 (continued)(continued)

Neutron scattering by light nuclei then the average energy loss and the average fractional energy loss

• How many collisions are needed to thermalize a 2 MeV neutron if the moderator was:

1H 2H 4He graphite 238U ?• What is special about 1H?• Why we considered elastic scattering?• When does inelastic scattering become important?

4Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

EE )1(21\

EEEE )1(21\

)1(21

E

E

Nuclear Fission

~200 MeV

Fission

Fusi

on

Coulomb effectSurface effect

5Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Nuclear Fission• B.E. per nucleon for 238U (BEU) and 119Pd (BEPd) ?• 2x119xBEPd – 238xBEU = ?? K.E. of the fragments 1011 J/g• Burning coal 105 J/g• Why not spontaneous?• Two 119Pd fragments just touching The Coulomb “barrier” is:

• Crude …! What if 79Zn and 159Sm? Large neutron excess, released neutrons, sharp potential edge, spherical U…!

MeVMeVfm

fmMeVV 2142502.12

)46(.44.1

2

6Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Nuclear Fission

• 238U (t½ = 4.5x109 y) for -decay.• 238U (t½ 1016 y) for spontaneous fission.• Heavier nuclei??• Energy absorption from a neutron (for example) could form an intermediate state probably above barrier induced fission.• Height of barrier is called activation energy.

7Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Nuclear Fission

Liquid Drop

Shell

Act

iva

tion

Ene

rgy

(MeV

)

8Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Nuclear Fission

Surface Term Bs = - as A⅔

Coulomb Term BC = - aC Z(Z-1) / A⅓

3

3

4R

2

3

4ab=

1

)1(

Rb

Ra23 abR

...)1( 252

...)1( 251

Volume Term (the same)

32

31

52

51 )1( AaAZZa SC fission

47~2

A

Z

Crude: QM and original shape could be different from spherical.

9Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).

Nuclear Fission

48300

)120( 2

Extrapolation to 47 10-20 s.

Consistent with activation energy curve for A = 300.

10Nuclear Reactor Theory, JU, Second Semester, 2008-2009 (Saed Dababneh).