Neutron-induced Reactions

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

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Neutron-induced Reactions

n-TOFn-TOFCERNCERN


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n_TOFn_TOFCERNCERN


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NuclearRadius

Charged Particle Reactions

What is the Gamow Peak?


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Electron Screening


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e2 = 1.44x10-12 keV.mTunneling probability:

In numerical units:

For -ray emission:

2eP v

eZZ

221

)(

)(29.312 21 keVE

uZZ

CM

Sommerfeld parameterGamow factor

12)( LLL EE

31)( EEDipole

Multipolarity

HW 37HW 37


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EE

1)( 2

2)( eE

)(1

)( 2 ESeE

E

Nuclear (or astrophysical) S-factor


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EC = ??


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Resonance Reactions

E tCN particle emission E E > spacing between virtual states continuum. (Lower part larger spacing isolated resonances).D bound states -emission E isolated states.


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Resonance Reactions

In the 19F(p,) reaction:• The Q-value is 8.??? MeV.• The Q-value for the formation of the C.N. is 12.??? MeV.• For a proton resonance at 668 keV in the lab system, the corresponding energy level in the C.N. is at 13.??? MeV.• If for this resonance the observed gamma energy is 6.13 MeV, what is the corresponding alpha particle energy?• If for this resonance there has been no gamma emission observed, what would then be the alpha particle energy?

HW 38HW 38


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Resonance Reactions

Entrance Channela + X

ExitChannelb + YCompound

Nucleus C*

ExcitedState

ExJ

a + X Y + b Q > 0b + Y X + a Q < 0

Inverse Reaction

22 )1()12)(12(

12XaHCCHbY

JJ

JIIIaX

XaaXaX

QM StatisticalFactor ()

Identicalparticles

• Nature of force(s).• Time-reversal invariance.

22 )1()12)(12(

12YbHCCHXa

JJ

JIIIbY

YbbYbY

??bY

aX

HW 39HW 39


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Resonance Reactions

Projectile

TargetQ-value

Projectile

Q-valueTarget

Non-resonant Capture

(all energies)

Resonant Capture

(selected energies with large X-section)

E = E + Q - Eex

2XaHY

Q + ER = Er

22XaHEEHE CNrrf

ba


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Resonance Reactions

bbplL

lb 222

1max, )12( lbb lll

)()(

7.656)(2

keVEub

CM HW 40HW 40

)1()12)(12(

122max aX

XaaX JJ

J


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Resonance Reactions

22

2 )()(

o

fresponse

Damped OscillatorDamped Oscillator

eigenfrequency

Dampingfactor

Oscillator strength

22

2 )()()(

R

ba

EEE

0

1

t

ot


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Resonance Reactions

22

2

2

)()()1(

)12)(12(

12)(

R

baaX

XaaX EEJJ

JE

Breit-Wigner formulaBreit-Wigner formula

• All quantities in CM system• Only for isolated resonances.

a

b

e

R

aae

baR

Reaction

Elastic scattering

HW 41HW 41 When does R take its maximum value?

ba

Usually a >> b.


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Resonance Reactions

Ja + JX + l = J(-1)l (Ja) (JX) = (J)

(-1)l = (J) Natural parity.

ExitChannelb + Y

Compound Nucleus C*

ExcitedState

ExJ

Entrance Channela + X


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Cro

ss s

ecti

on

EC a Energy

What is the “Resonance Strength” …?What is its significance?In what units is it measured?

ba

aXXa JJ

J)1(

)12)(12(

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Resonance Reactions

Charged particleradiative capture (a,)(What about neutrons?)

HW 42HW 42


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Resonance Reactions14N(p,)

• Q = ??• EC = ??• ER = 2.0 MeV

Formation via s-wave protons, Take J = ½, p = 0.1 MeV, dipole radiation E = 9.3 MeV, = 1 eV.Show that = 0.33 eV.

• If same resonance but at ER = 10 keVp = ?? E = ?? = ??Show that = 3.3x10-23 eV.

HW 43HW 43

Huge challenge to experimentalists


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Resonance J Estimated Energy (keV) (eV)

566 2+ 1.93- 0.154+ 0.01

470 0+ 0.6 1- 0.2

Experimental upper limit < 1.7 eV

-transfer reactionsAngular distribution

18O(, )22Ne

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Neutron-induced Reactions