Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

1

22 nXHCCHbY IIIn

Neutron-induced Reactions

X(n,b)Y

n(En)b(Q+En)

For thermal neutronsQ >> En

b(Q) constant

2

11

vE

)( nln EPvn

Probability to penetrate the

potential barrier

Po(Ethermal) = 1P>o(Ethermal) = 0

vEnn

1)( Non-resonant

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

2

Neutron-induced Reactions

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

3

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

4

Neutron-induced Reactions

n-TOFn-TOFCERNCERN

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

5

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

6

Neutron-induced Reactions

n_TOFn_TOFCERNCERN

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

7

Neutron-induced Reactions

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

8

NuclearRadius

Charged Particle Reactions

What is the Gamow Peak?

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

9

Charged Particle Reactions

Electron Screening

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

10

Charged Particle Reactions

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

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

11

Charged Particle Reactions

EE

1)( 2

2)( eE

)(1

)( 2 ESeE

E

Nuclear (or astrophysical) S-factor

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

12

Charged Particle Reactions

EC = ??

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

13

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.

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

14

Resonance Reactions

Entrance Channel

a + XExit

Channelb + 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 30HW 30

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

15

Resonance Reactions

Projectile

TargetQ-value

Projectile

Q-valueTarget

Direct Capture

(all energies)

Resonant Capture

(selected energies with large X-section)

E = E + Q - Eex

2XaHY

Q + ER = Er

22XaHEEHE CNrrf

ba

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

16

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

17

Resonance Reactions

bbplL

lb 222

1max, )12( lbb lll

)()(

7.656)(2

keVEub

CM HW 31HW 31

)1()12)(12(

122max aX

XaaX JJ

J

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

18

Resonance Reactions

22

2 )()(

o

fresponse

Damped OscillatorDamped Oscillator

eigenfrequency

Dampingfactor

Oscillator strength

22

2 )()()(

R

ba

EEE

0

1

t

ot

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

19

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 32 HW 32 When does R take its maximum value?

ba

Usually a >> b.

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

20

Resonance Reactions

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

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

ExitChannel

b + Y

Compound Nucleus C*

ExcitedState

ExJ

Entrance Channel

a + X

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

21

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(

12

Resonance Reactions

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

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

22

Resonance Reactions14N(p,)

• Q = ??• EC = ??• ER = 2.0 MeV

Formation via s-wave protons, 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 33HW 33

Huge challenge to experimentalists

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

23

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