compound nucleus reactions

Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

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Compound Nucleus Reactions

Direct

CN decays

• Time.• Energy.

• Two-step reaction. • CN “forgets” how it was formed.• Decay of CN depends on statistical factors that are functions of Ex, J.• Low energy projectile, medium or heavy target.

QCN

EaCM


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Compound Nucleus Reactions


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Compound Nucleus Reactions• Consider p + 63Cu at Ep

CM= 20 MeV.• Calculate Ep

CM + [m(63Cu) + m(p) – m(64Zn)]c2.• Divide by 64 available energy per nucleon << 8 MeV.• Multiple collisions “long” time statistical distribution of energy small chance for a nucleon to get enough energy EvaporationEvaporation.• Higher incident energy more particles “evaporate”.

See also Fig. 11.21 in Krane.


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• Random collisions nearly isotropic angular distribution.• Direct reaction component strong angular dependence.

See also Fig. 11.20 in Krane.

Direct Reactions


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Direct Reactions• Peripheral collision with surface nucleon.• 1 MeV incident nucleon ?? more likely to interact with the nucleus CN reaction.• 20 MeV incident nucleon ?? peripheral collision Direct reaction.• CN and Direct (D) processes can happen at the same incident particle energy. Distinguished by:

D (10-22 s) CN (10-18-10-16 s).[Consider a 20 MeV deuteron on A=50 target nucleus].

Angular distribution.


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Direct Reactions• (d,n) stripping (transfer) reactions can go through both processes.• (d,p) stripping (transfer) reactions prefer D rather than CN; protons do not easily evaporate (Coulomb). [(p,d) is a pickup reaction].• What about (,n) transfer reactions?HW 36HW 36 Show that for a (d,p) reaction taking place on the surface of a 90Zr nucleus, and with 5 MeV deuterons, the angular momentum transfer can be approximated by l = 8sin(/2), where is the angle the outgoing proton makes with the incident deuteron direction. (Derive a general formula first).

l 0 1 2 3

0º 14.4º 29º 44ºJ(90Zrgs) = 0+

J(91Zr) = l ± ½, = (-1)l

Optical model, DWBA, Shell model, Spectroscopic Factor.

calcmeas d

dS

d

d

Fig. 11.23 in Krane.


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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


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9


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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 = ??

compound nucleus reactions

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