Lesson 11

Nuclear Reactions --Part 2

Compound Nuclear Reactions

• The compound nucleus is a long-lived reaction intermediate that is formed by a complex set of interactions between the projectile and the target.

• The projectile and target nuclei fuse and the energy of the projectile is shared among all the nucleons of the composite system.

• The lifetime of the CN is ~ 10-18-10-16 s. This lifetime is directly measurable by crystal-blocking techniques.

Independence Hypothesis or “Amnesia Assumption” • The mode of decay of the CN is

independent of its mode of formation.

• Caveat: Conservation laws apply.• Experimental evidence: the Ghoshal

expt.• Angular distributions symmetric

about 90 in CN frame.

62Cu>63Zn>62Ni

ang. mom effects

€

σ =πD2 2l +1( )l =0

∞

∑ Tl

Cross Sections--General

€

probability =Tlβ Eβ( )Tlγ Eγ( )

l γ ,Eγ

∑

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

Cross Sections--Energy Dependence

/D << 1For reaction a + A Cb + B

€

σ =πD2 2JC +1( )2JA +1( ) 2Ja +1( )

ΓaAΓbB

ε −ε 0( )2 +

Γ2 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

Applying this to (n,) reactions

€

σn,γ = πD2 2JC +1( )2JA +1( ) 2( )

ΓnΓγ

ε −ε 0( )2 +

Γ2 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

/D >>1For reaction a + A Cb + B

σab = σC PC(b)

/D >>1• Assumption is that of statistical

equilibrium• For reaction a + A Cb + B

σab = σC PC(b)• So the problem is to calculate the

probability that C will decay to B + b.

Level densities

€

ρ(E*) =Cexp[2(aE*)1/ 2]

a = A12

to A8

E* = aT 2 −T

If emitted particles are neutrons

€

N(ε )dε =εT 2 exp −ε /T( )dε

If emitted particles are charged particles

€

N(ε )dε =ε −ε sT 2 exp −(ε −ε s )/T( )dε

Excitation functions

Photonuclear Reactions

Photonuclear Reactions• GDR-- a giant oscillation of the nuclear

protons vs the nuclear neutrons• dipole sum rule

€

σabs Eγ( )dEγ ∝NZA

≈ 0.058NZAMeV − barns

0

∞

∫

Heavy Ion Reactions• Classical motion• Dominated by high angular

momentum• Aproj > 4

Mechanisms

Mechanisms

Elastic scattering

Fusion

€

σR = πRint2 1−

V Rint( )Ecm

⎡ ⎣ ⎢

⎤ ⎦ ⎥

Rint = R1 + R2 + 3.2 fm

RI = 1.12 Ai1/3 - 0.94 AI

-1/3 fm

€

V Rint( ) = 1.44Z1Z2

Rint

− bR1R2

R1 + R2

Deep Inelastic Scattering

High Energy Reactions• Low energy (< 10 MeV/A)• Intermediate Energy ( 20-250

MeV/A)• High Energy (>250 MeV/A)

Spallation

New high energy mechanisms

• Spallation• IMF formation• Cascade processes• Participant-Spectator Picture

Cascadesnucleon-nucleon collisions

Participant-Spectator Physics

Multifragmentation• “Multifragmentation” refers to central

collisions where several IMFs are emitted.• Caloric curve