1. Nuclear Reactions - II A. Nucleon-Nucleus Reactions A.1 Spallation
A.2 Induced Fission
B. Nucleus-Nucleus Reactions
B.1 Fragmentation
B.2 Multifragmentation
B.3 Vaporization

2. Intermediate and Relativistic Energies
Nuclear Reactions - II
Intermediate and Relativistic Energies
Spallation
Induced Fission
Fragmentation
Multifragmentation
Vaporization

3. Introduction A-1 Spallation - 0 • Generalities
• Light particle emissions
• Residues
• The two stage of the spallation process
• The Intra-Nuclear Cascade
• Production of pions
• Evaporation
• Comparison with experimental results
• Main physical aspects
• Applications

4. Generalities A.1 Spallation – 1 projectile (p, n, p, ...) target
Definition (Encyclopedia Britannica): high-energy nuclear reaction in which a target nucleus struck by an incident (bombarding) particle of energy greater than about 50 million electron volts (MeV) ejects numerous lighter particles and becomes a product nucleus correspondingly lighter than the original nucleus. The light ejected particles may be neutrons, protons, or various composite particles equivalent…
projectile
(p, n, p, ...)
target
Drawing from the INC model

5. Generalities A.1 Spallation – 2
1947: E.O. Lawrence discovers that the number of emitted nucleons, especially neutrons, may be quite large depending upon the conditions of the spallation reaction.
90’s: new interest for spallation reactions  they are of pivotal importance for the development of powerful neutron sources for various purposes:
• hybrid systems, be devoted to energy production or to incineration of nuclear
wastes
• so-called multi-purpose spallation sources devoted to irradiation studies, material structure analysis, …
• future tritium production units
Other interest: the production of isotopes  spectroscopy
 reaction mechanisms
 astrophysics
Main aspects: • energy spectrum and angular distribution of emitted light particles
• production rate of residues

6. Light particle emission
A.1 Spallation – 3
Light particle emission
Neutron spectra 0°
7.5°
30°
60°
120°
150°
Cross section (mb/MeV-sr)
En (MeV)
p(800 MeV) + Pb
due to quasi-elastic scattering
 peripheral collisions
due to quasi-inelastic scattering
 neutron ejected by the proton which is excited to a D+ resonance
evaporation process
 independent of the angle!
Conclusion: the spallation reaction is a TWO STEP process!
Proton spectra
similar shapes as the neutron spectra

7. Residues A.1 Spallation – 4
They are observed in the very late stage of the process: after the cascade, the evaporation, and the possible b-decay of very-short-lived emitters.
208Pb + p at 1 AGeV
fission products
spallation residues
Intermediate
Mass
Fragments
(IMF)
very light fragments: produced by fast ejection (cascade) + evaporation of the remnant

8. A.1 Spallation – 6
Residues
208Pb + p at 1 AGeV

9. The two stages of the spallation process
A.1 Spallation – 7
The two stages of the spallation process
Individual nucleon-nucleon scattering
The incident proton loses part of its energy =
cascade (~ 10–22 s ~ 30 fm/c)
projectile
(p, n, p, ...)
target
Evaporation of the residue
(~ 10–20 - ~10-16 s)

10. The Intra-Nuclear Cascade
A.1 Spallation – 8
The Intra-Nuclear Cascade
1947: first suggestion of a Intra-Nuclear Cascade (INC) by R. Serber
An INC code describes p, p, p, … - nucleus and heavy ion reactions (see Multifragmentation)
nuclear collision = sequence of binary baryon-baryon collisions
occurring as in free space
Two approaches:
1. Liège1: All particles are propagating freely until two reach
the minimum relative distance of approach dmin. They scatter if dmin  (stot/p)
2. Bertini2/Isabel3: The target is seen as a continuous medium
providing the particles with a mean free path
l = (rs)-1
After a path, the particle is supposed to scatter on
a nucleon.
1. J. Cugnon, Phys. Rev. C 22(1980)1885
2. H.W.Bertini Phys.Rev.188(1969)1711
3. Y. Yariv and Z. Fraenkel, Phys. Rev. C 20(1979)2227

11. The Intra-Nuclear Cascade
A.1 Spallation – 9
The Intra-Nuclear Cascade
Liège
Bertini/Isabel D D p p
in the nucleus
in the nucleus

12. Production of Pions A.1 Spallation – 10
The pions are the decay products of the D resonances. They are mesons, exchange particles of the strong interaction between nucleons. The D resonances and pions are coming from inelastic nucleon-nucleon reactions at beam energies above few hundred of AMeV (Mp ~ 140 MeV).
Pion cycle ( D  Np  D )
• NN  DN hard D production
• D  Np D decay
• DN  NN D absorption
• Np  D soft D production
4 sorts of D’s
D++  1 (p+p+)
D+  2/3 (p+p0) + 1/3 (n+p+)
D0  2/3 (n+p0) + 1/3 (p+p-)
D-  1 (n+p-)
C. Hartnack et al., Nucl. Phys. A 495(1989)303

13. Evaporation A.1 Spallation – 11
These models are used to simulate the second step of the reaction, i.e. the decay of the excited residue.
Main features:
- the life-time of the excited residue is much longer than its formation time
T(residue) = several hundreds of fm/c
T(formation) ~ 30 fm/c
- the individual properties of the quantum states have a negligible effect at high
excitation energy, due to the small distance between the energy levels, in
particular in heavy nuclei.
All the states are equiprobable so the deexcitation of the nucleus may be treated in a statistical way.
In other words, a statistical model considers the probabilities of the different deexcitation possibilities with comparable weights, which correspond to individual processes of similar time length.

14. Evaporation A.1 Spallation – 12
Most of the current evaporation code describe the residue deexcitation according to the Weisskopf theory which is based on the energy conservation and the assumption of the micro-reversibility of the process.
This assumption is verified for the light particle emissions (n, p, d, t, 3He, 4He), but not for the emission of heavier nuclei or for fission.
Note: the average total neutron multiplicity is about 4 times the multiplicity of the neutrons coming from the cascade stage.

15. Comparison with experimental results
A.1 Spallation – 13
Comparison with experimental results

16. Comparison with experimental results
A.1 Spallation – 14
Comparison with experimental results

17. Main Physical Aspects A.1 Spallation – 15
The available incident energy is progressively shared by the incident particle itself, the ejectiles, the pions and the target.
The proton travels trough the target in 10 fm/c (1 fm/c = s)
A large amount of the energy is removed quickly (~ 20 fm/c) by the emission of a few fast nucleons and some pions.
The nuclear density is depleted when the proton enters the target.
A kind of “hole” is drilled into the target.
The density becomes more or less uniform before the ejection of the fast particles is over.
The relative energy transfer is maximum for incident energies between 1 and 2 GeV.
On average, the proton loses energy with a rate which is universal.
The number of fast ejected particles peaks around 2 GeV.

18. A.1 Spallation – 16
EURISOL
EURopean Isotope Separation On-Line radioactive nuclear beam facility 
 radioactive beams at very high intensities
Applications:
• proton & neutron
drip-lines
• changes in shell
structure
• halo structure
• high-spin physics
• isospin effects in
nuclear matter
• superheavy nuclei
• nuclear
astrophysics
• tests of the
standard model
• muons and
antiprotons
• solid state physics
• …

19. Spallation sources A.1 Spallation – 17
European Spallation Source (ESS) – EU 
????
Spallation Neutron Source (SNS) – Japan 
(2007)
Spallation Neutron Source (SNS) – USA 
(2006!)
Applications:
- chemistry
complex fluids
crystalline materials
disordered materials
engineering
magnetism and
superconductivity
polymers
- ….
Note: a proton of 1 GeV on Pb target with a thickness of 60 cm produces about 25 neutrons!