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

Nuclear Reactions - IIIntermediate and Relativistic Energies

1. Spallation

2. Induced Fission

3. Fragmentation

4. Multifragmentation

5. Vaporization

A-1 Spallation - 0Introduction

• 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

A.1 Spallation – 1Generalities

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, )

target

Drawing from the INC model

A.1 Spallation – 2Generalities

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

0°

7.5°

30°

60°120°150°

Cro

ss

se

cti

on

(m

b/M

eV

-sr)

1 10 100 1000En (MeV)

p(800 MeV) + Pb

A.1 Spallation – 3Light particle emission

Neutron spectra

Conclusion: the spallation reaction is a TWO STEP process!

Proton spectra similar shapes as the neutron spectra

evaporation process independent of the angle!

due to quasi-inelastic scattering neutron ejected by the proton which is excited to a resonance

due to quasi-elastic scattering peripheral collisions

208Pb + p at 1 AGeV

A.1 Spallation – 4Residues

They are observed in the very late stage of the process: after the cascade, the evaporation, and the possible -decay of very-short-lived emitters.

fission products spallation residuesIntermediate

Mass Fragments

(IMF)

very light fragments: produced by fast ejection (cascade) + evaporation of the remnant

A.1 Spallation – 6Residues

208Pb + p at 1 AGeV

A.1 Spallation – 7The two stages of the spallation process

1. Individual nucleon-nucleon scattering

The incident proton loses part of its energy =

cascade (~ 10–22 s ~ 30 fm/c)

2. Evaporation of the residue

(~ 10–20 - ~10-16 s)

projectile(p, n, )

target

A.1 Spallation – 8The Intra-Nuclear Cascade

1947: first suggestion of a Intra-Nuclear Cascade (INC) by R. Serber

An INC code describes 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 (tot/

2. Bertini2/Isabel3: The target is seen as a continuous medium providing the particles with a mean free path = ()-1

After a path, the particle is supposed to scatter on a nucleon.

1. J. Cugnon, Phys. Rev. C 22(1980)18852. H.W.Bertini Phys.Rev.188(1969)1711 3. Y. Yariv and Z. Fraenkel, Phys. Rev. C 20(1979)2227

A.1 Spallation – 9The Intra-Nuclear Cascade

Liège Bertini/Isabel

in the nucleus in the nucleus

A.1 Spallation – 10Production of Pions

The pions are the decay products of the resonances. They are mesons, exchange particles of the strong interaction between nucleons. The resonances and pions are coming from inelastic nucleon-nucleon reactions at beam energies above few hundred of AMeV (M ~ 140 MeV).

C. Hartnack et al., Nucl. Phys. A 495(1989)303

Pion cycle ( N

• NN N hard production• N decay• N NN absorption• N soft production

4 sorts of ’s

++ 1 (p++)+ 2/3 (p+0) + 1/3 (n++)0 2/3 (n+0) + 1/3 (p+-)- 1 (n+-)

A.1 Spallation – 11Evaporation

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/cT(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.

A.1 Spallation – 12Evaporation

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.

A.1 Spallation – 13Comparison with experimental results

A.1 Spallation – 14Comparison with experimental results

A.1 Spallation – 15Main Physical Aspects

1. 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 = 3.10-24 s)

A large amount of the energy is removed quickly (~ 20 fm/c) by the emission of a few fast nucleons and some pions.

2. 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.

3. The relative energy transfer is maximum for incident energies between 1 and 2 GeV.

4. On average, the proton loses energy with a rate which is universal.

5. The number of fast ejected particles peaks around 2 GeV.

A.1 Spallation – 16EURISOL

EURopean Isotope Separation On-Line radioactive nuclear beam facility http://www.ganil.fr/eurisol/

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• …

A.1 Spallation – 17Spallation sources

European Spallation Source (ESS) – EU http://www.neutron-eu.net/en/index.php????

Spallation Neutron Source (SNS) – Japan http://jkj.tokai.jaeri.go.jp/ (2007)

Spallation Neutron Source (SNS) – USA http://www.sns.gov (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!