Nuclear Reactions II A NucleonNucleus Reactions A 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

Nuclear Reactions - II Intermediate and Relativistic Energies 1. Spallation 2. Induced Fission 3. Fragmentation 4. Multifragmentation 5. Vaporization

A-1 Spallation - 0 Introduction • 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 – 1 Generalities 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 (Me. V) 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

A. 1 Spallation – 2 Generalities 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

A. 1 Spallation – 3 Light particle emission Cross section (mb/Me. V-sr) Neutron spectra p(800 Me. V) + Pb 0° 7. 5° 30° evaporation process independent of the angle! 1 10 150° 120° En (Me. V) 100 60° due to quasi-elastic scattering peripheral collisions due to quasi-inelastic scattering neutron ejected by the proton which is excited to a D+ resonance 1000 Conclusion: the spallation reaction is a TWO STEP process! Proton spectra similar shapes as the neutron spectra

A. 1 Spallation – 4 Residues 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. 208 Pb Intermediate Mass Fragments (IMF) + p at 1 AGe. V fission products spallation residues very light fragments: produced by fast ejection (cascade) + evaporation of the remnant

A. 1 Spallation – 6 Residues 208 Pb + p at 1 AGe. V

A. 1 Spallation – 7 The 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) projectile (p, n, p, . . . ) target 2. Evaporation of the residue (~ 10– 20 - ~10 -16 s)

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. Liège 1: All particles are propagating freely until two reach the minimum relative distance of approach dmin. They scatter if dmin (stot/p) 2. Bertini 2/Isabel 3: 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

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

A. 1 Spallation – 10 Production of Pions 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 AMe. V (Mp ~ 140 Me. V). Pion cycle ( D Np D ) • • NN DN D Np DN NN Np D hard D production D decay D absorption soft D production 4 sorts of D’s D++ 1 (p+p+) D+ 2/3 (p+p 0) + 1/3 (n+p+) D 0 2/3 (n+p 0) + 1/3 (p+p-) D- 1 (n+p-) C. Hartnack et al. , Nucl. Phys. A 495(1989)303

A. 1 Spallation – 11 Evaporation 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.

A. 1 Spallation – 12 Evaporation 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, 3 He, 4 He), but not for the emission of heavier nuclei or fission. Note: the average total neutron multiplicity is about 4 times the multiplicity of the neutrons coming from the cascade stage.

A. 1 Spallation – 13 Comparison with experimental results

A. 1 Spallation – 14 Comparison with experimental results

A. 1 Spallation – 15 Main 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 Ge. V. 4. On average, the proton loses energy with a rate which is universal. 5. The number of fast ejected particles peaks around 2 Ge. V.

A. 1 Spallation – 16 EURISOL 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 – 17 Spallation 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 Ge. V on Pb target with a thickness of 60 cm produces about 25 neutrons!