Nuclear-reaction models

Nuclear-reaction model ABRABLA07 and the universal empirical formula EPAX have been developed and are being maintained. These codes are not only of importance for understanding the nuclear reactions but also for estimating the intensities of the secondary beams that will be available at FAIR.

ABRABLA07

Contact person: Aleksandra Kelic-Heil

ABRABLA07 is a three-stage nuclear-reaction model developed for description of peripheral and semi-peripheral collisions at relativistic energies.
The first stage of the reaction is based on the abrasion picture, i.e. on the clean cut of the target nucleons by the interacting projectile (and vice versa). Because in the relativistic energy regime, the relative velocity
of the interacting nuclei exceeds the Fermi velocity of the constituent nucleons, the nucleon-nucleon 
collisions occur only within the overlapping zone between projectile and target. The rest of the projectile and target remain almost unaffected by the collision and continue to move with nearly the same velocities as before the collision. The number of nucleons, which are removed during the abrasion, depends only on the collision impact parameter. In ABRABLA, for a given mass loss, protons and neutrons are removed randomly from the projectile, and the N/Z ratio of the pre-fragment is subject to statistical fluctuations as given by the hyper-geometrical distribution. The excitation energy is related to the energies of the holes in the single-particle level scheme of the projectile after the collision as well as different collective effects. On the average, an excitation energy of 27MeV per abraded nucleon is induced. The angular momentum of the pre-fragment is obtained from the sum of the angular momenta of the removed nucleons on the basis of the shell model.
If the excitation energy per nucleon induced in the abrasion stage is larger than certain limiting value, then in the second stage the simultaneous emission of nucleons and clusters takes place due to thermal instabilities. This break-up stage is assumed to be very fast, the N/Z ratio of the initial pre-fragment is conserved, and the amount of energy released is parameterised on the basis on experimental data.
Once the excitation energy per nucleon falls below the limiting value, the sequential de-excitation, ablation, phase of the excited pre-fragments is modelled via an advanced evaporation code. The decay of the system is seen as a competition between evaporation of light particles - gammas, neutrons, 1,2,3H, 3,4,6He, IMFs and fission. Particle emission is based on the extended Wiesskopf-Ewing formalism with change in the angular momentum due to particle emission included. The fission probability is calculated at each evaporation step as a function of mass, nuclear charge, excitation energy and time with an elaborate analytical description based on the numerical solution of the Fokker-Plank equation. That permits a proper account for the early inhibition of fission caused by relaxation effects and, in this respect, it renders ABRABLA equivalent to a dynamical approach. In case the decaying system finally undergoes fission, the mass, nuclear charge, excitation energy and velocity of the primary fission fragments are calculated using a semi-empirical model. De-excitation of the primary fission fragments is then followed until they reach their
corresponding ground state.

The ablation-stage model - ABLA07, can be also used as a standalone model for description of low-energy compound nucleus reactions or can be combined with an adequate first-stage model and be used in other energy regimes (e.g. Fermi-energy regime) or for description of spallation reactions when combined with an intra-nuclear cascade model.

https://www.gsi.de/fileadmin/Kernreaktionen/238U_p.jpg
Comparison between measured and calculated with ABRABLA07 production cross sections in the reaction of 238U(1AGeV)+1H. Colour code shows cross sections in the logarithmic scale.
Comparison between measured and calculated with ABRABLA07 production cross sections in the reaction of 238U(1AGeV)+1H. Colour code shows cross sections in the logarithmic scale.

References for abrasion stage:

  • "A REEXAMINATION OF THE ABRASION-ABLATION MODEL FOR THE DESCRIPTION OF THE NUCLEAR FRAGMENTATION REACTION"
     J.-J. Gaimard, K.-H. Schmidt
     Nucl. Phys. A 531 (1991) 709-745
  •  "DISTRIBUTION OF Ir and Pt ISOTOPES PRODUCED AS FRAGMENTS OF 1 A GeV 197Au PROJECTILES - A THERMOMETER FOR PERIPHERAL NUCLEAR COLLISIONS"
    K.-H. Schmidt, T. Brohm, H.-G. Clerc, M. Dornik, M. Fauerbach, H. Geissel, A. Grewe, E. Hanelt, A. Junghans, A. Magel, W. Morawek, G. Muenzenberg, F. Nickel, M. Pfuetzner, C. Scheidenberger, K. Suemmerer, D. Vieira, B. Voss, C. Ziegler
     Phys. Lett. B 300 (1993) 313-316

References for break-up stage:

  •  "EXPERIMENTAL INDICATIONS FOR THE RESPONSE OF THE SPECTATOR TO THE PARTICIPANT BLAST"
    M. V. Ricciardi, T. Enqvist, J. Pereira, J. Benlliure, M. Bernas, E. Casarejos, V. Henzl, A. Kelic, J. Taieb, K.-H. Schmidt
    Phys. Rev. Lett. 90 (2003) 212302 / arXiv nucl-ex/0302024

References for de-excitation stage:

  • "ABLA07 - TOWARDS A COMPLETE  DESCRIPTION OF THE DECAY CHANNELS OF A NUCLEAR SYSTEM FROM  SPONTANEOUS FISSION TO MULTIFRAGMENTATION"
    A. Kelic, M.V. Ricciardi, K.-H. Schmidt
    Proceedings of the Joint ICTP-IAEA Advanced Workshop on Model Codes for Spallation Reactions, ICTP Trieste, Italy, 4-8 February 2008. Editors: D. Filges, S. Leray, Y. Yariv, A. Mengoni, A. Stanculescu, and G. Mank, IAEA INDC(NDS)-530, pagg. 181-221, Vienna, August 2008;
    arXiv_nucl-th/0906.4193v1; and references therein
  • "FRAGMENTATION OF SPHERICAL RADIOACTIVE HEAVY NUCLEI AS A NOVEL PROBE OF TRANSIENT EFFECTS IN FISISON"
    C. Schmitt, K.-H. Schmidt, A. Kelic, A. Heinz, B. Jurado,  P. N. Nadtochy
    Phys. Rev. C 81 (2010) 064602
  • "A CRITICAL ANALYSIS OF THE MODELLING OF DISSIPATION IN FISSION"
    B. Jurado, C. Schmitt, K.-H. Schmidt, J. Benlliure, A. R. Junghans.
    Nucl. Phys. A 747 (2005) 14-43, arXiv nucl-ex/0302003 (v2)
  • "EXPERIMENTAL EVIDENCE FOR THE SEPARABILITY OF COMPOUND-NUCLEUS AND FRAGMENT PROPERTIES IN FISSION"
     K.-H. Schmidt, A. Kelic, M.V. Ricciardi
     Europhys. Lett.    83 (2008) 32001;  arXiv nucl-ex/0711.3967v1
  •  "CALCULATED NUCLIDE PRODUCTION YIELDS IN RELATIVISTIC COLLISIONS OF FISSILE NUCLEI"
     J. Benlliure, A. Grewe, M. de Jong, K.-H. Schmidt, S. Zhdanov
     Nucl. Phys. A 628 (1998) 458-478

 

EPAX

Contact person: Klaus Suemmerer

EPAX is a universal analytical formula allowing to calculate the yields from fragmentation of all non-fissile
projectiles in the range of projectile masses between about 40 to 209. In particular, the formula tries to take properly into account the influence of the projectile proton or neutron excess onto the neutron-to-proton ratio of the fragments.
The EPAX parameterization is valid only in the limiting-fragmentation regime, where the fragmentation
yields do no longer depend on the projectile energy. This regime corresponds to energies well above the
Fermi energy (~40 A MeV), where the assumption of the limiting fragmentation is valid, and is thus well
satisfied in the relativistic energy regime investigated in our experiments. The EPAX parameterization aims at reproducing the bulk of the measured cross sections within a factor of two for fragment masses down to about half the projectile mass.  

References:

  • "IMPROVED EMPIRICAL PARAMETRIZATION OF FRAGMENTATION CROSS SECTIONS"
    K. Sümmerer
    Phys. Rev. C 86 (2012) 014601; Erratum Phys. Rev. C 87(2013) 039903
  • "MODIFIED EMPIRICAL PARAMETRIZATION OF FRAGMENTATION CROSS SECTIONS"
    K. Sümmerer and B. Blank
    Phys. Rev. C 61, 034607
  • "TARGET FRAGMENTATION OF Au AND Th BY 2.6 GeV PROTONS"
    K. Sümmerer, W. Brüchle, D. J. Morrissey, M. Schädel, B. Szweryn, and Yang Weifan
    Phys. Rev. C 42 (1990) 2546