Constance K. Walker Home Page


Program on Nuclear Reaction Phenomenology



Constance Kalbach Walker
(Senior Research Scientist, retired)


Program Overview

*          The TUNL Program on Nuclear Reaction Phenomenology has developed models to describe preequilibrium nuclear reactions. In these reactions, particle emission occurs before the energy brought into the system by the bombarding particle has become randomly distributed throughout the nucleus. The program is built around the exciton model, first proposed by J. J. Griffin in 1966, though this is supplemented by a number of auxiliary models. The models are implemented in the computer code preco. Versions of the code, written in Fortran-77, have been periodically released to the public along with extensive documentation of the physics and the code itself. Much of this work was conducted as part of the U.S. Nuclear Data Program, administered through the National Nuclear Data Center at Brookhaven National Laboratory, though this funding has been terminated and I am now retired. The work was carried out at the Triangle Universities Nuclear Laboratory or TUNL


*          The exciton model is a simple, statistical model for describing the continuum energy differential and double differential cross sections of particles emitted during energy equilibration in light particle induced reactions at incident energies of around 14 to 200 MeV. Because of its simplicity, its physical transparency, its utility, and its adaptability, the exciton model continues to be used in spite of the development of more microscopic and quantum mechanical models. In the preco code, the exciton model is supplemented by a number of smaller models treating direct reaction mechanisms not described by the exciton model. These direct reactions are particularly important for reactions with complex particles (deuterons, tritons, He-3, and alpha particles) in the entrance and/or exit channel. Model and code development uses simple physical concepts and relies on available data both to direct choices between alternative formulations of a model concept and to provide values for key model parameters that cannot be obtained from independent sources.


*          The code preco has been used around the world, either alone or in Hauser-Feshbach model codes, for both basic and applied research. The models, code and global input set are being refined and benchmarked against a broad range of energy spectra from the literature in order to allow the reliable calculation of unmeasured or unmeasurable spectra without the use of adjustable parameters. For many years the primary focus was on reactions with only nucleons (neutrons and protons) in the entrance and exit channels. More recently that focus has shifted to reactions involving complex particles. The description of these reactions was significantly updated in preco -2000 and again in preco -2006. One additional mechanism, projectile breakup, was missing from the code. A description of it was published in January 2017 in Physical Review C, but the model has not been incorporated into preco.

Code Features

*          Both preco -2000 and preco -2006 permit the simultaneous inclusion of shell structure, pairing, isospin conservation, and finite potential well depth effects in a two-component version of the exciton model. The finite well depth corrections include additional limitations that apply when the initial target-projectile interaction occurs primarily near the nuclear surface. Primary preequilibrium emission of all light particles from nucleons through alpha particles is considered, while secondary emission is only calculated for neutrons and protons.


*          Additional models in the code give a phenomenological statistical description of the direct transfer of one or more nucleons (stripping, pickup, and exchange reactions) and of direct knockout and inelastic scattering involving cluster degrees of freedom. The direct transfer model has been extensively updated for preco -2006. Excitation of strong collective states -- both discrete spectroscopic states and giant resonance states -- is also included, along with a highly over-simplified model for elastic scattering. Angular distributions at specific emission energies are calculated using global, empirical systematics. The model for projectile breakup is not yet included but will be important for a complete description of reactions induced by deuterons, tritons, He-3 ions, and, at higher incident energies, alpha particles.


*          Further details about the code are available in the extensive users manual which describes all of the incorporated physics as well as the structure and use of the code.

Projectile Breakup

*          A model was developed to describe the breakup of light complex-particle projectiles (deuterons, tritons, He-3 and alpha particles). This effort was part of a coordinated research project (CRP) with the International Atomic Energy Agency in Vienna. The goal of the CRP was to produce an expanded and updated data library, to be called FENDL-3, designed to fill the data needs of the fusion energy community. In particular, the design of the International Fusion Materials Irradiation Facility requires a knowledge of deuteron-induced reactions, in which projectile breakup is a dominant mechanism.  The model is described in Phenomenological Model for Light-Projectile Breakup, Phys. Rev. C 95, 014606 (2017) [abstract].

Code Availability

*          preco -2006 was formally released in July 2007 and is currently available as Fortran-77 source code plus a users manual from the Radiation Safety Information Computational Center at Oak Ridge National Laboratory (see the code description). Sample input and output files and a Windows executable file are also included in the code package.


Last modified 20 August 2021