Speaker
Description
Abstract
The ELECTR module of NJOY is designed to produce complete and accurate multigroup electroatomic cross sections from ENDF/B-IV, -V -VI or -VII data[1]. It will also work with the newer formats developed for ENDF/B-VII. ELECTR produces restricted cross sections consistent with a solution of the multigroup Boltzmann-Fokker-Planck (BFP) equation. Total, elastic, inelastic (collision and bremsstrahlung) cross sections can be averaged using a variety of group structures and weighting functions. The Legendre components of the within-group elastic and group-to-group inelastic collision cross sections are calculated using tabulated data in energy and analytic expressions of the angular deviation recovered from the CEPXS code[2]. Here, we propose an Open-Source implementation of this module, named ELECTR in NJOY-2012 and NJOY-2016.[3] ELECTR also computes partial energy deposition and charge deposition cross sections for each reaction and sum these partial contributions. The resulting multigroup constants are written on an intermediate GENDF file for later conversion to any desired format.
Introduction
ELECTR processes the following electroatomic reactions and collision laws from ENDF-102 evaluations:
- the impact electroionization is a correlated process including the (e,2e) inelastic collision differential cross section and relaxation production. Electrons scatter inelastically from the atomic electrons ejecting them from the $i-$th atomic shell with considerable kinetic energy. If $i\le 5$ ($K$, $L$ or $M$ shells), and if the atom is heavy, there is a production of additional relaxation radiation consisting of Auger electrons and fluorescence photons. These are produced in a cascade of shell transitions induced by the initial electron vacancy.
- the bremsstrahlung differential cross section. The bremsstrahlung process takes place when initial electron pass near atomic nuclei and inelastic radiative interaction occurs.
- the elastic collision differential cross section where the energy of the incident electron is conserved by the interaction. We consider the large angle elastic cross section (MT=525) corresponding to a deviation cosine with $-1 \le \mu \le 0.999999$. Forward peaked elastic scattering is further removed from the multigroup BFP equation using a transport correction.
- the microscopic stopping power $s(E)$ is the average rate at which the electrons lose energy at any point along their tracks, according to
\begin{equation}
s(E)= -{1\over N}{dE \over dx}
\end{equation}
where $N$ is the number of atoms per unit volume.
The stopping power represents components of atomic excitation, inelastic collision and bremsstrahlung processes. The stopping power is evaluated data, in units of Mev-barn, formally defined by the relation
\begin{equation}
s(E)=\int_{0^+}^E dE' \, (E-E')\, \sigma(E\rightarrow E')
\end{equation}
keeping in mind that $\sigma(E\rightarrow 0)$ or $\sigma(E\rightarrow E)$ may diverge. According to Ref [2], the lower energy limit must be set to $E/2$ for the collisional stopping power:
\begin{equation}
s^{\rm col}(E)=\int_{E/2}^E dE' \, (E-E')\,
\sigma_{\rm col}(E\rightarrow E') \ .
\end{equation}
- the energy and charge deposition cross sections are generated.
The electroatomic reactions are represented in ENDF-102 format with the MT numbers of Table 1. All reactions except 525 are written in restricted multigroup form on the GENDF tape. Reaction 525 is written in transport-corrected multigroup form. Restricted stopping powers are used to represent soft collisions in the Fokker-Planck operator. The excitation cross section representing a slowing down process through the electronic field of an atom (MT=528) is assumed to be soft. Other catastrophic reactions are used in the usual way. The soft component of the collisional and radiative stopping powers at group boundaries are written on the GENDF tape as MT=507 and MT=508.
Scattering laws of type LAW $=1$ for collision/ionization inelastic and bremsstrahlung reactions are stored in TAB2 records similar to those used for neutron-induced reactions in module GROUPR where tab1io data structures are replaced by listio data structures. The subroutine eetsed returns the secondary-energy distribution for electrons for all groups simultaneously, using an implementation similar to subroutines getsed of module GROUPR.
Table 1: Types of electroatomic material numbers
MT number: Class of data \
507: Collisional stopping power
508: Radiative (bremsstrahlung) stopping power
501: Total
525: Large angle elastic collision
527: Bremsstrahlung
534-572: Impact electroionization and relaxation production
530: Energy deposition by electrons
531: Charge deposition by electrons
References
[1] R. W. Roussin, J. R. Knight, J. H. Hubbell, and R. J. Howerton, ``Description of the DLC-99/HUGO Package of Photon Interaction Data in ENDF/B-V Format,'' Oak Ridge National Laboratory report ORNL/RSIC-46 (ENDF-335) (December 1983).
[2] L. J. Lorence, Jr., J. E. Morel and G. D. Valdez, ``Physics Guide to CEPXS: A Multigroup Coupled Electron-Photon Cross-Section Generating Code, Version 1.0,'' Sandia report SAND89-1685 (October 1989).
[3] R. E. MacFarlane and A. C. Kahler, ``Methods for Processing ENDF/B-VII with NJOY," Nuclear Data Sheets, 111, 2739 (2010).