Nuclear Reactions Group

1. Introduction

ERYA (Emitted Radiation Yield Analysis) is a Labview program dedicated to PIGE (Particle Induced Gamma-ray Emission). ERYA calculates the mass fraction of the elements present in a given sample, by integrating the relevant nuclear reaction cross sections along its depth.

The free version of ERYA can be found in here. Choose the Installer according to your screen resolution:

2. ERYA Calculation

The gamma yield Y emitted by an isotope i of an element e within a thick target bombarded by a proton beam of energy E0 may be written as:

Erya formula

where εabs(Eγ) is the absolute efficiency of the detection system at the emitted energy Eγ, Np is the number of incident protons, fm and A-1 are the mass fraction (concentration) and the inverse of the atomic mass of the element e, fi is the abundance of isotope i, Nav is the Avogadro's number, σ(E) is the nuclear reaction cross section and ε(E) is the stopping cross section of the sample in units of energy area per mass. The last two variables depend on the energy E of the incident proton. In order to perform the integration, the target is divided in n layers parallel to the sample surface. Stopping power calculations were made using semi-empirical equations of Ziegler et al. and the Bragg rule.


  • ERYA uses 1 μC for beam fluence;
  • ERYA will automatically normalize to 1 the atomic fraction.

ERYA package includes:

  • Detector Efficiency;
  • Ziegler parameters.

All these files can be changed by the user.
Bug reports and suggestions are very welcome.
Email me at micaelafonseca (add


This code was written in collaboration with Dr. Nuno Franco.

3. Related Bibliography

  • R. Mateus, A.P. Jesus, J.P. Ribeiro, Nucl. Instr. and Meth. B 229 (2005) 302.
  • PhD thesis: "Análise de elementos leves por reacções nucleares com produção de radiação gama", Maria Micaela Leal da Fonseca, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa (2010).
  • PhD thesis: "Recolha Automática de aerossóis e a sua análise por técnicas analíticas nucleares", Rodrigo Clemente Velez Mateus, Faculdade de Ciências da Universidade de Lisboa (2003).
  • J. F. Ziegler, J. P. Biersack, U. Littmark, in "The Stopping and Ranges of ions in Solids", Vol. 1, Pergamon Press, New York, 1985.
  • SRIM: ; J.F. Ziegler, Nucl. Instr. and Meth. B219-220 (2004) 1027.