Ionization Energy Loss — B. A. Weaver

The Article

This web-page is in support of Weaver & Westphal (2002) in Nuclear Instruments and Methods B. Subscribers to Science Direct can download our article here. If you do not know if you are subscribed to this service, please contact your university or other institutional library.

One of the primary features of our code is the implementation of the results of Lindhard & Sørensen (1996). This work used exact solutions to the Dirac equation to replace several previous corrections to the ionization energy loss formula. The code includes the ultrarelativistic limit, including finite nuclear size effects. These effects cancel other terms in the energy loss formula, so that at high energies, ionization energy loss becomes constant (Sørensen, 1998).

We have also recently added estimates of energy loss due to pair production and projectile bremsstrahlung by Sørensen (2002). This work has shown that bremsstrahlung energy loss is much smaller than the formula in our paper would suggest. This is due to our treatment of the projectile and target nuclei as point particles in the derivation of these formulas.

The Code

The source code is currently maintained on GitHub.

The code which has been developed so far is available as a GZIPPED TAR archive and can be downloaded from the links below. The code is fully documented, including full references, and will be updated as new effects are added. The current version is released under a 3-clause BSD-style license. Versions prior to 2.0.0 are released under the Lesser GNU Public License (LGPL).

The following versions are available:

You can also view the library of absorbing media used in the code.

Stopping Power Calculator

A web-based stopping power calculator is now available. It is based on the code above, but is still in an experimental state. Use with caution.


  1. J. Lindhard and A. H. Sørensen,Phys. Rev. A 53 (1996) 2443.
  2. A. H. Sørensen, in Photonic, Electronic and Atomic Collisions; Invited Papers XX Int. Conf. on the Physics of Electronic and Atomic Collisions, eds. F. Aumayr and H. Winter (World Scientific, Singapore, 1998) 475.
  3. A. H. Sørensen, in Application of Accelerators in Research and Industry: 17th Int. Conf. on the Application of Accelerators in Research and Industry, No. 680 in AIP Conference Proceedings, eds. J. L. Duggan and I. L. Morgan (Springer-Verlag, Berlin, 2002) 102.
  4. B. A. Weaver and A. J. Westphal, Nucl. Inst. Meth. B 187 (2002) 285.

Questions & Contact Information

Contact information.