Electron and Positron Chemical Potentials


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* The software tool in chem_poten.tbz returns the electron and positron chemical potentials as a function of temperature, density and Ye for a fully ionized stellar plasma.

The electron chemical potentials do not include the electron rest mass, so the value returned is the "kinetic chemical potential". This means that the positron chemical potential must have the rest-mass terms appear explicitly, ηpos = -ηele - 2mec2. You can see this being applied at the end of the routine.

This tool is derived from the Helmholtz equation of state, but as a stand-alone electron/positron chemical potential solver may be useful for computing weak reaction rates, reaction rate screening factors, etc where invoking the full machinery of an equation of state may not be desirable.

Top 10 tips about the chemical potential (from Peter Saeta)
  1. It expresses how eager a system is for particles.
  2. In equilibrium it is equal in two systems placed in diffusive contact.
  3. Particles move from a region of high chemical potential to a region of low chemical potential.
  4. It can be found by differentiating thermodynamic potentials with respect to N.
  5. It has an internal part and an external part; the external part is just a normal per-particle potential energy, such as mgh.
  6. It is the Gibbs free energy per particle, G/N.
  7. It is used to describe chemical equilibria.
  8. For a monatomic ideal gas, it is kT ln (νQ/ν).
  9. It is enormously useful in describing equations of state.
  10. It is the factor you use to get the particle number right!

Number 10 is probably the most pragmatic tip. In the above application, one balances the number density of electrons from fully ionized material with the net number density of electrons and positrons coming from the relevant Fermi-Dirac integrals.

Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.