For theoretical results, this is different. For the theoreticians, a o is defined as a combination of parameters. Therefore a o is constant only if all the parameters are constant. One then has to be careful in reading theoretical results and look at the method used to see if there really is a dependence of a o or if it is just a unit. Let us make sure that the physics is not lost in those calculations.
Most authors do their calculations in atomic units.
This means that the unit of mass is the electron mass. The authors then go on with numerical calculations to solve the equations. All the results in this appendix being theoretical, we made sure that their dependence in a o was real. The Dirac-Fock method gives no relativistic correction of the electron mass with respect to an external gravitational potential. This gives 2.00 a o .