For each neutral alkali atom (Li, Na, K), run the spherically-symmetric multi-shell RealQM solver to ground state, then read off the boundary M[NSHELLS−1]·h between the outermost core shell and the valence shell. That radius is the RealQM-native r_c for the empty-core + Neumann reduced model. Compare to the r_c values fitted in valence1_spectrum.html.

Note: The simulator's MAXSHELLS=6 limit covers Li, Na, K but not Rb, Cs.

Run Li, Na, K to convergence click Run