Input:

  T = 2000. K
  Z = 1
  R = 2.
  r_0 = 1.

n_av = 2.01381e+23 (per cc)
n_av_check = 2.01381e+23 (per cc)
mu/kT = 30.0712

  r/R       ePhi/kT      mu_eff/kT      n (per cc)

0.0200  3.792412e+03  3.822483e+03  7.6866882167e+25
0.0400  1.821855e+03  1.851926e+03  2.5908366515e+25
0.0600  1.166946e+03  1.197017e+03  1.3461188438e+25
0.0800  8.408919e+02  8.709630e+02  8.3540500243e+24
0.1000  6.463360e+02  6.764072e+02  5.7172726039e+24
0.1200  5.174940e+02  5.475652e+02  4.1640581229e+24
0.1400  4.261738e+02  4.562450e+02  3.1670210569e+24
0.1600  3.582804e+02  3.883516e+02  2.4870521446e+24
0.1800  3.059840e+02  3.360552e+02  2.0019750075e+24
0.2000  2.645876e+02  2.946588e+02  1.6436852595e+24
0.2200  2.311027e+02  2.611739e+02  1.3716149065e+24
0.2400  2.035376e+02  2.336088e+02  1.1603000079e+24
0.2600  1.805140e+02  2.105851e+02  9.9306534317e+23
0.2800  1.610476e+02  1.911188e+02  8.5860185982e+23
0.3000  1.444173e+02  1.744885e+02  7.4901075377e+23
0.3200  1.300825e+02  1.601536e+02  6.5863501310e+23
0.3400  1.176300e+02  1.477012e+02  5.8333461316e+23
0.3600  1.067389e+02  1.368101e+02  5.2002212315e+23
0.3800  9.715605e+01  1.272272e+02  4.6635667221e+23
0.4000  8.867918e+01  1.187503e+02  4.2053723292e+23
0.4200  8.114478e+01  1.112159e+02  3.8115990770e+23
0.4400  7.441928e+01  1.044904e+02  3.4711746545e+23
0.4600  6.839251e+01  9.846366e+01  3.1752737547e+23
0.4800  6.297285e+01  9.304401e+01  2.9167943786e+23
0.5000  5.808350e+01  8.815466e+01  2.6899712665e+23
0.5200  5.365963e+01  8.373079e+01  2.4900868264e+23
0.5400  4.964614e+01  7.971730e+01  2.3132523868e+23
0.5600  4.599593e+01  7.606709e+01  2.1562408553e+23
0.5800  4.266853e+01  7.273969e+01  2.0163574127e+23
0.6000  3.962896e+01  6.970012e+01  1.8913386692e+23
0.6200  3.684685e+01  6.691801e+01  1.7792733396e+23
0.6400  3.429575e+01  6.436691e+01  1.6785393480e+23
0.6600  3.195248e+01  6.202364e+01  1.5877535881e+23
0.6800  2.979668e+01  5.986784e+01  1.5057315139e+23
0.7000  2.781038e+01  5.788154e+01  1.4314544263e+23
0.7200  2.597770e+01  5.604886e+01  1.3640428307e+23
0.7400  2.428453e+01  5.435569e+01  1.3027346124e+23
0.7600  2.271831e+01  5.278947e+01  1.2468670657e+23
0.7800  2.126783e+01  5.133899e+01  1.1958620198e+23
0.8000  1.992306e+01  4.999422e+01  1.1492134691e+23
0.8200  1.867499e+01  4.874615e+01  1.1064772412e+23
0.8400  1.751553e+01  4.758669e+01  1.0672623291e+23
0.8600  1.643737e+01  4.650853e+01  1.0312235904e+23
0.8800  1.543392e+01  4.550508e+01  9.9805557463e+22
0.9000  1.449922e+01  4.457038e+01  9.6748728509e+22
0.9200  1.362786e+01  4.369902e+01  9.3927771831e+22
0.9400  1.281492e+01  4.288608e+01  9.1321205340e+22
0.9600  1.205593e+01  4.212709e+01  8.8909838600e+22
0.9800  1.134682e+01  4.141797e+01  8.6676492072e+22
1.0000  1.068386e+01  4.075502e+01  8.4605755070e+22