A gas proportional chamber has been employed to make precise observations o
f the low-energy portion of the H-3 beta spectrum in methane molecules. Thi
s spectrum has been well fit to the combination of an electron screening po
tential of 76 +/- 4 (stat) +/- 9 (sys) eV, simultaneously with - 22 +/- 3 (
stat) +/- 9 (sys) eV of molecular neutralization energy recovered in ioniza
tion of the gas. Both of these values are consistent with expectations base
d on self-consistent field predictions. [S0556-2813(99)02309-2].