Numerical Calculation of the Neutral Fermion Gap at $ u=5/2$

We present the first numerical computation of the neutral fermion gap, $Delta_psi$, in the $ u=5/2$ quantum Hall state, which is analogous to the energy gap for a Bogoliubov-de Gennes quasiparticle in a superconductor. We find $Delta_psi approx 0.027 frac{e^2}{epsilon ell_0}$, comparable to the charge gap, and discuss the implications for topological quantum information processing. We also deduce an effective Fermi velocity $v_F$ for neutral fermions from the low-energy spectra for odd numbers of electrons, and thereby obtain a correlation length $xi_{psi}={v_F}/Delta_{psi} approx 1.3, ell_0$. We comment on the implications of our results for electronic mechanisms of superconductivity more generally.