  We have determined a value for the $^1S_0$ neutron-neutron scattering length
($a_{nn}$) from high-precision measurements of time-of-flight spectra of
neutrons from the $^2H(\pi^-,n \gamma)n$ capture reaction. The measurements
were done at the Los Alamos Meson Physics Facility by the E1286 collaboration.
The high spatial resolution of our gamma-ray detector enabled us to make a
detailed assessment of the systematic uncertainties in our techniques. The
value obtained in the present work is $a_{nn} = -18$.63 $\pm $0.10
(statistical) $\pm$ 0.44 (systematic) $\pm$ 0.30 (theoretical) fm. This result
is consistent with previous determinations of $a_{nn}$ from the $\pi^-d$
capture reaction. We found that the analysis of the data with calculations that
use a relativistic phase-space factor gives a more negative value for $a_{nn}$
by 0.33 fm over the analysis done using a nonrelativistic phase-space factor.
Combining the present result with the previous ones from $\pi^-d$ capture
gives: $a_{nn} = - 18$.63 $\pm$ 0.27 (expt) $\pm$ 0.30 fm (theory). For the
first time the combined statistical and systematic experimental uncertainty in
$a_{nn}$ is smaller than the theoretical uncertainty and comparable to the
uncertainty in the proton-proton $^1S_0$ scattering length ($a_{pp}$). This
average value of $a_{nn}$ when corrected for the magnetic-moment interaction of
the two neutrons becomes -18.9 $\pm$ 0.4 fm which is 1.6 $\pm$ 0.5 fm different
from the recommended value of $a_{pp}$, thereby confirming charge symmetry
breaking at the 1% confidence level.
