  The filtered laser excitation technique was applied for measuring transition
frequencies of the Ca$_2$ B-X system from asymptotic levels of the
X$^1\Sigma_{\mathrm g}^{+}$ ground state reaching $v''=38$. That level has an
outer classical turning point of about 20~\AA which is only 0.2 \rcm below the
molecular $^1$S$+^1$S asymptote. Extensive analysis of the spectroscopic data,
involving Monte Carlo simulation, allowed for a purely experimental
determination of the long range parameters of the potential energy curve. The
possible values of the s-wave scattering length could be limited to be between
250$a_0$ and 1000$a_0$.
