  We examine a one-parameter family of analytical solutions representing
spherically symmetric collapse of a nonlinear massless scalar field with
self-interaction in an asymptotically flat spacetime. The time evolution
exhibits a type of critical behavior. Depending on the scalar charge parameter
$q$ as compared to a critical value $q^*$, the incoming scalar wave collapses
either to a globally naked central singularity if $q<q^*$ (weak field) or to a
scalar-hairy black hole if $q>q^*$ (strong field), both having finite
asymptotic masses. Near the critical evolution, the black hole mass follows a
product-logarithmic scaling law: $-M^2\ln M \sim q-q^*$ with $0<M\ll 1$ and
$q>q^*$. The solution admits no self-similarity and satisfies the null and the
strong energy conditions.
