  We consider the $L^{2}$-critical quintic focusing nonlinear Schr\"odinger
equation (NLS) on ${\bf R}$. It is well known that $H^{1}$ solutions of the
aforementioned equation blow up in finite time. In higher dimensions, for
$H^{1}$ spherically symmetric blow-up solutions of the $L^{2}$-critical
focusing NLS, there is a minimal amount of concentration of the $L^{2}$-norm
(the mass of the ground state) at the origin. In this paper we prove the
existence of a similar phenomenon for the one-dimensional case and rougher
initial data, $(u_{0}\in H^{s}, s<1)$, without any additional assumption.
