  Understanding the nature of the transition from the delocalized to the
many-body localized (MBL) phase is an important unresolved issue. To probe the
nature of the MBL transition, we investigate the universal properties of
single-particle excitations produced in highly excited many-body eigenstates of
a disordered interacting quantum many-body system. In a class of
one-dimensional spinless fermionic models with random disorder, we study the
finite size scaling of the ratio of typical to average values of the
single-particle local density of states and the scattering rates across the MBL
transition. Our results indicate that the MBL transition in this class of
one-dimensional models of spinless fermions is continuous in nature. For
various ranges of interactions in the system, the critical exponent $\nu$ with
which the correlation length $\xi$ diverges at the transition point $W_c$, $\xi
\sim |W-W_c|^{-\nu}$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound
$\nu \ge 2/d$ where $d$ is the physical dimension of the system. We also
discuss why the critical exponent obtained from finite-size scaling of the
conventional diagnostic of many-body localization, the level-spacing ratio,
strongly violates the CCFS bound while the single-particle density of states
and scattering rates are consistent with the CCFS criterion.
