  Extensive research has been lavished on effects of spin-orbit couplings (SOC)
in attractively interacting Fermi systems in both neutral cold atom systems and
condensed matter systems. Recently, it was suggested that a SOC drives a new
class of BCS to BEC crossover which is different than the conventional one
without a SOC. Here, we explore what are the most relevant physical quantities
to describe such a new BCS to BEC crossover and their experimental detections.
  We extend the concepts of the pairing length and "Cooper-pair size" in the
absence of SOC to Fermi systems with SOC. We investigate the dependence of
chemical potential, pairing length, "Cooper-pair size" on the SOC strength and
the scattering length at $ 3d $ (the bound state energy at $ 2d $) for three
attractively interacting Fermi gases with 3 dimensional (3d) Rashba, 3d Weyl
and 2d Rashba SOC respectively. We show that only the pairing length can be
used to characterize this new BCS to BEC crossover. Furthermore, it is the only
length which can be directly measured by radio-frequency dissociation spectra
type of experiments. We stress crucial differences among the pairing length,
"Cooper-pair size " and the two-body bound state size. Our results provide the
fundamental and global picture of the new BCS to BEC crossover and its
experimental detections in various cold atom and condensed matter systems.
