  The temperature dependent measurements of the thermodynamic critical field
and the specific heat for the pressure stabilized Ga-II phase of elemental
Gallium are presented. The discussion of these and other Ga phases data in the
context of elemental and binary phonon-mediated type-I superconductors allowed
to establish simple scaling relations between BCS quantities such as $B_{\rm
c}(0)/T_{\rm c}\sqrt{\gamma_{\rm e}}$ and the specific heat jump at $T_{\rm c}$
versus the coupling strength $2\Delta/k_{\rm B} T_{\rm c}$ [$\Delta$ and
$B_{\rm c}(0)$ are the zero-temperature values of the superconducting energy
gap and the thermodynamic critical field, respectively, $T_{\rm c}$ is the
transition temperature, and $\gamma_{\rm e}$ is the electronic specific heat].
The scaling relations can be analytically expressed by taking into account
strong-coupling corrections to BCS theory. Such correlations can naturally
explain the linear relation between $B_{\rm c}(0)$ and $T_{\rm c}$, which holds
for type-I superconducting materials.
