  The work describes the properties of the high-pressure superconducting state
in phosphor: $p\in\{20, 30, 40, 70\}$ GPa. The calculations were performed in
the framework of the Eliashberg formalism, which is the natural generalization
of the BCS theory. The exceptional attention was paid to the accurate
presentation of the used analysis scheme. With respect to the superconducting
state in phosphor it was shown that: (i) the observed not-high values of the
critical temperature ($\left[T_{C}\right]_{p=30{\rm GPa}}^{\rm max}=8.45$ K)
result not only from the low values of the electron - phonon coupling constant,
but also from the very strong depairing Coulomb interactions, (ii) the
inconsiderable strong - coupling and retardation effects force the
dimensionless ratios $R_{\Delta}$, $R_{C}$, and $R_{H}$ - related to the
critical temperature, the order parameter, the specific heat and the
thermodynamic critical field - to take the values close to the BCS predictions.
