  We report a comprehensive study of the noncentrosymmetric superconductor
Mo$_3$P. Its bulk superconductivity, with $T_c = 5.5$ K, was characterized via
electrical resistivity, magnetization, and heat-capacity measurements, while
its microscopic electronic properties were investigated by means of muon-spin
rotation/relaxation ($\mu$SR) and nuclear magnetic resonance (NMR) techniques.
In the normal state, NMR relaxation data indicate an almost ideal metallic
behavior, confirmed by band-structure calculations, which suggest a relatively
high electron density of states, dominated by the Mo $4d$-orbitals. The
low-temperature superfluid density, determined via transverse-field $\mu$SR and
electronic specific heat, suggest a fully-gapped superconducting state in
Mo$_3$P, with $\Delta_0= 0.83$ meV, the same as the BCS gap value in the
weak-coupling case, and a zero-temperature magnetic penetration depth
$\lambda_0 = 126$ nm. The absence of spontaneous magnetic fields below the
onset of superconductivity, as determined from zero-field $\mu$SR measurements,
indicates a preserved time-reversal symmetry in the superconducting state of
Mo$_3$P and, hence, spin-singlet pairing.

Superconductivity;Materials Science;Strongly Correlated Electrons