The PD(X3Σ−) interaction potential is constructed using the CCSD(T) theory and the basis set, aug-cc-pV5Z. Using this potential, the spectroscopic parameters are accurately determined. The present Do, De, Re, ωe, ωeχe, αe, and Be are of 3.056 99 eV, 3.161 75 eV, 0.142 39 nm, 1701.558 cm−1, 23.6583 cm−1, 0.085 99 cm−1, and 4.3963 cm−1, respectively, which almost perfectly conform with the measurements. A total of 26 vibrational states is predicted when J = 0 by solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which favorably agree with the experiments. The total and various partial-wave cross sections are calculated for the elastic impact between two ground-state P and D atoms at 1.0 × 10−12 – 1.0 × 10−4 a.u. when they approach each other along the PD(X3Σ−) potential. No shape resonances exist in the total elastic cross sections, though the peaks can be found for each partial wave until l = 6. The shape of the total elastic cross sections is dominated by the s partial wave at very low temperatures. Due to the weakness of the shape resonances of each partial wave, they are all passed into oblivion by the strong total elastic cross sections.