Polarizabilities of $^3$P atoms and van der Waals coefficients for their interaction with helium atoms

The effectiveness of the buffer gas cooling depends on the relative efficiency of elastic and inelastic collisions of the atoms with $^3$He atoms at temperatures below 0.4 K. Inelastic collisions lead to trap loss. The inelastic cross sections are controlled by the energy separations of the interaction potentials of the different symmetries of the molecular system formed by the approach of the helium atom and the gas atom. Scattering at low temperatures is sensitive to the interactions at large internuclear distances R and the range of candidate atoms can be explored through calculations of the long range anisotropy. Time-dependent density functional theory with self-interaction correction is applied to obtain the scalar and tensor dynamic polarizabilities of atoms in $^3$P states. The static polarizabilities are in good agreements with previous values. The dynamic polarizabilities are then used to evaluate the leading term in the long range interaction between the $^3$P atoms and helium. They are significant in determining the likelihood that the $^3$P atoms can be trapped in a helium buffer gas.