Static and dynamic polarizabilities of the non-relativistic hydrogen molecular ion

Static and dynamic polarizabilities are calculated for the non-relativistic hydrogen molecular ion by solving the three-body Schrödinger equation in perimetric coordinates with the Lagrange-mesh method. The static dipole polarizabilities of the ground-state rotational band are computed for total orbital (or rotational) angular momenta from L = 0 to 39 with an absolute accuracy of about 10-9 au. For L = 0, 1 and 2, slightly less accurate results are also given for the first three vibrational excited levels. For the ground state, dynamic dipole polarizabilities as well as static and dynamic quadrupole polarizabilities are computed. To illustrate the versatility of the method, the static dipole polarizability of the hydrogen molecular ion in a Debye plasma is also determined.