  Relativistic dipolar to hexadecapolar polarizabilities of the ground state
and some excited states of hydrogenic atoms are calculated by using numerically
exact energies and wave functions obtained from the Dirac equation with the
Lagrange-mesh method. This approach is an approximate variational method taking
the form of equations on a grid because of the use of a Gauss quadrature
approximation. The partial polarizabilities conserving the absolute value of
the quantum number $\kappa$ are also numerically exact with small numbers of
mesh points. The ones where $|\kappa|$ changes are very accurate when using
three different meshes for the initial and final wave functions and for the
calculation of matrix elements. The polarizabilities of the $n=2$ excited
states of hydrogenic atoms are also studied with a separate treatment of the
final states that are degenerate at the nonrelativistic approximation. The
method provides high accuracies for polarizabilities of a particle in a Yukawa
potential and is applied to a hydrogen atom embedded in a Debye plasma.

Atomic Physics