Induced toroid structures and toroid polarizabilities

The frequency-dependent toroid dipole polarizability {γ}({ω}) of a (nonrelativistic, spinless) hydrogenlike atom in its ground state is calculated analytically in terms of two Gauss hypergeometric functions. The static result reads {γ}({ω}=0)=(23/60)α²{Z}^{{-}4}a₀{}⁵(α=fine-structure constant, Z=nucleus charge number,{a}₀$=Bohr radius). Comparing the present evaluations for atoms with previous ones for pions, one sees that the role of the induced toroid moments (as against that of the usual electric ones) increases considerably towards smaller distances (or higher characteristic excitation energies). It might become dramatic at the subhadronic level.