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A new general formalism for determining the electric multipolepolarizabilities of quantum (atomic and nuclear) bound systems based on the useof the transition matrix in momentum space has been developed. As distinct fromthe conventional approach with the application of the spectral expansion of thetotal Green's function, our approach does not require preliminary determinationof the entire unperturbated spectrum; instead, it makes possible to calculatethe polarizability of a few-body bound complex directly based on solvingintegral equations for the wave function of the ground bound state and thetransition matrix at negative energy, both of them being real functions ofmomenta. A formula for the multipole polarizabilities of a two-body boundcomplex formed by a central interaction potential has been derived and studied.To test, the developed $T$-matrix formalism has been applied to the calculationof the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.

Direct T-Matrix Approach to Determination of the Electric Polarizabilities of Quantum Bound Systems