Abstract
A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green’s function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed t-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.
Highlights
Study of the few-body quantum systems persists a perspective line of the advancement of the modern physics
A new general formalism for determining the electric multipole polarizabilities of quantum bound systems based on the use of the transition matrix in momentum space has been developed
There exists a discrepancy between the direct experimental result for the electric dipole polarizability of the nucleus 3He and the result deduced from the data for the total 3He photoabsorption cross section using the sum rule 2 [9]
Summary
Study of the few-body quantum systems persists a perspective line of the advancement of the modern physics. In this paper we formulate the direct t-matrix approach to determination of the electric polarizabilities of a bound system that relies on the solution of the integral equations for both the bound-state wave function and corresponding components of the partial transition matrix of the system. It is shown that the electric 2 -pole polarizability of the two-particle S -state bound complex contains information both on derivatives (of the order and lower) of the wave function in momentum space and on the partial component of the transition matrix that corresponds to the orbital state with l.
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