A new analytical solving for electric polarizabilities of hydrogen-like atoms

The direct transition-matrix approach to the description of the electric polarization of the quantum bound system of particles is used to determine the electric multipole polarizabilities of the hydrogen-like atoms. It is shown that in the case of the bound system formed by the Coulomb interaction the corresponding inhomogeneous integral equation determining an off-shell scattering function, which consistently describes virtual multiple scattering, can be solved exactly analytically for all electric multipole polarizabilities. Our method allows to reproduce the known Dalgarno-Lewis formula for electric multipole polarizabilities of the hydrogen atom in the ground state and can also be applied to determine the polarizability of the atom in excited bound states.

Deuteron electric quadrupole and octupole polarizabilities

The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my recent work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.

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

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 Greens 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.

On the Electric Dipole Polarizability of the Three-Hadron Bound System

A simple analytical expression for the electric dipole polarizability of the three-hadron bound system having only one stable bound state has been derived neglecting by the higher orbital components of the off-shell three-body transition matrix at the energy of the bound state. As a case in point, we have estimated the electric dipole polarizability of the triton, using a cluster triton wave function and the Hulthen potential to describe the related p-n and n-d bound states.

Hypertriton Electric Polarizability

A rigorous formalism for determining the electric dipole polarizability of a three-hadron bound complex in the case that the system has only one bound (ground) state has been elaborated. On its basis, by applying a model wave function that takes into account specific features of the structure of the lightest hypernucleus and using the known low-energy experimental data for the p-n and lambda-d systems as input data, we have calculated the value of the electric dipole polarizability of the lambda hypertriton. It follows from our study that the polarizability of the lambda hypertriton is close to 3 fm^3 exceeding the polarizabilities of the ordinary three-nucleon nuclei by an order of magnitude.