ИСТИНА

The properties of the ground state of the hydrogen atom confined in a vacuum spherical cavity with third type boundary condition for the electron wave function are studied by numerical simulation. From the results of computational experiments follow that in the adiabatic approximation depending on the parameters of the cavity, atom could be in stable equilibrium at the center of the cavity or shifts towards its periphery, i.e. there is a spontaneous breaking of spherical symmetry. If the shift exists, an increasing size of the cavity will cause the tendency of the binding energy of the atom and the distance between it and the boundary to the limiting values determined by the task of an atom over the plane with third type boundary condition. To achieve the required accuracy in certain ranges of values of the cavity parameters arbitrary-precision arithmetic was used. Also on the basis of calculations with cutoff parameter for the angular momentum varying in the range 28-40, the special smooth extrapolating function was selected that allows take into account the contributions of the angular momenta up to 1000 properly.