Energy and sreening constants of the one-dimension helium atom

To calculate the energy and screening constants of a one-dimensional helium atom, the same mathematical formalism was used that was previously applied by the authors in the case of the “ordinary” three-dimensional helium atom. Such electronic configurations of the helium atom were considered when one of the electrons is in the ground state, and the second electron in one of the excited states when the principal quantum number takes on values. For these configurations, it was found that the screening constant monotonically decreases with increasing, tending to zero in the formal limit, and the energy modulus in the same limit tends to a constant value in complete analogy with a three-dimensional atom. The results of numerical calculations of and in this range of variation of the principal quantum number are presented both in the form of tables and graphically. It can be expected that in the near future the conclusions made in this work can be verified, since one-dimensional atoms in the Bose-Einstein condensate phase have already been obtained experimentally, and it is quite possible that one-dimensional atoms can also be obtained.

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