Our previous papers provided a classical description of one-electron diatomic molecules and of charge exchange. In the present paper we advanced these studies by providing a classical description of two-electron diatomic molecules, consisting of the two nuclei of charges Z and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$Z' \ge $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>Z</mi> <mo>′</mo> </msup> <mo>≥</mo> </mrow> </math></EquationSource> </InlineEquation> Z and two electrons. In particular, in laboratory and astrophysical plasmas, in the process of charge exchange between multicharged ions, there can form transient two-electron diatomic quasi-molecules containing nuclei of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$Z' \ge Z>> 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>Z</mi> <mo>′</mo> </msup> <mo>≥</mo> <mi>Z</mi> <mo>></mo> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We analyzed classical two-electron diatomic molecules in two configurations: one where the two electrons rotate in the same circular orbit, being at the opposite ends of the diameter; another where the two electrons rotate in two different quasi-circular orbits. We demonstrated that in the first configuration, the two-electron system is characterized by a lower energy in all cases than the corresponding one-electron system. Besides, we showed that the equilibrium range of the projection of the electrons orbit on the internuclear axis is smaller than in the corresponding one-electron case. We also analyzed the stability of the system against small fluctuations of the parameters of the electrons orbit and gave the ranges of the stability. Most importantly, for the first configuration we described classically the double charge exchange in plasmas. The feasibility of the classical description of the double charge exchange represents a counterintuitive result. For the second configuration, we demonstrated that it is stable when one electron is relatively close to one of the nuclei while the other electron is relatively close to the other nucleus.

Classical Description of Two-Electron Diatomic Molecules and of the Double Charge Exchange

期刊论文
出版模式：

开放获取
发表日期：

2026年7月31日

查看全文

N. Kryukov,
E. Oks

摘要

Our previous papers provided a classical description of one-electron diatomic molecules and of charge exchange. In the present paper we advanced these studies by providing a classical description of two-electron diatomic molecules, consisting of the two nuclei of charges Z and $Z' \ge $ $Z^{'} \geq$ Z and two electrons. In particular, in laboratory and astrophysical plasmas, in the process of charge exchange between multicharged ions, there can form transient two-electron diatomic quasi-molecules containing nuclei of $Z' \ge Z>> 1$ $Z^{'} \geq Z > > 1$ . We analyzed classical two-electron diatomic molecules in two configurations: one where the two electrons rotate in the same circular orbit, being at the opposite ends of the diameter; another where the two electrons rotate in two different quasi-circular orbits. We demonstrated that in the first configuration, the two-electron system is characterized by a lower energy in all cases than the corresponding one-electron system. Besides, we showed that the equilibrium range of the projection of the electrons orbit on the internuclear axis is smaller than in the corresponding one-electron case. We also analyzed the stability of the system against small fluctuations of the parameters of the electrons orbit and gave the ranges of the stability. Most importantly, for the first configuration we described classically the double charge exchange in plasmas. The feasibility of the classical description of the double charge exchange represents a counterintuitive result. For the second configuration, we demonstrated that it is stable when one electron is relatively close to one of the nuclei while the other electron is relatively close to the other nucleus.