H2+, HD+, D2+ hydrogen molecular ions

Abstract

The article is devoted to the study of statistical polarizability of molecular ions H₂⁺, HD⁺, D_2⁺ . Particularly DC Stark effect (at constant electric field) in the nonrelativistic approximation was calculated. Our calculation takes into account the dependence of the rotational-vibrational states, and the dependence of the hyperfine splitting of levels. We have considered special cases that allow obtain explicit analytical solutions associated with the algebra of angular momentum.

The results of the work have a great importance in metrology. At first to clarify the fundamental physical constants, primarily to improve the value of the mass ratio of the electron to the proton m_e/m_p. Precise calculations of the values of static polarizabilities will be of a great importance for verification experiments of variations of fundamental constants in time in a laboratory. Recently has been proposed to use molecular hydrogen ions H₂⁺  and HD⁺ for development of high-precision clock with a relative stability of order of 10^-18 at room temperature. For comparison, the best accuracy achieved in cesium clocks (the current standard time) implemented by the National Institute of Standards and Technology in 2011: 2.3 * 10^-16.