Rovibrational energy levels of the hydrogen molecule through nonadiabatic perturbation theory

Abstract

We present an accurate theoretical determination of rovibrational energy levels of the hydrogen molecule and its isotopologues in its electronic ground state. We consider all significant corrections to the Born-Oppenheimer approximation, obtained within nonadiabatic perturbation theory, including the mixed nonadiabatic-relativistic effects. Quantum electrodynamic corrections in the leading α 5 m and the next-to-leading α 6 m orders, as well as finite nuclear size effect, are also taken into account but within the Born-Oppenheimer approximation only. Final results for the transition wavelength between rovibrational levels achieve accuracy of the order of 10 −3 -10 −7 cm −1 , and are provided by simple to use computer code.

Precision tests of nonadiabatic perturbation theory with measurements on the DT molecule

“…We solve Eq. (8) with a discrete variable representation method [47,48] for χ , which is then used in a perturbative manner to calculate the rovibrational energy contributions χ |E (i,k) (R)|χ , where E (i,k) (R) denotes a correction of the order α i m(m/μ n ) k to the electronic potential. Regarding E (2) , its BO approximation E (2,0) is surely not accurate enough for our purposes.…”

“…The fine-structure constant α, Rydberg constant R ∞ , and Bohr radius a 0 are taken from [52], as are the respective proton, deuteron, and triton electron mass ratios: m p /m = 1 836.152 673 43 (11) (4) 0.014 837 5(1) 0.016 339 6(1) 0.019 890 6(1) E (4,0) 0.014 806 83 0.016 296 89 0.019 804 22 E (4,1) 0.000 030 62 0.000 042 72 0.000 086 36 E (5) −0.012 686 6(79) −0.014 105 2(96) −0.017 606 9(156) E (6) −0.000 113 5(3) −0.000 126 2(4) −0.000 157 8(5) E (7) 0.000 006 1 All the functions μ (R), μ ⊥ (R), W (R), and Y (R) in the above are defined and provided as analytic fits in Refs. [9,46,48]. Note that Y (R) incorporates both the adiabatic and nonadiabatic effects, and the g/u-mixing term from Eq.…”

“…All needed potentials are taken from the following: E (2,0) (R), Refs. [8,48]; E (2,1) (R), Ref. [49]; the nonadiabatic potentials in Eq.…”

“…More details concerning particular potentials are available in Ref. [48]. The theoretical uncertainty of an E (i) component includes the missing next term E (i,k max +1) ≈ E (i,k max ) m/μ n , where k max is the highest included term in the m/μ n expansion.…”

A study of New Physics searches with tritium and similar molecules

“…Precise theoretical predictions of rovibrational lines for hydrogen isotopologues have been made publicly available in the computer code H2Spectre [22,23] and are nicely reviewed in Ref. [24].…”