Hyperfine-interaction-induced g/u mixing and its implication on the existence of the first excited vibrational level of the A+ Σu+2 state of H2+ and on the scattering length of the H + H+ collision

Abstract

Ab initio calculations of the energy level structure of H2+ that include relativistic and radiative corrections to nonrelativistic energies and the diagonal part of the hyperfine interaction have predicted the existence of four bound rovibrational levels [(v = 0, N = 0 − 2) and (v = 1, N = 0)] of the first electronically excited (A+ Σu+2) state of H2+, the (v = 1, N = 0) level having a calculated binding energy of only Eb = 1.082 219 8(4)·10−9 Eh and leading to an extremely large scattering length of 750(5) a0 for the H+ + H collision [J. Carbonell et al., J. Phys. B: At., Mol. Opt. Phys. 37, 2997 (2004)]. We present an investigation of the nonadiabatic coupling between the first two electronic states (X+ Σg+2 and A+ Σu+2) of H2+ induced by the Fermi-contact term of the hyperfine-coupling Hamiltonian. This interaction term, which mixes states of total spin quantum number G = 1/2, is rigorously implemented in a close-coupling approach to solve the spin-rovibronic Schrödinger equation. We show that it mixes states of gerade and ungerade electronic symmetry, that it shifts the positions of all weakly bound rovibrational states of H2+, and that it affects both the positions and widths of its shape resonances. The calculations demonstrate that the G = 1/2 hyperfine component of the A+ (v = 1, N = 0) state does not exist and that, for G = 1/2, the s-wave scattering lengths of the H+ + H(1s) collision are −578(6) a0 and −43(4) a0 for the F = 0 and F = 1 hyperfine components of the H(1s) atom, respectively. The binding energy of the G = 3/2 hyperfine component of the A+ (v = 1, N = 0) state is not significantly affected by the hyperfine interaction and the corresponding scattering length for the H+ + H(1s, F = 1) collision is 757(7) a0.

Determination of the Interval between the Ground States of Para- and Ortho- H2

“…Linking the energy-level structures of both nuclear-spin isomers is thus extremely challenging. A significant mixing of states of ortho and para (and gerade and ungerade) character is predicted to only occur in the highest vibrational states, because the hyperfine interaction of the atomic fragments becomes dominant at large internuclear separations and decouples the two nuclear spins [8][9][10][11]. The N þ ¼ 1 ← N þ ¼ 0ðv þ ¼ 19Þ pure rotational transition in H þ 2 was measured with an accuracy of 1.1 MHz (2σ) by Critchley et al and represents today the only experimental connection between states of ortho-and para-H þ 2 [12].…”

“…The N þ ¼ 1 ← N þ ¼ 0ðv þ ¼ 19Þ pure rotational transition in H þ 2 was measured with an accuracy of 1.1 MHz (2σ) by Critchley et al and represents today the only experimental connection between states of ortho-and para-H þ 2 [12]. The frequency of this transition was also determined in first-principles calculations that included quantum-electrodynamics corrections and hyperfineinduced ortho-para mixing [9,11]. This connection enables one to relate the energy-level structure of ortho-and para-H þ 2 through high-level first-principles calculations [13], which have been validated by precision spectroscopy in molecular hydrogen ions [14,15].…”

“…A list of the measured nf0 3 ð0Þ-GKð0; 2Þ intervals with corresponding experimental uncertainties and fit residuals is provided in the Supplemental Material [41]. [9,11,13].…”

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2+

“…A basis set of 2 vibrational (v = 0, 1), 3 rotational (N = 0, 2, 4), 2 nuclear-spin (I = 0, 2) and all resulting fine, hyperfine and Zeeman states was used yielding a total of 360 states. We note that the hyperfine interaction can in principle also mix states of gerade and ungerade electronic symmetry, 54 but this effect is expected to be insignificant for the lowest vibrational levels of the X 2 S + g state of N 2 + and was, therefore, neglected in the present work.…”

Relating Binding Energy and Scattering Length of Weakly Bound Dimers of Strontium

“…[23,24]); only a tiny variation of may introduce or remove a bound vibrational state causing the value of a to pass between as a result (see e.g., refs. [25,26]); a reliable mass scaling between different isotopomers requires respecting of the Born–Oppenheimer breakdown (BOB) correction terms. [ 20,27,28 ]…”