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.
\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.30]{maby_ortho_h2-01.eps} \end{wrapfigure} We use high Rydberg states to measure the properties of H
2+ and HD
+ in the vicinity of their dissociation limits H
++H, H
++D and H+D
+, with particular emphasis on quasibound rovibrational levels above the dissociation threshold of the X
+ 2Σg+ ground state. Although the existence of these quasibound levels has been predicted a long time ago, they have never been observed. Positions and widths of the lowest resonances have not been calculated either. Given the role that such states play in the three-body and radiative recombination of H(1s) and H
+ to form H
2+, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels (shape resonances) of H
2+, located close to the top of the centrifugal barriers and which decay by quantum-mechanical tunneling. For HD
+ we present measurements of rovibrational levels of the A
+ 2Σu+ state, located between the two dissociation limits. Because of the g-u-symmetry breaking in HD
+, these levels are coupled to the H
++D continuum by nonadiabatic interactions (Feshbach resonances). The experimental results will be compared with the positions and widths we calculate for these levels using a potential model for the X
+ and the A
+ state of H
2+ and HD
+ which includes adiabatic, nonadiabatic, relativistic and radiative corrections to the Born-Oppenheimer potential energies.
We analyse the influence of the attractive tail of the p–H two-body potential on the energy progression of the near-threshold rotationless bound states of the H molecular ion. For the 1sσ g configuration we study different definitions of the reference potential describing the potential tail. In each case, the scattering length consistent with the energies of the highly excited vibrational states, as calculated by Hilico et al. [Eur. Phys. J. D 12, 449 (2000)], is found to lie in the range between −30.5 and −31 au. In the 2pσ u configuration, for which there is an extremely weakly bound v = 1 vibrational state [Carbonell et al., Europhys. Lett. 64, 316 (2003)], we obtain a scattering length near 762.8 au. In contrast to previously conveyed impressions, the weakly bound v = 1 state can be satisfactorily described as the excited state in a distant shallow potential well of the p–H two-body potential, provided that a sufficient number of terms is included in the representation of the large-distance behaviour of this potential.
The binding energies of the five bound rotational levels
J=0−−4 in the highest vibrational level
v=14 in the ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ ground electronic state of
H2 were measured in a three-step ultraviolet-laser experiment. Two-photon UV photolysis of
H2S produced population in these high-lying bound states that were subsequently interrogated at high precision via Doppler-free spectroscopy of the ${F}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}\text{\ensuremath{-}}{X}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ system. A third UV laser was used for detection through auto-ionizing resonances. The experimentally determined binding energies were found to be in excellent agreement with calculations based on nonadiabatic perturbation theory, also including relativistic and quantum electrodynamical contributions. The
s-wave scattering length of the
H+H system is derived from the binding energy of the last bound
J=0 level via a direct semi-empirical approach, yielding a value of
as=0.2724(5)a0, in good agreement with a result from a previously followed theoretical approach. The subtle effect of the $m{\ensuremath{\alpha}}^{4}$ relativity contribution to
as was found to be significant. In a similar manner a value for the
p-wave scattering volume is determined via the
J=1 binding energy yielding ${a}_{p}=\ensuremath{-}134.0000\phantom{\rule{0.16em}{0ex}}(6)\phantom{\rule{0.16em}{0ex}}{a}_{0}^{3}$. The binding energy of the last bound state in
H2, the (
v=14,J=4) level, is determined at 0.023 (4) ${\mathrm{cm}}^{\ensuremath{-}1}$, in good agreement with calculation. The effect of the hyperfine substructure caused by the two hydrogen atoms at large internuclear separation, giving rise to three distinct dissociation limits, is discussed.
Shape resonances in H_{2}, produced as reaction intermediates in the photolysis of H_{2}S precursor molecules, are measured in a half-collision approach. Before disintegrating into two ground state H atoms, the reaction is quenched by two-photon Doppler-free excitation to the F electronically excited state of H_{2}. For J=13, 15, 17, 19, and 21, resonances with lifetimes in the range of nano- to milliseconds were observed with an accuracy of 30 MHz (1.4 mK). The experimental resonance positions are found to be in excellent agreement with theoretical predictions when nonadiabatic and quantum electrodynamical corrections are included. This is the first time such effects are observed in collisions between neutral atoms. From the potential energy curve of the H_{2} molecule, now tested at high accuracy over a wide range of internuclear separations, the s-wave scattering length for singlet H(1s)+H(1s) scattering is determined at a=0.2735_{31}^{39} a_{0}.
Accurate scattering lengths and effective ranges for hydrogen atomic collisions are determined from effective range theory. The precise ab initio b3Σ+u potential energy curve values of H2 calculated by Kolos and Wolniewicz and C6, C8, C10 long-range expansion coefficients are used in obtaining accurate representation of the two-body interaction potential. The s-wave scattering length obtained for this potential (A =1/33455 ao) is used to calculate the zero temperature energy as a function of density of electron spin-polarized ("spin-aligned") atomic hydrogen (H+) using previous many-body perturbation theory results for bosons. Neglecting small potential shape dependent terms, one obtains E/N (energy per particle ) as a function of density, which may be compared with similar results obtained from Monte-Carlo or variational calculations. The scattering lengths and effective ranges for the other hydrogen isotopic systems are also presented. It is shown that the first bound state for the b3Σ+u potential (within the Born-Oppenheimer approximation) only exists for a hypothetical isotopic species with mass larger than a value m = 3.258176 g/mole (where the scattering length becomes infinite). In terms of the quantum parameter, η ≡ [MATH]2/ (2µεσ2), two-body binding occurs in the b3Σ+u potential only for η < 0.17094. The second order liquid-to-gas transition (corresponding to the onset of infinite-body binding) occurs at the accurately determined critical value of the quantum parameter ηCB = 0.43891. This corresponds to zero scattering length.
The scattering lengths and effective ranges for collisions of ground state Be atoms interacting via the X 1Σ + g molecular state of the Be 2 dimer are calculated for two published X 1Σ + g potentials. A new ab initio X 1Σ + g potential is presented with its vibrational energies and rotational constants. The scattering parameters calculated with it and with the existing potentials are compared. Simple formulae showing how the scattering parameters are influenced by adiabatic coupling to electronic motion are derived within the semi-classical formulation and evaluated for the potentials considered. The formulae imply that a semi-classical account of adiabatic coupling can be made by increasing each atomic mass by one electron mass. © 2007 IOP Publishing Ltd.