The transition wave number from the EF 1 ⌺ g + ͑v =0,N =1͒ energy level of ortho-H 2 to the 54p1 1 ͑0͒ Rydberg state below the X + 2 ⌺ g + ͑v + =0,N + =1͒ ground state of ortho-H 2 + has been measured to be 25 209.997 56Ϯ ͑0.000 22͒ statistical Ϯ ͑0.000 07͒ systematic cm −1 . Combining this result with previous experimental and theoretical results for other energy level intervals, the ionization and dissociation energies of the hydrogen molecule have been determined to be 124 417.491 13͑37͒ and 36 118.069 62͑37͒ cm −1 , respectively, which represents a precision improvement over previous experimental and theoretical results by more than one order of magnitude. The new value of the ionization energy can be regarded as the most precise and accurate experimental result of this quantity, whereas the dissociation energy is a hybrid experimental-theoretical determination.

Highly accurate results from frequency measurements on neutral hydrogen molecules H2, HD and D2 as well as the HD + ion can be interpreted in terms of constraints on possible fifth-force interactions. Where the hydrogen atom is a probe for yet unknown lepton-hadron interactions, and the helium atom is sensitive for lepton-lepton interactions, molecules open the domain to search for additional long-range hadron-hadron forces. First principles calculations in the framework of quantum electrodynamics have now advanced to the level that hydrogen molecules and hydrogen molecular ions have become calculable systems, making them a search-ground for fifth forces. Following a phenomenological treatment of unknown hadron-hadron interactions written in terms of a Yukawa potential of the form V5(r) = β exp(−r/λ)/r current precision measurements on hydrogenic molecules yield a constraint β < 1 × 10 −7 eV·Å for long-range hadron-hadron interactions at typical force ranges commensurate with separations of a chemical bond, i.e. λ ≈ 1Å and beyond.

The fundamental ground tone vibration of H2, HD, and D2 is determined to an accuracy of 2 × 10 −4 cm −1 from Doppler-free laser spectroscopy in the collisionless environment of a molecular beam. This rotationless vibrational splitting is derived from the combination difference between electronic excitation from the X 1 Σ + g , v = 0 and v = 1 levels to a common EF 1 Σ + g , v = 0 level. Agreement within 1σ between the experimental result and a full ab initio calculation provides a stringent test of quantum electrodynamics in a chemically-bound system.Quantum electrodynamics (QED), the fully quantized and relativistic version of electromagnetism, solves the problem of infinities associated with charged point-like particles and includes the effects of spontaneous particleantiparticle generation from the vacuum. QED is tested to extreme precision by comparing values for the electromagnetic coupling constant α obtained from measurements of the g-factor of the electron [1] and from interferometric atomic recoil measurements [2]. These experiments and the Lamb shift measurements in atomic hydrogen [3,4] have made QED the most accurately tested theory in physics. Concerning molecules, significant progress has been made recently in theoretical [5] and experimental [6,7] investigations of QED phenomena in the HD + molecular ion, where multiple angular momenta (rotational, electronic and nuclear spins) play a role. Neutral hydrogen has also recently been targeted for QED-tests, via a measurement of the dissociation energy of the H 2 [8], HD [9], and D 2 [10] molecules, and the experimental determination of rotationally excited quantum levels inThe rotationless fundamental ground tone (i.e. the vibrational energy splitting between the v ′′ = 0, J ′′ = 0 and v ′ = 1, J ′ = 0 quantum states) of the neutral hydrogen molecule is an ideal test system for several reasons. The total electronic angular momentum is zero for the X 1 Σ + g ground state and the total nuclear spin for the rotationless J = 0 state of para-H 2 is also zero resulting in a simple spectrum without hyperfine splitting. The hyperfine splitting is extremely small in HD (down to the Hz level [12]) and D 2 in the absence of an I · J interaction for the J = 0 ground state. The recent progress in theory allows for calculations involving relativistic and QED-effects up to order α 4 [13,14]. Energy contributions in the calculation cancel to a large degree for the fundamental ground tone, leading to a significant reduction in the uncertainty, thereby allowing for accurate QED tests.The present study focuses on a precise laser spectroscopic measurement of the rotationless fundamental quantum of vibration in H 2 , HD and D 2 . In the absence of rotation a one-photon transition between the FIG. 1. (Color online)A schematic layout of the experimental setup. The oscillator cavity is seeded by a cw Ti:Sa laser, the pulsed output of which makes multiple passes in an amplifier stage. The amplified output is frequency up-converted in two frequency doubling (SHG) stages leadin...