By combining results from a Doppler-free two-photon laser excitation study on several lines in the EF 1 ' þ g À X 1 ' þ g (0,0) band of H 2 with results from a Fourier-transform spectroscopic study on a low-pressure discharge in hydrogen, absolute level energies, with respect to the X 1 AE þ g , v ¼ 0, N ¼ 0 ground level, were determined for 547 rovibronically excited states in H 2 . While for some of the levels in the EF 1 AE þ g and B 1 AE þ u states the uncertainties are as low as 0.0001 cm À1 , the accuracy of other levels is lower. The general improvement in the accuracy for the comprehensive data set of level energies is by an order of magnitude with respect to previous measurements. An updated listing of transition wavelengths of the spectral lines in the Lyman and Werner bands is presented, based on combination differences between the presently obtained B 1 AE þ u and C 1 Å u level energies and those in the X 1 AE þ g ground state.

Two distinct high-accuracy laboratory spectroscopic investigations of the H 2 molecule are reported. Anchor lines in the EF 1 AE þ g À X 1 AE þ g system are calibrated by two-photon deep-UV Doppler-free spectroscopy, while independent Fourier-transform spectroscopic measurements are performed that yield accurate spacings in the B 1 AE þ u À EF 1 AE þ g and I 1 Å g À C 1 Å u systems. From combination differences accurate transition wavelengths for the B À X Lyman and the C À X Werner lines can be determined with accuracies better than $5 Â 10 À9 , representing a major improvement over existing values. This metrology provides a practically exact database to extract a possible variation of the proton-to-electron mass ratio based on H 2 lines in high-redshift objects. Moreover, it forms a rationale for equipping a future class of telescopes, carrying 30-40 m dishes, with novel spectrometers of higher resolving powers. DOI: 10.1103/PhysRevLett.101.223001 PACS numbers: 33.20.Àt, 06.20.Jr, 95.30.Dr, 98.80.Bp Fundamental physical constants may be subject to change on cosmological time scales. For the fine structure constant , evidence for a temporal drift with a 5 significance has been reported [1]. Recently, an indication of a possible decrease of the dimensionless proton-to-electron mass ratio ¼ m p =m e was reported at Á= ¼ ð2:45 AE 0:59Þ Â 10 À5 over a time interval of 12 Â 10 9 years, based on a comparison of spectra of molecular hydrogen [2,3]. The latter findings require three crucial input ingredients. First, a theory is required that relates possible changes in to observable shifts in the spectrum of H 2 . For this purpose sensitivity coefficients K i ¼ d ln i =d ln, which indicate how each line in the H 2 spectrum would drift as a result of a variation in the mass ratio , can be deduced either in a semiempirical fashion [3] or through quantum chemical ab initio calculations [4]. The second ingredient is the accurate determination of spectral line positions at high redshifts. Of the thousands of known quasar systems at redshifts z > 2, H 2 absorption features have only been observed in some 10 to 15 systems thus far. Of these, only Q0405-443 and Q0347-383 have high-quality and well-calibrated spectra containing many H 2 lines [5], which formed the basis of the finding on Á= [2]. Recently, HE0027-184 was established as another system with many resolved H 2 lines [6], and hence a potential source in deriving further constraints on Á. The final ingredient is a database comprising of high-precision laboratory measurements that represent present-day (z ¼ 0) H 2 spectra. The limited amount of available astrophysical data accentuates the need for a set of laboratory data that would not contribute to the uncertainties in estimating a possible drift in .The principle behind the novel determination of laboratory transition wavelengths in theWerner band systems is depicted in Fig. 1. Two entirely independent experiments are performed. First, the level energies of the lowest rotational states in. Schematic of the combi...