Towards measuring the ionisation and dissociation energies of molecular hydrogen with sub-MHz accuracy

The most precise determination of the ionisation and dissociation energies of molecular hydrogen H-2 was carried out recently by measuring three intervals independently: the X -> EF interval, the EF -> n = 54p interval, and the electron binding energy of the n = 54p Rydberg state. The values of the ionisation and dissociation energies obtained for H-2, and for HD and D-2 in similar measurements, are in agreement with the results of the latest ab initio calculations [Piszczatowski et al., J. Chem. Theory Comput., 2009, 5, 3039; Pachucki and Komasa, Phys. Chem. Chem. Phys., 2010, 12, 9188] within the combined uncertainty limit of 30 MHz (0.001 cm(-1)). We report on a new determination of the electron binding energies of H2 Rydberg states with principal quantum numbers in the range n 51-64 with a precision of better than 100 kHz using a combination of millimetre-wave spectroscopy and multichannel quantum-defect theory (MQDT). The positions of 33 np (S = 0) Rydberg states of ortho-H-2 relative to the position of the reference 51d (N+ = 1, N = 1, G(+) = 1/2, G = 1, F = 0) Rydberg state have been determined with a precision and accuracy of 50 kHz. By analysing these positions using MQDT, the electron binding energy of the reference state could be determined to be 42.3009108(14) cm(-1), which represents an improvement by a factor of similar to 7 over the previous value obtained by Osterwalder et al. [J. Chem. Phys., 2004, 121, 11810]. Because the electron binding energy of the high-n Rydberg states will ultimately be the limiting factor in our method of determining the ionisation and dissociation energies of molecular hydrogen, this result opens up the possibility of carrying out a new determination of these quantities. By evaluating several schemes for the new measurement, the precision limit is estimated to be 50-100 kHz, approaching the fundamental limit for theoretical values of similar to 10 kHz imposed by the current uncertainty of the proton-to-electron mass ratio.