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 H2 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 H2, and for HD and D2 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-H2 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 -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 -10 kHz imposed by the current uncertainty of the proton-to-electron mass ratio.