No abstract

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 ¼ 54p interval, and the electron binding energy of the n ¼ 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 À1 ). We report on a new determination of the electron binding energies of H 2 Rydberg states with principal quantum numbers in the range n ¼ 51-64 with a precision of better than 100 kHz using a combination of millimetre-wave spectroscopy and multichannel quantumdefect theory (MQDT). The positions of 33 np (S ¼ 0) Rydberg states of ortho-H 2 relative to the position of the reference 51d (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 À1 , 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.

The transition wave numbers from selected rovibrational levels of the EF 1 ⌺ g + ͑v =0͒ state to selected np Rydberg states of ortho-and para-D 2 located below the adiabatic ionization threshold have been measured at a precision better than 10 −3 cm −1 . Adding these wave numbers to the previously determined transition wave numbers from the X 1 ⌺ g + ͑v =0, N =0,1͒ states to thestates of D 2 and to the binding energies of the Rydberg states calculated by multichannel quantum defect theory, the ionization energies of ortho-and para-D 2 are determined to be 124 745.394 07͑58͒ cm −1 and 124 715.003 77͑75͒ cm −1 , respectively. After re-evaluation of the dissociation energy of D 2 + and using the known ionization energy of D, the dissociation energy of D 2 is determined to be 36 748.362 86͑68͒ cm −1 . This result is more precise than previous experimental results by more than one order of magnitude and is in excellent agreement with the most recent theoretical value 36 748.3633͑9͒ cm −1 ͓K. Piszczatowski, G. Łach, M. Przybytek et al., J. Chem. Theory Comput. 5, 3039 ͑2009͔͒. The ortho-para separation of D 2 , i.e., the energy difference between the N = 0 and N = 1 rotational levels of the X 1 ⌺ g + ͑v =0͒ ground state, has been determined to be 59.781 30͑95͒ cm −1 .

The adiabatic ionization energy [in units of hc, [Ei=124 568.485 81(36) cm−1] and the dissociation energy [D0=36 405.783 66(36) cm−1] of HD have been determined using a hybrid experimental-theoretical method. Experimentally, the wave numbers of the EF(v=0,N=0)→np[X+(v+=0 and 1, N+=0)] and EF(v=0,N=1)→np[X+(v+=0,N+=1)] transitions to singlet Rydberg states were measured by laser spectroscopy and used to validate predictions of the electron binding energies by multichannel quantum defect theory. Adding the transition energies, the electron binding energies and previously reported term energies of the EF state led to a determination of the adiabatic ionization energy of HD and of rovibrational energy spacings in HD+. Combining these measurements with highly accurate theoretical values of the ionization energies of the one-electron systems H, D, and HD+ further enabled a new determination of the dissociation energy of HD.

Precision measurement of the rotational energy-level structure of the three-electron molecule He 2 + The data were combined with spectroscopic data on low-lying triplet np and nf Rydberg states from the literature to derive energy-and internuclear-distance-dependent eigenquantum-defect parameters of multichannel quantum-defect theory (MQDT). The MQDT calculations reproduce the experimental data within their experimental uncertainties and enabled the derivation of potential-energy curves for the lowest triplet p Rydberg states (n = 2-5) of He 2 . The eigenquantum-defect parameters describing the p -f interaction were found to be larger than 0.002 at the energies corresponding to the high-n Rydberg states, so that the p -f interaction plays an important role in the autoionization dynamics of np Rydberg states with