Precision spectroscopy of high rotational states in H2 investigated by Doppler-free two-photon laser spectroscopy in the EF 1Σg+-X 1Σg+ system

Recently a high precision spectroscopic investigation of the EF1 Sigma(+)(g)-X-1 Sigma(+)(g) system of molecular hydrogen was reported yielding information on QED and relativistic effects in a sequence of rotational quantum states in the X-1 Sigma(+)(g) ground state of the H-2 molecule [Salumbides et al., Phys. Rev. Lett. 107, 043005 (2011)]. The present paper presents a more detailed description of the methods and results. Furthermore, the paper serves as a stepping stone towards a continuation of the previous study by extending the known level structure of the EF1 Sigma(+)(g) state to highly excited rovibrational levels through Doppler-free two-photon spectroscopy. Based on combination differences between vibrational levels in the ground state, and between three rotational branches (O, Q, and S branches) assignments of excited EF1 Sigma(+)(g) levels, involving high vibrational and rotational quantum numbers, can be unambiguously made. For the higher EF1 Sigma(+)(g) levels, where no combination differences are available, calculations were performed using the multichannel quantum defect method, for a broad class of vibrational and rotational levels up to J = 19. These predictions were used for assigning high-J EF levels and are found to be accurate within 5 cm(-1).