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Recently a high precision spectroscopic investigation of the EF^1\Sigma_g^+ -X^1\Sigma_g^+ system of molecular hydrogen was reported yielding information onQED and relativistic effects in a sequence of rotational quantum states in theX^1\Sigma^+_g$ ground state of the H_2 molecule [E.J. Salumbides et al., Phys.Rev. Lett. 107, 043005 (2011)]. The present paper presents a more detaileddescription of the methods and results. Furthermore, the paper serves as astepping stone towards a continuation of the previous study by extending theknown level structure of the EF^1\Sigma^+_g state to highly excitedrovibrational levels through Doppler-free two photon spectroscopy. Based oncombination differences between vibrational levels in the ground state, andbetween three rotational branches (O, Q and S branches) assignments of excitedEF^1\Sigma^+_g levels, involving high vibrational and rotational quantumnumbers, can be unambiguously made. For the higher EF^1\Sigma^+_g levels, whereno combination differences are available, calculations were performed using themulti-channel quantum defect method, for a broad class of vibrational androtational levels up to J=19. These predictions were used for assigning high-JEF-levels and are found to be accurate within 5 cm^-1.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Precision spectroscopy of high rotational states in H_2 investigated by  Doppler-free two-photon laser spectroscopy in the EF^1\Sigma_g^+ -  X^1\Sigma_g^+ system