The excimer-pumped sodium laser (XPNaL) is very important for its application in sodium guide star. However, the absorption coefficients (for the pumping source) of traditional excimer pairs, such as Na-He and Na-Ar, are very small. In this work, four systems (Na-Ar, Na-Xe, Na-CH_{4}, and Na-C_{2}H_{6}) are investigated based on both fluorescence experiment and theoretical binding energies obtained from highly accurate quantum chemistry calculations to determine better excimer pairs. The experiment results show that the peak area ratio of fluorescence intensity curves for the excimer pairs of Na-Ar, Na-Xe, Na-CH_{4}, and Na-C_{2}H_{6} was 1.0 : 6.4 : 4.9 : 10.4. Meanwhile, using the CCSD(T) approach and basis set extrapolation, binding energies for these four systems were calculated as 52.8, 124.5, 117.7, and 150.0 cm^{-1}, respectively. Therefore, predication by quantum chemistry calculation was consistent with experimental results. The Na-C_{2}H_{6} system was found to be the most efficient system both experimentally and theoretically, and has the potential to be used in the development of a high power XPNaL. This work also demonstrates that the binding energy from highly accurate quantum chemistry calculations with a large basis set is a very good criterion for the selection of excimer pairs for the excimer-pumped alkali laser (XPAL).