Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain

We have measured the absolute frequency of the hydrogen 1S-2S two-photon resonance with an accuracy of 3.4 parts in 10(13) by comparing it with the 28th harmonic of a methane-stabilized 3.39 mu m He-Ne laser. A frequency mismatch of 2.1 THz at the 7th harmonic is bridged with a phase-locked chain of five optical frequency interval dividers. From the measured frequency f(1S-2S); = 2 466 061 413 187.34(84) kHz and published data of other authors we derive precise new values of the Rydberg constant, R-infinity = 10973 731.568 639(91) m(-1) and of the Lamb shift of the 1S ground state, L-1S = 8172.876(29) MHz. These are now the most accurate values available.