a New Value for the Rydberg Constant by Precision Measurement of the Hydrogen Balmer-Beta Transition.

The Rydberg constant {rm R }_infty is determined to a very high accuracy of 3 parts in 10^{10 } by a direct comparison of the four hydrogen and deuterium Balmer-beta transitions with a standard laser from the National Bureau of Standards. This experiment is now the most precise measurement for {rm R}_infty and approaches the limits of accuracy for wavelength or frequency measurements in the visible region. The result is {rm R}_infty = 109 737.315 73 (3) {rm cm}^{-1} with the definition of the meter: c = 299 792 458 m/sec. The experiment also yields the following results: The fine structure splittings 4{rm P}_ {1/2} rightarrow {rm 4P}_{3/2} in H: 1370.9 (3) MHz and in D: 1371.8 (3) MHz. The isotope shifts between H and D in the transitions {rm 2S}_{1/2} rightarrow {rm 4P}_{1/2}: 167 752.4 (3) MHz and {rm 2S}_{1/2 } rightarrow {rm 4P}_{3/2}: 167 753.3 (3) MHz. The experiment utilizes atomic beam laser spectroscopy. A beam of atomic hydrogen (or deuterium) is excited by electron bombardment to the metastable {rm 2S }_{1/2} state and is detected by a secondary electron emission detector. A chopped cw dye laser beam crosses the atomic beam at an angle of 90^circ to eliminate Doppler broadening. The metastables are quenched by laser excitation to {rm 4P}_{1/2} or {rm 4P}_{3/2 } states. The signal is monitored by a lock -in amplifier with the chopper as reference. An iodine (^{127}{ rm I}_2) stabilized helium-neon (He-Ne) laser is the primary standard with an accuracy of 1.6 times 10^{ -10}. Another He-Ne laser is locked to the standard laser with a variable offset frequency controlled by an oscillator. A frequency chain is established by locking together a dye laser, a piezoelectrically controlled measuring etalon and the offset laser. This chain allows the dye laser to scan across the Balmer-beta line in a precisely controllable manner. The lineshape and offset frequency are recorded simultaneously. Possible sources of systematic shifts and errors are carefully investigated. Hydrogen energy levels are calculated according to most recent values of physical constants. {rm R}_infty is obtained by comparing the measured and calculated hydrogen Balmer-beta transition. The result is in good agreement with the two most recent, but less precise experiments.