Electron proton mass

Classical electron radius Compton wavelength of the electron Proton mass Neutron mass... 

Note the emergence of the last term in (3.4) which lifts the characteristic degeneracy in the Dirac spectrum between levels with the same j and / = j 1/2. This means that the expression for the energy levels in (3.4) already predicts a nonvanishing contribution to the classical Lamb shift E 2Si) — E 2Pi). Due to the smallness of the electron-proton mass ratio this extra term is extremely small in hydrogen. The leading contribution to the Lamb shift, induced by the QED radiative correction, is much larger. 

Here the first contribution to the uncertainty is due to the experimental error of the isotope shift measurement, the second uncertainty is due to the error of the electron-proton mass ratio determination, and the third is generated by the theoretical uncertainty of the isotope shift. 

A higher order correction [36] is added to the number previously given in R.ef. [32] and the uncertainty is now dominated by two sources the electron proton mass ratio (1.5 kHz) [37] and higher order deuteron structure effects (0.5 kHz). 

The accuracy of computed energy levels is further limited by uncertainties of fundamental constants and by nuclear size and structure effects. The dominant contributor to the uncertainty of the 1S-2S frequency ( 500 kHz) is still the Rydberg constant. However, the electron/proton mass ratio, known within 2-10 8 [37], introduces an additional uncertainty of about 30 kHz. The rms charge radius of the proton contributes at least another 50 kHz [38], assuming that it has been measured to within 2.5% estimates of this accuracy still differ widely. 

To give an example, we could measure the isotope shifts Af of two separate transitions such as 1S-2S and 2S-nS. By forming the linear combination 7Af(2S-nS)-(l-8/n3)-Af(lS-2S), we obtain a new composite frequency which no longer contains terms proportional to 1/n3. It is thus independent of nuclear size and can be calculated much more precisely than iis constituents. A CuSipniiSCii of experiment and theory can then yield an improved electron-proton mass ratio. 

Ma = mass of nucleus a rtii (or m) = mass of electron = proton mass... 

Cold, trapped HD+-ions are ideal objects for direct spectroscopic tests of quantum-electrodynamics, relativistic corrections in molecules, or for determining fundamental constants such as the electron-proton mass ratio. It is also of interest for many applications since it has a dipole moment. The potential of localizing trapped ions in Coulomb crystals has been demonstrated recently with spectroscopic studies on HD+ ions with sub-MHz accuracy. The experiment has been performed with 150 HD+ ions which have been stored in a linear rf quadrupole trap and sympathetically cooled by 2000 laser-cooled Be+ ions. IR excitation of several rovibrational infrared transitions has been detected via selective photodissociation of the vibra-tionally excited ions. The resonant absorption of a 1.4/itm photon induces an overtone transition into the vibrational state v = A. The population of the V = A state so formed is probed via dissociation of the ion with a 266 nm photon leading to a loss of the ions from the trap. Due to different Franck-Condon factors, the absorption of the UV photon from the v = A level is orders of magnitude larger than that from v = 0. 

With the envisioned higher resolution, it should be possible to determine a better value of the electron/proton mass ratio from a precise measurement of the isotope shift. And a measurement of the absolute frequency or wavelength should provide a new value of the Rydberg constant with an accuracy up to 1 part in 10, as limited by uncertainties in the fine structure constant and the mean square radius of the proton charge distribution. A comparison with one of the Balmer transitions, or with a transition to or between Rydberg states could provide a value for the IS Lamb shift that exceeds the accuracy of the best radiofrequency measurements of the n=2 Lamb shift. Such experiments can clearly provide very stringent tests of quantum electrodynamic calculations, and when pushed to their limits, they may well lead to some surprising fundamental discovery. 

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