Breit-Rabi diagram

Fig. 5. a) Breit-Rabi diagram of the hydrogen ground state in a magnetic field, b) dependence of the magnetic moment of he four states on the magnetic field... 

The energy levels are shown in the form of the Breit-Rabi diagram in Fig. 1. At low magnetic fields, the total angular momentum F and Mp are good quantum numbers. At high fields, however, the individual spin quantum numbers m and m describe the system. 

The eigenvectors of this Hamiltonian (for the H atom) have been familiar for about 50 years now the energy eigenvalues are shown in frequency units in the Breit-Rabi diagram of Figure 14. The hyperfine frequency of Mu in vacuum is vq = 4463.302 35(52) MHz,24 which can be compared with the corresponding value for the H atom, i o(H) = 1420.405751(1) MHz, to give almost exactly the ratio predicted by Equation 31 when g M i s replaced by OaH-p. for the proton. In fact, a more detailed calculation, combined with the experimental values of g and provides the best test of quantun electro-... 

In zero field, the Hamiltonian of Equation 43 predicts three frequencies, since the I F = 1 M = 0> substate is shifted in energy with respect to the degenerate case depicted in the Breit-Rabi diagram of Figure 14. These frequencies are given by and 1/2 ... 

Fig.2.20. Breit-Rabi diagram for an alkali state with J = 1/2 and I = 3/2. (Ground state of...

Figure 2 Breit-Rabi diagram for muonium with transverse-field transitions indicated by arrows. The zero-field splitting corresponds to the muon hyperfine coupling constant (/A = 4463 MHz for Mu). In high fields, the four eigenstates become pure Zeeman states ( 1 >= a a >, 2 >= P a >, 3 > = P P >, 4>= a P .

Fig. 1 Breit-Rabi energy level diagram for the ground state of muonium.

Fig. 2.19. Breit—Rabi hyperfine energy level diagram for ground-state hydrogen, showing the magnetic energy of the atom A IF normalised to the hyperfine splitting at zero field (5 W).

The Breit-Rabi energy level diagram for ground state muonium is shown in Fig. 13. The history of the various determinations of Av and of is shown in Fig. 14. 

Figure 7.4 Breit-Rabi energy level diagram for a muonium like (or a muoniated radical) system. is the muon-electron hyperflne constant and Ws is the total quantum number.

---