Transition probabilities magnetic dipole radiation

The second term in the expansion of the classical vector potential for an oscillating distribution of current and charge, equation (2.81), contains contributions from both magnetic dipole and electric quadrupole distributions, as shown in sections 2.10 and 2.11, We therefore expect these different distributions to radiate at similar rates. Thus, whenever the electric dipole transition probabilities from a given level are identically zero we must consider the possibility of decay by electric quadrupole radiation in addition to the magnetic dipole radiation discussed in... 

The probability of a transition being induced by interaction with electromagnetic radiation is proportional to the square of the modulus of a matrix element of the form where the state function that describes the initial state transforms as F, that describing the final state transforms as Tk, and the operator (which depends on the type of transition being considered) transforms as F. The strongest transitions are the El transitions, which occur when Q is the electric dipole moment operator, — er. These transitions are therefore often called electric dipole transitions. The components of the electric dipole operator transform like x, y, and z. Next in importance are the Ml transitions, for which Q is the magnetic dipole operator, which transforms like Rx, Ry, Rz. The weakest transitions are the E2 transitions, which occur when Q is the electric quadrupole operator which, transforms like binary products of x, v, and z. 

Here is yet another bizarre result of quantum mechanics for you to ponder. The lx wavefunction for a hydrogen atom is unequal to zero at the origin. This means that there is a small, but nonzero probability that the electron is inside the proton. Calculation of this probability leads to the so-called hyperfine splitting —the magnetic dipoles on the proton and electron interact. This splitting is experimentally measurable. Transitions between the hyperfine levels in the lx state of hydrogen are induced by radiation at 1420.406 MHz. Since this frequency is determined by... 

In a multipole expansion of the interaction of a molecule with a radiation field, the contribution of the magnetic dipole is in general much smaller than that of the electric dipole. The prefactor for a magnetic dipole transition probability differs from the one for an electric dipole by a2/4 1.3 x 1 () 5. Magnetic dipoles may play an important role, however, when electric dipole transitions are symmetry-forbidden as, e.g., in homonuclear diatomics. 

The quality of the SOC calculation in O2 can be checked by estimation of the fc Sj" — A3E transition probability. The transition is forbidden by selection rules for electric dipole radiation with account of SOC, and occurs as magnetic dipole spin-current borrowing intensity from microwave transitions between spin-sublevels of the ground state [41]. 

Because circular dichroism is a difference in absorption for left and right circularly polarized light, its theoretical description includes subtraction of the transition probabilities induced by left and right circularly polarized radiation. The interaction Hamiltonian that determines transition probability includes electric, , and magnetic, B, fields of electromagnetic circularly polarized radiation, and the electric, /i, and magnetic, m, dipole moments of the molecule. 

We thus see that the probability of transition due to magnetic dipole or electric quadripole radiation will be negligible in comparison to the probability of transition due to electric dipole radiation. The higher terms in 8-35 will therefore be of importance only in those cases in which... 

The transition probabilities for magnetic dipole and electric quadrupole radiation are important since they can be combined with measurements of the absolute and relative intensities of forbidden lines emitted by nebulae, the aurora, or the solar corona to yield estimates of the number density, composition, and temperature existing in these various sources. We therefore proceed to obtain explicit expressions for these transition probabilities, making use of the expressions for the power radiated from the corresponding classical current and charge distributions which we obtained in sections 2.10 and 2.11. 

Unfortunately no generally applicable method of measuring the transition probabilities of forbidden lines has been developed. This is mainly because the lifetimes of the metastable levels which can decay only by magnetic dipole or electric quadrupole radiation in the visible region of the spectrum are of the order of 10 s or longer. 

---