Magnetic transition dipole

In the remainder of this section, we will consider only electric-dipole transitions. These are the strongest transitions, and account for most of the observed atomic and molecular spectroscopic transitions. (Magnetic-dipole transitions occur in magnetic-resonance spectroscopy.) When the integral d vanishes, we say that a transition between states n and m is forbidden. 

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

One of the consequences of this selection rule concerns forbidden electronic transitions. They caimot occur unless accompanied by a change in vibrational quantum number for some antisynnnetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally synnnetric they have no antisymmetric vibrations to make the transitions allowed. 

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

Callomom J H and Innes K K 1963 Magnetic dipole transition in the electronic spectrum of formaldehyde J. Mol. Spectrosc. 10 166-81... 

The electric dipole selection rule for a hannonic oscillator is Av = 1. Because real molecules are not hannonic, transitions with Av > 1 are weakly allowed, with Av = 2 being more allowed than Av = 3 and so on. There are other selection niles for quadnipole and magnetic dipole transitions, but those transitions are six to eight orders of magnitude weaker than electric dipole transitions, and we will therefore not concern ourselves with them. 

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

Laporte rule because they are magnetic dipole transitions the rule applies only to electric dipole transitions. 

For the sake of simplicity and a more instructive description, we shah restrict ourselves to the case of unpolarized single line sources of 7 = 3/2v / = 1/2 magnetic dipole transitions (Ml) as for example in Fe, which has only a negligible electric quadrupole (E2) admixture. It will be easy to extend the relations to arbitrary nuclear spins and multipole transitions. A more rigorous treatment has been given in [76, 78] and [14] in Chap. 1. The probability P for a nuclear transihon of multipolarity Ml (L=l) from a state I, m ) to a state h, m2) is equal to... 

In [49, 76], the line intensities for electric quadrupole and Zeeman (magnetic dipole) splitting and including the anisotropy of the /-factor are also given for / = 2 <-> 7g = 0 transitions (even-even isotopes, e.g., in the rare earth region or in W, Os). 

Spin-spin relaxation is primarily induced by magnetic dipole interactions between paramagnetic ions. Usually, the most important spin-spin relaxation process is the so-called cross-relaxation process in which a transition of an ion / from the state K) to toe state is accompanied by a transition of another ion j from the... 

Fig. 7.3 Effect of magnetic dipole interaction (7/m), electric quadmpole interaction (Hq), and combined interaction// = Hu + //q, Em> q on the Mossbauernuclear levels of Ni. The larger spacings between the sublevels of the ground state are due to the somewhat larger magnetic dipole moment of the nuclear ground state as compared to the excited state. The relative transition probabilities for a powder sample as well as the relative positions of the transition lines are indicated by the stick spectra below...

MS2 Study of magnetic dipole and electric quadrupole interactions, two Ni sites differing in angle between H and EFG axis phase transitions in NiS2.oo NiS 1 96... 

Apart from the determination of nuclear parameters, the Mossbauer transition in Os, especially the 36.2 and 69.6 keV transitions, are suited for chemical applications. As shown below, the 36.2 keV level, in spite of its large half-width, can be well used for the measurement of isomer shifts, whereas the 69.2 keV state is favorable for the characterization of electric quadrupole or magnetic dipole interactions. Both Mossbauer levels are populated equally well by the parent isotope lr, and simultaneous measurement is possible by appropriate geometrical arrangement. 

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