Zeeman quantum number

The Zeeman quantum number q is conserved during evolution under a high field Hamiltonian. Thus neglecting relaxation... 

The number of energy levels found to date, with the aid of the Zeeman effect and the isotope shift data, is 605 even and 586 odd levels for Pu I and 252 even and 746 odd for Pu II. The quantum number J has been determined for all these levels, the Lande g-factor for most of them, and the isotope shift for almost all of the Pu I levels and for half of those of Pu II. Over 31000 lines have been observed of which 52% have been classified as transitions between pairs of the above levels. These represent 23 distinct electron configurations. 

A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

The principal interaction experienced is the Zeeman interaction (Hz), which describes the interaction between the magnetic moment of the nucleus and the externally applied magnetic field, B0 (tesla). The nuclear magnetic moment, p (ampere meter2) is proportional to the nuclear spin quantum number (/) and the magnetogyric ratio (y, radian telsa-1 second-1) ... 

This is the usual situation in a high field. It is characterized by the fact that transitions between different M bands of the spectrum are highly improbable because of the vanishingly small relevant density of states or because of the high number of spins that have to be rearranged in order to distribute a Zeeman quantum over... 

This method is equally applicable to atoms 26) and to molecules 22). In molecules the Zeeman splitting depends on the quantum number / of the total angular momentum and therefore the fluorescence from a single rotational level (v, f) need be observed. Because of this necessarily selective excitation, these molecular level-crossing experiments can be performed much more easily with lasers than with conventional light sources and have been sucessfully performed with Naj 2 > and NaK 29). 

In the presence of magnetic field a further splitting into (2J+l) equispaced energy levels occurs. These correspond to the number of values that can be assumed by the magnetic quantum number M ranging from +J>M>—J (Zeeman effect). 

The first- and second-order Zeeman effect coefficients in the expansion of equation (62) are defined by the quantum numbers which specify the atomic energy level. They are in general a function of the direction of the magnetic field with respect to the axis of quantization of the wave functions. They are obtained by the use of the magnetic moment operator for the appropriate direction, q = x,y ox z ... 

Fig. 16.10 Quantum beat signals of high lying 2D states of Na obtained by time resolved selective field ionization. The variation of the beat frequency with principal quantum number is shown. Several quantum beat frequencies appear due to a Zeeman splitting of the fine structure levels in the earth s magnetic field (from ref. 43).

Let us first consider the normal Zeeman effect, which applies to transitions between electronic states with zero total spin magnetic moment, so-called singlet states. Like the projection Ms of S in the Stern-Gerlach experiment, the projection Ml of the spatial angular momentum L is space quantized in the external magnetic field. We shall describe the quantization of the spatial angular momentum by means of quantum mechanical methods in detail later. Suffice it to say that each state with spatial angular momentum quantum number L splits into 2L + 1 components, i.e., a P state (L = 1) splits into three components with... 

Carrying on the investigation of the anomalous Zeeman effect and the Paschen-Back effect on the spectra of the alkali atoms, Pauli postulated that an electron in an external magnetic field has to be described by four independent quantum numbers. Moreover, in order to justify the Bohr-Sommerfeld Aufbau (building-up) principle of the periodic system of the elements, he came up with his famous exclusion principle (Ausschliefiungsprinzip). In its original formulation it reads 10... 

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