According to selection rules, the same parity of the two states suggests magnetic dipole transition is allowed.

For magnetic dipole transition, [DELTA]S = 0, [DELTA]L = 0, and if J' = J - 1, the reduced matrix element can be calculated as follows.

A mechanism on the basis of electric and magnetic dipole transitions in gas media was proposed recently [14, 15].

Electric dipole, quadrupole, and magnetic dipole transition probabilities of ions isoelectronic to the first-row atoms, Li through F.

Moreover, in our earlier work we presented an investigation including the level energies and electric dipole transitions for neutral boron (Karacoban et al.

In the electric dipole approximation, if the polarization of an electromagnetic radiation is chosen in z-direction, the dipole transition matrix element between ith state (lower) and fth state (upper) is given by

Figures 1 and 2 display the square of dipole transition matrix element between ith and fth states and differences between energy levels in the dipole transitions as a function of dot radius at x = 0.

The reason is that as the energy difference of the levels is more dominant in small dot radii, the dipole transition matrix element is more dominant in large dot radii, see Figure 1 and Figure 2.

We have used a core polarization potential in a Dirac-Fock wave function code to calculate target atom wave functions and a matching form of the dipole transition operator to calculate oscillator strengths and Born cross sections.

In other words, the correction for the dipole transition operator can also be used to introduce the correction for the core polarization in plane-wave Born cross sections.

4), as well as the matching form of the dipole transition operator, Eq.

The book begins with the basic knowledge of the theories of nuclei and angular momentum, develops through the standard description of the fine and magnetic hyperfine interactions, and their impact on the energy structure of the lanthanide ions, and includes advanced description of f to f electric and magnetic

dipole transitions.