Configuration state functions parity

Forced electric dipole emission occurs if it is possible to mix even functions into the uneven 4/ functions, so that the parity selection rule is relaxed. It is usually assumed that this occurs by 4f—5d mixing. For Eu +, however, the 4/ 5high energy (see Table 3). Since the electric-dipole emission dominates for Eu3+ on sites without inversion S5unmetry, it seems obvious to assume that another state is used to relax the parity selection rule. This must occur by mixing the 4/ configuration with the levels of opposite parity of the c.t. state. 

The parity of atomic states is important in spectroscopy. A radial function is an even function [see (1.113)] the spherical harmonic Y(m is found to be an even or odd function of the Cartesian coordinates according to whether / is an even or odd number. For a many-electron atom, it follows that states arising from a configuration for which the sum of the / values of all the electrons is an even number are even functions when 2,/, is odd, the state has odd parity. 

In the following it will be outlined, how the parity violating potentials are computed within a sum-over-states approach, namely on the uncoupled Hartree-Fock (UCHF) level, and within the configuration interaction singles approach (CIS) which is equivalent to the Tamm-Dancoff approximation (TDA), that avoids, however, the sum over intermediate states. Then a further extension is discussed, namely the random phase approximation (RPA) and an implementation along similar lines within a density functional theory (DFT) ansatz, and finally a multi-configuration linear response approach is described, which represents a systematic procedure that... 

The ground level electronic configuration of trivalent europium is / . Transitions within the / shell are responsible for the crystal spectra. Transitions are forbidden in a free ion by the parity rule for electric dipole transitions. In a crystal or glass, forced electric transitions become allowed as a consequence of coupling of odd electronic wave functions due to the odd parity terms in the crystal field expansion. Considering the static field approximation in the theory developed by Judd (4) and Ofelt (5), the contribution of the odd parity part of the cr5rstal field is calculated by mixing states of different parity. 

Excited state wave functions are constructed in a similar way. The low-lying, J=l, odd parity state is described approximately by two configurations 2s2pi 2 2s2p3 2 this cas, there are... 

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