Radiative Transitions in Rare Earth Elements

Radiative relaxation from an excited state /J of a lanthanide ion usually occurs in various lower lying state giving rise to several lines in the emission spectrum. For example, the red luminescence of Eu is a result of transitions from its Dq state to all of the lower lying Fj levels. The spontaneous emission probability, A, of the transition /J is related to its dipole strength according to 

The elementary charge e is 4.803 x 10 ° esu. The Q, parameters belong the particular combination of the RE ion and its coordinating environment, end are usually determined experimentally. P are the square reduce dmatrix 

Transitions arising from the Dq level of the 41 electronic configuration of are intensities between the magnetic dipolar Dq Fi ( 590 nm) and the electric dipolar Dq — p2 ( 610 nm) transitions. The higher this ratio, the closer the local symmetry around Eu is to an inversion center. In the standard theory, the spontaneous emission of a integrated coefficient of the transition between two manifolds / and / is given by 

Where to is a angular frequency of the transition, e is the electronic charge, c is the velocity of light, h is Planck s constant over 27t and n is the refractive index of the medium. The electric and magnetic dipole strengths, respectively, Sed and 8 4 (in units of e ), are given by 

Where the quantities 2 are the Judd-Ofelt intensity parameters as described before and m is the electron mass. 

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