Background to Lifetime Measurements

On several previous occasions we have discussed measurement techniques yielding information on natural radiative lifetimes. We now discuss the motivation behind such measurements. In Fig. 9.24 some important relations between radiative properties are presented. 

In many contexts, transition probabilities, A fc, (Sect. 4.1) are the quantities of primary interest. As we will see in the next section, relative transition probabilities, Uik, can be determined by several methods. A direct, absolute determination is considerably more difficult. However, lifetimes can be used to determine the relevant constant c, used to normalize relative transition probabilities to absolute ones 

There are many reasons for studying radiative properties  

The natural lifetime determines the fundamental limit of resolution Ai/n — l/27rr in spectroscopic investigations. 

Transition probabihties can be used for sensitive testing of atomic wave functions. Aif. is related to the matrix element of the electric dipole operator er between the two wave functions (Sect. 4.1). Note that Aik is especially sensitive to the outer part of the wave function (at larger r values) because of the r weighting. 

In many contexts, transition probabilities (Sect.4.1) are the quantities of primary interest. As we will see in the next section, relative transi- 

3) As we have mentioned in Sect.6.7, transition probabilities and the related oscillator strengths fj are of utmost importance for astrophysics, e.g. for calculations of the relative abundances of the elements in the sun and stars. 

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