Basic notions of autoionizing Rydberg states

It is straightforward to extend the picture of the spinless Ba atom given in Chapter 17 to autoionizing states. We again use the Hamiltonian of Eq. (17-1), which separates into 

Here p is a Ba+ wavefunction and xp is a hydrogenic wavefunction. The wavefunction of Eq. (19.6a) is a good zero order representation of the Ba atom as long as the inner turning point of the outer n(. electron is at a larger radius than the outer turning point of the Ba+ n C electron. 

Since the two wavefunctions are independent, the energies do not depend on m, m, or , and we can write the energy of the n t nt state relative to the ground state of Ba2+ as 

Physically, the wavefunction of Eq. (19.6a) corresponds to adding one electron to Ba2+ to make the Ba+ n C states and then adding the second n electron to form the neutral Ba n Cni states. On each state of Ba+ there is built an entire system of Rydberg states and continua, as shown in Fig. 19.1 for the three lowest lying states of Ba+. Note that the Rydberg states converging to the 5d and 6p states of Ba+ are above the Ba+ 6s state. With the independent electron Hamiltonian H0 these states can only decay radiatively. They are not coupled to the degenerate continua above the Ba+ 6s state. 

Ba Rydberg energy levels (—) and continua (///) obtained by adding the second valence electron to these Ba+ levels. The horizontal arrows show the possible interactions between channels associated with different ion levels. Interactions with other bound states lead to series perturbations while interactions with continua lead to autoionization. 

---