Minima in the emission oscillator strengths of alkali Rydberg states

Abstract

Minima have been found in the calculated emission oscillator strengths of excited Rydberg states of the alkali atoms. These minima appear only in the D states of potassium and F states of caesium. Their crigin and implications are discussed. In the process of calculating Rydberg state lifetimes (Theodosiou 1979) we came across surprisingly sharp minima in the transition probabilities and emission oscillator strengths from all excited D states in potassium to lower P states. These minima are analogous to the well known 'Cooper minima' in photoionisation cross sections and in generalised oscillator strengths (Fano and Cooper 1968, Kim et a1 1968). They are absent in the S and P states and in Na and Rb. A minimum in the transition probability, or equivalently in the emission oscillator strength, from an excited to a lower state appears when the dipole matrix element between the respective states becomes, for some reason, vanishingly small. The matrix element, in turn, depends critically on the overlap between initial- and final-state wavefunctions. In our case of nd to n'p transitions in potassium the dipole matrix element assumes alternatively positive and negative values depending on the number of nodes the n'p state has. (We assume here a positive wavefunction slope near the origin.) At some principal quantum number n' the contributions to the matrix element from the positive and negative lobes of the n'p wavefunction cancel each other out, thus resulting in the calculated minima. We shall explain later why this happens only for certain states. The transition probability A and emission oscillator strength -f are given, respec- tively, by