Exponentially Correlated Hylleraas–Configuration Interaction Studies of Atomic Systems—IV: Energies for the Five Lowest 1S and 1P States of He and Oscillator Strengths, Including Bounds, for Their Allowed Transitions

The Exponentially Correlated Hylleraas–Configuration Interaction method (E-Hy-CI) is a generalization of the Hylleraas–Configuration Interaction method (Hy-CI), in which the single \(r_{ij}\) is generalized to a form of the generic type \(r_{ij}^{\nu_{ij}}\text{e}^{-\omega_{ij}r_{ij}}\). This paper extends our earlier work of exploring whether wave functions containing both linear and exponential \(r_{ij}\) factors converge more rapidly. In the present study, we calculate the five lowest \(^1S\) and \(^1P\) states of He I in two wave functions. These two wave functions are used to calculate oscillator strengths, including upper and lower bounds, for the allowed transitions between these states. The results of this study are oscillator strengths for the \(n\) \(^1S\) \(\rightarrow\) \(m\) \(^1P\) transitions for \(n = 1-5\), \(m= 2-6\) with rigorous upper and lower bounds, which in the best case (1 \(^1S \rightarrow 2\ ^1P\)) are 0.00000001 % and probable precision ≤ 0.0000000001.