---
abstract: 'The bound state spectra of the doublet states in three-electron atomic systems are investigated. By using different variational expansions we determine various bound state properties in these systems. Such properties include the electron-nucleus and electron-electron delta-functions and cusp values. The general structure of the bound state spectra in several three-electron atomic systems (Li, Be$^{+}$, C$^{3+}$ and F$^{6+}$) is investigated with the use of the Hylleraas-Configuration Interaction and the Configuration Interaction wave functions. The advantage of our Configuration Interaction based procedure is that it provides high numerical accuracy for all rotationally excited states, including the bound states with $L \ge 7$.'
author:
- 'Alexei M. Frolov'
- María Belén Ruiz
- 'David M. Wardlaw'
title: 'Bound state spectra and properties of the doublet states in three-electron atomic systems'
---

Introduction {#intro}
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In this study we investigate the bound doublet states in the three-electron atoms and ions by using a few different variational expansions written in the relative coordinates, or interparticle distances $r_{ij} =  \mid {\bf r}_i - 
{\bf r}_j \mid = r_{ji}$, where ${\bf r}_i$ ($i$ = 1, 2, 3) are the Cartesian coordinates of the three electrons, while ${\bf r}_4$ are the Cartesian coordinates of the positively 