Several extended Rydberg series have been experimentally identified in triply excited states of hollow lithium, by use of electron spectrometry and synchrotron radiation at the Advanced Light Source. Energies, partial cross sections, and quantum defects have also been calculated using the R-matrix approximation. Our results show that the two inner electrons stay in a core-excited state of given symmetry while the behavior of the third electron is mostly governed by the nuclear potential screened by the two inner electrons. [S0031-9007(97)03826-X] PACS numbers: 32.80. Hd, 32.80.Fb, 32.80.Rm We present here the first experimental evidence demonstrating the existence of several extended Rydberg series in the hollow triply excited states of lithium. These new results, obtained using electron spectrometry and synchrotron radiation, are supported by our theoretical calculations made using the R-matrix approximation. We also explain why these Rydberg series have not been observed previously.The inner shell (K, or 1s) in a hollow atomic or ionic state is empty. Simultaneous excitation of all three electrons can create hollow lithium states of the type nᐉn 0 ᐉ 0 n 00 ᐉ 00 with n $ 2 [1-5]. A calculation of some low-lying hollow lithium states in hyperspherical coordinates has been recently carried out [6] as a step towards the development of a classification scheme for triply excited states, analogous to the ͑K, T͒ A radial and angular correlation quantum numbers [7,8] used to describe the doubly excited states of helium [9]. For future understanding an important question is whether hollow lithium states exist which can be regarded as heliumlike doubly excited Li 1 terms plus a running outer electron or is the configuration mixing so great that Rydberg states of this type are absent? An earlier experiment [3] measuring the yield of Li 1 ions by photoion spectrometry did not reveal such series features. In fact, the authors specifically stated [3] "that the most striking aspect of the ion spectrum is the complete absence of any identifiable Rydberg series structure." Later measurements taking advantage of the final-state selectivity of photoelectron spectroscopy [4,5] suggested, however, that some of the observed structures could be identified as first members of Rydberg series. But their effect on partial cross sections for photoionization into final Li 1 ionic states with one vacancy in the 1s shell was very weak and no higher terms of any series were observed.We have carried out new theoretical R-matrix calculations which predict the existence of eight Rydberg series between 150 and 160 eV, i.e., 1s 2 2s 2 S 1 hn ! ͓͑2s 2 1 S͒np͔ 2 P, ͓͑2s2p 3 P͒ns or nd͔ 2 P, ͓͑2p 2 3 P͒np͔ 2 P, ͓͑2p 2 1 D͒np͔ 2 P, ͓͑2s2p 1 P͒ns or nd͔ 2 P, and ͓͑2p 2 3 1 S͒np͔ 2 P. In Fig. 1, we show the calculated partial cross section for photoionization into the 1s2ᐉ final Li 1 FIG. 1. R-matrix calculation of partial cross section for photoionization of Li atoms into the ͑1s2ᐉ͒ 1,3 L final states of the Li 1 ion.