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The fully correlated calculations of the Zeeman gJ factors for the first three quartet S states of lithium are presented, including relativistic and radiative corrections of orders α2, α2 m/M, and α3. The isotope shifts in gJ are predicted precisely for various isotopes of lithium.

Nonrelativistic energies for the low-lying states of lithium are calculated using the variational method in Hylleraas coordinates. Variational eigenvalues for the infinite nuclear mass case with up to 34 020 terms are $\ensuremath{-}7.478\phantom{\rule{0.16em}{0ex}}060\phantom{\rule{0.16em}{0ex}}323\phantom{\rule{0.16em}{0ex}}910\phantom{\rule{0.16em}{0ex}}147(1)$ a.u. for $1{s}^{2}2s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.354\phantom{\rule{0.16em}{0ex}}098\phantom{\rule{0.16em}{0ex}}421\phantom{\rule{0.16em}{0ex}}444\phantom{\rule{0.16em}{0ex}}37(1)$ a.u. for $1{s}^{2}3s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.318\phantom{\rule{0.16em}{0ex}}530\phantom{\rule{0.16em}{0ex}}845\phantom{\rule{0.16em}{0ex}}998\phantom{\rule{0.16em}{0ex}}91(1)$ a.u. for $1{s}^{2}4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.410\phantom{\rule{0.16em}{0ex}}156\phantom{\rule{0.16em}{0ex}}532\phantom{\rule{0.16em}{0ex}}652\phantom{\rule{0.16em}{0ex}}41(4)$ a.u. for $1{s}^{2}2p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}P$, and $\ensuremath{-}7.335\phantom{\rule{0.16em}{0ex}}523\phantom{\rule{0.16em}{0ex}}543\phantom{\rule{0.16em}{0ex}}524\phantom{\rule{0.16em}{0ex}}688(3)$ a.u. for $1{s}^{2}3d{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}D$. The selection of the minimum set of angular momentum configurations is discussed, with the $2P$ and $3D$ states as examples to demonstrate the impact of various configurations on the variational energies. It is shown by numerical example that the second spin function (i.e., coupled to form a triplet intermediate state) has no significant effect on either the variational energies or the spin-dependent Fermi contact term. Results of greatly improved accuracy for the Fermi contact term are presented for all the states considered.

We present improved calculations of variational energy eigenvalues for the $1{s}^{2}2s {}^{2}S$, $1{s}^{2}3s {}^{2}S$, and $1{s}^{2}2p {}^{2}P$ states of lithium using basis sets with up to 30 224 terms in Hylleraas coordinates. The nonrelativistic energies for infinite nuclear mass are $\ensuremath{-}7.478 060 323 910 143 7(45)$ a.u. for $1{s}^{2}2s {}^{2}S$, $\ensuremath{-}7.354 098 421 444 316 4(32)$ a.u. for $1{s}^{2}3s {}^{2}S$, and $\ensuremath{-}7.410 156 532 651 6(5)$ a.u. for $1{s}^{2}2p {}^{2}P$, which represent the most accurate variational upper bounds to date. An important advantage of the basis sets with multiple distance scales is their exceptional numerical stability.

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-lived ‘halo’ nuclei 6He and 11Li in order to determine their nuclear charge radii from high precision spectroscopic measurements. It is shown that the results provide a unique measurement tool that is capable of discriminating amongst a variety of theoretical models for nuclear structure. In view of the high precision that is now obtainable, helium and lithium, along with hydrogen, can be regarded as fundamental atomic systems whose spectra are well understood for all practical purposes.