Predicted spectrum of atomic nobelium

Abstract

The electronic spectrum of atomic nobelium (element 102) is calculated in preparation for a planned experiment. The intermediate-Hamiltonian (IH) coupled-cluster method is applied to the ionization potential and excitation energies of the atom, using a large basis set $(37s\phantom{\rule{0.2em}{0ex}}31p\phantom{\rule{0.2em}{0ex}}26d\phantom{\rule{0.2em}{0ex}}21f\phantom{\rule{0.2em}{0ex}}16g\phantom{\rule{0.2em}{0ex}}11h\phantom{\rule{0.2em}{0ex}}6i)$ and correlating the outer 42 electrons. All the levels studied are obtained simultaneously by diagonalizing the IH matrix. The rows and columns of this matrix correspond to all excitations from correlated occupied orbitals to virtual orbitals in a large $P$ space $(8s\phantom{\rule{0.2em}{0ex}}6p\phantom{\rule{0.2em}{0ex}}6d\phantom{\rule{0.2em}{0ex}}4f\phantom{\rule{0.2em}{0ex}}2g\phantom{\rule{0.2em}{0ex}}1h)$, and the matrix elements are ``dressed'' by including excitations to the higher virtual orbitals ($Q$ space) at the coupled cluster singles-and-doubles level. Lamb shift corrections are included. The accuracy is assessed by applying the same method to ytterbium, the lighter homologue of No. The calculated ionization potential of Yb is within $3\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ of experiment, and the average error in the lowest 20 excitation energies of the atom is $300\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. Nobelium is the heaviest element for which a reliable semiempirical estimate of the ionization potential exists, $6.65(7)\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$; the calculated value of $6.632\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ is in excellent agreement. Transition amplitudes are obtained from an extensive relativistic configuration interaction calculation. The outstanding feature of the predicted nobelium spectrum is a very strong line at $30\phantom{\rule{0.2em}{0ex}}060\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, with an amplitude $A=5.0\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.3em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, corresponding to the $7s7p$ $^{1}P_{1}\ensuremath{\rightarrow}7{s}^{2}$ $^{1}S_{0}$ transition. Putting the error limit conservatively at $0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, we predict a strong feature in the No spectrum at $30\phantom{\rule{0.2em}{0ex}}100\ifmmode\pm\else\textpm\fi{}800\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.