Geometric quantities of lower doubly excited bound states of helium |
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Affiliation: | 1.School of Physics and Technology, Wuhan University, Wuhan 430072, China;2.College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China |
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Abstract: | Expectation values of single electron and interelectronic geometric quantities such as $langle rrangle$, $langle r_{12}rangle$, $langle r_rangle$, $langle costheta_{12}rangle$ and $langle theta_{12}rangle$ are calculated for doubly excited $2{rm p}n{rm p},{}^1P^{,rm e},(3leq nleq5),, 2{rm p}n{rm p},{}^3!P^{,rm e},(2leq nleq5)$ and $2{rm p}n{rm d},{}^{1,3}D^{,rm o},(3leq nleq5)$ states of helium using Hylleraas-$B$-spline basis set. The energy levels converge to at least 10 significant digits in our calculations. The extrapolated values of geometric quantities except for $langle theta_{12}rangle$ reach 10 significant digits as well; $langle theta_{12}rangle$ reaches at least 7 significant digits using a multipole expansion approach. Our results provide a precise reference for future research. |
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Keywords: | doubly excited states unnatural parity Hylleraas-$B$-spline geometric quantities |
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