类氦和类锂等电子序列的超紧凑精确波函数与变分计算. II. 氦序列的自旋单重态（激发）和自旋三重态（最低）态
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. II. Spin-singlet (excited) and spin-triplet (lowest) states of the Helium sequence
A. V. Turbiner, J. C. Lopez Vieyra, J. C. del Valle, D. J. Nader
备注：
27 pages, 6 figures, 4 tables: typos fixed, 8 extra references added, the text essentially extended, to be published at Int Journ Quantum Chemistry
As a continuation of Part I \cite{Part-1:2020} (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, a few ultra-compact wave functions in the form of generalized Hylleraas-Kinoshita functions are constructed, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for the energies (4-5 significant digits (s.d.)) of two excited states of He-like ions: the spin-singlet (first) excited state $2^1 S$ and the lowest spin-triplet $1^3 S$ state. For both states it provides absolute accuracy for energy $\sim 10^{-3}$\,a.u., exact values for cusp parameters and also for 6 expectation values the relative accuracy $\sim 10^{-2}$. The Bressanini-Reynolds observation about the special form of the nodal surface of the $2^1 S$ state of Helium is confirmed and extended to He-like ions with $Z > 2$. Critical charges $Z=Z_B$, where ultra-compact trial functions lose their square-integrability, are estimated: $Z_B(1^1 S)\approx Z_B(2^1 S)\sim 0.905$ and $Z_B(1^3 S)\sim 0.902$. For both states the Majorana formula - the energy as a second degree polynomial in $Z$ - provides accurately 4-5 significant digits for $Z \leq 20$.
We report a calculation of relativistic corrections of order $mα^7$ to the Bethe logarithm for the $2^3S$ and $2^3P$ states of helium-like ions. The calculation is required for improving the accuracy of theoretical energies of helium-like ions and for checking the evaluation of the $mα^7$ effects in helium performed in [V. Patkóš, V. A. Yerokhin, K. Pachucki, Phys. Rev. A 103, 042809 (2021)], where a significant discrepancy with experimental results was found. The large-$Z$ limit of the relativistic Bethe logarithm is determined numerically, in excellent agreement with the analytical results o…
For decades, improved theory and experiment of the $n=2$ $^3$P fine structure of helium have allowed for increasingly-precise tests of quantum electrodynamics, determinations of the fine-structure constant $α$, and limitations on possible beyond-the-Standard-Model physics. Here we use the new frequency-offset separated-oscillatory-fields (FOSOF) technique to measure the $2^3$P$_2\!\!\to\!2^3$P$_1$ interval. Our result of $2\,291\,176\,590(25)$~Hz represents a major step forward in precision for helium fine-structure measurements.
We have derived the complete formula for the $α^7\,m$ contribution to energy levels of an arbitrary triplet state of the helium atom, performed numerical calculations for the $2^3S$ and $2^3P$ states, and thus improved the theoretical accuracy of ionization energies of these states by more than an order of magnitude. Using the nuclear charge radius extracted from the muonic helium Lamb shift, we obtain the theoretical prediction in excellent agreement with the measured $2^3S - 2^3P$ transition energy [X.~Zheng et al., Phys. Rev. Lett. {\bf 199}, 263002 (2017)]. At the same time we observe sign…
Theoretical predictions for the Lamb shift in helium are limited by unknown quantum electrodynamic effects of the order $α^7m$, where $α$ is the fine-structure constant and $m$ is the electron mass. We make an important step towards the complete calculation of these effects by deriving the most challenging part, which is induced by the virtual photon exchange between all three helium particles, the two electrons, and the nucleus. The complete calculation of the $α^7m$ effect including the radiative corrections will allow comparing of the nuclear charge radii determined from the electronic and …
We perform ab initio calculations of the QED effects of order $mα^7$ for the $2^3S$ and $2^3P$ states of He-like ions. The computed effects are combined with previously calculated energies from [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], thus improving the theoretical accuracy by an order of magnitude. The obtained theoretical values for the $2^3S$-$2^3P_{0,2}$ transition energies are in good agreement with available experimental results and with previous calculations performed to all orders in the nuclear binding strength parameter $Zα$. For the ionization energies, howe…
The dynamic dipole polarizabilities for the four lowest triplet states ($2\,^3S$, $3\,^3S$, $2\,^3P$ and $3\,^3P$) of helium are calculated using the B-spline configuration interaction method. Present values of the static dipole polarizabilities in the length, velocity and acceleration gauges are in good agreement with the best Hylleraas results. Also the tune-out wavelengths in the range from 400 nm to 4.2~$μ$m for the four lowest triplet states are identified, and the magic wavelengths in the range from 460~nm to 3.5~$μ$m for the $2\,^3S \to 3\,^3S$, $2\,^3S \to 2\,^3P$, and $2\,^3S \to 3\,^…
We have obtained accurate ab initio quartet potentials for the diatomic metastable triplet helium + alkali-metal (Li, Na, K, Rb) systems, using all-electron restricted open-shell coupled cluster singles and doubles with noniterative triples corrections [CCSD(T)] calculations and accurate calculations of the long-range $C_6$ coefficients. These potentials provide accurate ab initio quartet scattering lengths, which for these many-electron systems is possible, because of the small reduced masses and shallow potentials that results in a small amount of bound states. Our results are relevant for u…
Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states
University of Windsor（温莎大学）；Drake University（德雷克大学）
Low-energy positron scattering from metastable helium
Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences（中国科学院精密测量科学与技术创新研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Discharge and electron-impact excitation lead to the production of metastable helium atoms in two metastable states, 2$^1$S$_0$ and 2$^3$S$_1$. However, many applications require pure beams of one of these species or at least a detailed knowledge of the relative state populations. In this paper, we present the characterization of an original experimental scheme for the optical depletion of He(2$^1$S$_0$) in a supersonic beam which is based on the optical excitation of the 4$^1$P$_1 \leftarrow 2^1$S$_0$ transition at 397 nm using a diode laser. From our experimental results and from a compariso…
In an ultracold, optically trapped mixture of $^{87}$Rb and metastable triplet $^4$He atoms we have studied trap loss for different spin-state combinations, for which interspecies Penning ionization is the main two-body loss process. We observe long trapping lifetimes for the purely quartet spin-state combination, indicating strong suppression of Penning ionization loss by at least two orders of magnitude. For the other spin-mixtures we observe short lifetimes that depend linearly on the doublet character of the entrance channel. We compare the extracted loss rate coefficient with recent predi…
Nonzero angular momentum states of the helium atom in a strong magnetic field
在B=0- 100 a. u.的磁场范围内，氦原子的电子结构。的研究，使用全组态相互作用的方法，这是基于非线性优化的各向异性高斯基组的单粒子函数。相应的广义本征值问题的磁量子数M=-1和z宇称的奇偶性以及单重态和三重态自旋对称性。精确的总电子能量的基态和前四个激发在每个子空间，以及它们的单电子电离能的磁场的函数。此外，我们提出的能量内的M =-1子空间和M=-1子空间和M=0子空间之间的电磁跃迁在以前的工作中处理。一个完整的表的波长和场强检测到的驻点。
We report on the realization of an ultracold (<25~muK) mixture of rubidium ({87}Rb) and metastable triplet helium ({4}He) in an optical dipole trap. Our scheme involves laser cooling in a dual-species magneto-optical trap, simultaneous MW- and RF-induced forced evaporative cooling in a quadrupole magnetic trap, and transfer to a single-beam optical dipole trap. We observe long trapping lifetimes for the doubly spin-stretched spin-state mixture and measure much shorter lifetimes for other spin-state combinations. We discuss prospects for realizing quantum degenerate mixtures of alkali-metal and…
