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Journal of Physics B Atomic Molecular and Optical Physics

Oscillator strengths and radiative decay rates for spin-changing S–P transitions in helium: finite nuclear mass effects

D. C. Morton, Eva Schulhoff, G. W. F. Drake

Published Dec 14, 2014• 7 citations
Publisher

Abstract

Abstract We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for 24 spin-changing transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron augmented by the recently derived Pachucki term. The specific transitions for 4 He are and with and for For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on both numerical accuracy and validity of the transition operators. The corrections for the nuclear mass and the electron anomaly tend to cancel, indicating that if one is included, then so should be the other. The tables give mass- and anomaly-dependent coefficients permitting the easy generation of results for the other isotopes of helium.

DOI
10.1088/0953-4075/48/23/235001

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Abstract We have calculated the electric dipole (E1) and magnetic quadrupole (M2) oscillator strengths and spontaneous decay rates for 24 spin-changing transitions of atomic helium. We included the effects of the finite nuclear mass and the anomalous magnetic moment of the electron augmented by the recently derived Pachucki term. The specific transitions for 4 He are and with and for For the E1 calculations we used the Breit approximation and pseudostate expansions to perform the perturbation sums over intermediate states in both the length and velocity gauge as a check on both numerical accuracy and validity of the transition operators. The corrections for the nuclear mass and the electron anomaly tend to cancel, indicating that if one is included, then so should be the other. The tables give mass- and anomaly-dependent coefficients permitting the easy generation of results for the other isotopes of helium.
A large-scale full-configuration-interaction calculation based on the Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the 21S02{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}21S0​ and 23S12{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}23S1​ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved nnn (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states, and a series of magic wavelengths with QED and hyperfine effects included for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ transition of helium are identified. In addition, the high-order ac Stark shift determined by the dynamic hyperpolarizabilities at the magic wavelengths are also evaluated. Since the most promising magic wavelength for application in experiment is 319.8 nm, the high-accuracy magic wavelength of 319.815 3(6) nm of 4He^{4}\mathrm{He}4He is in good agreement with the recent measurement value of 319.815 92(15) nm [R. J. Rengelink et al., arXiv:1804.06693], and the present magic wavelength of 319.830 2(7) nm for 3He^{3}\mathrm{He}3He would provide theoretical support for experimentally designing an optical dipole trap to precisely determine the nuclear charge radius of helium in the future.
The relaxation rates of the monopole, magnetic dipole, and electric quadrupole moments have been determined for the 31{3}^{1}31P state of helium excited by electron impact, The data are determined from atomic lifetimes using linear and circular polarization analyzed radiation with the electron-photon delayed coincidence technique. This has permitted the direct observation of the time dependence of all the off-diagonal elements of the density matrix of the excited state. The implications for atomic state information determined from polarization and angular correlation methods are indicated.
A series of magic wavelengths for the forbidden transition of $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}$ in helium are determined by performing large-scale full relativistic configuration interaction calculations based on Dirac-Coulomb-Breit Hamiltonian with the mass shift operator included. QED corrections to magic wavelengths are taken into account by using the perturbation theory in nonrelativistic configuration interaction calculations. The 1335.55(2)-nm magic wavelength for the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{S}_{1}(M=\ifmmode\pm\else\textpm\fi{}1)\ensuremath{\rightarrow}2{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}(M=0)$ transition is found to be sensitive to the finite nuclear mass, relativistic, and QED effects, and its measurement might provide a test of atomic structure theory.
Introduction The selection rules discussed in Sec. 3.5 forbid many kinds of transitions that are frequently observed or exploited. It must be remembered that these “rules” are based on the approximations of Sec. 3.2, but of course, those can be extended. Such expansions to higher orders of approximation may seem to be little more than a tedious exercise, but this chapter will show that the results are extremely important, because they cause qualitatively different kinds of transitions. Since they involve both the electric and magnetic components of the light, their atomic dipole moments will be identified with the superscript E and B for the remainder of this chapter. The magnetic dipole transitions, called M1, discussed in Sec. 4.2.1 that arise from extension of the electric dipole approximation encompass all of magnetic resonance, including atomic clocks, forced evaporative cooling in Bose–Einstein Condensation (BEC), MRI, and astrophysical processes such as generation of the all-important 21 cm radio frequency line. The electric quadrupole transitions, called E2, discussed in Sec. 4.2.2 describe myriad stellar spectral features as well as the vast majority of nuclear γ-ray transitions. Even with these extensions there are many cases where the relaxation of the electric dipole (E1) selection rules to include M1 and E2 transitions as in Sec. 4.2 still do not account for observed processes. Thus other approximations have to be extended so that their limitations can be relaxed as well. Extension of the perturbation approximation (see Sec. 4.3.1) provides an analytical description of most of non-linear optics, including second harmonic generation, four wave mixing, Raman spectroscopy, and the fabled decay of the hydrogen 2S state. A semi-classical description of the interaction between radiation and atoms can begin with a multipole expansion of the Hamiltonian. The lowest-order term is just from the point charges α located at, and vanishes for neutral atoms. The next-order term is the electric dipole interaction that arises from the non-isotropic distribution of charges induced by the electric field of the light. This term produces the electric dipole transitions (E1) that have been described in some detail in Chap. 3.
For pt.I see ibid., vol.17, p.29-52 (1984). Wavelengths, dipole strengths, oscillator strengths and transition probabilities for electromagnetic transitions between low-lying states of the hydrogen atom embedded in a magnetic field of arbitrary strength (0<B<or=4.70*10 8 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B values using the wavefunctions and energy values determined in paper I by expanding the wavefunctions in terms of spherical harmonics (weak and moderate fields), or in terms of Landau states (strong and very strong fields). Effects caused by the finiteness of the proton mass are taken into account, and the scaling laws are quoted by the aid of which the results presented can be utilised to cover quantitatively the whole hydrogenic sequence in intense magnetic fields; finally, the quality of the results of previous calculations is checked.
Given growing interest in optical-frequency magnetic dipole transitions, we use intermediate coupling calculations to identify strong magnetic dipole emission lines that are well suited for experimental study. The energy levels for all trivalent lanthanide ions in the 4fn4{f}^{\text{n}}4fn configuration are calculated using a detailed free ion Hamiltonian, including electrostatic and spin-orbit terms as well as two-body, three-body, spin-spin, spin-other-orbit, and electrostatically correlated spin-orbit interactions. These free ion energy levels and eigenstates are then used to calculate the oscillator strengths for all ground-state magnetic dipole absorption lines and the spontaneous emission rates for all magnetic dipole emission lines including transitions between excited states. A large number of strong magnetic dipole transitions are predicted throughout the visible and near-infrared spectrum, including many at longer wavelengths that would be ideal for experimental investigation of magnetic light-matter interactions with optical metamaterials and plasmonic antennas.