Measurement of Hyperfine Structure and the Zemach Radius in

We investigate the 2^{3}S_{1}-2^{3}P_{J} (J=0, 1, 2) transitions in ^{6}Li^{+} using the optical Ramsey technique and achieve the most precise values of the hyperfine splittings of the 2^{3}S_{1} and 2^{3}P_{J} states, with smallest uncertainty of about 10 kHz. The present results reduce the uncertainties of previous experiments by a factor of 5 for the 2^{3}S_{1} state and a factor of 50 for the 2^{3}P_{J} states, and are in better agreement with theoretical values. Combining our measured hyperfine intervals of the 2^{3}S_{1} state with the latest quantum electrodynamic (QED) calculations, the improved Zemach radius of the ^{6}Li nucleus is determined to be 2.44(2) fm, with the uncertainty entirely due to the uncalculated QED effects of order mα^{7}. The result is in sharp disagreement with the value 3.71(16) fm determined from simple models of the nuclear charge and magnetization distribution. We call for a more definitive nuclear physics value of the ^{6}Li Zemach radius.

Precision Spectroscopy of the Pionic Helium-4.

The transition frequency of (n,ℓ)=(17,16)→(16,15) in pionic helium-4 is calculated to an accuracy of 4 ppb (parts per billion), including relativistic and quantum electrodynamic corrections up to O(R_{∞}α^{5}). Our calculations significantly improve the recent theoretical values [Hori et al., Phys. Rev. A 89, 042515 (2014)PLRAAN1050-294710.1103/PhysRevA.89.042515]. In addition, collisional effects between pionic helium and target helium on transition frequencies are estimated. Once measurements reach the ppb level, our Letter will improve the value of the π^{-} mass by 2-3 orders of magnitude.

Precision Calculation of Hyperfine Structure and the Zemach Radii of

The hyperfine structures of the 2^{3}S_{1} states of the ^{6}Li^{+} and ^{7}Li^{+} ions are investigated theoretically to extract the Zemach radii of the ^{6}Li and ^{7}Li nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.243001] and disagree with them by about 1.5 and 2.2 standard deviations for ^{6}Li and ^{7}Li, respectively. Furthermore, our Zemach radius of ^{6}Li differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)PLRAAN1050-294710.1103/PhysRevA.78.012513] by more than 6σ, indicating an anomalous nuclear structure for ^{6}Li. The conclusion that the Zemach radius of ^{7}Li is about 40% larger than that of ^{6}Li is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the 2^{3}P_{J} states of ^{6,7}Li^{+}, where an order of magnitude improvement over the previous theory has been achieved for ^{7}Li^{+}.

Relativistic corrections to the ground states of HD and D2 calculated without using the Born-Oppenheimer approximation.

The Schrödinger equation for the ground states of the hydrogen molecules HD and D2 is solved variationally by treating the constituent particles of HD or D2 on the same footing without assuming the Born-Oppenheimer approximation. The variational basis sets are constructed using Hylleraas coordinates that are traditionally adopted for few-electron atomic systems. The nonrelativistic energy eigenvalues are converged to the level of 10-6 cm-1. The leading-order relativistic corrections, including relativistic recoil terms, are calculated rigorously. Together with the higher-order relativistic and quantum electrodynamic corrections obtained by the Pachucki's group [Phys. Rev. A., 2017, 95, 052506; Phys. Rev. Lett., 2018, 120, 153001], we determine the dissociation energy of D2 to be 36748.36240(28) cm-1, which agrees with the recent experimental result of Liu et al. [J. Chem. Phys., 2010, 132, 154301] 36748.36286(68) cm-1. For HD, the dissociation energy determined by us is 36405.78252(27) cm-1, which deviates from the most accurate experimental result of Sprecher et al. [J. Chem. Phys., 2010, 133, 111102] 36405.78366(36) cm-1 by about 2σ.

Fine structure and ionization energy of the 1s2s2p 4P state of the helium negative ion He-.

The fine structure and ionization energy of the 1s2s2p (4)P state of the helium negative ion He(-) are calculated in Hylleraas coordinates, including relativistic and QED corrections up to O(α(4)mc(2)), O((µ/M)α(4)mc(2)), O(α(5)mc(2)), and O((µ/M)α(5)mc(2)). Higher order corrections are estimated for the ionization energy. A comparison is made with other calculations and experiments. We find that the present results for the fine structure splittings agree with experiment very well. However, the calculated ionization energy deviates from the experimental result by about 1 standard deviation. The estimated theoretical uncertainty in the ionization energy is much less than the experimental accuracy.

Oscillator strengths between low-lying ro-vibrational states of hydrogen molecular ions.

It is important for experimental design to know the transition oscillator strengths in hydrogen molecular ions. In this work, for HD(+), HT(+), and DT(+), we calculate the ro-vibrational energies and oscillator strengths of dipole transitions between two ro-vibrational states with the vibrational quantum number ν = 0-5 and the total angular momentum L = 0-5. The oscillator strengths of HT(+) and DT(+) are presented as supplementary material.

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms.

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

Long-range dispersion coefficients for Li, Li(+), and Be(+) interacting with the rare gases.

The long-range dispersion coefficients for the ground and excited states of Li, Li(+), and Be(+) interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, Li(+), and Be(+), while pseudo-oscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and Be(+) and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and Li(+) states and the recommended (7)Li(+) polarizability including both finite-mass and relativistic effects was 0.192 486 a.u. The impact of finite-mass effects upon the dispersion coefficients has been given for some selected interatomic interactions.

Carrier-envelope phase dependence of non-sequential double ionization in few-cycle pulses.

The influence of carrier-envelope phase (CEP) of a few-cycle laser pulse on non-sequential double ionization (NSDI) of an atom is investigated by applying the three-dimensional semi-classical re-scattering method. The asymmetric momentum distribution of the double-charged ion parallel to the laser polarization, which depends on the CEP, is explained by comparing the contributions from several half-cycles in the laser pulse. The ionization rate and the returning kinetic energy of the first electron dramatically affect the contributions from each half-cycles, and play different roles in different laser intensity regimes.

Bethe logarithm and QED shift for lithium.

A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 (2)S(1/2) and excited 3 (2)S(1/2) states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order alpha(3) Ry. The calculated 3 (2)S(1/2)-2 (2)S(1/2) transition frequency for 7Li is 27 206.092 6(9) cm(-1), and the ionization potential for the 2 (2)S(1/2) state is 43 487.158 3(6) cm(-1). The 7Li-6Li isotope shift is also considered, and all the results compared with experiment.