Hyperfine Mixing Research Articles

Spin-state mixing in InAs double quantum dots

We quantify the contributions of hyperfine and spin-orbit-mediated singlet-triplet mixing in weakly coupled InAs quantum dots by electron transport spectroscopy in the Pauli spin-blockade regime. In contrast to double dots in GaAs, the spin-orbit coupling is found to be more than two orders of magnitudes larger than the hyperfine mixing energy. It is already effective at magnetic fields of a few mT, where deviations from pure hyperfine mixing are observed.

Observation of Hyperfine Mixing in Measurements of a Magnetic OctupoleDecay in Isotopically Pure Nickel-LikeXe129andXe132Ions

We present measurements of high statistical significance of the rate of the magnetic octupole (M3 ) decay in nickel-like ions of isotopically pure 129Xe and 132Xe. On 132Xe, an isotope with zero nuclear spin and therefore without hyperfine structure, the lifetime of the metastable level was established as (15.06+/-0.24) ms. On 129Xe, an additional fast (2.7+/-0.1 ms) decay component was established that represents hyperfine mixing with a level that decays by electric quadrupole (E2 ) radiation.

Magic-wave-inducedS01−P03transition in even isotopes of alkaline-earth-metal-like atoms

The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the $^{3}P_{1}$ state into the long-living metastable state $^{3}P_{0}$, thus enabling the strictly forbidden $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{0}$ ``clock'' transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional ``state-mixing'' wave, including estimations of the ``magic'' wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.

Hyperfine splittings of infrared lines of the cubic centre in CaF2:Ho3+

Hyperfine structure is observed on three transitions of the 5I8 → 5I7 absorption spectrum of the cubic-symmetry centre in CaF2:Ho3+. Hyperfine mixing between the two lowest levels of the 5I8 ground multiplet produces a complex and rich spectrum, which is only partially resolved. Simulated spectra are generated using one parameter to determine electronic crystal-field wavefunctions and one for the crystal-field splitting of the near-degenerate ground state. The simulated spectra correspond well with the measured spectra and demonstrate that the complex structure is well accounted for by dipole-hyperfine mixing between the lowest triplet and doublet states in the 5I8 ground multiplet.

Theoretical evaluation of the 7,9Be− 2s2p2 4P1/2,3/2,5/2hyperfine structure parameters and Be 2s2p 3Poelectron affinity

The hyperfine structures of 7,9Be− 2s2p2 4P1/2,3/2,5/2are investigated theoretically using the multiconfiguration Hartree–Fock and configurationinteraction methods. The effects of the hyperfine mixing between the fine-structureJ-levelsare discussed. The feasibility of some atomic spectroscopyexperiments, allowing determination of the 7Bequadrupole moment from the observed hyperfine structure of the 7Be− negativeion and from the present electronic parameters, is investigated. The Be 2s2p 3Poelectron affinity is monitored as a function of the orbital and configuration spacesto assess the reliability of the wavefunctions of the neutral atom and the negativeion. The theoretical value nicely converges towards the most recent theoreticaland experimental results.

High-resolution spectroscopy of a singleIn+ion: Progress towards an optical frequency standard

The ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{0}$ transition of a single laser-cooled ${}^{115}{\mathrm{In}}^{+}$ ion in a miniature radiofrequency trap is investigated as a possible optical frequency standard. This line at a frequency of 1267 THz (wavelength 236.5 nm) is highly immune to frequency shifts due to external perturbations so that the expected systematic uncertainties can be reduced to the millihertz level. Experimentally, we obtained a fractional resolution $\ensuremath{\Delta}\ensuremath{\nu}/\ensuremath{\nu}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ (linewidth 170 Hz), limited by the frequency instability of the laser used for excitation. The g factor and the lifetime of the metastable ${}^{3}{P}_{0}$ level were measured as ${g(}^{3}{P}_{0})=\ensuremath{-}9.87(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ and $\ensuremath{\tau}{(}^{3}{P}_{0})=0.195(8) \mathrm{s}.$ Both values are in good agreement with perturbative calculations, based on hyperfine mixing between the ${}^{1}P$ and ${}^{3}P$ levels.

A three-body force model for the electromagnetic excitation of the nucleon

We have performed a calculation of the helicity amplitudes for the electromagnetic excitation of nucleon resonances based on a three-body force model for baryon structure. All parameters have been previously fixed studying the baryon spectrum and therefore this is a parameter free calculation. We have taken into account the hyperfine mixing in all the baryon states and we present our results in comparison with those given by other approaches proposed in the literature. A brief discussion on open problems is also given.

A new hyperfine operator in the Dirac equation

A recently found additional hyperfine interaction in the Dirac equation extends the validity of this equation to comparable masses of its two spin- 1/2 particles. For equal masses as in positronium, it ensures CP conservation. The new operator simplifies the hyperfine mixing of states with different j. Anomalous magnetic moments are incorporated, and an application to helium-like Rydberg states is mentioned. CPT invariance is demonstrated and discussed, including the extension to n-electron atoms.

Reflection symmetries of linear-molecular rovibronic levels

Coriolis forces break the infinite-fold axis of symmetry of a linear molecule, but leave a residual plane of symmetry normal to the axis of rotation. This plane is subject to quantum uncertainties at low rotation, but becomes semiclassically well defined at high rotation. The spin-rovibronic wavefunctions can be classified according to their behavior under reflection of the spin-vibronic variables in this plane, whose orientation depends on the coupling case. In Hund's case (a) or (c) the plane is through the molecular axis normal to the perpendicular component of the angular momentum J, while in Hund's case (b) it is normal to the perpendicular component of N. The former gives a symmetry classification that is exact in the absence of hyperfine mixing, and is equivalent to the e f classification of J. M. Brown et al. [ J. Mol. Spectrosc. 55, 500–503 (1975)], while the latter gives the A′ A″ approximate symmetry classification proposed by M. H. Alexander et al. [ J. Chem. Phys. 89, 1749–1753 (1989)]. This latter classification is equivalent to a generalization to nonsinglet states of the c d classification of G. Herzberg [“Spectra of Diatomic Molecules”, 2nd ed., Van Nostrand, Princeton, NJ (1950)], in which c and d levels are defined to have parities +(−1) N and −(−1) N , respectively. Usually N is not a perfect quantum number, but this notation provides a useful characterization whenever N is well defined. The classification of case (d) rovibronic levels in terms of the symmetries of the levels of the core is considered briefly.

Relaxation and recombination in spin-polarized atomic hydrogen.

We have studied relaxation and recombination processes in compressed, doubly polarized atomic hydrogen at temperatures from 0.13 to 0.60 K and magnetic fields from 3 to 9 T. The gas and surface dipole three-body recombination rate constants at a field of 7.6 T are measured to be, respectively, ${L}_{g}$=8.9(8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ ${\mathrm{cm}}^{6}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${L}_{s}$=1.2(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ ${\mathrm{cm}}^{4}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. They decrease slowly with field and ${L}_{s}$ exhibits no significant angular dependence. The three-body recombination rate due to hyperfine mixing has also been measured. Electronic and nuclear relaxation rates have been measured; the b-c electronic relaxation rate constant in the gas is ${G}^{\mathrm{bc}}$=1.03(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$exp(-${E}_{\mathrm{bc}}$/${k}_{B}$T). The temperature and field dependence of the nuclear relaxation rate in the gas are observed to be in excellent agreement with recent theoretical calculations. Three-body surface recombination-rate measurements using $^{3}\mathrm{\ensuremath{-}}^{4}$He surfaces indicate that as little as one monolayer of $^{3}\mathrm{He}$ on the liquid $^{4}\mathrm{He}$ surface appreciably decreases the adsorption energy of atomic hydrogen. Densities achieved include 4.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.55 K (pure $^{4}\mathrm{He}$ walls), and 1.4\ifmmode\times\else\texttimes\fi{}${10}^{18}$ atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.19 K (8 at. ? sup 3---He).

Isotope effects in low-pressure Hg-rare-gas discharges.

Measurements of the Hg (253.7 nm) output (${P}_{\mathrm{uv}}$) and output per arc watt (${P}_{\mathrm{uv}}$/${P}_{W}$) as a function of $^{196}\mathrm{Hg}$ concentration in a low-pressure Hg-Ar electrical discharge are reported. A peak increase of 7.9% and 6.8% for ${P}_{\mathrm{uv}}$ and ${P}_{\mathrm{u}\mathrm{v}/\mathrm{PW}}$, respectively, has been found at 2.6 wt. % $^{196}\mathrm{Hg}$. A modified Holstein-Biberman formalism that takes into account emission and absorption line shapes, energy transfer between Hg isotopes, rare-gas hyperfine mixing, and overlap between different isotopic components has been developed. Based on this formalism the calculated hyperfine structure (hfs) of the Hg(6 $^{3}P_{1}$\ensuremath{\rightarrow}6 $^{1}S_{0}$) transition is in very good agreement with our measured hfs. Furthermore our calculations predict a saturation in ${P}_{\mathrm{uv}}$ and ${P}_{\mathrm{uv}/{P}_{W}}$ for relatively low $^{196}\mathrm{Hg}$ concentrations. This formalism is applicable to various problems involving resonance radiation transfer in metal-vapor--rare-gas combinations containing more than one isotope.

Precision measurement of the off-diagonal hyperfine interaction.

We have measured the hyperfine mixing of the $6S$ and $7S$ states of cesium using a new high-precision experimental technique. By comparing the diagonal and off-diagonal hyperfine interaction for these states, we find that a single-particle description of the states is accurate to better than 2%.

Quadrupole moment in the ground state of atomic hydrogen

The quadrupole moment of the atomic hydrogen ground state is calculated. It arises due to a hyperfine interaction. Its true value is 20 times larger than the result obtained only taking into account the hyperfine mixing with the lowest d level.

Effects of nuclear structure and triplet-singlet interaction in the 1s2s3S1 hyperfine multiplet of Li+

From combined laser-microwave spectroscopy of the 1s2s3S1 hyperfine structure (hfs) splittings in helium-like6,7Li+ ions, the magnetic dipole hfs interaction constantA and a small displacement σ of theF=1 substate, caused by 1s2s3S1−1s2s1S0 hyperfine mixing, have been obtained. Analysis ofA yields nuclear structure effects in the hfs splittings of the isotopes6,7Li+. The result of a calculation of6,7δ with accurate integral-transform 21S0 and 23S1 wave functions is presented.

Hanle effect detection of the [formula omitted] single-photon transition of cesium, without electric field

Although the oscillator strength of the 6S 1 2 −7S 1 2 transition is only 4.0×10 -15, by the Hanle effect in a zero electric field this transition gives rise to a very specific signal well above noise and background. From the hfs profile, we can test the magnetic dipole nature of the transition and obtain direct evidence for its perturbation by hyperfine mixing between the two S states. Our new values of M hf 1/ M 1 and M 1 and M 1/β agree with previous results, and the accuracy of M hf 1/ M 1 is improved.

Muonium formation and the “missing fraction” in vapors

The vapor phase fractional polarizations of positive muons thermalizing as the muonium atom (PM) and in diamagnetic environments (PD) has been measured in H2O, CH3OH, C6H14, C6H12, CCl4, CHCl3, CH2Cl2 and TMS, in order to compare with the corresponding fractions measured in the condensed phases. There is a marked contrast in every case, with the vapor phase results being largely understandable in terms of a charge exchange/hot atom model. Unlike the situation in the corresponding liquids, there is no permanent lost fraction in the vapor phase in the limit of even moderately high pressures (≈1 atm); at lower pressures, depolarization is due to hyperfine mixing and is believed to be well understood. For vapor phase CH3OH, C6H14, C6H12, and TMS therelative fractions are found to be pressure dependent, suggesting the importance of termolecular hot atom (or ion) reactions in the slowing down process. For vapor phase H2O and the chloromethanes, the relative fractions are pressure independent. For CCl4,PM=PD≈0.5 in the vapor phase vs.PD=1.0 in the liquid phase; fast thermal reactions of Mu likely contribute significantly to this difference in the liquid phase. For H2O,PM ≈ 0.9 andPD≈0.1 in the vapor phase vs.PD≈ 0.6 andPM≈0.2 in the liquid phase. Water appears to be the one unequivocal case where the basic charge exchange/hot atom model is inappropriate in the condensed phase, suggesting, therefore, that radiation induced “spur” effects play a major role.

Stark interference effects in a weak magnetic field on the 6S–7S forbidden transition of cesium

Hyperfine mixing in a weak magnetic field gives rise to new interference terms between the Stark-induced amplitudes of the 6S–7S forbidden transition of cesium. Compared with typical allowed transitions, effects of unusual size (circular dichroism of ∼10% in a 10 G field) and/or symmetry (3% upper state spin polarization induced by linearly polarized light in a direction normal to both the beam and the magnetic field) are observed. The circular dichroism yields a new method to determine the scalar to vector polarizability ratio; our result (α/β=-10.0±0.15) agrees with those of other techniques. The analysis of systematic effects in our recent measurement of parity violation required an understanding of these hyperfine mixing effects. One of them will be utilized to calibrate a new version of the parity experiment.

M1transitions in charmonium and the anomalous magnetic moment of the charm quark

Magnetic transitions in charmonium are calculated by use of the Bethe-Salpeter formalism in the pseudopotential approximation. The relativistic corrections suppress the nonrelativistic widths by about 25% for the allowed decays. Allowing for hyperfine mixing, good agreement with the recent experimental measurements is obtained for both allowed and hindered transitions with an anomalous magnetic moment $|\ensuremath{\mu}|\ensuremath{\approx}0.6$ of the $c$ quark.

K − nuclear interactions and yields of kaonic X-rays

We examine the K − nuclear interaction in kaonic atoms in the light of recent presumed evidence for an anomalous neutron distribution in the nuclear surface. A K − nuclear potential, proportional to the KN scattering lengths and nuclear density, reproduces observed X-ray yields within experimental uncertainty. With With a nuclear matter distribution proportional to the known proton distribution, no ad no additional freedom is needed at present. The variation of the capture width with radius and surface thickness parameters are discussed in detail. Estimates for energy shifts in the kaonic levels are given. Dynamical hyperfine and Stark mixing of kaonic orbits are discussed. Distortion effects of the K − wave function by the strong interaction are important and may well dominate all other effects. The renormalization of the KN scattering lengths by multiple scattering in nuclear matter is estimated. Approximations and limitations of the model are discussed.

2P→1STransitions in Muonic Tl, Pb, and Bi

The mixing of states of a muonic atom with the nucleus in an excited state into the states with the nucleus in the ground state, for natural Tl, Pb, and Bi (due to the multipole interactions between the nucleus and the muon), is calculated. This effect fails to explain the ratio of the number of $2{P}_{\frac{1}{2}}\ensuremath{\rightarrow}1{S}_{\frac{1}{2}}$ to $2{P}_{\frac{3}{2}}\ensuremath{\rightarrow}1{S}_{\frac{1}{2}}$ transitions (expected to be 0.5 in the absence of mixing) as observed by Frati and Rainwater. In Bi, the calculation shows that the mixing is negligible, but the observed ratio was 0.75\ifmmode\pm\else\textpm\fi{}0.05; in Tl (where the ratio was 0.97\ifmmode\pm\else\textpm\fi{}0.09) the off-diagonal matrix elements of the Hamiltonian, required for this effect to be the sole cause of the change of ratio, differs from theory by two standard deviations. For Pb the observed ratio agrees with theory and the calculated mixing is, indeed, negligible. If we assume that some unknown effect is acting in Bi and is of the same order of magnitude in Tl, then the difference between the ratio in Tl from that in Bi is explained by the above mixing. This assumption is suggested by the fact that Tl is one proton below and Bi is one proton above a magic number closed shell (82). We suppose that this unknown effect is absent in Pb since it is a magic number nucleus (82 protons). It is proven that nonresonant effects, due to spin-independent operators, cannot affect the radiative-transition sum rules. This is applied to nonresonant hyperfine mixing and a hypothetical nuclear-Auger effect.