Singlet-triplet Mixing Research Articles

High-resolution uv laser spectroscopy of the 1s2s 3S1-->1snp (n=5-79) transitions in 3He and 4He.

The /sup 4/He fine structure and /sup 3/He hyperfine structure as well as the isotope shift between /sup 4/He and /sup 3/He in the 1s2s /sup 3/S/sub 1/..-->..1snp (n = 5--79) transitions have been measured using an atomic beam and an intracavity frequency-doubled coumarin ring dye laser near 270 nm. The observed 1snp /sup 3/P /sup 4/He fine structure is in agreement with (extrapolations of) existing experimental results and theoretical calculations. The 1snp /sup 3/He hyperfine structure has been analyzed using the /sup 4/He fine-structure parametrization and the Fermi-contact interaction of the screened 1s electron. For n>35 hyperfine components of the 1snp /sup 1/P levels are also excited as a consequence of hyperfine-induced singlet-triplet mixing. Calculated hyperfine splittings agree with experiment for n 20. These are shown to be due to hyperfine-induced n-mixing effects. The experimental results are excellently reproduced in a three-channel two-limit quantum-defect model without any adjustable parameter. The observed 1s2s /sup 3/S/sub 1/..-->..1snp /sup 3/P isotope shifts can be fully explained using recent mass polarization calculations for the 1s2s /sup 3/S/sub 1/ and 1snp (n = 3--8) /sup 3/P levels and confirm an isotope dependence of for the 1s2smore » /sup 3/S/sub 1/ level.« less

Double-resonance studies of rotational autoionization of H2

Two-color resonantly enhanced multiphoton ionization combined with photoelectron spectroscopy detection was used to study rotational autoionization of np Rydberg states of H2 near the first ionization threshold. In this two-step experiment, one laser was used to excite a two-photon transition to the E,F 1Σ+g, v′=E0, J′=0–4 levels, and a second laser was used to probe single photon transitions to the rotationally autoionized np Rydberg series coverging to the X 2Σ+g, v+=0, N̄+=1–6 rotational levels of the ion. Assignments were made for a large number of Rydberg states converging to v+=0 and for several interlopers converging to v+=1 and 2. Of the five dipole allowed Rydberg series converging to v+=0 excited from each intermediate J′ level (J′>2), two are allowed to rotationally autoionize in a coupling scheme that assumes ejection of pure p waves in the ionization process and singlet coupling of the spins of the ion core and the outgoing electron. Members of these Rydberg series have large half-widths, and the v dependence of the half-widths is in good agreement with simple quantum defect theory predictions. Ionization via the change of four quanta of rotational energy was found to be significantly slower than ionization via the change of two quanta of rotational energy. Ionization was also observed for the series that are forbidden to rotationally autoionize according to this simple coupling scheme, and it is shown that both the inclusion of f waves in the autoionization process and singlet–triplet mixing may be required to explain these observations.

High-resolution Rydberg-state spectroscopy of stable alkaline-earth elements

High-resolution Rydberg-state spectroscopy was applied to investigate high-lying Rydberg states of the alkaline-earth elements Mg, Ca, Sr, and Ba up to principal quantum numbers n > 200. In this energy range interactions dominate that are negligible at low n. It is shown that the hyperfine interaction can be used as a sensitive probe for configuration interactions, singlet–triplet mixing, and hyperfine-induced n mixing.

Multiphoton spectroscopy of doubly excited, bound, and autoionizing states of strontium.

We present a theory attempting an interpretation of existing data on three- and four-photon ionization of Sr in the wavelength range 557--575 nm and at 532 nm. Two-photon resonances with bound excited states and three-photon resonances with doubly excited autoionizing states are studied. ac Stark shifts and broadening of resonances, as well as singlet-triplet transitions, are shown to yield interesting new information on atomic structure. The absorption of a fourth photon above the threshold leads to excited final ionic states, with autoionizing states having served as intermediate three-photon resonances. The calculation is based on a configuration-interaction scheme, with singlet-triplet mixing taken into account either through jl coupling or phenomenologically by adjustment to some aspects of the data. The apparatus of resonant multiphoton theory is combined with the above scheme. Depending on the quantity in question, the agreement between theory and experiment ranges from good to semiquantitative.

Hyperfine structure and multichannel quantum defect theory analysis of the 6sng rydberg series of barium

High resolution laser-atomic-beam spectroscopy has been applied to study the hyperfine structure of the barium 6sng Rydberg series forn=6−40. The singlet-triplet mixing of the two 6sng J=4 series is deduced through a diagonalisation of the total Hamiltonian. Multichannel Quantum Defect Theory (MQDT) has been used to reproduce both experimental level energies of the 6sng J=3,4 and 5 series and the extracted singlet-triplet mixing. The close-coupling channels of the 6sng Rydberg series turn out to be nearly purejj-coupled channels in contradistinction to lowerl Rydberg series. Furthermore MQDT is used to analyse the observed isotope shifts and peak intensities of the 6sng Rydberg series.

High resolution laser spectroscopy of Ba Rydberg atoms

The purpose of the present paper is to illustrate some selected aspects of high resolution laser spectroscopy of Rydberg atoms, rather than giving an extensive review of the state of the art. The following topics will be discussed: (i) Excitation and detection of Ba Rydberg atoms with principal quantum numbers up ton≲300; (ii) Stark effect and atomic diamagnetism of high-n Ba Rydberg states in thel-mixing region, (iii) Resonance in singlet-triplet mixing of 6snp1P1 and 6snd1D2 Ba Rydberg states deduced from hyperfine structure measurements.

Effects of Nuclear Spin Polarization on Reaction Dynamics in Photosynthetic Bacterial Reaction Centers

Singlet-triplet mixing in the initial radical-pair state, P[unk]I[unk], of photosynthetic bacterial reaction centers is due to the hyperfine mechanism at low magnetic fields and both the hyperfine and Deltag mechanisms at high magnetic fields (>1 kG). Since the hyperfine field felt by the electron spins in P[unk]I[unk] is dependent upon the nuclear spin state in each radical, the relative probabilities of charge recombination to the triplet state of the primary electron donor, (3)PI, or the ground state, PI, will depend on the nuclear spin configuration. As a result these recombination products will have non-equilibrium distributions of nuclear spin states (nuclear spin polarization). This polarization will persist until the (3)PI state decays. In addition, due to unequal nuclear spin relaxation rates in the diamagnetic PI and paramagnetic (3)PI states, net polarization of the nuclear spins can result, especially in experiments that involve recycling of the system through the radical-pair state. This net polarization can persist for very long times, especially at low temperatures. Nuclear spin polarization can have consequences on any subsequent process that involves re-formation of the radical-pair state.Numerical calculations of the nuclear polarization caused by both of these mechanics are presented, including the effect of such polarization on subsequent yields of (3)PI, (3)PI decay rates, the decay rate of the radical pair, and saturation behavior. The effect of this polarization under certain circumstances can be very dramatic and can explain previously noted discrepancies between experiments and theories that do not include nuclear spin polarization effects. Our analysis suggests new classes of experiments and indicates the need to reinterpret some past experimental results.

Proton-impact excitation of HeI triplet levels

We investigated the excitation of the λ(1s3d3D−1s2p3P)=588 nm line of atomic helium by proton and deuteron impact for projectile energies 10 keV≦Ep≦25 keV. In apparent contradiction to Wigner's spin conservation rule, the emission cross section does not vanish. By measuring the intensity of the impact radiation as a function of homogeneous magnetic and electric fields applied to the collision volume, it has been shown thatp- andd-impact excitation of the 1s3d3D level of HeI proceeds via 1snl states withl≧3, which populate the 33D states by cascade decays. The well-known strong singlet-triplet mixing of these 1snl states enables a population of triplet states in accord with Wigner's rule. Accordingly, we determine the excitation cross section of the 1s4f multiplet from the measured emission cross section of the 588 nm line. The field-dependent signals give evidence that predominantly substates with |mL|≦1 are excited.

A time-domain EPR study of the SO−3 combination reaction: Radical pair CIDEP without singlet–triplet mixing

The radical ion ⋅SO−3 was studied by in situ pulsed radiolysis of aqueous alkaline sodium sulfite solutions in a pulsed EPR spectrometer. Initial radical concentrations on the order of 5×10−4 M were generated, and detailed measurements of the decay of ⋅SO−3 magnetization were performed on the microsecond time scale. It was found that the second order decay of both longitudinal and transverse magnetization lags behind the second order decay of radical population when the reaction rate approaches the relaxation rates 1/T1,2. The observations may be explained in terms of the spin-pairing requirements for formation of a singlet reaction product. The spin pairing gives rise to a ‘‘passive’’ form of radical pair mechanism (RPM) chemically induced dynamic electron polarization (CIDEP) which has previously gone unrecognized. RPM polarization therefore occurs in ⋅SO−3 encounters despite the lack of hyperfine dependent singlet–triplet mixing between radical reencounters, which is necessary for the accepted RPM mechanism. The implications of these observations for the interpretation of time-resolved EPR experiments are discussed.

Visible absorption and magnetic-rotation spectroscopy of 1CH2: The analysis of the b̃ 1B1 state

The b̃1B1←ã 1A1 spectrum of CH2 radical has been recorded with Doppler-limited resolution in the 15 600–18 650 cm−1 wavelength region by laser flash-kinetic absorption spectroscopy. Singlet methylene is produced by photolysis of ketene at 308 nm. Assignments for 477 transitions originating from 1A1(0,0,0) and (0,1,0) levels with J≤8 and Ka≤5 are reported from some 10 000 lines observed. Term values are given for these 1A1 levels and 1B1(0,v2,0) levels with 13≤v2≤17. Magnetic-rotation signals were observed for 60% of the 424 lines studied. This anomalous Zeeman effect is explained by singlet–triplet mixing in both ã and b̃ states. Extensive singlet–triplet mixing occurs for 1B1 levels with Ka≠0; this mixing is allowed in second order by Renner–Teller coupling of b̃ 1B1 with ã 1A1 and by spin-orbit coupling via ã 1A1 to X̃ 3B1. The consequent shifts prevent determination of accurate rovibrational structural parameters for the 1B1 state.

Theory of the upper critical field of a magnetic superconductor.

We have derived a general set of microscopic equations for the upper critical field of a magnetic superconductor which is valid for any concentration of normal impurity scattering and includes fully the dynamics of the phonons and of the spin fluctuations. As spin correlations can be long range, we avoid, in our derivation, the usual contact approximation and get an expression which behaves properly near the magnetic transition. Numerical estimates for various possible values of the magnetic parameters reveal that, for some regimes, the dynamics of the spin diffusions can be important. In addition it is found, from general symmetry considerations, that singlet-triplet amplitude mixing can occur in dirty superconductors with large band-splitting effects due to internal magnetization.

Shifts of the 4snd 1,3DJ Levels of the Naturally Abundant, Even Ca Isotopes

The level isotope shifts of the 4snd 1,3DJ have been measured in the singlet-triplet mixing region around n = 15 applying the resonant Doppler-free 2-photon laser spectroscopy and the thermionic diode as a detector. From the isotope shift as well as from the intensities of the lines the singlet-triplet mixing was found to be larger than previously determined from fine structure measurements and the study of the hyperfine structure in the odd isotope 43Ca.

ESR study of the complexes [ClO, O2] and [BrO, O2] formed by decomposition of ClO−3 and BrO−3 in solid KClO4

The ESR spectra of defects arising from photolysis at 214 or 229 nm of ClO−3 and BrO−3 embedded in KClO4 crystals and subsequent radiolysis at 26 K are interpreted in terms of the complexes [XO, O2], X=Cl, Br, formed in the reactions XO−3 →hν [XO−,O2], [XO−,O2] +(ClO4)−2 →[XO,O2] +2ClO−4, where (ClO4)−2 represents the mobile holes produced during radiolysis of the host crystal. The main features of the spin Hamiltonian of [XO,O2] correspond to XO(2Π) in a crystal field, coupled through an isotropic exchange interaction to O2(3Σ−g ) to form a spin-doublet ground state, but the observed halogen and 17O hyperfine splittings are considerably smaller than expected for [XO,O2]. Moreover, the splitting of the 2Π states of XO inferred from the g tensor is an order of magnitude larger than that observed earlier in a similar system. Both findings indicate an interaction, which splits the degenerate pairs of antibonding π orbitals on XO and O2 by ∼104 cm−1. In O2 this may lead to near degeneracy of the lowest singlet state with 3Σ−g , thus allowing a significant singlet–triplet mixing which reduces the net spin density in the complex. The spin Hamiltonian indicates that the axes of XO and O2 are perpendicular. The strong interaction between XO and O2 furthermore suggests a planar T configuration of the complex.

Hyperfine-dependent lifetimes induced by singlet-triplet mixing.

Hyperfine-dependent lifetimes induced by singlet-triplet mixing.

Hyperfine structure and isotope shifts in odd-parity 6snp and 6snf Rydberg series of Ba I

Hyperfine structure and isotope shifts in transitions to odd-parity 6snp and 6snf Rydberg configurations of barium have been investigated using laser-atomic-beam spectroscopy. For the 6snf Rydberg configurations with n=13-42 the complete hyperfine multiplet is observed. The data on isotope shifts have been used to test the total perturber character mixed in the 6snp and 6snf Rydberg states predicted by existing multichannel quantum defect theory (MQDT) treatments of the odd-parity J=0, 1, 2, 3 and 4 spectra. The MQDT predictions are shown to be reliable in this respect. The hyperfine structure of the singlet and triplet states is analysed in terms of singlet-triplet mixing. The extracted mixing coefficients disagree with the predictions of existing MQDT models, even when an interaction between 'singlet' and 'triplet' 6snl channels is introduced. New MQDT models have been developed in which both energies and mixing coefficients are reproduced well. Hyperfine structure data provides information on interactions between mutually perturbing channels. Finally an earlier analysis of the hyperfine structure of the 6snf 3F states in terms of effective parameters is discussed.

Proton- 3He elastic scattering: A phase-shift analysis by a separable potential model

All the available experimental data (cross sections, projectile and target polarizations, polarization transfer coefficients) on p- 3He elastic scattering up to ~10 MeV are analyzed on a unified basis in the framework of a separable potential model. This allows a phase-shift analysis which is model dependent, but is averaged over a wide energy interval (757 experimental points are reproduced by 27 model parameters). The calculations confirm some indications, already present in the literature, of a weak S-D tensor mixing, and strong singlet-triplet mixing in the P-states. Our conclusions are that probably the leading non-central effect is given by the coupling s 1 · l between the incident proton spin s 1 and the orbital angular momentum of relative motion. Finally, the phase shifts and observables are recalculated using the p- 3He potential parameters, but switching off the Coulomb interaction. The results are compared with the (few) n- 3H experimental cross sections of the literature, and the agreement is good, as expected on the basis of the charge-symmetry law.

Excitation cross sections of Li +(1s nl) 3L, 1L states in collisions of Li + with He

We report for the first time specific (1s nl) 1L and 3L projectile excitation cross sections of 280 keV ( v=1.26 a.u.) Li ++He collisions. Strong production of triplet states is observed in the (1s nl) distribution of the Li II Rydberg states. We suggest that final state singlet-triplet mixing of the Rydberg manifold in conjunction with cascade repopulation may considerably modify the population of high spin states.

Proximity and Josephson effects for heavy-fermion superconductors

At an interface or junction, strong spin-orbit coupling combined with pairing inhomogeneity and small pair size on the heavy-electron side mean that proximity or Josephson effects occur for singlet to triplet as well as for singlet to singlet pairing states. Large electron mass contrast at a metal-metal interface means that transmission of electron probability current is at most of order one percent. Singlet-triplet mixing of pair states by inhomogeneous magnetism is much smaller than mixing due to strong spin-orbit coupling combined with small pair size.

The radiative lifetime of the1D2state of Ca and Sr: a core-valence treatment

Theoretical studies of the lowest 1S, 1,3P and 1,3D states of calcium and strontium are presented. The excitation energies, dipole-allowed transition moments and the 1D-1S quadrupole moment are studied as a function of the one-particle and molecular orbital bases and level of correlation treatment. Including core-valence correlation significantly reduces the magnitude of the dipole and quadrupole transition moments, producing oscillator strengths that lie within the experimental error bars. On the basis of relativistic effective-core potential calculations, the authors find that, unlike barium, the strontium transition moments are not significantly changed when relativistic effects are included. Spin-forbidden transitions were assumed to occur entirely as a result of the breakdown of LS coupling. The magnitude of the singlet-triplet mixing was determined both by ab initio calculation and from the observed deviations from the Lande interval rule. The calculated 1D2 state lifetime for Ca is 3.1+or-0.3 ms, which is in reasonable agreement with the experimental value of 2.3+or-0.5 ms (with an absolute upper bound of 4 ms). The dominant decay mechanism is spin-forbidden dipole-allowed transitions, with only 12% arising from quadrupole transitions. Similarly for the 1D2 state of Sr, the authors compute a radiative lifetime of 0.49+or-0.04 ms with only 2% of the decay from quadrupole transitions.

Proton-He elastic scattering: A phase-shift analysis by a separable potential model

All the available experimental data (cross sections, projectile and target polarizations, polarization transfer coefficients) on p- 3 He elastic scattering up to ~10 MeV are analyzed on a unified basis in the framework of a separable potential model. This allows a phase-shift analysis which is model dependent, but is averaged over a wide energy interval (757 experimental points are reproduced by 27 model parameters). The calculations confirm some indications, already present in the literature, of a weak S-D tensor mixing, and strong singlet-triplet mixing in the P-states. Our conclusions are that probably the leading non-central effect is given by the coupling s 1 · l between the incident proton spin s 1 and the orbital angular momentum of relative motion. Finally, the phase shifts and observables are recalculated using the p- 3 He potential parameters, but switching off the Coulomb interaction. The results are compared with the (few) n- 3 H experimental cross sections of the literature, and the agreement is good, as expected on the basis of the charge-symmetry law.