Mechanism of “GSI oscillations” in electron capture by highly charged hydrogen-like atomic ions

We suggest a qualitative explanation of oscillations in electron capture decays of hydrogen-like ¹⁴⁰Pr and ¹⁴²Pm ions observed recently in an ion experimental storage ring (ESR) of Gesellschaft für Schwerionenforschung (GSI) mbH, Darmstadt, Germany. This explanation is based on the electron multiphoton Rabi oscillations between two Zeeman states of the hyperfine ground level with the total angular momentum F = 1/2. The Zeeman splitting is produced by a constant magnetic field in the ESR. Transitions between these states are produced by the second, sufficiently strong alternating magnetic field that approximates realistic fields in the GSI ESR. The Zeeman splitting amounts to only about 10^?5 eV. This allows explaining the observed quantum beats with the period 7 s.     

Exchange interaction of S state ions with charge carriers in SnTe

ESR investigations of Mn, Eu and Gd in highly degenerate SnTe - a p-type semiconductor with metallic behaviour - prove the existence of an exchange interaction between localized magnetic moments and charge carriers. The ratio of the exchange parameters J_Mn and J_Eu between charge carriers and Mn or Eu ions, respectively, amounts to |J_Mn/J_Eu| = 8 ± 1.5. The consequence this result has on long range spin-spin interaction via charge carriers as well as on hyperfine interaction is discussed.     

Interpretation of multifrequency transient EPR spectra of the P 700 + A0Q K − state in photosystem I complexes with a sequential correlated radical pair model: Wild type versus A0 mutants

Transient electron paramagnetic resonance (TR-EPR) spectra of the electron-hole pair state P ₇₀₀ ⁺ A₀Q _K ^? in photosystem I are numerically calculated. Parameter variation concerns mainly the exchange integralJ of the precursor spin pair state P ₇₀₀ ⁺ A ₀ ^? Q_K and its lifetime τ. A prominent emissive feature in the high-field region (P ₇₀₀ ⁺ part) of the EPR spectrum turns out to be diminished with increasing lifetime τ of the precursor pair state in the case of positive exchange couplingJ>0 (ferromagnetic type). Correspondingly, the emissive feature becomes more pronounced with increasing lifetime τ in the case of negative exchange couplingJ<0 (antiferromagnetic type). These results can be used to interpret the changes in the pattern observed in TR-EPR spectra comparing wild-type and specific A₀ mutants. The central ligating amino acid residue to the A₀ chlorophyll cofactor is mutated from native methionine (M) to leucine (L) in either the PsaA or the PsaB branch. Changes are observed only for the A-side mutant: M688L(PsaA). They are consistent with the following parameters in the precursor pair P ₇₀₀ ⁺ A ₀ ^? :J≈0.5÷1.0 mT and τ=1.5÷2 ns (as compared to τ～0.05 ns in the wild type).     

Evidence for Quantum Beats generated by a photo-induced charge transfer reaction

Photo-initiated charge transfer reactions in solution proceed via a radical pair intermediate which in most cases will separate on a time scale of several nanoseconds. The non-adiabicity of this process is the source of coherences in the spin system. A quantitative discussion of the observability of the resulting quantum beats using Fourier-transform EPR is presented. We also show experimental evidence for the predicted quantum beats using the photo-initiated charge transfer reaction of Zn-Tetraphenylporphyrin and benzoquinone in 2-propanol. The analysis of the beat frequency leads to an estimate of the exchamge couplingJ≈2.6·10⁶ s^?1 of the Coulomb-coupled radical pair.     

EPR measurements of weak exchange interactions coupling unpaired spins in model compounds

I review electron paramagnetic resonance (EPR) measurements performed to evaluate very weak exchange interactions (defined as ?_ex(i, j) = ?J _ij S _i S _j , with 10^?3 cm^?1<|J _ij|<1 cm^?1) between unpaired spins, transmitted through long and weak chemical pathways typical of protein structures. They are performed in appropriate model compounds, mainly copper derivatives of amino acids and peptides, making use of the phenomenon of exchange narrowing and collapse of the resonances. I describe the theoretical basis and the implementations of the method to different situations, including selected experimental values of the exchange couplingsJ between metal centers, and briefly discuss correlations betweenJ and the structure of the paths. Results obtained in relatively simple EPR experiments performed at room temperature in single-crystal samples are compared with those obtained from thermodynamic magnetic measurements having higher experimental difficulties. The experimental information allows describing the role of molecular segments typical of biomolecules (H bonds, aromatic ring stacking, cation-π contacts, etc.) in the transmission of the exchange interaction. The values ofJ obtained in some model compounds are compared with those obtained in proteins to conclude that the magnitudes of the exchange interactions are useful to characterize long and weak biologically relevant chemical pathways. One observes that these exchange couplings are weakly dependent on the nature of the unpaired spins and strongly dependent on the chemical pathway. Thus, measurements of exchange couplings in model compounds may provide useful information about biological function, particularly about electron transfer in proteins.     

Radical cations of n-alkanes in irradiated solutions as studied by time-resolved magnetic field effects

The time-resolved magnetic field effect in the recombination fluorescence of spin-correlated radical ion pairs has been measured to study n-alkane radical cations in irradiated solutions at room temperature. The magnetic field effect was recorded as a ratio of fluorescence decay curves in the 0.1 T and zero magnetic fields for solutions of C₈, C₉, C₁₀, C₁₂, and C₁₆ n-alkanes in n-hexane with addition of 3 × 10^?5 M p-terphenyl-d ₁₄. A distinct maximum at 10–30 ns followed by a slowly decaying plateau was observed for all the solutions. Simulation shows that the maximum corresponds to an unresolved ESR spectrum with the peak-to-peak line-width ranging from about 1.6mT to 0.5mT for C₈ to C₁₆ radical cations. The unresolved structure is believed to result from the hyperfine couplings with many protons of the radical cation, the increase in the number of interacting protons compared with low temperature matrices being caused by the methyl group rotation and conformational motion of the carbon chain. With increase in concentration of dissolved n-alkane, the maximum in the curves first moves to longer times and finally disappears; this was attributed to the narrowing of ESR spectrum contour due to degenerate electron exchange.     

Exchange and hyperfine fields acting on dilute Eu In SmCo5, Sm2(Co1-xFex)17 and Sm2CoxMy( rm M = Fe, Cu, Zn, Zr)

Mössbauer source experiments of dilute ¹⁵³Eu and ⁵⁷Fe in SmCo₅ and ¹⁵³Eu in Sm₂(Co_1-xFe_x)₁₇ and Sm₂ Co_x M_y at 4.1 K were performed. After the ${}^{153}\text{Sm}\text{→β?}{}^{153}$ decay the Eu ion is trivalent and exhibits extremely large hyperfine interactions due to strong exchange fields. Since the exchange interactions are comparable to the Eu³⁺ spin-orbit coupling, we calculated the expectation values of the Eu³⁺ spin, magnetic hyperfine field and electric field gradient as a function of exchange field and second order crystalline field, by diagonalization of the full Hamiltonian of spin orbit, exchange and crystalline field. For SmCo₅ and Sm₂(Co_1-xFe_x)₁₇ the exchange and crystalline fields are known and thus allow us to analyze our experimental results and obtain the polarized conduction electron contributions to the magnetic hyperfine field. The contribution due to magnetic neighbour polarization of conduction electrons is found to be linear in exchange field. The experimental results together with the theoretical analysis yield the Eu electric field gradient 4f Sternheimer shielding factor R_Q to be 0.26±04. It is shown that Mössbauer studies of two probes (¹⁵⁵Gd and Eu³⁺) in magnetic systems yield directly the second order crystalline field, the exchange field and the various contributions to the hyperfine field acting on the Eu nucleus. From the experimentally measured magnetic hyperfine fields alone, approximate values for the exchange fields in the mixed systems Sm₂Co_xM_y were determined.     

Resonanzstreuung von Licht in magnetischen und elektrischen Feldern zur Untersuchung der Hyperfeinstruktur des 7d 2 D 3/2-Terms im Thallium I-Spektrum

Observing the resonance fluorescence of the transition 7d ² D _3/2-6p ² P _1/2 (λ=2379 Å) in the Tl I-spectrum the level crossing technique with combined electric and magnetic fields was used to investigate the hyperfine structure and the Stark effect of the 7d ² D _3/2-state. For electric field strengthsE?25 kV/cm the Stark shifts are considerably greater than the hyperfine splitting. Therefore the crossing signals for the case of decoupled hyperfine structure could be detected. The following values of the magnetic hyperfine constantA and the Stark parameterβ were deduced: ¦A¦=55(1) Mc/sec·g _J /0.8, ¦β¦=0.20(4) Mc/sec/(kV/cm)²·g _J /0.8 andA/β>0. The widths of the signals yielded the mean lifetimeτ=2.7(5)·10^?8 sec· 0.8/g _J . Sign and values ofA andβ are discussed.     

ESR line shift in NiSnCl6·6H2O at very low temperatures

Electron spin resonance in a single-ground-state magnet, NiSnCl₆·6H₂O, has been studied at temperatures between 83 mK and 4.2 K. Below 1 K, the resonance lines show marked shifts, which can be described quantitatively in terms of exchange shift due to polarization effects treated by McMillan and Opechowski. The shifts give 2J = ?(0.55 ± 0.15) × 10^?2 cm^?1 for the antiferromagnetic exchange interaction among the Ni²⁺ ions in this crystal. The value of 2J is sub-critical in the sense that no spontaneous long-range order can be expected in this singlet-ground-state magnet.     

Spin dynamics in strongly coupled spin-correlated radical pairs: Stochastic modulation of the exchange interaction and ST−1 mixing in different magnetic fields

We investigate the effect of stochastic modulation of the exchange interaction J_ex on singlet (S)-triplet (T) transitions in radical pairs. These transitions limit the lifetime of the photo-generated radical pairs in covalently linked porphyrin-quinone systems that have been developed for biomimetic modeling of photosynthetic electron transfer processes. In order to explain transient electron paramagnetic resonance (EPR) results in different magnetic fields, i.e., with X-band ((0.34 T)/ (9.5 GHz)) and W-band ((3.4 T)/(95 GHz)) time-resolved EPR, we have to assume that J_ex is modulated over a range of 20000 G, which is wide enough that S is temporarily almost degenerate with T₀ as well as with T_?1. This large modulation of J_ex is caused by restricted rotational diffusion of the quinone subunit with respect to the porphyrin subunit. However, because of the small interradical distance of about 1.0–1.4 nm, the radical pair is continuously kept in the strong coupling limit and, therefore, we observe only EPR transition between the triplet sublevels. We find an approximation to solve the stochastic Liouville equation valid for rotational diffusion on an intermediate time scale, i.e., the diffusion rate D_R is smaller than the singlet electron recombination rate K_S ～ 10⁹ s^?1, but larger than the ST transition rates κ₀, κ_?1 < 10⁶ s^?1.     

Bilinear and biquadratic exchange interactions and their effect on magnetic susceptibilities of KMgF3: Mn and KZnF3: Mn

Exchange interaction constants of nearest (J₁) and next-nearest-neighbor (J₂) Mn²⁺ in KMgF₃: Mn and KZnF₃: Mn have been evaluated from the magnetic susceptibilities. For KZnF₃: Mn, J₁ = 8.2 ± 0.5 K; this is consistent with the ESR value if biquadratic exchange is present.     

Mössbauer studies of dilute Au:Er alloys: Obervation of hyperfine structure of ground and excited CEF levels

The hyperfine structure of dilute ¹⁶⁶Er impurities in Au has been investigated between 1.8 and 60 K by Mössbauer spectroscopy. The hyperfine spectrum of the Γ₇ electronic ground state is clearly observed below 4.2 K while at higher temperatures there is an indication of the contribution from the excited CEF-states Γ⁽¹⁾₈ and Γ₆. Using Hirst's relaxation theory for the Γ₇ ground state the magnetic hyperfine coupling constant A=(247±3) MHz and the exchange coupling constant J_sf=(0.10±0.02)eV were derived. A quadruple coupling constant B of about 1 MHz was estimated from the hyperfine pattern of the Γ⁽¹⁾₈ quartet.     

Evaluation of exchange interaction in binuclear copper(II) chelates of amide-based cyclophanes

Temperature dependence of the electron paramagnetic resonance (EPR) spectra of binuclear Cu(II) complexes with amide-based cyclophanes, Cu₂(bis-EDTAPDN), Cu₂(bis-EDTANAP) and Cu₂(bis-EDTABPE), in 60% methanol (pH ca. 10) has been studied at a frequency of 9.43 GHz in the temperature range of 77–4.2 K; the cyclophanes are macrocyclic compounds in which four amide bonds link two ethylenediaminetetraacetate (EDTA) units and two units of the aromatic diamine 1,4-phenylenediamine (DPN), 1,5-diaminonaphthalene (NAP) or bis(4-aminophenyl) ether (BPE). Exchange integrals found from the EPR measurements are ca. 70–105 cm^?1, 22 cm^?1 andJ ≤ 0, for Cu₂(bis-EDTAPDN), Cu₂(bis-EDTANAP) and Cu₂(bis-EDTABPE), respectively; the sign ofJ is defined to be positive for antiferromagnetic interaction. The variation of exchange interactions in these compounds is related to the nature of the bridging organic groups.     

NMR and magnetic susceptibility of CeCu6

NMR and magnetic susceptibility of CeCu₆ intermetallic compound were investigated. The most important contributions to the magnetic susceptibility are the Curie-Weiss term, expressing the paramagnetism of the localized f-electrons, and a temperature independent term for which all the contributions were estimated. The phenomenological exchange constantJ _sf between 4f — electron spins and conduction — electron spins is derived to be ?0·012 eV. The Knight shift and Curie temperature are discussed in terms of the Ruderman-Kittel-Kasuya-Yosida theory and in the Rocher's virtual bound states model. The s — f exchange integralΓ and the Fermi wavevectork _F are derived to be — 0·8 eV and 1·32 Å^?1, respectively.     

Far-infrared absorption of MgO: Fe2+ in magnetic fields

We have measured the far-infrared absorption of iron-doped MgO in the wavenumber region 10–200 cm^?1 and in magnetic fields up to 6 T. Absorption peaks found at 107.0 and 110.5 cm^?1 are assigned to magnetic dipole transitions between the spin-orbit Г_5g groundstate (J = 1) and the Г_3g, Г_4g excited states (J = 2) of the Fe²⁺ -ion at a cubic site. The observed magnetic field dependence shows that Г_4g is the higher excited level, so that the crystal field order of the levels is not changed by the reduction of the spin-orbit splitting attributed to a dynamic Jahn-Teller effect. An additional absorption peak at 33.4 cm^?1 is found to split in magnetic field.In iron-doped KMgF₃ absorption peaks at 52 and 87 cm^?1 that have previously been attributed to the same transitions of Fe²⁺ are found to remain unshifted and unsplit in magnetic fields up to 6 T.     

Dynamic phenomena in layer superconducting cuprate and organic metals

Dynamic electron spin resonance (ESR) and extended x-ray absorption edge fine structure (XAFS) measurements suggest that layered organic metals and cuprate superconductors behave similarly. The response to microwave radiation in a modulated external magnetic field indicates that: (i) triplet state, T * ESR is observed below T_c for both; (ii) the condensation of free spin doublet D to T* occurs above the transition temperature to superconductivity T_c (10 ± 1 K for the organic metal (BEDT-TTF)₃Ta₂F₁₁ and 92 to 12 K for YBa₂Cu₃O_7-δ and its rare earth derivatives); (iii) antiferomagnetic (AF) resonance is detected above T_c for the organic metal. Here the exchange field between the aligned AF domains: J_AF(150 K) = 130.7 mT (153 mK) is greater than the exchange term J(150 K) ≈ 15 mT (20 mK) between free spins (S = 1/2) leading to T* states; the lifetime of AF domains τ_AF decreases below 150 K and resonance is not detected below 44 K (i.e. τ_AF < 10^-10 s) allowing a superconducting transition to appear below 10 K; (iv) the relaxation time τ₁ for the half field, triplet state ESR absorption increases fourfold near 10 K for the organic metal and, (v) the onset of superconductivity is detected in all superconductors by the appearance of an energy loss at exactly H=0 and, magnetization oscillations observed versus H below T_c when the samples are cooled in a non-zero field H. The spin-lattice relaxation time for the organic metal triplet state, half field ESR near 10 K is interpreted using the Gorter phenomenological relation τ₁ = C_H /α_H, C_H and α_H are respectively the heat capacity and the thermal contact coefficient to the lattice by the spin system, at constant field H . Complementary changes in x-ray edge widths near T_c are correlated to electron-phonon interactions.     

Magnetic and ESR studies of Er3+ in lanthanum dihydride LaH2

Er³⁺ electron spin resonance ESR and magnetic susceptibility have been studied in metallic lanthanum dihydride host. The ESR spectrum contains a single asymmetrical line with g-factor g = 6.68 ± 0.05 close to that expected for Γ₇ as ground state. The experimental magnetic susceptibility was interpreted on the base of LLW cubic crystal field Hamiltonian. The best fit of the experimental data has been obtained for the following B₄ and B₆ crystal field parameters: B₄ = ?5.2 × 10^?3 K; B₆ = 3.8 × 10^?5 K which support the anionic-like character hydridic model of hydrogen atoms in this hydride.     

A theorem on electromagnetic properties of leptons

The following theorem is proven: Every lepton with the mass m, electric charge q and spin J belonging to any representation of a non-abelian gauge group must have the magnetic moment μ = qJm^?1, electric mean squared radius r² = qJ(J + 1)m^?2 and electric quadrupole moment Q = qJ(2J ? 1)m^?2 in the first order of the electromagnetic effects in an arbitrary renormalizable theory with the non-abelian gauge group symmetry which permits the validity of the Gerasimow-Drell-Hearn and Cabibbo-Radicati sum rules. The formula for the magnetic moment applies also for an abelian symmetry and remains valid even if the gauge symmetry is spontaneously broken.