EPR and ENDOR study of porphyrins and their covalently linked dimers in the photoexcited triplet state

The triplet states of several substituted porphyrins (Tetraphenylporphyrin (H₂TPP), Zinc-Tetramethylporphyrin (ZnTMP), Octaethylporphyrin (H₂OEP) and the Dication of H₂TPP (H₄TPP²⁺)) and two covalently linked dimers with H₂TPP-subunits in disordered solid solution were studied by EPR and ENDOR at liquid helium temperature. The measurement yields theA _zz component of the hyperfine tensors of all α-protons in the reference frame of the zero field splitting tensor. Dipolar and isotropic contributions toA _zz are discussed and spin densities derived. The spin densities are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/S). One of the dimers shows indications of triplet energy transfer between the porphyrin subunits. The order of magnitude of the transfer rate is estimated to be 5 · 10⁵ s^?1.     

On the electronic structure of N,N′-ethylenebis(acetylacetonatiminato)Co(II), Co(II)acacen

Single crystal E.P.R. and cobalt ENDOR measurements on N,N′-ethylenebis(acetylacetonatiminato)Co(II), Coacacen, diluted in Niacacen·1/2 H₂O are reported. Forbidden Δm _Co = 1,2 transitions in the E.P.R. spectra have been observed. The g-tensor (E.P.R.) and the cobalt hyperfine and quadrupole tensors (ENDOR) have been determined. The g- and cobalt hyperfine tensors are discussed. They support the |² A ₂,yz? groundstate proposed for four coordinated low-spin Schiff base complexes of cobalt(II). The measured quadrupole coupling is also compatible with a |² A ₂,yz? groundstate, if anisotropic contraction of the cobalt 3d orbitals is taken into consideration.     

Elektronen-Kern-Doppelresonanz-Untersuchung vonU 2-Zentren in Kaliumchlorid

U ₂-centers in alkali halides are neutral hydrogen atoms in interstitial lattice sites, as has been shown by EPR measurements. The hyperfine interactions with the proton and with the four nearest halogen nuclei are resolved in the EPR spectrum. In order to resolve hyperfine interactions with further nuclei of the surrounding lattice ENDOR measurements have been performed onU ₂-centers in KCl at 77 °K. The analysis of the ENDOR spectra gave precise values for the hyperfine and quadrupole interaction constants of the nearest neighbour chlorine and potassium nuclei. The isotropic hyperfine constant of the chlorine neighbours is 24 times larger than that of the potassium neighbours although both nuclei are on equivalent first shell lattice positions. The hyperfine interactions of second shell potassium nuclei [(1/2, 1/2, 3/2)-position] show an unexpectedly large isotropic hyperfine constant. One expects a pure magnetic dipole-dipole interaction for the outer shell nuclei because of the concentrated hydrogen wave function. Two further chlorine shells could be approximately analysed. A theoretical estimate of the hyperfine and quadrupole interaction constants was made by orthogonalizing the 1s hydrogen wave function to the cores of the surrounding ions. If one takes into account the mutual overlap of neighbouring potassium and chlorine ions, one gets the right order of magnitude of the measured constants and a value of 10.4∶1 for the ratio of the isotropic hyperfine constants of the first shell chlorine and potassium nuclei. The relatively large isotropic constant of the second shell potassium nuclei can also be explained on this basis.     

Probabilistically perfect quantum cloning and unambiguous state discrimination

We consider the N → M probabilistically perfect quantum cloning machine that perfectly produces M faithful copies from N identical input states, where the input states are selected, with prior probabilities η₁and η₂ = 1 − η₁, from a given set of the two linearly independent states |ψ₁〉^⊗ N = (cosθ|0〉 + sinθ|1〉)^⊗ N and |ψ₂〉^⊗ N = (sinθ|0〉 + cosθ|1〉)^⊗ N (θ∈(0,π/2)). We derive the optimal distribution of the success probabilities. When M approaches infinite, the probabilistically perfect quantum cloning can be regarded as a kind of the unambiguous state discrimination, and theoretically provides the upper bound of the unambiguous state discrimination. By using the optimal distribution of the success probabilities of the optimal asymmetric 1 → M probabilistically perfect quantum cloning, we can derive the maximum average success probability of the unambiguous discrimination of two nonorthogonal quantum states |ψ₁〉and|ψ₂〉. As an example, we give the explicit transformation of the optimal symmetric 1 → M probabilistically perfect quantum cloning to copy the two input states |ψ₁〉 and |ψ₂〉.     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Crystalline fields,exchange interactions and spin reorientations in TmxHo1−xFe2 systems,studied by a Yb170 Mössbauer probe

Mössbauer studies of the 84.3 keV gamma ray of Yb¹⁷⁰ emitted from Yb in Tm_xHo_1?xFe₂ at various temperatures were performed. These yield the crystalline field parameters (A₄〈r⁴〉 = 36 ± 5 K, A₆〈r⁶〉 = -3 ± 2K, the exchange field (μ_BH_exch = 116 ± 4 K) and the Yb³⁺ free ion hyperfine constants (H_4f = 4100 ± 150 kOe, eqQ = 2400 ± 250 MHz and H (conduction electrons) = 350±100 kOe). Spin relaxation phenomena observed in TmFe₂ at low temperatures give a value of ～ 0.03 for |?(E_F)J_sf|. Spectra observed in Tm_0.2Ho_0.8Fe₂ in the spin reorientation transition region indicate that the transition is of second order.     

Angle-selective measurements of spin soliton in ladder polydiacetylene by pulsed 94 GHz EPR

Angle-selection experiments of a spin soliton in randomly oriented ladder polydiacetylene were carried out by pulsed electron paramagnetic resonance (EPR) at W-band. EPR measurement using 94 GHz microwaves increased the difference in the resonance field due tog anisotropy of the spin soliton to allow the orientation dependence of transient nutation, electron nuclear double resonance (ENDOR) and spin relaxations to be investigated. The shape of theg anisotropy-resolved nutation spectrum was discussed on the basis of the EPR transition moments and the differences between spin relaxation times. Reliable assignments of hyperfine couplings to the β protons (H_β) of the alkyl side chains were achieved with the support of W-band ENDOR measurements. No significant orientational dependence in theT ₁ andT ₂ processes was found in terms of isotropy of the H_β-hyperfine interaction.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

EPR study of impurity iron ion clusters in BaF<Subscript>2</Subscript> crystals

Tetragonal paramagnetic centers with spin S = 7/2 were detected in x-ray-irradiated BaF₂: Fe (c_Fe ≈ 0.002 at. %) crystals using the EPR method. Electronic transitions between the |±1/2〉 states of a Kramers doublet were observed in the X and Q ranges. In the EPR spectra of the tetragonal centers, a ligand hyperfine structure (LHFS) was observed corresponding to the interaction of the electron magnetic moment of the tetragonal center with eight equivalent ligands. The large spin moment, significant anisotropy of the magnetic properties, and the characteristic LHFS indicate that the tetragonal center is a Fe^1.5+?Fe^1.5+ dimer in which the two iron ions are bound via superexchange interaction. It is assumed that, before crystal irradiation, this dimer was in the Fe³⁺(3d⁵)?Fe⁺(3d⁷) state.     

Mössbauer effect study of hyperfine interactions in145Nd

The magnetic hyperfine splitting of the 72.5 keV γ rays of¹⁴⁵Nd was investigated in intermetallic compounds of Nd and in the paramagnetic salts Nd _x Y _1-x Cl₃·6H₂O (withx=0.02 andx=0.05) at 4.2 K. With the magnetic hyperfine tensorA of Nd_0.01Y_0.99Cl₃·6H₂O known from EPR spectroscopy, the analysis of the unresolved magnetic hyperfine spectra yieldsI _e =5/2 for the spin of the 72.5 keV state, in contradiction to a previous result. The multipolarity of the 72.5 keV γ transition was found to be essentiallyM1 with δ²=0.010±0.014, and the magnetic moment of the 72.5 keV state was determined as μ(5/2)=?0.319±0.004 nm. For various divalent and trivalent Nd compounds as well as for metallic Nd the isomer shift IS of the 72.5 keV γ line was measured. A value for the change of the mean square nuclear charge radius during the 72.5 keV γ transition of Δ〈r ²〉=+(1.9±0.9)·10^?3fm² was deduced using electron density differences from free-ion Hartree-Fock calculations.     

Perturbation theory with a tridiagonal zeroth-order hamiltonian

We generalize the Rayleigh-Schrödinger perturbation formalism to the hamiltonians H=H₀+λH₁ where the correction λH₁ is small and the unperturbed operator H₀ is represented by an infinite tridiagonal matrix. This enables us to construct the solutions E=E₀+λE₁+λ²E₂+… and |ψ〉 = |ψ₀〉+λ|ψ₁〉+λ²|ψ₂〉+… in terms of the analytic continued fractions.     

Refined MCHF evaluations of field isotope shift and hyperfine structure in the calcium atom

In the calcium atom, the MCHF method has been applied for evaluating the field-shift electronic parts of both 4s ²-4s4p lines, and the hyperfine-structure electronic effective parameters of the 4s4p ³ P ₂ and¹ P ₁ levels. For the hyperfine structures, the far-configuration mixing corrections have been computed with the assumption that the lower state is itself a two-componentsp+dp state in close-configuration mixing.     

Proton ENDOR of VO(H2O)5 2+ in Mg(NH4)2(SO4)2)26H2O

ENDOR measurements at 25 K have been used to determine the hyperfine coupling tensors for all ten protons in the VO(H₂O)₅ ²⁺ ion in single crystals of Mg(NH₄)₂(SO₄)₂6H₂O. The traceless components of all the tensors are close to axial and their use in a point dipole treatment enables a very plausible geometrical model of the complex ion to be constructed. Six of the protons in the equatorial water molecules have substantial positive isotropic couplings and it is suggested that these reflect the direct admixture of hydrogen 1s components into the singly occupied orbital.     

The missing mass squared dependence of the average charged particle multiplicity in the reaction K+p → KoX++ from 5–16 GeV/c

The average charged particle multiplicity, 〈n_ch(M_X²)〉, in the reaction K⁺p→K^oX⁺⁺ is studied as a function of the mass squared, M_X², of the recoil system X and also as a function of the K^o transverse momentum, p_T, at incident momenta of 5.0, 8.2 and 16.0 GeV/c. The complete data samples yield distributions which are not independent of c.m. energy squared, s, They exhibit a linear dependence on log (M_X²_X/M_o²)[M_o²=1 GeV²] with a change in slope occurring for M_X²≈s/2, and do not agree with the corresponding distributions of 〈n_ch〉 as a function of s for K⁺ p inelastic scattering. Sub-samples of the data for which K^o production via beam fragmentation, central production and target fragmentation are expected to be the dominant mechanisms show that, within error, the distribution of 〈n_ch(M_X²)〉 versus M_X² is independent of incident momentum for each sub-sample separately. In particular in the beam fragmentation region the 〈n_ch(M_X²)〉 versus M_X² distribution agrees rather well with that of 〈n_ch〉 versus s for inelastic K⁺p interactions. The latter result agrees with recent results on the reactions pp → pX and π^?p → pX in the NAL energy range. Evidence is presented for the presence of different production mechanisms in these separate regions.     

X-Band Pulsed ENDOR Study ofFe-Substituted Sodalite— The Effect of the Zero-Field Splitting

X-band (∼9.3 GHz) pulsed ENDOR measurements were carried out on⁵⁷Fe-substituted sodalite (FeSOD) which contains only one type of Fe(III) (S=) located at a framework site. The ENDOR spectrum recorded atg= 2 shows three doublets corresponding to the sixM_Smanifolds. The assignment of these signals was confirmed by hyperfine-selective and triple ENDOR experiments. The components of each of the doublets had different intensities, reflecting the different populations of the EPR energy levels at the measurement temperature, 1.8 K. ENDOR spectra were recorded at magnetic fields within the EPR powder pattern, and the field dependence observed showed an anisotropic behavior, unexpected from the isotropic character of the⁵⁷Fe(III) hyperfine coupling. This dependence was attributed to the high-order effects of the zero-field splitting (ZFS) interaction on the ENDOR frequencies. Three different theoretical approaches were used to account for the dependence of the ENDOR spectrum on the ZFS interaction. The first involves the exact diagonalization of the total spin Hamiltonian, the second uses third-order perturbation approximations, and the third employs an effective nuclear Hamiltonian for each of theM_Smanifolds. The simulations showed that the ENDOR signals of theM_S= ±5/2 (ν_±5/2) manifold are the least sensitive to the magnitude of the ZFS parameterDand are therefore the most appropriate for the determination ofa_iso. It is shown that at X band anda_isovalues of about 30 MHz, the perturbation approach is valid up toDvalues of 500 MHz if all three doublets are concerned. However, if only the ν_±5/2doublet is considered, then this approach is valid forD< 1000 MHz. The third approach was found inappropriate fora_isovalues of ∼30 MHz. Using the method of exact diagonalization together with orientation selectivity, the trends observed in the experimental spectra could be reproduced. The ENDOR spectra of the⁵⁷Fe-substituted zeolites ZSM5, L, and mazzite showed broad and ill-defined peaks since the ZFS of Fe(III) in these zeolites is significantly larger than that of FeSOD. Because this broadening is a high-order effect, it can be significantly reduced at higher spectrometer frequencies.     

Hyperfine structure and isotope shift of high-lying metastable states of rhenium

Fourteen transitions in ReI, starting from high-lying metastable states belonging to the configurations (5d+6s)⁷, have been studied by laser-induced fluorescence in a collimated atomic beam, and accurate values for the isotope shifts in these transitions as well as for the hyperfine structure constants of 13 metastable and 9 excited states have been obtained. In addition, high precision measurements of the hyperfine structure of the states 5d ⁵ 6s ^{2 4} D _7/2 and 5d ⁶ 6s ⁶ D _{1/2, 3/2, 5/2, 9/2} have been performed using the atomic beam magnetic resonance technique coupled with laser-induced state-selective detection of metastable atoms. The analysis of the hyperfine structure data yields experimental evidence for far configuration mixing effects on the off-diagonal spin-dipole matrix elements. The phenomenological interpretation of the isotope shifts shows the significance of off-diagonal field-shift effects.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

On the influence of spin-orbit scattering on the Kondo effect

It is shown that the hyperfine splitting of the levels 2s _1/2 and 2p _1/2 of atomic hydrogen has a measurable influence on the mixing of these levels in a weak electric field.     

169Tm NMR study of the high-Tc superconductor TmBa2Cu3O6.92

The ground state of Tm³⁺ ion (4t²,³H₆) in a crystal electric field (CEF) of TmBaCuO is a singlet, separated from the lowest excited states by an energy gap of 100÷130 cm^?1. The pulsed NMR of¹⁶⁹Tm nuclei (spinI=1/2) in a magnetically-oriented TmBa₂Cu₃O_6.92 power is studied at temperatures 1.5÷4.2 K. Two sorts of Tm nuclei are observed: rapidly relaxing Tm1 (≥80% of total amount, having relaxation timesT ₁ ⁽¹⁾ ≈35 ms,T ₂ ⁽¹⁾ =80÷250 μs) and slowly relaxing Tm2 nuclei (≦20%,T ₁ ⁽²⁾ =300÷1000 μs). The¹⁶⁹Tm NMR spectra are described by the spin-Hamiltonian ?₁ = ??Σγ _i H _i I _i (i = x,y,z), where |γ _x ⁽¹⁾/2π| = 5.3(1), |γ _y ⁽¹⁾/2π| = 6.6(1), |γ _x ⁽²⁾/2π| = |γ _y ⁽²⁾/2π| = 5.1(1), |γ _z ⁽¹⁾/2π| = |γ _z ⁽²⁾/2π| = 2.3(1) kHz/Oe, and axesx, y, z coincide with the crystal axesa, b, c. The Tm1 and Tm2 nuclei are identified as those belonging to orthorhombic (CEF of D_2h symmetry) and tetragonal (D_4h) phases of the TmBaCuO compound, respectively. Two-exponential and nearly temperature-independent nuclear relaxation is observed at temperatures 1.5÷4.2 K. The smallestT ₂ ⁽¹⁾ -values (≈80 μs) found for the orthorhombic (superconducting) phase in an external field H perpendicular to the crystalc-axis agree fairly well with those one could expect due to the dipole-dipole interaction of thulium nuclei. However, the slowing down of this rapid relaxation of the nuclear transverse magnetization in a field H‖c as well as the origin of unusually largeT ₂ ⁽²⁾ -values remain unclear.     

Exchange currents in electric transitions and the rôle of siegert's theorem: A case study in deuteron photodisintegration

The hyperfine structure (hfs) splittings of the metastable 1s2s ³ S ₁ state of⁷Li⁺ have been measured with combined laser optical pumping and microwave resonance. A lowenergy Li⁺ ion beam, optically excited by an intersecting laser beam, passed a waveguide where radio frequency transitions were induced. The resulting population transfer among the hfs levels of the³ S ₁ was detected via the change in intensity of the fluorescence light from a second crossing region of laser light and ion beam located past the waveguide. The magnetic hfs constantA(⁷Li⁺, 1s2s ³S₁) was measured and compared with theory. A deviation of the two transition frequenciesν(F=3/2?F=5/2) andν(F=1/2?F=3/2) from the interval rule is due to a depression of theF=3/2 hfs sublevel, caused by mixing of the 2³ S ₁ and 2¹ S ₀ states via hyperfine interaction. This shift was never observed so far in a two-electron spectrum, because of absence ofI>1/2 isotopes in He, the only two-electron atom investigated spectroscopically with high precision. The size of the shift is in fair agreement with a theoretical estimate.