Excitation conditions for quantitative determination of quadrupolar spins with one pulse or spin-echo sequences in solid-state NMR

One of the major problems concerning quadrupolar spins in solid-state NMR is their quantification. If the optimal excitation conditions with one radio-frequency pulse are widespread known now, this is not the case with the spin-echo sequences. This paper reports some theoretical predictions and their limitations concerning quantification with the echo obtained with spin-echo resonances. To realize that, first, the relative line intensity of a transition (m+1,m) is defined in order to allow the comparison of results, from different authors. Then results concerning one pulse excitation on a spinI=3/2 are summarized. The condition of short pulse excitation is generalized to higher spins using the Pauli matrices applied to the two extreme cases: hard pulse or non selective excitation, and selective excitation. Finally the same procedure has been followed for the spin-echo sequence involving twox-pulses. It was shown that the optimum conditions are: both the pulse length must be sufficiently short, and the interpulse delay should be taken as short as the duration of the FID provided the phase of the second pulse alternates without changing the receiver phase. In these conditions, the relative echo amplitude depends linearly on the first pulse length and quadratically on the second. The limitations are: the homonuclear magnetic dipolar interaction must be much smaller than the heteronuclear case which must be itself much smaller than the amplitude of the pulse. Furthermore, quantification with the echo requires the determination of the spin-spin relaxation time as well.     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

Electron-positron pair production by electromagnetic pulses

Electron-positron pair production in vacuum by a single focused laser pulse and by two counter-propagating colliding focused pulses is analyzed. A focused laser pulse is described using a realistic three-dimensional model based on an exact solution of Maxwell’s equations. In particular, this model reproduces an important property of focused beams, namely, the existence of two types of waves with a transverse electric or magnetic vector (e-or h-polarized wave, respectively). The dependence of the number of produced pairs on the radiation intensity and focusing parameter is studied. It has been shown that the number of pairs produced in the field of a single e-polarized pulse is many orders of magnitude larger than that for an h-polarized pulse. The pulse-intensity dependence of the number of pairs produced by a single pulse is so sharp that the total energy of pairs produced by the e-polarized pulse with intensity near the intensity I _S = 4.65 × 10²⁹ W/cm² characteristic of QED is comparable with the energy of the pulse itself. This circumstance imposes a natural physical bound on the maximum attainable intensity of a laser pulse. For the case of two colliding circularly polarized pulses, it is shown that pair production becomes experimentally observable when the intensity of each beam is I ～ 10²⁶ W/cm², which is one to two orders of magnitude lower than that for a single pulse.     

A study of branching ratios of cross sections in the charge symmetric reactions10B(d,p)11B and10B(d,n)11C

High-spin states in¹⁵⁶Er have been populated using the (α, 8n) and (¹⁶O, 4n) reactions. In the ground state band a strong backbending effect was observed atI ^π=12⁺. Four states of a secondK=0 band with spins 9, 11, 13 and 15 were found. This second band depopulates completely into the 8⁺ and 10⁺ members of the ground state band. This is explained by the fact that the upper states of this second band are yrast states and that this band crosses the (gsb)-line atI ?11.     

Modeling of transient electroluminescence overshoot in bilayer organic light-emitting diodes using rate equations

When a voltage pulse is applied under forward biased condition to a spin-coated bilayer organic light-emitting diode (OLED), then initially the electroluminescence (EL) intensity appearing after a delay time, increases with time and later on it attains a saturation value. At the end of the voltage pulse, the EL intensity decreases with time, attains a minimum intensity and then it again increases with time, attains a peak value and later on it decreases with time. For the OLEDs, in which the lifetime of trapped carriers is less than the decay time of the EL occurring prior to the onset of overshoot, the EL overshoot begins just after the end of voltage pulse. The overshoot in spin-coated bilayer OLEDs is caused by the presence of an interfacial layer of finite thickness between hole and electron transporting layers in which both transport molecules coexist, whereby the interfacial energy barrier impedes both hole and electron passage. When a voltage pulse is applied to a bilayer OLED, positive and negative space charges are established at the opposite faces of the interfacial layer. Subsequently, the charge recombination occurs with the incoming flux of injected carriers of opposite polarity. When the voltage is turned off, the interfacial charges recombine under the action of their mutual electric field. Thus, after switching off the external voltage the electrons stored in the interface next to the anode cell compartment experience an electric field directed from cathode to anode, and therefore, the electrons move towards the cathode, that is, towards the positive space charge, whereby electron–hole recombination gives rise to luminescence. The EL prior to onset of overshoot is caused by the movement of electrons in the electron transporting states, however, the EL in the overshoot region is caused by the movement of detrapped electrons. On the basis of the rate equations for the detrapping and recombination of charge carriers accumulated at the interface expressions are derived for the transient EL intensity I, time t_m and intensity I_m corresponding to the peak of EL overshoot, total EL intensity I_t and decay of the intensity of EL overshoot. In fact, the decay prior to the onset of EL overshoot is the decay of number of electrons moving in the electron transporting states. The ratio I_m/I_s decreases with increasing value of the applied pulse voltage because I_m increases linearly with the amplitude of applied voltage pulse and I_s increases nonlinearly and rapidly with the increasing amplitude of applied voltage pulse. The lifetime τ_t of electrons at the interface decreases with increasing temperature whereby the dependence of τ_t on temperature follows Arrhenius plot. This fact indicates that the detrapping involves thermally-assisted tunneling of electrons. Using the EL overshoot in bilayer OLEDs, the lifetime of the charge carriers at the interface, recombination time of charge carriers, decay time of the EL prior to onset of overshoot, and the time delay between the voltage pulse and onset time of the EL overshoot can be determined. The intense EL overshoot of nanosecond or shorter time duration may be useful in digital communication, and moreover, the EL overshoot gives important information about the processes involving injection, transport and recombination of charge carriers. The criteria for appearance of EL overshoot in bilayer OLEDs are explored. A good agreement is found between the theoretical and experimental results.     

Oscillatory free induction decay in angular distribution of nuclear radiation

A theoretical consideration of the free induction decay (FID) signal formation in the angular distribution of radiation, emitted by oriented nuclei after excitation by a long radiofrequency resonance pulse t_p ? T¹₂, is carried out. The well-known theorem on the oscillatory FID signal is expanded for the case of second rank tensors.     

Formation of impurity bands in iodine cation substitutionally doped TiO2 and its effects on photoresponse and photogenerated carriers

First-principles calculations based on the plane-wave pseudopotential (PWP) method were performed to investigate the electronic structure of iodine cation substitutionally doped anatase TiO₂ (referred to as I_sTiO₂). A 2×2×1 anatase supercell, in which one Ti atom was substituted by one iodine atom, was constructed for calculations. The calculated results reveal that iodine dopant contributes part of its 5s states to form one isolated impurity band in band gap and part of its 5p states to form some impurity bands at the bottom of conductive bands. The visible light response of I_sTiO₂ should be the consequence of the excitation between the two types of impurity bands (2.77 eV, about 450 nm). According to the distribution of impurity states, iodine dopant is considered to serve as a recombination center or an efficient trap for photogenerated carriers. This deduction was partly approved by water photosplitting under visible light irradiation.     

Separation of quadrupolar and magnetic contributions to spin-lattice relaxation in the case of a single isotope

We present a NMR pulse double-irradiation method which allows one to separate magnetic from quadrupolar contributions in the spin–lattice relaxation. The pulse sequence fully saturates one transition while another is observed. In the presence of a Δm = 2 quadrupolar contribution, the intensity of the observed line is altered compared to a standard spin-echo experiment. We calculated analytically this intensity change for spins I = 1, , , thus providing a quantitative analysis of the experimental results. Since the pulse sequence we used takes care of the absorbed radiofrequency power, no problems due to heating arise. The method is especially suited when only one NMR sensitive isotope is available. Different cross-checks were performed to prove the reliability of the results obtained. The applicability of this method is demonstrated by a study of the plane oxygen ¹⁷O (I = ) in the high-temperature superconductor YBa₂Cu₄O₈: the ¹⁷O spin–lattice relaxation rate consists of magnetic as well as quadrupolar contributions.     

Calculation of the eigenvalues of pure quadrupole interaction in Mössbauer effect studies

Summary Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in M?ssbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spinI=3/2÷9/2 and the electric-field gradient with different asymmetry parameter (η=0÷1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spinI=5/2.     

Exciton molecule in semiconductors by phonon-assisted two-photon absorption

Direct creation of bi-excitonic states by photon-assisted two-photon absorption in indirect-gap semiconductors is investigated theoretically. The symmetry of the indirect bi-exciton states and of the phonon used are given for the case of Ge. A numerical application to the case of Si shows that the indirect two-photon absorption coefficient for bi-excitonic α²_I (bi-ex) transitions is several orders of magnitude larger than both indirect two-photon interband, α²_I (band), and excitonic, α²_I (exc), transitions. It becomes smaller than both indirect one-photon interband, α¹_I (band), and excitonic, α¹_I (exc), transitions for available laser intensities. The essential contribution to this enhancement of α²_I (bi-ex) is found to be from the resonance effect in the first process and from both the resonance effect and matrix elements included in the second process.     

Relaxation Effects in a System of a Spin-1/2 Nucleus Coupled to a Quadrupolar Spin Subjected to RF Irradiation: Evaluation of Broadband Decoupling Schemes

We have investigated the suitability and performance of various decoupling methods on systems in which an observed spin-1/2 nucleusI(¹³C or¹⁵N) is scalar-coupled to a quadrupolar spinS(²H). Simulations and experiments have been conducted by varying the strength of the irradiating radiofrequency (RF) field, RF offset, relaxation times, and decoupling schemes applied in the vicinity of theS-spin resonance. TheT₁relaxation of the quadrupolar spin has previously been shown to influence the efficiency of continuous wave (CW) decoupling applied on resonance in such spin systems. Similarly, the performance of broadband decoupling sequences should also be affected by relaxation. However, virtually all of the more commonly used broadband decoupling schemes have been developed without consideration of relaxation effects. As a consequence, it is not obvious how one selects a suitable sequence for decoupling quadrupolar nuclei with exotic relaxation behavior. Herein we demonstrate that, despite its simplicity, WALTZ-16 decoupling is relatively robust under a wide range of conditions. In these systems it performs as well as the more recently developed decoupling schemes for wide bandwidth applications such as GARP-1 and CHIRP-95. It is suggested that in macromolecular motional regimes, broadband deuterium decoupling can be achieved with relatively low RF amplitudes (500–700 Hz) using WALTZ-16 multiple pulse decoupling.     

Three-nucleon yrast states in145Sm

In-beamγ-ray and conversion electron measurements with (α, xn) reactions have established the¹⁴⁵Sm highspin states up toI ^π=25/2⁺ at 3.5 MeV excitation. A shell model analysis using empirical two- and one-body energies from neighbouring nuclei classifies the low-lying odd-parity levels as 3-quasiparticle states formed by the¹⁴⁴Sm two-proton-hole excitations and thef _7/2 valence neutron. The higher-lying positive-parity states involve particle-hole core excitations with one proton inh _11/2.     

Second-harmonic conversion of partially coherent radiation of neodymium glass laser

The experimental results on the conversion of multimode radiation of a neodymium glass laser with controlled spatial and temporal coherence to the second optical harmonic in nonlinear KDP crystal during the oee interaction implementation are presented. The dependence of the efficiency of the conversion to the second harmonic on the fundamental radiation power density on the crystal in the range I = 0.2 ? 5 GW/cm² is studied at the number of transverse modes in the cavity N = 1000; the radiation divergence φ = 3.5, 4.7, and 5 mrad; the emission spectral width δλ = 5and 42 Å; and the pulse duration of 2.5 ns. The breakdown power density of the KDP crystal is determined, the interference properties of the converted radiation of the second harmonic are studied.     

Application of a quadrupole-coupling model to doublet bands in doubly-odd nuclei

A simple model is applied to the yrast and yrare states based on the νh _11/2 ⊗ πh _11/2 configuration in the doubly-odd nuclei around the mass 130. In the model, the basis state is constructed by one neutron and one proton both in the 0h _11/2 orbital, and by the collective core which couples with the two particles through a quadrupole interaction. The model reproduces quite well the overall energy levels and the electromagnetic transitions. The analysis of the yrast and yrare states reveals that the angular-momentum configuration of the neutron and the proton in the yrast states is different from that in the yrare states, when the two particles are weakly coupled with the quadrupole collective excitations of the core. The strong even-odd staggering of the ratios B(M1;I → I - 1)/B(E2;I → I - 2) for the yrast states is described by the chopsticks-like motion of two angular momenta of the neutron and the proton.     

Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω²〉 and the frequency of only one singularity ω₂ of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.     

Recoil distance lifetime measurements in82Kr

The lifetimes τ=124±12, 6 _?2 ⁺⁴ and 380±100 ps of theE _x (I ^π )=3.46(8⁺), 2.92(6⁺) and 3.04(6^?) MeV states, respectively, populated by the reaction⁷⁶Ge(¹²C,α2n) were measured with the recoil distance method. In addition upper lifetime limits were obtained for nine states. The measured lifetimes and energies indicate a band crossing at aboutI ^π =8⁺, probably arising from the alignment of twog _9/2 neutrons. For the 3.04 MeV 6^? state as a second member of a band built on the 2.65 MeV 4^? state the measured lifetime points to a two-quasiparticle configuration. The positive-parity states have been discussed in the frame of the interacting boson approximation, nuclear field theory and the cranked shell model.     

Nuclear reactions as an example of the quantum theory of irreversible processes

A modification of the atomic beam magnetic resonance method for investigation of the hyperfine structure of excited atomic states will be described. Radiofrequency transitions between the hyperfine structure niveaus of the excited state, which are unequally populated by circularly polarized light, are detected by observing the resulting change in population number of the hyperfine structure niveaus of the ground state using magnetic deflection in an inhomogeneous field and additional radiofrequency transitions in the ground state as analyzers. As an application the hyperfine structure of the excited 4² P _3/2-state of K³⁹ has been investigated in an almost strong magnetic field of about 65 G with a constant frequency of the applied radiofrequency field of 125.50 Mc/s. The analysis of the radiofrequency signal of the excited state detected as a change in the amplitude of a radiofrequency transition in the ground state yielded the valuesA=(6.10±0.25) Mc/s andB=(1.8±1.2) Mc/s for the hyperfine structure constants of the 4² P _3/2-state of K³⁹. Further possibilities for observing signals of the excited state with the apparatus used in this experiment are also discussed.     

Photocontrol of magnetization in Al-substituted Fe3O4 thin films

Thin films of (111)-oriented spinel ferrite Al_0.5Fe_2.5O₄ have been prepared by a pulsed-laser deposition (PLD) technique on α-Al₂O₃ (0001) substrates. The films exhibit cluster-glass behaviors with a spin-freezing temperature, T_g, near or above room temperature. The magnetization was found to increase following light irradiation below T_g, which indicates the photoinduced melting of cluster-glass states. An analysis comparing the dynamic behavior of magnetic response to light irradiation between zero-field-cooled (ZFC) states and field-cooled (FC) states at 10 K under various light intensities, I, revealed that the direct photoexcitation of spins occurs when I≤0.78 mW/mm², while the thermal heating effect following the light absorption of the samples also contributes to the enhancement of magnetization when I≥1.22 mW/mm². The magnetization of the films could be controlled by light irradiation even at room temperature. This suggests the possibility of utilizing these films in the development of novel magneto-optical memory devices.     

Influence of the shape of the exciting laser pulse on fluorescence saturation in the quantitative analysis of dissolved trace organic substances

Theoretical investigations of the influence of the exciting laser pulse shape on fluorescence saturation in the quantitative analysis of a single-component fluorescing solution, when the Raman signal of the solvent is usedas a reference, are carried out. A quantity α is introduced, responsible for the influence of laser pulse shape on the precision of the analysis. The dependences of α on the exciting radiation photon flux density I_m in the range I_m = 10²² ? 10²⁸ photons/cm²?s and on the duration of the exciting pulses τ_p in the range τ_p = 0.6 ? 60 ns are computed for different pulse shapes in the case of rhodamine 6G dissolved in water. Conditions when α is, in practice, independent of τ_p and of the pulse shape are found. A general analytical expression is found for α, which produces errors not greater than several percent when compared to the computed values of α. An experimental verification of the theoretical results in the case of a rectangular-shaped pulse in the spatial domain and a Gaussian-shaped pulse in the temporal domain is realized.