Dynamical study of triplet-triplet energy transfer in rigid solution

Triplet-triplet (T-T) energy transfer from acetophenone to naphthalene-d₈ has been studied in EPA rigid-glass solution at 77 K by masuring the decay of donor phosphorescence and the rise of acceptor T-T absorption over a wide range of time. The results were analyzed in terms of the theory proposed by Inokuti and Hirayama on the basis of a point molecular model. Two parameters, R_O and γ, were determined which are involved in their expression for the rate constant of T-T energy transfer, i.e. n(R) = (1/τ_D) exp[γ(1?R/R_O)], where R and τ_D denote the donor-acceptor distance and the lifetime of donor triplet in the absence of acceptor, respectively. It was found that, in contrast to the Inokuti-Hirayama theory in which γ is assumed to have a constant value, γ increases significantly as the time (t) after flash excitation of the donor becomes smaller: γ ≈ 25 for t/τ_D=10^-2?1, ≈ 35 for t/τ_D = 10^-3? 10^-2, and ≈ 45 for t/τ_D = 10^-4?10^-3. This finding suggests that the true rate constant increases with decreasing R value to a greater extent than the n(R) employed by Inokuti and Hirayama.     

On the dynamical coupling between the dipolar and tunneling system of CH3-groups in solids at high temperatures

For methyl groups a dynamical coupling has been predicted between the dipolar and tunnelling systems, also at high temperatures where the observable tunnelling frequency at thermal equilibrium ω_t is zero. This is experimentally confirmed by observed non-exponential dipolar relaxation for ω₀²τ_c² ? 1.     

Radiative decay and autoionization in the4 D-states of the 3d 94s5s configuration in CuI

The CuI 3d ⁹4s5s ⁴ D-states, which lie above the ionization limit, were populated by stepwise collisional and laser excitation. With respect to their total angular momentum, the⁴ D-states have completely different decay modes. Whereas the lifetimesτ(⁴ D _7/2)=8.2(4)·10^?9s andτ(⁴ D _1/2)=7.9(6)·10^?9 s are determinrd by radiative transitions and were measured by time-resolved spectroscopy, the lifetimesτ(⁴ D _5/2)=1.59(6)·10^?12s andτ(⁴ D _3/2)=1.28(5)·10^?12s are due to autoionization and were deduced from the widths of the excitation signals observed by ion detection.     

Multiple quadrupolar spin echoes in the La-filled skutterudite LaOs4As12

We report experimental results of ¹³⁹La pulse NMR studies in LaOs₄As₁₂. Measurements have been performed on a powder sample obtained from high quality single crystals. For the first time the pattern of quadrupole echoes for ¹³⁹La nuclei (I=7/2) was obtained. All the allowed quadrupolar echoes expected for spin I=7/2 were observed at times t=(4/3)τ, (3/2)τ, (5/3)τ, 2τ, (5/2)τ, 3τ, 4τ. The presence of quadrupolar echoes is the fingerprint of the deviation from perfect cubic symmetry of the structure and can be used as a simple and fast test of the sample quality.     

Lebensdauern und Oszillatorstärken im Sr I- und Ca I-Spektrum

Radiative lifetimes of some highly excited levels in Sr I were measured by zero-field level crossing technique. These levels have been populated using optical excitation starting from the metastable 4d 5s ¹ D ₂ or 5s5p ³ P _2,1,0 states. The high population of these metastable levels necessary for the experiments was obtained by a discharge in the pure Sr vapour burning in the atomic beam oven. The following lifetimes have been determined (in units of 10^?8 sec):τ(5s 6s³ S ₁)=1.09±0.11,τ(5s 5d ³D₁)=1.67±0.10,τ(5s4f¹ F ₃)=3.43±0.28,τ(4d5p ¹ D ₂)=2.19±0.16,τ(5p ^{2 3}P₁)=0.88±0.12,τ(5p ^{2 3} P ₂)=0.78 _?0.10 ^+0.26 . These results are compared with lifetimes derived from oscillator strengths given in the literature, and the reliability of different oscillator strengths tables is discussed. A corresponding discussion is given for radiative lifetimes of some levels in Ca I published previously. Good agreement with data derived from arc emission oscillator strengths has been found. Ca lifetimes are fairly well consistent with oscillator strengths calculated with semiempirical scaled Thomas-Fermi-wave functions.     

Stark-Effekt-Untersuchungen in der Hyperfeinstruktur der 3s 2 3d 2 D 5/2- und2 D 3/2-Terme des Al I-Spektrums

The resonance fluorescence of the transitions 3d ² D _5/2,3/2 3p ² P _3/2,1/2 in the Al I-spectrum was observed as a function of a magnetic field. Adding an electric field parallel to the magnetic field the shifts of level crossing signals caused by the Stark effect of the electric field were used to separate overlapping signals of the 3d ² D _5/2- and 3d ² D _3/2-states. The following values of the Stark parametersβ of both states and the hyperfine structure constantsA andB of the 3d ² D _3/2-states were deduced: 3d ² D _3/2∶ ¦A¦=99(1) Me/sec · g_J/0,8,B/A=?0,22(12), ¦β¦=0.45 (8) Mc/sec/(kV/cm)² · g_J,/0.8, A/β< 0 3d²D_5/2∶ ¦β¦=0.16 (4) Mc/sec/(kV/cm)² · g_J/1.2, A/β>0. Some qualitative aspects of interconfiguration mixing in the 3d²D-states are discussed.     

Lifetimes of some highly excited levels in the Pb-I spectrum measured by the hanle method

Natural lifetimes of some highly excited levels in the Pb-I spectrum have been measured by the zero field level crossing (Hanle) method. The levels were reached by optical excitation from the metastable 6p ^{2 3} P ₂ and 6p ^{2 3} P ₁ states, were a considerable population had been created by means of adc discharge in a Pb atomic beam. An atomic beam source producing atoms in metastable states is described. For the lifetimes τ of the investigated levels we find:τ(6p(1/2)6d ³ D ₁)=3.74(28) ns,τ(6p(1/2)6d ³ F ₂)=25.8(1.3) ns,τ(6p(1/2)6d ³ D ₂)=4.17_(?31) ^(?49) ns,τ(6p(1/2)6d ³ F ₃)=6.08(26) ns,τ(6p(3/2)7s)³ P ₂=5.85(27) ns. These results are compared with lifetimes derived from oscillator strengths given in the literature.     

New aspects of the rotational model in25Mg

Spin assignments have been made to the²⁵Mg levels in theE _x=5–6 MeV region fromγ-ray angular distributions measured in the²²Ne(α, n y) reaction atE _α=8.0 and 8.8 MeV and fromp-γ angular correlations measured in the²⁴Mg(d, p γ) reaction atE _d=6 MeV. Unique spin assignments ofJ=7/2, 5/2, 5/2, and 9/2 could be made to the levels atE _x=5005, 5511, 5851, and 5967 keV, respectively. Ambigious assignments have been made to the levels atE _x=5245, 5524, 5785, 6032 keV (J=11/2, 7/2), 5455 keVJ=13/2, 9/2), and 5738 keV (J=3/2, 5/2). The present data confirm previous assignments ofJ=1/2 to the levels atE _x=5108 and 5466 keV, respectively. Lifetime estimates have been obtained, using the Doppler-shift attenuation method, for the levels atE _x=5245 keV (τ=30–60 fs), 5785 keV (τ=50–100 fs), 5967 keV (τ=50–100 fs), and 5455 keV (τ>1ps). All other levels in theE _x=5–6 MeV region haveτ<60 fs. A breakdown of theK-selection rule has been observed in theγ-decay of some high spin states, indicating a deviation from the strong coupling model.     

Stark-Effekt-Untersuchungen der Hyperfeinstruktur der 5s25d2D3/2- und 5s25d2D3/2-Terme im In I-Spektrum

The level-crossing technique with combined electric and magnetic fields was used to investigate the hyperfine structure of the 5s ²5d ² D _3/2- and 5s ²6d ² D _3/2-stedes of the In I-spectrum. From the shifts of the level-crossing signals due to the Stark effect of the electric field the Stark constantsβ of both states were deduced: 5s ²5d ² D _3/2: ¦β¦=0.33(3) Mc/(kV/cm)² 5s ²6d ² D _3/2: ¦β¦=6(1) Mc/(kV/cm)². By theoretical calculations with wave functions of the Coulomb approximation one can show, that the Stark effect in both states is mainly due to admixtures of the 5s ²6p- resp.5s ²7p-configuration.     

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.     

Exact results for two-dimensional coarsening

We consider the statistics of the areas enclosed by domain boundaries (‘hulls’) during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area, n _h (A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form n _h (A, t) = 2c _h /(A + λ _h t)², demonstrating the validity of dynamical scaling in this system. Here $ c_h = {1 \mathord{\left/ {\vphantom {1 8}} \right. \kern-0em} 8}\pi \sqrt 3 $ is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λ _h is a material parameter. The distribution of domain areas, n _d (A, t), is apparently very similar to that of hull areas up to very large values of A/λ _h t. Identical forms are obtained for coarsening from a critical initial state, but with c _h replaced by c _h /2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of c _h . By applying a ‘mean-field’ type of approximation we obtain the form n _d (A, t) ? 2c _d [λ _d (t+t ₀)] ^τ?2/[A+λ _d (t+t ₀)] ^τ , where t ₀ is a microscopic timescale and τ = 187/91 ? 2.055, for a disordered initial state, and a similar result for a critical initial state but with c _d → c _d /2 and τ → τ _c = 379/187 ? 2.027. We also find that c _d = c _h + O(c _h ² ) and λ _d = λ _h (1 + O(c _h )). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.     

Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime

In this paper, we study the problem of continuous time option pricing with transaction costs by using the homogeneous subdiffusive fractional Brownian motion (HFBM) Z(t)=X(S_α(t)), 0<α<1, here dX(τ)=μX(τ)(dτ)^2H+σX(τ)dB_H(τ), as a model of asset prices, which captures the subdiffusive characteristic of financial markets. We find the corresponding subdiffusive Black-Scholes equation and the Black-Scholes formula for the fair prices of European option, the turnover and transaction costs of replicating strategies. We also give the total transaction costs.     

A tilted rotatory frame method for the measurement of nuclear spin diffusion coefficients in solids doped with paramagnetic centers: Mn-Doped CaF<Subscript>2</Subscript>

Nuclear magnetic resonance (NMR) experiments recording the recovery of the magnetization of the nuclei in one phase, following the excitation of the nuclei in the other phase, is a classical way of studying blends inhomogeneous at the nanometer scale. Interpretation of the time recovery in terms of the spatial dimension requires knowledge of the two-phase spin diffusion coefficientsD ₀. A new method of measurement of_{D 0} is proposed on the basis of variable angle-tilted rotatory frame relaxation in homogeneous samples doped with paramagnetic centers. The choice of the tilt angle allows one to finely balance the direct relaxation by the paramagnetic center and the spin diffusion. The shape of the relaxation is analyzed with the solution for the diffusion-limited regimeM(t)/M(0)=exp[?(r ₂ t)^1/2?r ₁ t] andD ₀ then calculated fromr ₁,r ₂ and the concentration of paramagnetic centers. Conditions where reliable results can be obtained both theoretically and numerically are explored. The method has been implemented and applied to polycrystalline Mn-doped CaF₂ leading toD ₀=540±60 nm²/s, in agreement with existing values on this model compound.     

Proton spin relaxation in hexagonal ice

Measurements of the rotating frame proton spin relaxation timeT _1p in hexagonal ice single crystals as a function of temperature ? for various rotating magnetic field strengths reveal the expectedT _1p minimum at the lowest practicable field values. This allows a very precise determination of the proton correlation (? molecular jump) time τ_c and the related activation energy ΔE by means of the theoretical reasoning of relaxation spectroscopy. We find the Arrhenius-law temperature dependenceτ _c=1.99×10^?17exp(0.603/8.61×10^?5 ?)sec, which is in good agreement with our earlier indirect derivation.     

Frozen photoconductivity in PbTe films

We have studied PbTe films of thicknessd=200/10000 A made with telluride vapour deposition on glass substrate at room temperature. The estimate of the donor concentration ～10¹⁹ cm^?3 of the fresh-deposited film compared with the impurity content in the bulk raw material ～10¹⁷ cm^?3 shows that the donors were mainly film defects or nonstoichiometric Pb atoms. Electrical conductivity of the freshly deposited film increased with lowering of the temperature. After deposition the donors were compensated with an oxidation in the laboratory air. Transition to the thermally activated conductivity resulted from oxidation. At temperatures belowT≈100 K the resistance of the compensated films followed Mott’s ruleR=R ₀ exp(T ₀/T)^1/3. The square film value 1 Mohm andT ₀≈100 K ford=1000 A. At low temperatures an exposure to light resulted in sharp decrease of the film resistance. At liquid helium temperatures the resistance dropped 10³–10⁶ times and stayed at the low value for an indeterminate time. The heating of the film aboveT=100 K gave rise to an initial high resistive state. The critical temperatureT _c, when the frozen photoconductivity became negligible, varied with samples in the temperature region 90–120 K. Near the critical temperature we could measure the time dependence of the film resistance after the light exposure, which followed the equationR=A+B.lnt fort>1 sec with the empirical constantsA andB. After a time intervalτ the resistance gained the initial “dark” value and remained stationary. The value lnτ≈α.(T _c?T), where the factorα approximately wasα≈0.5 K^?1. Some results of these experiments were published earlier (Krylov and Nadgorny 1982; Krylov and Pojarkov 1984).     

Electric dipole moments and nuclear hyperfine interactions for H2S,HDS, and D2S

Electric dipole moments and nuclear hyperfine coupling constants for several low-energy rotational states of the ground vibrational state of H₂S, HDS, and D₂S have been determined by molecular beam electric resonance spectroscopy. Analysis of the Stark effects for radiofrequency spectra of the lowest rotational levels gives dipole moments of 0.978325 (10) D for H₂S (J = 1, τ = 0), 0.977294 (20) D for D₂S (J = 1, τ = 0), and 0.977484 (60) D for HDS (J = 1, τ = 1 and J = 2, τ = 0). The electric field gradient tensor at the deuterium nucleus, the nuclear spin-spin tensor, and the spin-rotation tensor were evaluated from the hyperfine components of the radiofrequency spectra. The accuracy of these tensors was moderately improved over earlier measurements. From the H₂S spin-rotation tensor, the average paramagnetic shielding for the protons was found to be σ_av^p = ?104.84 (40) ppm. Combining this result with the proton NMR absolute chemical shift allowed the average diamagnetic shielding to be calculated as σ_av^d = 135.7 (5) ppm.     

Eine Hyperfeinstruktur-Analyse der Grundkonfigurationen 5d 8 6s 2 und 5d 9 6s des Pt-I Spektrums

The hyperfine structure of the ground configurations 5d ⁸ 6s ² and 5d ⁹ 6s of the stable Platin isotopes 194, 195, 196, 198 was analyzed. For the isotope 195 a complete set of the magnetic splitting constantsA is given. TheA constants of the levels 5d ⁸ 6s ^{2 3} P ₁ and¹ D ₂ were determined for the first time. From these data the electronic splitting constants a_{6 s}=l010(10) mK, a_{d 3/2}=57 (6) and a_{d 5/2}=27 (2) mK could be evaluated. The effect of core polarization is discussed and a fieldκ _cp=?5.6(1.0) a.u. per 5d-electron spin is found. Also the isotopic shift is determined and for the mean quadratic nuclear charge radius the valueΒδ <r ²>=0.095 (10) fm² is derived.     

Associated relaxation time and the correlation function for a tumor cell growth system subjected to color noises

The associated relaxation time Tc and the normalized correlation function C(s) for a tumor cell growth system subjected to color noises are investigated. Using the Novikov theorem and Fox approach, the steady probability distribution is obtained. Based on them, the expressions of Tc and C(s) are derived by means of projection operator method, in which the effects of the memory kernels of the correlation function are taken into account. Performing the numerical computations, it is found: (1) With the cross-correlation intensity |λ|, the additive noise intensity α and the multiplicative noise self-correlation time τ₁ increasing, the tumor cell numbers can be restrained; And the cross-correlation time τ₃, the multiplicative noise intensity D can induce the tumor cell numbers increasing; However, the additive noise self-correlation time τ₂ cannot affect the tumor cell numbers; The relaxation time Tc is a stochastic resonant phenomenon, and the distribution curves exhibit a single-maximum structure with D increasing. (2) The cross-correlation strength λ weakens the related activity between two states of the tumor cell numbers at different time, and enhances the stability of the tumor cell growth system in the steady state; On the contrast, τ₁ and τ₃ enhance the related activity between two states at different time; However, τ₂ has no effect on the related activity between two states at different time.     

Level-Crossing-Experimente zur Untersuchung der Hyperfeinstruktur des 5d 2 D 5/2-Terms im Indium I-Spektrum

The resonance fluorescence of the transition 5d ² D _5/2?5p ² P _3/2 (λ=3256Å) in the In I-spectrum was observed as a function of an external magnetic field. From the level crossing signals the following values of the hyperfine constantsA andB of the 5d ² D _5/2-state were deduced: ¦A¦=148(8) Mc/sec·g _J/1.2 and ¦B/A¦≦0.3. The widths of the signals yielded the mean lifetimet=7.1 (6)·10^?9 sec · 1.2/g _J . From the shifts of the signals caused by a constant electric field parallel to the magnetic field the value of the Stark parameter ¦β¦=0.19(4) Mc/sec/(kV/cm)² ·g _J /1.2 and the sign of the ratioA/β<0 were determined. Calculations with Coulomb wave functions show that the Stark shifts of the electric field are mainly due to admixtures of the 6p ² P _3/2-state.