Effect of Ps-phonon interaction on the momentum distribution of positronium atoms in a crystal

In single crystals, posttronium can exist both in the localized and delocalized states [1–8]. Delocalized positronium is revealed by peaks in the angular distribution in the annihilation of quanta (AD), which occupy positions corresponding to the projections of the reciprocal lattice vectors onto a direction determined by the setup. The peaks indicated show the Bloch states of positronium [1–3]. As the temperature increases, the fraction of delocalized positronium decreases, while the peaks stemming from it broaden (see [3–7]). The broadening of the momentum distribution n(k) of positronium atoms (compared to the Maxwellian distribution with the particle mass equal to the rest mass (m_o) of the Ps atom), as shown by Ikary [9], viewing the Ps atom as an exciton, can be explained as the decay of quasiparticle positronium states due to the Ps-phonon interaction.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 63–66, November, 1981.     

Analysis of positron diffusion data

In this paper we present and discuss experimental methods to determine the positron diffusion coefficient from slow positron beam measurements. We also evaluate the use of the annihilation line Doppler-broadening technique in positron diffusion measurements, as compared on the more commonly used method of positronium fraction. The effects of incomplete positron thermalization and uncertainties of the positron implantation profile at low-positron incident energies to the measured data are discussed. We apply the presented methods to the model case of A1(110) system in the temperature range from 20 to 500 K. This data shows that Doppler-broadening and positronium fraction measurements give consistent results for the positron diffusion coefficient in A1(110), where D₊(300 K) = 1.7(2) cm²/s with the temperature dependence D₊ T ^–0.62(3).     

Positron annihilation in free volume elements of polymer structures

Free volume effects are important for positronium formation, pickoff annihilation and chemical reactions. In order to make the method of positron annihilation an effective technique for quantitative studies of molecular solids, for example polymers, the relation between the intensity of the longlived component of lifetime distribution of positron annihilation and the number of defects (elementary free volumes) was considered. The analysis assumes selective trapping of positrons and positronium in the defects of ordered and disordered (crystalline and amorphous) sites, respectively, the sizes of nonhomogeneities are assumed to be lower than positron diffusion length. The results on positronium annihilation in porous poly(phenylene oxide) allow one to estimate nontrapped positronium diffusion coefficient which is equal to . The relation between the positronium lifetime and effective size of free volume for large pores (effective radius 1 nm) is considered. Experimental results were obtained using the CONTIN program; some comments on its application for calculations of size distribution of elementary free volumes in polymers are discussed.     

Positronium interactions with gases in pores of silicagels

Positronium interaction with O₂, NO, Cl₂ molecules in pores of silicagels has been investigated by the methods of lifetime and angular correlation. For silicagel with diameter of pores ≈100 Å it was obtained that the rate constant of positronium conversion on oxygen was (2.4±0.2)10⁷ sec^?1 atm^?1 and on nitrogen oxide (2.6±0.2)10⁷ sec^?1 atm^?1. The rate constant of the positronium chemical reaction with Cl₂ was found to be ≈10^?11 sec^?1 atm^?1. The results of investigation of positronium interactions with oxygen in the gas phase, organic liquids, zeolites, liquid argon, and nitrogen are explained in terms of the formation of an excited complex PsO ₂ ^* . The decay of this complex to Ps and O₂ makes possible positronium conversion, and stabilization of the complex leads to annihilation in the bound state (chemical reaction). Study of positronium interaction with O₂ in silicagels (diameters of pores 100, 30 and 16 Å) confirms the assumption of the complex formation. The rates of chemical reaction and of conversion become equal for pores of diameter of 20 Å. The estimated lifetime of the PsO ₂ ^* complex is τ _k ? 10^?12 sec.     

Positron mobility in polyethylene in the 60–400 K temperature range

We have determined the positron mobility (₊) in polyethylene samples (67.2% crystalline, glass transition temperatureT _g=151 K) in the 64–400 K temperature range by Doppler shift measurements. A method based on the simulataneous observation of two lines from¹³³Ba and¹³⁷Cs radioactive sources together with the positron annihilation line, was employed to measure the Doppler shift of the 511 keV line as a function of the electric field applied to the samples. With this method we were able to measure at the same time the drift velocity of positrons and theS parameter. This parameter is very important in the interpretation of the mobility trend in samples where the positron states change with temperature. The positron mobility was corrected for positronium formation. ₊ at 64 K is 31.7±0.8 cm² V^–1 s^–1 then decreases up to 123 K, increases at 148 K and decreases again up to 170 K (₊=26.9±0.8 cm² V^–s^–). This sharp change in mobility is centred around the glass transition temperature of our samples. Then the mobility remains almost constant up to 230 K. From 250 K to 377 K, ₊ increases and reaches the value of 38.4±1.0 cm² V^–1s^–1. The corrected experimental data were well fitted by a simple model taking into account scattering and a thermally activated process (hopping mechanism).     

Positron-lithium scattering with the inclusion of positronium formation

Detailed studies have been made of elastic scattering and positronium formation in low energy collisions of positrons with lithium atoms for the two partial wavesl=0,1. For this system, as for all alkali atoms, the positronium formation channel is open even at zero positron energy. A two-channel version of the Kohn variational method is used with trial functions containing many variational parameters, and reasonably well converged results are obtained. The s-wave positronium formation cross section is infinite at zero positron energy but it then falls rapidly to become several orders of magnitude smaller than the elastic scattering cross section which has a maximum value of approximately 100 ₀ ² at a positron energy of 0.5 eV. For p-wave scattering the positronium formation cross section rises to a value of approximately 10 ₀ ² at an energy of 0.1 eV, with the elastic scattering cross section rising to a maximum of approximately 60 ₀ ² just below the first excitation threshold at 1.84 eV.     

Scattering of positronic atoms on optical phonons in ionic crystals. Positron thermalization

The time for positron thermalization in ionic crystals due to the interaction of positronic atoms with polarizational optical oscillations of the lattice is calculated. The positronic atom is considered as a dipole with moment p induced by the internal crystal field. The dipole moment is evaluated from the value of the positronic-atom deformation parameter determined from data on the magnetic quenching of positronium. For an NaCl crystal, p 1.91D. The positronium thermalization time in ionic, crystals (for the example of NaCl) is estimated at 10^–1 sec. After this time, not only ortho positronium but also para positronium reached total thermalization.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizida, No. 5, pp. 66–70, May, 1979.     

Kinetics of positron annihilation in ionic crystals

A kinetic scheme of decay of positron and positronium states for the general case — a real ionic crystal with point lattice defects and a developed surface — is examined. The properties of positron and positronium states in the volume of the crystal, positron and positronium color centers, and surface positron and positronium states, are analyzed. It is shown that all the available experimental data qualitatively confirm the conclusion of an annihilation mechanism based on the postulated kinetic scheme of positron annihilation in real ionic crystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 50–55, September, 1977.     

Spectroscopy of excited state positronium

Electric dipole transitions in the microwave range have been induced between the fine-structure levels of positronium in the excited staten=2. As an indication of the transitions, we used the increase in Lyman- radiation when the metastable 2³S₁-level is depopulated. The results for the transitions 2³S₁2³P_0,1,2 are ₀=18499.65±1.20±4.00 MHz, ₁=13012.42 ±0.65±1.54 MHz and ₂=8624.38±0.54±1.40 MHz. The first error is statistical and the second systematic. The precision of the present measurement has improved by a factor of 3, compared to previous data. Recent bound state QED-calculations have been extended to the orderR _t8 ⁴ln ^–1. The not yet completely calculated orderR _t8 ⁴ is estimated to contribute less than 1 MHz. Our experimental results are in good agreement with theory. By applying a weak magnetic field, we were able to observe the transition 2³S₁2¹P₁ which is strictly forbidden byC-invariance in zero field. Our result, corrected for Zeeman- and motional Starkeffect, is ₃=11180.0±5.0±4.0 MHz. An upper limit for theC-violating matrix element of MHz could be deduced. Our experiment used moderated slow positrons from the bremsstrahlung and pair production of a pulsed electron linear accelerator (TEPOS facility at the university of Giessen).     

Surface positron and positronium states in real ionic crystals

Positron annihilation has been used to examine the positron and positronium states at the surfaces of (100) and (110) faces of KCl and KCl-5% AgCl single crystals. The measured and theoretical parameters differ from the analogous bulk values; exposure of KCl to Ps atoms produces mainly A₊, F₊, and D₊ centers. It is shown that this method can be used to examine surface states and surface electron-density distributions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 76–81, January, 1978.     

Kinetics of Prompt Fluorescence Decay in Rubrene Films. Manifestations of the Migration of T Excitons

The kinetics of fast fluorescence decay in organic semiconductors due to the splitting of the excited singlet state S₁ into a pair of triplet (T) excitons is significantly influenced by the process of reverse TT annihilation. It is shown that a correct interpretation of this effect requires taking into account the stochastic migration of T excitons. A two-state model (TSM) is proposed for describing the effect of migration on the kinetics of TT annihilation and, thus, on the kinetics of the fission of the S₁ state. In the TSM, the migration effect is interpreted in terms of transitions between the [TT] state of the interacting excitons (at small T?T distances) and the [T + T] state of freely diffusing excitons (at large T?T distances). Within the framework of the TSM, an analytical expression for the fluorescence decay kinetics (FDK) \(I_{S_1 } (t)\) from the S₁ state is derived. This expression is used to describe the FDK measured in amorphous rubrene films in the absence of the magnetic field (B = 0) and in the magnetic field B = 8.1 kG. Adjusting the parameters of the model makes it possible to reproduce the experimentally measured FDK with good accuracy. An analysis of the theoretical FDK obtained revealed a significant contribution of T migration to \(I_{S_1 } (t)\), which manifests itself, in particular, in the characteristic dependence \(I_{S_1 } (t) \sim t^{ - 3/2}\) at long times.     

Dynamical selection rules from $p \bar p$ annihilation at restin three meson final states

The hadronic annihilation branching-ratios in quasi-two-body final states have been obtained from the observation of the reactions , at rest in hydrogen targets at different densities. The enhancement or suppression of specific hadronic channels connected to dynamical selection rules is observed in the production of different resonances both in protonium S and P-waves, systematically investigated for the first time. Besides the well known and enhancement from ³S₁ and ¹S₀ partial waves, the dominance of one isospin source in production, well established from S-waves, is confirmed also in P-waves (¹S₀, I = 0; ³S₁, I = 1; ¹P₁, I = 0; ³P₁, I = 0; ³P₂, I = 1). In addition, the experimental data clearly show a strong suppression of and final states from P-wave which has a remarkable coincidence with pattern production.Received: 4 February 2004, Published online: 5 May 2004     

Decay of the positronium molecule into a positronium atom and photons

Decays of the positronium molecule Ps₂ into para- or orthopositronium Ps in the ground state and photons are investigated. The differential probabilities of the decays are determined. The total probabilitiesw _2γ ^(Ps2) andw _3γ ^(Ps2) of Ps₂ annihilation with the production of two and three photons and positronium are calculated to be $$w_{2\gamma }^{(P_{S_2 } )} = 1.6 \cdot 10^{10} \sec ^{ - 1} ,w_{3\gamma }^{(P_{S_2 } )} = 0.43 \cdot 10^8 \sec ^{ - 1} $$ . The curve of the angular correlation of the γ rays on the decay of Ps₂ into two photons and parapositronium is studied. The width of this curve is Δ¦P¦=0.128 a.u. (¦P¦ is the total photon momentum), which corresponds to a deviation of the emission angle of the γ rays from π: θ ? 0.934 mrad. The maximum in the distribution of the photons with respect to the momenta ¦P¦ in the center of mass of the annihilating pair is attained at ¦P¦=0.175 a.u. The calculations were made on an M-222 computer, and their accuracy is determined by the choice of the wave function of the positronium molecule and the accuracy in the computer calculation of the integrals.     

Ultrahigh-resolution laser spectroscopy of the S1B2u ← S0Ag transition of perylene

A rotationally resolved ultrahigh-resolution fluorescence excitation spectrum of the S₁ ← S₀ transition of perylene has been observed using a collimated supersonic jet technique in conjunction with a single-mode UV laser. We assigned 1568 rotational lines of the band, and accurately determined the rotational constants. The obtained value of inertial defect was positive, accordingly, the perylene molecule is considered to be planar with D_2h symmetry. We determined the geometrical structure in the S₀ state by ab initio theoretical calculation at the RHF/6-311+G(d,p) level, which yielded rotational constant values approximately identical to those obtained experimentally. Zeeman broadening of each rotational line with the external magnetic field was negligibly small, and the mixing with the triplet state was shown to be very small. This evidence indicates that intersystem crossing (ISC) in the S₁¹B_2u state is very slow. The rate of internal conversion (IC) is also inferred to be small because the fluorescence quantum yield is high. The rotational constants of the S₁¹B_2u state were very similar to those of the S₀¹A_g state. The slow internal conversion (IC) at the S₁ zero-vibrational level is attributed to a small structural change upon electronic transition.     

Excited States of Magnesium Complexes of Porphin and Bacteriochlorin

Quantum-chemical calculations of magnesium complexes of porphin (D _4h , C _4v ) and bacteriochlorin (D _2h , C _2v ) have been carried out for three variants of Mg parameters used in the CNDO/S method. It is shown that the Mg parameters and z _Mg weakly influence the results of the calculations of these complexes in the excited S _i states localized on the macrocycles in contrast to the calculations for the S _i ^CT states. The G S _i ^CT transitions are transitions with intramolecular electron transfer (CT) from the macrocycles to Mg. The energies of the S _i ^CT states can be close to the energies of the B levels and differ by a value from 1600 to 6400 cm^–1 depending on the Mg parameters. A displacement of Mg (z _Mg) 0) from the midplane of the macrocycles and hydrogenation of the pyrrole rings decrease the energies of the lower G S _i ^CT transitions and enhance their CT character.     

Thermopower of spin glasses

We calculate the thermopowerS _d(T) of spin glasses on the basis of thesd exchange model with additional interactions between the impurity spins by means of time dependent perturbation theory. Similarly to the Kondo effect, the observed giant thermopower can only be explained if one also takes into account the spin independent interactionV between the magnetic impurities and the conduction electrons. We obtain a Kondo termS _d ⁽¹⁾ (T) (which reduces for vanishing spin interactions to the thermopower of Kondo systems) and in addition a resonance termS _d ⁽²⁾ (T) of opposite sign which vanishes for vanishing interactions. The superposition of both terms leads to an additional extremum of the total thermopower and to a change of sign at a temperatureT ₀ which depends on the Kondo temperature and on the magnetic excitations of the spin glass and therewith on the freezing temperatureT _f. We obtain at low temperatures for oscillating and relaxing spin glass modesS _d ⁽¹⁾ T² andS _d ⁽²⁾ T. At high temperaturesS _d ⁽¹⁾ (T) decreases as |lnT|^–3 andS _d ⁽²⁾ asT ^–1. A close relationship between the temperature dependent resistivity in Born approximation andS _d ⁽¹⁾ (T) is pointed out.SFB 125 Aachen-Jülich-Köln     

Four-baryon weak interactions with ΔS = 1 and SU (6) symmetry

Relations are found among the amplitudes for four-baryon processes with S = 1 under the assumption that the Lagrangian for s-wave weak interactions has the transformation properties of a component of the SU(6) 35-plet. In particular, it is found that the amplitudes for the¹S₀ ¹S₀ and³S₁ ³S₁ transitions for the p pn reaction are the same, within a sign.Translated from Izvestiya VUZ. Fizika, No. 10, pp. 70–77, October, 1969.     

On the annihilation rate of positronium in dense rare gases

The dependence of the positronium decay rate on the gas density is considered. It is known that the positronium can be localized in a dense gas with the formation of a cavity “bubble” around the positronium. It results in a significant delay of the annihilation. The paper containes the quantitative theory of this phenomenon. A comparison is made with the experimental data for He⁴, He³, Ne.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Quantum beats in the 3γ annihilation decay of Positronium observed by perturbed angular distribution

We have applied conventional Time Differential Perturbed Angular Correlation (TDPAC) method to observe the anisotropy oscillations in the 3γ annihilation decay of polarized Positronium in a weak magnetic field. The effect, as predicted theoretically and experimentally demonstrated by Barishevsky et al. [V.G. Barishevsky, O.N. Metelitsa, V.V. Tikhomirov, Oscillations of the positronium decay γ-quantum angular distribution in a magnetic field, J. Phys. B: At. Mol. Opt. Phys.22 (1989) 2835], is induced by the coherent admixture of the m = 0 states of ortho-Positronium (o-Ps) and para-Positronium (p-Ps) in interaction with the magnetic field.The following experimental characteristics are to be considered:

(i)

the oscillation frequency corresponds to the difference in energy of the Ps atom levels in magnetic field and is proportional with H²;

(ii)

in a fixed geometry the modulation depth (oscillations amplitude) depends on the mean positron polarization;

(iii)

privileged angles of the polarization vector, magnetic field and detectors are required for optimizing the observed oscillations amplitude.

The normalized difference spectrum function (R(t)) obtained from time spectra measured in vacuum and in different gaseous atmospheres (Ar, H₂, N₂) have the oscillations amplitude constant and we conclude that the Ps atoms are not fully thermalized over a time interval of about 400 ns.The R(t) functions obtained for o-Ps annihilation decays, in dry air or Ar-O mixture, have the oscillations amplitude time dependent due, probably, to the paramagnetism of the Oxygen molecules.