The oscillator representation and the stability of three-body Coulomb systems

Within nonrelativistic quantum mechanics the Wick-ordering method, called the oscillator representation, is suggested for calculating the energy spectrum for a wide class of potentials allowing the existence of a bound state. As test cases, anharmonic (V(r)=r ²) and screened Coulomb potentials are considered. In particular, the method is applied to three-body Coulomb systems to obtain the dependence of the bound-state energy on the masses and charges of the particles. The calculations of the bound-state energies for the moleculesH ^–=(pee),H ₂ ⁺ =(ppe), (e ^–e^–e⁺) and (pp), (dd), (dt) prove the accuracy of the zeroth approximation to be better than one per cent. For the three-body Coulomb system with charges +, –, – and arbitrary masses the region of stability is determined. For the systems (pe ^–C⁺), (A ⁺e^–e⁺), and (pB ^–e^–) the critical masses are calculated to beM _c=1.945m_e,M _A=4.350m_e andM _B=1.575m_e. It turns out that the system (pe ^–e⁺) is unstable.     

Recoil effect on multiplicity correlation

The kinematical constraint due to energymomentum conservation reduces the multiplicity correlation ine ⁺ e ^–-annihilation (recoil effect). The correction starts at the second order in the expansion in powers of [i.e.O(_s)]. TheO(_s) correction to the squared dispersionr ₂ of the scaled multiplicity distribution is evaluated. It is found so large that the truncated expansion is inadequate at current energies. An evaluation without the expansion gives a reduced correction, with which the prediction remains positive down to low energies. The recoil effect makes the prediction closer to the experimental data.     

Angular correlation of photons ine + e − collision in QED: Planar processes

The angular correlation for two monochromatic photons produced ine ⁺ e ^– collision has been calculated to lowest order in the fine-structure constant in QED for planar processes. The angular correlation is defined as the average of the cosine of the angle between the directions of momenta of the two photons. This is done by computing, in the process, thee ⁺ e ^–-spin-momentum-averaged,-polarization-averaged conditional probability. In particular, we learn that for energies of the photons above a certain critical value, the angular correlation is strictly positive, for planar processes, indicating that the photons tend to travel in the same direction in a statistical sense for such processes.On sabbatical leave from Royal Military College, Kingston, Ontario, K7K 5LO, Canada.     

Production of hard photons in electron-positron annihilation into hadrons

Frequency of emission of prompt, hard photons radiated by the fast-moving quarks (antiquarks) ine ^– e ⁺ annihilation into hadrons is estimated for the string model. The differential probability of emission of such photons is obtained from a sum rule which takes for the initial state of the emitter a classical trajectory. It is found that the string models are quite effective in production of hard photons (i.e., photons whose energies are substantial fractions of the energies of the initiale ^– e ⁺ pair) associated with production of hadrons. For 100 GeVe ⁺ e ^– initial energy the frequency of emission,v, of 10 GeV<><40gev photons=" is=" estimated=" to=" be=">^–4v<>^–3.Supported in part by the Polish Ministry of Education, Grant DNS-P-04/215/90-2 and KBN Grant No 2-00054-91-01     

Solution of three-dimensional Faddeev equations for three-body Coulomb bound states

A new method of directly solving the three-dimensional Faddeev equations in the total-angular-momentum representation for the pure Coulomb bound-state problem is developed. The method is based on the tri-quintic Hermite spline expansion of the Faddeev components. The ground states of thee ^– e ^– e ⁺ system and thepp ^– mesic molecule are calculated.     

Polarization effects in the photoproduction of a fermion pair and a gamma quantum on nuclei

Integration of the cross section of the process+(Ze)(Ze)+₁+e^–+e⁺ over the angles of emission of the electron and positron was carried out, and the angular, energy, and spin dependences of the cross section were obtained. The cross section for photoproduction of a lepton-antilepton pair and a quantum on nuclei in the case where the emitted photon moves in the same direction as the incident quantum can exceed the Bethe-Heitler cross section for ordinary photoproduction of an e^–e⁺ pair. The probabilities of some electron and positron spin states are analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 106–110, June, 1972.In conclusion I express my thanks to A. A. Sokolov and A. I. lViukhtarov for valuable advice.     

Search for contact interactions in the reactionse+e?→l+l? ande+e?→γγ

Contact interactions are searched for using the differential cross sections for the reactionse ⁺ e ^–e ⁺ e ^–,e ⁺ e ^–µ ⁺ µ ^–,e ⁺ e ^{– + –} ande ⁺ e ^– measured at 12 energies around theZ peak and corresponding to about 20 pb^–1 of cumulated luminosity. Four-fermion contact term models assuming various chiralities of lepton currents are fitted to the lepton data and lower limits on the energy scale of such terms are set at 95% c.l. The limits vary in the range 0.9–4.7 TeV, depending on the model and on the lepton flavour. Theee contact terms are searched for assuming various chiralities. Limits on the energy scale between 79 and 130 GeV are extracted from the data. The results are compared and combined with those reported at lower energies.Deceased     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

Cantor spectrum and singular continuity for a hierarchical Hamiltonian

We study the spectrum of the HamiltonianH onl ₂() given by (H)(n)=(n+1)+(n–1)+V(n)(n) with the hierarchical (ultrametric) potentialV(2 ^m (2l+1))=(1–R ^m )/(1–R), corresponding to 1-, 2-, and 3-dimensional Coulomb potentials for 0<R<1,R=1 andR>1, respectively, in a suitably chosen valuation metric. We prove that the spectrum is a Cantor set and gaps open at the eigenvaluese _n (1)<e _n (2)<...<e _n (2 ⁿ –1) of the Dirichlet problemH=E, (0)=(2 ⁿ )=0,n1. In the gap opening ate _n (k) the integrated density of states takes on the valuek/2 ⁿ . The spectrum is purely singular continuous forR1 when the potential is unbounded, and the Lyapunov exponent vanishes in the spectrum. The spectrum is purely continuous forR<1 in (H)[–2, 2] and =0 here, but one cannot exclude the presence of eigenvalues near the border of the spectrum. We also propose an explicit formula for the Green's function.Work supported by the Fonds National Suisse de la Recherche Scientifique, Grant No. 2.042-0.86 (H.K. and R.L.) and 2.483-0.87 (A.S.)On leave from the Dipartimento di Fisica, Università degli Studi di Firenze, Largo E. Fermi 2, I-50125 Firenze, Italy     

Differential cross sections for in the CM energy range from 2.0 to 3.1 GeV

Exclusive production of proton-antiproton pairs by two photon scattering at CM energies between 2.0 GeV and 3.1 GeV has been measured with the TASSO detector at the e⁺e⁻ storage ring PETRA. The angular distribution is flat within the accepted CM angular range |cos Θ^*|0.7. The integrated cross section (|cos Θ^*|0.6) drops from about 4 nb at 2 GeV to less than 0.5 nb above 3 GeV. For the two-photon production of the η_c(2984) and its subsequent decay into proton-antiproton the upper limit

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(95% CL) is found.     

Mixing of toponium and Z° boson in elastic e+ − annihilation

If toponium with a mass close to the mass of a Z meson exists, it could be studied on the basis of the interference pattern which would be produced in the differential cross section for elastic e⁺e^– annihilation with unpolarized initial beams. The energy and angular dependence of the quantity which determines the relative contribution of vector toponium to the differential cross section for the process e⁺e^– e⁺e^– has been studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika,No. 10, pp. 38–42, October, 1988.     

R andRτ ratios at the five-loop level of perturbative QCD

We study perturbative QCD at the five-loop level. In particular we considerR = _tot(e ⁺ e ^– hadrons)/(e ⁺ e ^{– + –}) andR = ( v+hadrons)/( ev). We use our method to estimate the five-loop coefficients. As a result, we obtain _s (M _z ) = 0.1186(11) and _s (34 GeV) = 0.1396(16), which are accurate at the 1% level. We also findR = 3.8350(18), which is consistent withR and is accurate to 0.05%.     

Study of the process ee→ππγ in c.m. energy range 600–970 MeV at CMD-2

The cross section of the process e⁺e⁻→π⁰π⁰γ has been measured in the c.m. energy range 600–970 MeV with the CMD-2 detector. The following branching ratios have been determined:

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and

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. Evidence for the ρ⁰→f₀(600)γ decay has been obtained:

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. From a search for the process e⁺e⁻→ηπ⁰γ the following upper limit has been obtained: at 90% CL.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Photon-photon angular correlation ine +e− collision in QED

The angular correlation of two monochromatic photons produced ine ⁺e^– collision (annihilation), defined as the average of the cosine of the angle of separation between their outgoing momenta, is studied completely in momentum space to lowest order in the fine structure constant in QED. This is done from the expression of thee ⁺e^–-momentum-spin,-polarization-averaged conditional probability density for the angular distributions of the photons, given that the process has occurred. Although the density is in general nonvanishing for less than as well as greater than/2, the angular correlation is found to be strictly negative for all energies, indicating that the photons tend to travel in opposing directions in a statistical sense. The back-to-back motion, however, is very quickly unfavored as we move to higher energies.     

Precise calculation of coulomb binding energies of mesomolecules

The best variational energies obtained to date for the ground states of all -mesomolecules are presented. The results are of rather high accuracy and can serve as a theoretical basis for the experimental study of three-body systems. The energies of thee ^– e ⁺ e ^–,H^– and 1¹ S, 2³ S, 2³ P, 2³ P states ofHe are calculated using the same method.     

Muon lifetimes and weak interaction coupling constants

Improvements in determining muon lifetimes that are possible with the pulsed muon beam at the ISIS accelerator complex near Oxford, UK, are examined. The requirements of the standard model do not require an improvement in (µ⁺)[G_µ], which is fortunate as the low repetition rate of ISIS make such difficult. However, for stopping µ^± in liquid hydrogen the differences [(µ⁺) –(µ^–, observing decay e^–)] and [(µ^–, e^–) – (µ^–, observing capture n)] can be well improved to give the induced pseudo-scalar coupling constant,g _P, to ±2% and hence the first test of the chiral structure of the nucleon.On leave from Department of Physics, William & Mary, VA, USA.     

The183Re ground state dipole moment and nuclear spin-lattice relaxation of Re in Fe

The hyperfine interaction of the system¹⁸³Re(70d)Fe has been investigated with the NMR/ON technique. With the hyperfine field valueB _hf(ReFe)=–76.0(1.5) T the ground state magnetic moment was determined as: (5/2⁺,¹⁸³Re)=+3.12(6) _N. The field dependent nuclear spin-lattice relaxation time has been measured. The result for the high-field relaxation rateR _exp=1.65(5)·10^–15 T ²s K^–1 is explained in terms of indirect spin-wave interaction.     

Gluon and quark jets in deep-inelastic scattering of electrons by nucleons

The paper considers the formation of gluon and quark jets in the inelastic scattering of electrons by nucleons with large momentum transfers. It is assumed that these jets are created by the processes e^–+qe^–+q+g and e^–+ g e^–+q+q, where q is a quark and g is a gluon. The angular distributions of gluon and quark jets are calculated in the lowest order in the quark-gluon coupling constant. It is shown that after integration the processes e^–+qe^–+q+g and e^–+g e^–+q+¯q lead to violation of the scaling invariance of deep-inelastic scattering of electrons by nucleons.Translated from Izvestiya Vysshkikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 68–73, September, 1981.     

Spatial distribution of albedo particles on altitudes ∼500 km

Spatial distributions of energetic charged particles, neutrons and gamma rays at altitude 500 km (below the radiation belts of the Earth), obtained by the measurements of two apparatuses on board the Intercosmos-17 satellite, are presented. The latitudinal dependences, [i.e. the variation of flux with vertical cut-off rigidity of the measurement point], for neutrons (E _n = 1 –30 MeV), gamma rays (E =0·15–6 MeV), secondary electrons (E _e > 100 MeV) and for primary protons coming from the west and the east, respectively, are given. The main characteristic, the ratioN _p/N _e of the counting rate of the particles in the polar regionN _p(R_vert< <0·1 GeV/c) and on the equatorN _e(R_vert > 16 GeV/c), is obtained for the various types of particles. This value is 10 for neutrons, 3.7 for gamma rays, 1·8 for electrons, 11 for protons in westward direction, 10 for protons in eastward direction. The latitude profile of neutrons and gamma rays is in a good agreement with calculations assuming their production by nuclear reactions of primary cosmic rays with nuclei of the atmosphere. The weakening of rigidity dependence of protons coming from east in comparison with those coming from the west, is interpreted as the cause of additional proton albedo flux. The equality of albedo electron fluxes (E_e = 100–3500 MeV) from these directions is observed. With the use of the shadowing effect the obtained data on electron-positron component are consistent with the flux of albedo positrons (E_e + > 3·5 GeV) of the value (0·5±0·2) m^–2. s^–1. ster^–1. The possibility of abundance of albedo positrons above electrons at these altitudes for the energy intervalE=0·2÷0·3 GeV is indicated.