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.     

Behavior of a test body in a plane gravitational (gravity) wave

The motion of a test particle in a plane gravity wave characterized by the metricds ²=e ^y c ² dt ² –e ^y dx ² –dy ² –dz ². is considered. It is shown that, in the case of velocities smaller than the velocity of light, when and vary harmonically, the test particle will execute harmonic oscillations along the x, y, and z axes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 112–115, January, 1975.     

Approach to a theory for the masses of the electron,muon, and heavier charged leptons

The electron mass valuem=9.093 × 10^–28 g is shown to be obtainable from the QED self-energy formula amended to include gravitational selfenergy and restricted by the space-time equipartition lawm/n ₀=4/3. Held together by gravity, the electron has a radiusr _e =8Gm/9e ² c=2.588 × 10^–53 cm. An extension of the analysis yields the theoretical muon-electron mass ratio of 206.241 and predicts heavier charged leptons with mass values of 1.915 GeV, 15.67 GeV, and above.     

Photoproduction of and of high mass in ultra-peripheral Au + Au collisions at

We present the first measurement of photoproduction of J/ψ and of two-photon production of high-mass e⁺e⁻ pairs in electromagnetic (or ultra-peripheral) nucleus–nucleus interactions, using Au + Au data at . The events are tagged with forward neutrons emitted following Coulomb excitation of one or both Au nuclei. The event sample consists of 28 events with m_e⁺e⁻>2 GeV/c² with zero like-sign background. The measured cross sections at midrapidity of and for m_e⁺e⁻[2.0,2.8] GeV/c² have been compared and found to be consistent with models for photoproduction of J/ψ and QED based calculations of two-photon production of e⁺e⁻ pairs.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Imaginary-time path integral for a relativistic spinless particle in an electromagnetic field

A rigorous path integral representation of the solution of the Cauchy problem for the pure-imaginary-time Schrödinger equation _t (t, x)=–[H–mc ²](t,x) is established.H is the quantum Hamiltonian associated, via the Weyl correspondence, with the classical Hamiltonian [(cp–eA(x))²+m ² c ⁴]^1/2+e(x) of a relativistic spinless particle in an electromagnetic field. The problem is connected with a time homogeneous Lévy process.     

Trace norm convergence of exponential product formula

LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH K. We show the norm inequality (e^–rH/2 e^–rK e^–rH/2)^1/r forr > 0 and any symmetric norm . WhenH +K is essentially self-adjoint and e^–K is of trace class, we prove that (e^–rH/2e^–rK e^–rH/2)^1/r converges asr 0 to e^–(H+K) in the trace norm.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

Dilepton mass spectra in collisions at and the contribution from open charm

PHENIX has measured the electron–positron pair mass spectrum from 0 to 8 GeV/c² in p+p collisions at . The contributions from light meson decays to e⁺e⁻ pairs have been determined based on measurements of hadron production cross sections by PHENIX. Within the systematic uncertainty of 20% they account for all e⁺e⁻ pairs in the mass region below 1 GeV/c². The e⁺e⁻ pair yield remaining after subtracting these contributions is dominated by semileptonic decays of charmed hadrons correlated through flavor conservation. Using the spectral shape predicted by PYTHIA, we estimate the charm production cross section to be 544±39(stat)±142(syst)±200(model) μb, which is consistent with QCD calculations and measurements of single leptons by PHENIX.     

A solvable model exhibiting a glass-like transition

A nonlinear equation of motion of an overdamped oscillator exhibiting a glass-like transition at a critical coupling constant _c is presented and solved exactly. Below _c , in the fluid phase, the oscillator coordinatex(t) decays to zero, while above _c , in the amorphous phase, it decays to a nonzero infinite time limit. Near _c the motion is slowed down by a nonlinear feedback mechanism andx(t) decays exponentially to its long time limit with a relaxation time diverging as (1 – / _c )^–3/2 and (/ _c –1)^–1 for < _c and > _c respectively. At _c x(t) exhibits a power law decay proportional tot ^– with exponent -1/2.     

Study of the Β decay of6He with allowance for second-class currents and the antineutrino mass

The effects of the rest mass of the electron antineutrino are studied with allowance for the induced tensor form-factor F_c of the second-class current according to the Weinberg classification during the decay of the⁶He nucleus. We calculate the contribution of m and F_c to the electron-antineutron angular correlation coefficient A_e and the degree of longitudinal polarization P_e of the decay electrons. When m is nonzero, the coefficient A_e tends asymptotically to zero both at the beginning and endpoint of the spectrum, whether or not the second-class currents are taken into account. The series of qualitatively new experiments planned for the near future to measure the e- correlation for pure Gamow-Teller transitions (the⁶He nucleus could be a suitable nucleus here) with an accuracy of the order of 1% would allow the available estimate of the form-factor F_c to be improved substantially.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 62–67. September, 1989.     

Coordinate-dependent 3+1 formulation of the general relativity equations for a perfect fluid

This paper defines mass, momentum, and energy densities for a perfect fluid, and derives a coordinate-dependent 3+1 decomposition of the equation of motion in terms of a scalar potential c ² [(–g _g44) 1/2 –1] and a vector potentialA _i cg _4i /(–g ₄₄)^1/2. The momentum equation has the form of the Euler equation except there is an additional force proportional to the vector potential and the rate of change of kinetic energy per unit volume. The momentum and energy equations are integrated to obtain the equations previously derived for a particle. The momentum equation is solved for the total acceleration of a fluid element. The equations are exact and do not depend on the choice of coordinate system.     

A bag model calculation of the electroweaks→dγ loop

We consider the CP-conserving electroweak transitionssd. To include confinement effects below the charm scale, we perform the loop calculations within the bag model. According to the calculation, confinement effects are rather important and give amplitudes three orders of magnitude bigger than that obtained from the free quark loop, which is eG _F m _c ² /M _W ² . Moreover, the amplitude is of the same order of magintude as the perturbative two loop amplitude eG _{F s} ln(m _c /). For the decay mode ^{– –} we obtain a branching ratio 4.4·10^–5. Other radiative decays of strange baryons are known to be dominated by pole diagrams.     

Supersymmetric Box Contributions toe + e −→Z 0 h 0 ande + e −→A 0 h 0

Within the MSSM we calculate the electroweak 1-loop box contributions to the processese ⁺ e ^–Z ⁰ h ⁰ ande ⁺ e ^–Z ⁰ h ⁰. We present detailed results for c.m. energies and as well as for tan =2 and tan =50. The box contributions to the processe ⁺ e ^–Z ⁰ h ⁰ are, depending on and tan , of the order –2 to –20% and toe ⁺ e ^– A ⁰ h ⁰ of 2 to 10%.     

Processes of associated production of the Higgs boson with the Z boson in a superstrong magnetic field

We compute probabilities for the processes ee+Z+H, and e⁺+e^–Z+H in a superstrong magnetic field. It is shown that the magnetobremsstrahlung of the Higgs boson with the Z boson in the magnetic field Bs>B₀=m²/e=4.41·10¹³ G may be a relatively probable process, and that the superstrong magnetic field significantly influences the process e⁺+e^–Z+H, which is possible even in the absence of the field.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 104–108, January, 1991.The author thanks V. Ch. Zhukovskii and A. V. Borisov for discussions on the results of this work.     

Four-quark and hybrid mixing in the light-quark vector sector

The data one ⁺ e ^– annihilation are shown to be incompatible with an interpretation of the observed vector mesons as excitations. It is necessary to consider mixing with some system. Two specific models are considered: either four-quark states or hybrid states mixing with the conventional quark-antiquark excitations. Both models are compatible with the presente ⁺ e ^– annihilation data. It is possible to incorporate the 1.3 GeVJ ^PC =1^–– state seen by LASS in the channel in the four-quark model, but this is not possible with the hybrid model.     

Search for possible anapole and electric dipole moments of the proton on the basis of the pp ⇌ e+ e− annihilation reaction

Differential and total cross sections are found for the formation of an electron-positron pair during the annihilation of longitudinally polarized protons and antiprotons (pp e⁺ e^–) and for the inverse reaction (e⁺ e^- pp) in the single-photon approximation, account is taken of the anapole and electric dipole moments of the proton, which violate C, P, and T parity. Possible ways to determine the square moduli of the form factors for the anapole [G₁(q²)] and electric dipole [G₂(q²)] moments and to determine the relative phase of the form factors F_e(q²) and G₂(q²) [F_m(q²) and G₁(q²)] are pointed out. Estimates are found for ¦(G₁q²)¦² and ¦G₂(q²) ¦² with q² = –6.8 (GeV/c)².Translated from Izvestiya VUZ. Fizika, No. 8, pp. 59–65, August, 1970.The authors thank Professor A. A. Sokolov, Professor I. M. Ternov, and Yu. M. Loskutov for discussions of these results.     

Estimates for the efficient production of antihydrogen by lasers of very high intensities

Starting from the non-linear relativistic equations of motion for charged particles in the very high intensity fields of laser radiation, the maximum kinetic energy _kin of the resulting oscillation is derived exactly. In non-relativistic conditions _kin agrees with the well-known valuee ² E _v ²/(2m₀²|n|), showing a dependence on the rest massm ₀ of the particle. In the relativistic case, the mass dependence vanishes. The multipole radiation is calculated on the basis of Sommerfeld's formula for relativistic conditions. It is shown that this radiation is not important for oscillation energies up to =70m ₀ c ² for electrons in neodymium glass laser radiation and up to higher values for CO₂ lasers and for protons. With the limitationm ₀ c ² < _kin < , the formula for _kin is used to calculate the pair production (a) for singly oscillating particles in vacuum without collisions and (b) for plasmas with collisions. Taking into account the local increase of the effective electric laser field near the cut-off density due to the decrease of ¦n¦ (n is the complex refractive index), there is the possibility of efficient proton pair production at intensities of 10¹⁹ W cm^–2 for neodymium glass lasers and of 10¹⁷ W cm^–2 for CO₂ lasers, besides electron pair production.     

Critical currents of type ii superconductors in non-transversal magnetic fields

The force on flux lines near narrow defects elongated in the direction of the transport current is calculated. This force, together with the maximum interaction forcek _m on the central flux line element, gives the volume pinning forceF _p on the flux line lattice. The dependence ofk _m (and of the critical current densityj _c ) on the angle between the magnetic field and the transport current is calculated for different defect dimensions (with respect to the coherence length of the superconductor) and compared with the experimental results. We obtainj _c sin^–n , where 1n3 in dependence on the defect dimensions and on the angle interval. The possibility of testing theF _p k _m ² dependence of the statistical theory of pinning is proposed.     

The interpretation of the C metric. The charged case whene 2 ≤m 2

The charged C metric involves three parametersm, e andA representing mass, charge and acceleration respectively. Using a method developed in a previous paper, we show that whene ² m ² the metric may be interpreted in terms of two Reissner-Nordström particles, each of massm and with charges +e and –e, in accelerated motion and connected by a spring. The method depends on the fact that for certain regions of the coordinate space the charged C metric may be transformed into the Weyl form for a static axisymmetric system. In this form the horizons of the C metric become line sources. One of the regions leads to a Weyl metric with two line sources, one of finite length which corresponds to the outer horizon of a Reissner-Nordström particle and the other semi-infinite corresponding to a horizon associated with uniform accelerated motion. A further coordinate transformation leads to a metric valid for a larger region of space-time in which there are two charged particles in accelerated motion. WhenAm is small, the electromagnetic invariants approximate to those for the Born field for two accelerated charges in special relativity.