Variation of the local field through the liquid-vapour interface

We derive an integral equation for the self-consistent local field E^loc(z) within an inhomogeneous non-polar fluid, with particular application to the liquid-vapour interface. Approximate solutions are given for the cases of induced atomic dipoles oriented perpendicular and parallel to the interface. For the perpendicular case we relate the average field to the local field and thus obtain an equation for the static dielectric constant ?(z) in terms of the density profile n(z). The departures of the local field from Lorentz form $\text{E}{}^{\mathrm{<mtext>ext</mtext>}}\text{/(1 + (}\text{8}\text{3}\text{)παn(z))}$ and of the dielectric constant from the Clausius-Mossotti form ($\text{1 + (}\text{8}\text{3}\text{)πan(z))/(1 ? (}\text{4}\text{3}\text{)παn(z))}$ are shown to be small. For the parallel case we discuss fringing of the external field and show that the dipoles align themselves with the average field, not the external field. The departure of the local field from $\text{E}{}^{\mathrm{<mtext>ave</mtext>}}\text{/(1 ? (}\text{4}\text{3}\text{παn(z))}$ is shown to be small.     

New form of dynamics and current algebra

We study a new form of dynamical system, in which the commutation relations for the dynamical variables of a quantized field are defined on a “lightlike surface $\text{τ≡}\text{(t+z)}\text{2}\text{=0}$ rather than at one instant of time t = 0. We clarify the physical implications of the use of the new variables x¹ = x, x² = y, $\text{x}{}^{\mathrm{+}}\text{=}\text{(t+z)}\text{2}\text{, x}{}^{\mathrm{?}}\text{=}\text{(t?z)}\text{2}$ and explore its significance as a new form of relativistic dynamics, which holds in any Lorentz frame but not in the so-called “infinite momentum frame.” Using the quark model, we build up a new algebra of currents, in which the current commutators are defined at equal τ. The sum rules and other results of the usual current algebra can be obtained without taking the unjustifiable limit of infinite momentum. In particular, we obtain the Gell-Mann-Okubo mass formulas in quadratic form for both mesons and baryons without the trouble due to momentum dependence. We derive the reduction formula and find the physical high energy limit (not the Bjorken limit) of an amplitude is determined by the equal τ commutator.     

Muon capture in atoms,crystals and molecules

The slowing down and capture of negative muons in solids is discussed on the basis of classical equations of motion where the energy dissipation is described in terms of frictional forces. Transport equations determining the energy distribution of the muons in the target are formulated and solved for various models. Using a statistical model of the atom it is shown that the muons are captured typically at energies of a few tens of electron volts, that the angular momentum distribution of the muons at capture is almost statistical, and that this distribution is not expected to be qualitatively changed by the subsequent cascade to the tightly bound orbits. In mixtures of atoms with atomic numbers Z₁ and Z₂ the capture ratio is to a good approximation proportional to the atomic concentration and, in the statistical model, proportional to $\text{(}\text{Z}{}_1\text{Z}{}_2\text{)}{}^{\mathrm{<mtext>7</mtext><mtext>6</mtext>}}$. Calculations are also performed with more accurate atomic models, and it is shown that capture ratios as well as angular momentum distributions are influenced by the ionicity of the atomic bonds and the atomic shell structure. No systematic study of these effects has been made but the few results obtained seem to be in reasonable agreement with experiments.     

Like-sign dimuon events produced in narrow-band neutrino and antineutrino beams

Forty seven events of the type v + Fe → μ^? + μ^? + X and nine events of the type $\text{v}\text{+}\text{Fe}\text{→ μ}{}^{\mathrm{+}}\text{+ μ}{}^{\mathrm{+}}\text{+}\text{X}$ have been observed, and zero events with like-sign muons of the opposite sign. Most of the observed events can be attributed to the background of normal charged current events, in which one of the pions or kaons of the hadron shower decays, and so produces a second muon. The remaining events correspond to rates of the order of (3 ± 2) × 10^?4 of those for charged current events. They may very well be due to the hadronic production of a charm-anticharm pair, with subsequent decay of one member of the pair. The observed rates correspond to charm-anticharm pair production in 0.5–1% of the hadron showers. No evidence can be found for a lepton-cascade origin of the observed events.     

Measurements of the polarization of the 2p and 1s states in muonic atoms and the helicity of the muon in pion decay

We have measured the polarization of the 2p and 1s states in muonic selenium (amorphous and metallic modifications), cadmium, palladium and iodine, in order to study the depolarization of muons in the cascading process and to measure the helicity of the μ^?. In the cases of cadmium, palladium and amorphous selenium good agreement between the measurements and cascade calculations is found. There is an unexpected depolarization of the 2p_{$\text{1}\text{2}$} state in metallic selenium. The helicity of the muon after the pion decay was measured to h_μ^? = + 0.99 ± 0.16.     

Experimental detection and investigation of muon catalyzed fusion of deuterium and tritium

Measurement of the neutron yield of the reaction $\text{dt}\text{μ →}{}^4\text{He}\text{+ μ}{}^{\mathrm{?}}\text{+ 17.6}\text{MeV}$, induced by negative muons in a mixture of gaseous D₂ and T₂, has shown that the rate of muon transfer from deuterium to tritium is λ_dt = (2.7 ± 0.9) × 10⁸s^?1 and that the lower limit of the formation rate of dt_μ molecules is λ_dtμ > 10⁸s^?1.     

Evidence for heavy leptons from anomalous μe production in e+e− annihilation

Events of the type $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→μ}{}^{\mathrm{\pm }}\text{+e}{}^{\mathrm{?}}\text{+}\text{“nothing”}$ have been observed in the magnetic detector PLUTO at the storage ring DORIS at DESY. The data support the hypothesis of the pair production of heavy leptons, and allow to determine decay parameters. Decay rates into muons and electrons are equal within error, and argue for a new lepton number of the heavy lepton.     

Relativistic effect on magnetic moments of negative muons bound to high-Z nuclei

The g factors of the negative muons bound to Zn, Cd, and Pb nuclei have been determined. The observed values after the corrections for the internal fields have shown substantial deviations from the free-muon g factor: $\text{(g}{}_{\mathrm{<mtext>free</mtext>}}\text{-g)}\text{g}{}_{\mathrm{<mtext>free</mtext>}}$ is (1.3±0.6)% for Zn, (2.2±1.4) % for Cd, and (5.0±2.2)% for Pb. These shifts are in good agreement with the relativistic binding corrections for finite-size nuclei calculated by Ford et al.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

Separable expansions of thet-matrix

A recent result of Osborn on the non-convergence of separable expansions of the t-matrix $\text{(}\text{p}\text{,}\text{p}\text{′;z)}$ is discussed. It is shown that the theoretical difficulties arise from large values of $\text{p}$ and $\text{p}\text{′}$, and cause no difficulties in practical situations.     

Critical scaling function for long-range interactions to order 1/n

A universal scaling function of the order-parameter correlation function for an n-vector system in d dimensions, with long-range interactions $\text{～1/z.sfnc}\text{r}\text{z.sfnc}{}^{\mathrm{d+\sigma }}$, is discussed on the basis of explicit zero-field calculations to order 1/n, for T?T_c and σ<d<2σ.     

Muon capture by hydrogen and 3He

We present a new calculation of the capture rates, polarizations and asymmetry parameters of the final nucleus in the capture of muons by any $\text{spin}\text{-}\text{1}\text{2}\text{,}\text{isospin}\text{-}\text{1}\text{2}$ nucleus in the non-breakup channel. We treat nuclei as elementary particles and give explicitly the transition amplitude for any spin configuration. We apply our formulae to hydrogen and ³He, obtaining agreement with the experimental data.     

Scaling violation favouring high multiplicity events at 540 GeV CMS energy

New data are presented on the charged multiplicity distribution for non single-diffractive events produced in pp? interactions at a CM energy $\text{s}\text{= 540}\text{GeV}$. The distribution in the full pseudorapidity range is compared with data from the ISR. Using the scaling variable $\text{z =}\text{n}\text{〈n〉}$ a change of shape is observed. The effect is manifested as an increase from 2% to 6% in the proportion of high multiplicity (z > 2) events. For the central pseudorapidity range, |η| ? 1.5, scaling is approximately valid up to $\text{s}\text{= 540}\text{GeV}$.     

Upper limits on D0-D0 mixing and BB production from muon-nucleon scattering

In deep inelastic interactions of 200 GeV muons with a carbon target, we have found 17 events of the type μ^±N→μ^±μ^?μ^?X (“wrong-sign” dimuons). We derive upper limits of 1.2% (90% CL) on $\text{D}{}^0\text{-}\text{D}{}^0$ transitions (mixing) or, alternatively, of 9 pb (90% CL) cross section for $\text{B}\text{B}$ pair production as possible sources of such events.     

Inclusive muon production reactions as a test of neutral currents

With right and left handed polarized muons scattering on an unpolarized target we discuss possible asymmetries of inclusive cross sections induced by neutral weak currents. Using general positivity arguments we derive rigorous upper bounds to the asymmetries. Numerical estimates of the bounds are already possible if use is made of the branching ratios NC/CC)_ν, $\text{v}$ observed in the CERN Gargamelle bubble chamber. Upper and lower bounds to the asymmetries, specific to the Weinberg-Salam model, are also discussed.     

An equation of state of the Ising systems

In the framework of the spin operators diagram technique the method of taking into account the correlation effects in magnetic system based on the idea of $\text{1}\text{z}$ expansion (z is the number of the nearest neighbours) is proposed. An equation of state of 3-dimensional Ising systems with the arbitrary spin values S in the first order in $\text{1}\text{z}$ is presented which considerably improves the mean field theory (being the zeroth order approximation). For various lattices the calculated values of Tc coinside within 1% with the results of the high-temperature expansions.     

Searching for the spin-0 leptons of supersymmetry

The production and subsequent decay of spin-0 electrons and muons in e⁺e^? annihilation leads to distinctive noncoplanar e⁺e^? or μ⁺μ^? production, with missing energy carried away by photinos or goldstinos. We give the cross section predicted by supersymmetry for creating pairs of these new spin-0 particles. Present e⁺e^? annihilation experiments imply that their masses must be larger than $\text{3}\text{1}\text{2}\text{GeV}\text{/c}{}^2$, and in the near future PETRA experiments will either observe them or raise this limit to ～15 GeV/c².     

Electromagnetic effects in the production of dimuons at large transverse momentum

The effects of single-photon corrections to the simple Drell-Yan mechanism $\text{(}\text{q}\text{q}\text{→ γ}{}^1\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{)}$ are studied for massive dimuons at large transverse momentum in the processes $\text{π}{}^{\mathrm{?}}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X and}\text{p}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{X}$. It is found that single-photon emission by the muons constitutes an important correction to the effects of single-gluon emission by the quarks for very massive (M_μμ² ? m_μ²) muon pairs.Interference of the amplitude for photon emission from the muons with that for radiation from the quarks generates an asymmetry in the muon angular distribution. The forward-backward asymmetry is studied in detail as a function of pair mass and transverse momentum.     

Quantum theory of longitudinal dielectric response properties of a two-dimensional plasma in a magnetic field

An analysis of dynamic and nonlocal longitudinal dielectric response properties of a two-dimensional Landau-quantized plasma is carried out, using a thermodynamic Green's function formulation of the RPA with a two-dimensional thermal Green's function for electron propagation in a magnetic field developed in closed form. The longitudinal-electrostatic plasmon dispersion relation is discussed in the low wavenumber regime with nonlocal corrections, and Bernstein mode structure is studied for arbitrary wavenumber. All regimes of magnetic field strength and statistics are investigated. The class of integrals treated here should have broad applicability in other two-dimensional and finite slab plasma studies.The two-dimensional static shielding law in a magnetic field is analyzed for low wavenumber, and for large distances we find $\text{V(}\text{r}\text{) ～}\text{Q}\text{k}{}_0{}^2\text{r}{}^3$. The inverse screening length $\text{k}{}_0\text{=}\text{2πe}{}^2\text{??}\text{?ξ}$ (? = density, ξ = chemical potential) is evaluated in all regimes of magnetic field strength and all statistical regimes. k₀ exhibits violent DHVA oscillatory behavior in the degenerate zero-temperature case at higher field strengths, and the shielding is complete when $\text{ξ = r′}\text{l}\text{z.shtsls;}\text{ω}$, but there is no shielding when $\text{ξ ≠ r′}\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}$. A careful analysis confirms that there is no shielding at large distances in the degenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> ξ}$. Since shielding does persist in the nondegenerate quantum strong field limit $\text{l}\text{z.shtsls;}\text{ω}{}_{\mathrm{c}}\text{> KT}$, there should be a pronounced change in physical properties that depend on shielding if the system is driven through a high field statistical transition. (It should be noted that the static shielding law of semiclassical and classical models has no dependence on magnetic field in two dimensions, as in three dimensions.) Finally, we find that the zero field two-dimensional Freidel-Kohn “wiggle” static shielding phenomenon is destroyed by the dispersal of the zero field continuum of electron states into the discrete set of Landau-quantized orbitals due to the imposition of the magnetic field.