Step algebras of semi-simple subalgebras of Lie algebras

For each pair (G,K) where G is a complex finite-dimensional Lie algebra and K a semi-simple subalgebra of G, we construct an associative algebra (step algebra) $\text{Y}$ (G,K) and a homomorphism i_*: $\text{Y}$ (G,K)→E(G) is the enveloping algebra of G. $\text{Y}$ (G,K) has the following properties: (1) If V is any G-module and x ? V a K-maximal vector, then sx = i_* (s)x is K-maximal for any s ? $\text{Y}$ (G,K); (2) If V is irreducible and a certain simple criteria is fulfilled, then any K-maximal vector can be written in the form sx_m, s ? $\text{Y}$ (G,K), where x_m is some fixed K-maximal vector. Because of these properties $\text{Y}$ (G,K) has great practical value when constructing irreducible representations of Lie algebras in a form which makes the reduction with respect to a semi-simple subalgebra explicit.     

Momentum transfer distributions of some diffractive enhancements in K−p interactions at 14.3 GeV/c

We discuss the structure of the momentum transfer distributions for the diffractive dissociation processes p → nπ⁺, p → Δ⁺⁺π^? and $\text{K}{}^{\mathrm{?}}\text{→}\text{K}{}_{890}{}^{10}\text{π}{}^{\mathrm{?}}$. In the near-threshold mass region a clear break of slope is found around t′KK ～ 0.25 GeV² for the two baryonic channels, whereas no comparable structure is seen for the mesonic system. The $\text{K}\text{→}\text{K}{}^1\text{π}$ differential cross section exhibits a nearly exponential behaviour up to t′_pp ～ 0.6 GeV², falling over three orders of magnitude. The slope variations and breaks are strongly correlated both to the mass region considered and to the decay angle of the fragmentation system.     

Depolarization in proton inclusive inelastic scattering and in the (d,p) reaction on medium-weight nuclei

The energy-averaged depolarization parameter K_y^y′ has been measured for the inelastic scattering of 18 MeV protons from ⁵⁴Fe, ⁶³Cu and ⁹²Mo at 45°, 90° and 135°, and for 14.35 MeV protons from ⁶³Cu at 45° and 135°. In all cases K_y^y′ varies from approximately unity for scattering with low energy loss to approximately zero for inelastic scattering to high excitation energies. The change from one of these values to the other occurs over a region ≈ 6 MeV wide centered at about 5 MeV excitation. A simple two-component model fits both the K_y^y′ and inelastic crosssection data. K_y^y′ has also been measured for the ⁵⁴Fe($\text{d}$, $\text{p}$)Fe reaction with 16 MeV deuterons incident. Here K_y^y′ changes from approximately the maximum possible value, $\text{2}\text{3}$, to about zero in a 6 MeV region centered at roughly 13 MeV excitation. The ($\text{d}$,$\text{p}$) data can be fitted by an extension of the model used for the proton scattering data.     

Observation of a KK enhancement at 1.85 GeV in the reaction K−p → KKΛ at 8.25 GeV/c

In a high statistics $\text{(}\text{～150 eV}\text{μb}\text{)}$ bubble chamber experiment on K^?p interactions at 8.25 $\text{GeV}\text{c}$, the study of the reaction K^?p → KKΛ provides evidence for an enhancement in the KK system with a mass of (1850 ± 10) MeV and a width of (80_?30⁺⁴⁰) MeV. Its possible identification with the missing isosinglet of the 3^? nonet is discussed. A K¹$\text{K}$ decay mode is also observed.     

Polarization transfer in the deuteron break-up reaction at 56 MeV

The polarization transfer coefficients K^yy′ of the break-up spectra in the reactions ¹²C, ⁵⁸Ni, ²⁰⁹Bi($\text{d}$, $\text{p}$X) were measured at 56 MeV. In the forwardd angles (13.5° and 20.0°), the K_y^y′ data at the break-up peak are nearly equal to $\text{2}\text{3}$ (the spectator model prediction) and they decrease at both sides of the peak. The deviation due to the deuteron D-state is estimated, using PWBA and DWBA.     

Angular distribution of polarization transfer in 2H(d, p)3H

Measurements have been made of seven polarization transfer coefficients for the ²H($\text{d}$, $\text{p}$)³H reaction. The experiment used a polarized deuteron beam from the Los Alamos Scientific Laboratory Lamb-shift polarized ion source, a liquid-nitrogen cooled deuterium gas target, a magnetic quadrupole triplet for focusing the reaction protons and a helium filled polarimeter for simultaneously measuring the proton polarization along two transverse axes. Results have been obtained at 10 MeV and for lab angles of 15, 30, 45 and 60 degrees for the vector transfer coefficients K_x^x′, K_y^y′ and K_z^x′, and the tensor transfer coefficients K_xx^y′, K_yy^y′, K_zz^y′ and K_xz^y′.     

Rotational analyses and vibrational assignments of the 463- and 474-nm bands of NO2

The excitation spectrum of NO₂ was investigated in the blue region by using a Nd:YAG laser-pumped dye laser. The 463- and 474-nm bands of the ²B₂-²A₁ system were identified and analyzed using the simplification that occurs if the excitation spectrum is monitored at particular wavelengths. Band origins and rotational constants were obtained. Vibrational assignments have been given to these bands by comparing the Franck-Condon Factors calculated for the ²B₂-²A₁ system with the fluorescence intensities of bands going to different vibrational levels of the ground state. The vibrational assignments and molecular constants obtained in this work are (v′₁, v′₂, v′₃) = (3, 11, 0)ν₀(K′ = 0) = 21584.1, $\text{B}\text{= 0.405}$, and $\text{∥}\text{?}\text{′∥ = 0.05}\text{cm}{}^{\mathrm{?1}}$ for the 463-nm band; and (v′₁, v′₂, v′₃) = (2, 12, 0), ν₀(K′ = 1) = 21104.9, $\text{B}\text{= 0.408}$, and $\text{∥}\text{?}\text{′∥ = 0.03}\text{cm}{}^{\mathrm{?1}}$ for the 474-nm band.     

Rotational analysis and radiative lifetime measurement on the 2B1 (K′ = 0) excited state of NO2 with v′2 = 6, 7, 8, and 9

The rotational structure of the ²B₁ (K′ = 0) subbands of NO₂ with v′₂ = 6, 7, 8, and 9 were analyzed by means of the time-gated excitation spectrum. The excitation spectrum monitored at ν₂, 2ν₂, or 3ν₂ fluorescence band was fairly simplified in comparison to its corresponding absorption spectrum. The band origins and rotational constants are evaluated from the observed data: ν₀ = 20205.0 cm^?1, $\text{B}\text{′ = 0.374}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 6; ν₀ = 21104.4 cm^?1, $\text{B}\text{′ = 0.374}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 7; ν₀ = 22001.9 cm^?1, $\text{B}\text{′ = 0.375}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 8ν₀ = 22898.0 cm^?1, $\text{B}\text{′ = 0.375}\text{cm}{}^{\mathrm{?1}}$ for v′₂ = 9. The value of $\text{B}\text{′}$ extrapolated to v′ = 0 is 0.370 cm^?1. This value corresponds to the bond length of 1.19 Å. Fluorescence decays of these excited levels were also studied. Radiative lifetimes obtained by extrapolation to zero pressure from the $\text{1}\text{τ}\text{– P}$ plots were 25–40 μsec. The short-lived excited levels previously reported by some authors were not found.     

Microwave optical double resonance and continuous wave dye laser excitation spectroscopy of NO2: Rotational assignment of the K = 0−4 subbands of the 593 nm band

A rotational assignment of approximately 80 lines with K_a′ = 0, 1, 2, 3, and 4 has been made of the 593 nm ${}^2\text{A}{}_1\text{→}{}^2\text{B}{}_2$ band of NO₂ using cw dye laser excitation and microwave optical double-resonance spectroscopy. Rotational constants for the ²B₂ state were obtained as A = 8.52 cm^?1, B = 0.458 cm^?1, and C = 0.388 cm^?1. Spin splittings for the K_a′ = 0 excited state levels fit a simple symmetric top formula and give $\text{(?}{}_{\mathrm{bb}}\text{+ ?}{}_{\mathrm{cc}}\text{)}\text{2}\text{= ?0.0483}\text{cm}{}^{\mathrm{?1}}$. Spin splittings for K_a′ = 1 (N′ even) are irregular and are shown to change sign between N′ = 6 and 8. Assuming that the large inertial defect of 4.66 amu Ų arises solely from A, a structure for the ²B₂ state is obtained which gives $\text{r}\text{(NO) = 1.35}\text{A}\text{?}$ and an ONO angle of 105°. Alternatively, weighting the three rotational constants equally gives $\text{r = 1.29}\text{A}\text{?}$ and θ = 118°.     

Information on the dynamics of the reaction KN → K1N from KLN interactions

If $\text{K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{is a K}{}^1$ resonance decaying into K_S,L (the short- and long-lived kaon) and a neutral system S^o of pions, one can isolate the C-even and C-odd, crossed-channel contributions to $\text{KN → K}{}^1\text{N}$ by using the reactions $\text{K}{}_{\mathrm{L}}\text{N → K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{N}$ whether S^o is a C-eigenstate, or a mixture of C-even and C-odd states. Applications to the production of K¹(890) and the Q-meson are discussed, and simple numerical predictions made for Q_S,L production. Q-production data indicate approximate t-channel helicity conservation for the ω and P' exchanges at vertices involving a spin change, in similarity to the belief for the pomeron. Q_S,L production data can give information also on Q-decays.     

Resonance production in the reaction π±p→Ks0K±p at 30 and 50 GeV/c

The mass and momentum transfer spectra of the charged $\text{K}\text{K}$ system produced in the reaction π^±p→K_s⁰K^±p are analyzed. The data have been collected at the CERN SPS with the Geneva-Lausanne two-arm, non-magnetic spectrometer at 30 and 50 GeV/c incident momenta. The general features of the reactions at these energies and the results of partial-wave analyses of the two kaon system are presented.The channel is dominated by the diffractive production of even spin resonances. The spin 4 recurrence of the A₂(1320) is clearly observed at 2040 MeV (Γ=380 MeV. A new resonance is observed with a mass M=2450MeV and a width Γ=400 MeV; the quantum numbers of this state are found to be I^G(J^PC)=1^?(6++). The analysis also shows the decay of the decay of the meson ?′(1600) through the $\text{K}\text{K}$ channel at both energies.The production amplitudes are determined both as a function of the $\text{K}\text{K}$ effective mass and of the momentum transfer. Isoscalar natural parity exchange is dominant. The energy dependence between 10 and 50 GeV/c is shown to be well described by a Regge pole model based on the f-dominated pomeron hypothesis. We compare the production mechanisms of the 2⁺ resonances A₂(1320) and K¹(1430). Finally, we estimate the $\text{K}\text{K}$ branching ratios of the spin 4 A₂(2040) and spin 6 A₂(2450) resonances.     

A measurement of the branching ratios of the A2− meson produced in 3.9 GeV/cπ−ϱ interactions

We have measured the branching fractions of the A₂^? meson, produced in the reaction π^?p → pA₂^? at 3.9 GeV/c incident momentum. The rates for the ηπ and K$\text{K}$ modes relative to ?π are 0.211 ± 0.044 and 0.056 ± 0.014, respectively. The upper limit for the η′π mode is 0.056 at the 90% confidence level. We have also looked for an ωππ decay of the A₂^? and our data are consistent with a rate of 0.10 ± 0.05, relative to ?π.     

|ΔI| = 12 rule in non-leptonic weak interactions with Han-Nambu quarks

Gauge theories of weak and electromagnetic interactions involving Han-Nambu quarks are constructed with the following features: small $\text{K}{}_{\mathrm{<mtext>L</mtext>}}\text{→ μ}\text{μ}$ amplitude and K_L - K_S mass-splitting; a non-leptonic effective Lagrangian ΔY = ± 1 leading to the usual soft-pion theorems and obeying a fundamental $\text{|ΔI| =}\text{1}\text{2}$ rule, with corrections of order θ²_Cabibbo.     

Longitudinal polarization transfer in the T→p, →n)3He reaction

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.     

Variational calculations of realistic models of nuclear matter

We report variational calculations of nuclear matter with a semi-realistic Reid v₁₂ model, and a realistic v₁₄ model of the two-nucleon interaction operator. The v₁₄ model fits the available nucleon-nucleon scattering data up to 425 MeV lab energy, and has relatively weak L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions in addition to the standard central, tensor and ($\text{L}\text{·}\text{S}$). The L² and $\text{(}\text{L}\text{·}\text{S}\text{)}{}^2$ interactions are treated semiperturbatively; their contribution reduces the overbinding of nuclear matter. However, the equilibrium k_F = 1.7 fm^?1 and E₀ = ?17.5 MeV obtained with the v₁₄ model are both higher than their empirical values k_F = 1.33 fm^? and E₀ = ?16 MeV. We assume that the difference between the calculated and empirical E(ρ) is entirely due to three-nucleon interactions (TNI). The TNI contributions are phenomenologically added to the nuclear matter energy, and their parameters are adjusted to obtain the correct equilibrium energy, density and compressibility. The required TNI contributions appear to be of reasonable magnitude.     

On (πμ) atoms produced in K0L decay

The branching ratio for producing (πμ) atoms in K⁰_L decay is calculated. Using the approximate solution of the Bethe-Salpeter equation for the (πμ) atom, the S-matrix element of this process is written in a more precise form than that obtained intuitively. Furthermore, all corrections of $\text{O}\text{(α) (α =}\text{e}{}^2\text{4π}\text{)}$ are considered. As a result, the branching ratio may be used to determine the form factor ζ = f_?(0)/f₊(0) of K⁰_L.     

Semiconductor-metal transition in doped (CH)x: Thermoelectric power

Thermoelectric power studies of polyacetylene have been carried out as a function of dopant concentration and temperature. The thermopower of pure trans-(CH)_x is large $\text{(S =}\text{+850 μ V}\text{°K}\text{)}$ and positive consistent with p-type material. With iodine doping, (CHI_y)_x, the thermopower remains positive over the full range of concentration 0 < y < 0.22. The semiconductor-metal transition is clearly observed at n_c ? 3 mole %; S falls dramatically from $\text{S =}\text{+850 μ V}\text{°K}$ at y = 0.003 to $\text{S =}\text{+30 μ V}\text{°K}$ at y = 0.03. At higher concentrations, S remains nearly constant saturating at $\text{+18 μ V}\text{°K}$ in the heavily doped metallic polymer. Temperature dependences are consistent with metallic behavior at the highest dopant concentrations and hopping transport in the undoped and lightly doped polymer.     

s-State potts model on a Cayley tree

The Potts model is shown to exhibit a phase transition of continuous order on a Cayley tree. The leading nonanalytic part of the free energy ∣L∣ ^$\text{K}$_s involves a critical exponent $\text{K}$_s going from one to infinity as the coupling goes f rom infinity to K_BP, the Bethe-Peierls critical coupling.