Ground state properties of the two impurity Anderson model in a 1/N expansion

The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/N. The dependence of this contribution on the interimpurity separation has an R^?1 or R^?3 envelope for distances smaller or larger than a length ν_F/T_A ranges from a value equal to the bare ?-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).     

An effective chiral Lagrangian model for the τ-decay into three charged pions

An effective chiral Lagrangian for the π-ρ-A ₁-system is used to study the decayτ ^±→ν _τπ⁺π^?π^±. Demanding that the hadronic current 〈0|J _μ|3π〉 agrees at the low energy limit with the one obtained from the corresponding pseudoscalar meson Lagrangian ?(π), an ambiguity linked to free parameters in ?(π,ρ,A ₁) is eliminated. The decay spectrum and branching ratio of τ^±→ν _τπ⁺π^?π^± are calculated as functions of theA ₁-mass and compared with the experimental results. So conclusions can be drawn concerning theA ₁-parameters, which are found to be $$m_{A_1 } = (1180 \pm 50)MeV;\Gamma _{A_1 } = (450 \pm 100)MeV.$$ . The mass-value is smaller than recently published ones. This is attributed to the effect of suppressed decay channels not seen in the experiments up to now. A contribution from direct, non-(ρ ⁰π^±) resonanceA ₁-decay is obtained, being about 15%.     

On the origin of like-sign dimuons in neutrino-nucleon and antineutrino-nucleon interactions

The so-called quasi-parton mechanism is considered taking into account nonperturbative effects in QCD and enabling one to explain like-sign dimuon production inv _μ( \(\bar v_\mu\) )N interactions. The rates of production cross sections of like-sign dimuons and trimuons of nonelectromagnetic origin to inclusive cross sections, as well as the average kinematical characteristics of the fast muon are obtained. The contribution of quasi-parton mechanism in γN, μN, π^± p,pp channels is considered. The energy distribution for slow muon inv _μ N interaction is received.     

Gluon-exchange currents: The nucleon axial-vector coupling constant and magnetic moments in bag models

Possible numerical importance of the two-body currents arising from exchange of one hard gluon between two constituent quarks is investigated by studying the evaluation of the nucleon axial-vector coupling constantg _A and magnetic moments μ _p ^tot , μ _n ^tot in the context of the MIT bag model. The double counting problem is resolved only to the extent that, in accord with the standard wisdom, hard gluons have nothing to do with the formation of bags (quark confinement) and so are not included in bag-model wave functions. For reasonable choices of the parameters, we find that (1) the contribution tog _A arising from one-gluon-exchange currents (OGEC) could account for the discrepancy between the observed value and the one-body bag-model prediction, and that (2) whereas the OGEC contribution to μ _n ^tot is negligible, the contribution to μ _p ^tot could be important but does not allow further understanding of the observed μ _p /μ _n ratio.     

Microwave spectrum and barrier to internal rotation of 1-chloro-2-butyne

Rotational transitions of the μ_a and μ_b type have been identified with microwave-microwave double resonance measurements for 1-chloro-2-butyne in the ground vibrational state. In the first excited state of the methyl torsion only μ_a-type transitions have been identified. The A-type transitions of the ground vibrational state can be described perfectly by the rigid rotor approximation with centrifugal corrections. Using the internal axis method the barrier to internal rotation was determined from the A,E splittings: V₃ = 10.05 ± 0.09 cm⁻¹. A model which allowed for geometry relaxation upon internal rotation was used to fit one set of parameters to the transition frequencies of both ground state and first excited torsional state. The sixfold contribution to the barrier was found to be negligible: V₆ = −0.4 ± 0.3 cm⁻¹.     

Mössbauer spectroscopic studies of spin crossover in tris(N, N′-dialkyldithiocarbamato) iron (III) complexes: effect of alkyl substituents

Spin crossover behavior in tris(N,N′-dialkyldithiocarbamato) iron(III) complexes with varying alkyl groups has been studied by variable temperature magnetic moment and Mössbauer spectral studies. All the complexes may be divided into three broad groups; high spin (μ _eff > 4.8 BM), intermediate spin (μ _eff?=?3.5???4.6 BM) and low spin (μ _eff?< 3.2 B.M). Room temperature (RT) Mössbauer spectra exhibit an asymmetric doublet resolved into two doublets corresponding to high and low spin states. Estimated % contributions of HS and LS states and calculated μ _eff were comparable with the experimentally determined values. It has been shown that some complexes undergo spin crossover, ⁶A₁g→²T₂g whereas others exhibit spin transitions ⁶A₁g →⁴T₁g or ⁴T₁g → ²T₂g. IR spectra show characteristic ν _(Fe???S) bands in the region 208–285 (HS) and 311–380 cm^???1 (LS). Nature of alkyl groups affects the spin state.     

Ten-dimensional Maxwell-Einstein supergravity,its currents,and the issue of its auxiliary fields

The d=10, N=1 Yang-Mills system is coupled to d=10, N=1 supergravity in a locally scale-invariant way. An analysis of the currents agrees with the Noether coupling results and reveals the existence of two ordinary axial and more low-dimension auxiliary fields. The coupling of the photon A_μ to antisymmetric tensors A_μν is consistent because the Maxwell transformation δA_μ=?_μΛ is extended to δA_μν=κΛF_μν.     

Diagnosis of OH radical by optical emission spectroscopy in a wire-plate bi-directional pulsed corona discharge

The emission spectrum of the molecule OH (A²Σ→X²Π, 0–0) during a high-voltage, bi-directional pulsed corona discharge consisting of a gas mixture of N₂ and H₂O in a wire-plate reactor has been successfully recorded under severe electromagnetic interference at atmospheric pressure. The relative vibrational populations and the vibrational temperature of N₂ (C, v′) have also been determined. Due to the difficulty of determining the exact overlapping spectral line shape function of the OH (A²Σ→X²Π, 0–0) and the Δv=+1 vibrational transition band of N₂ (C³Π_u→B³Π_g), a practicable Gaussian form is used for calculating the emission intensity of OH (A²Σ→X²Π, 0-0) and the Δv=+1 vibrational transition band of N₂ (C³Π_u→B³Π_g). The emission intensity of OH (A²Σ→X²Π, 0–0) has been evaluated with a satisfactory accuracy by subtracting the emission intensity of the Δv=+1 vibrational transition band of N₂ (C³Π_u→B³Π_g) from the overlapping spectra. The relative population of OH (A²Σ) has been obtained by the emission intensity of OH (A²Σ→X²Π, 0–0) and Einstein's transition probability. The influences of peak voltage, pulse repetition rate and O₂ flow rate on the relative population of OH (A²Σ) radicals have also been investigated. We found that the relative population of OH (A²Σ) rises with an increase in both the peak applied voltage and the pulse repetition rate. When oxygen is added to an N₂ and H₂O gas mixture, the relative population of OH (A²Σ) radicals decreases exponentially with an increase in added oxygen. The main physicochemical processes involved are also discussed in this paper.     

Intervalley transfers of hot electrons in silicon below 77 K

Intervalley rate transfer along 〈100〉 directions is deduced from conductivity measurements versus electric field for different impurity concentrations N_D-N_A at lattice temperatures T ? 77 K. The maximum rate transfer plotted versus T reaches 1 at T < 25 K and does not depend on N_D-N_D for N_D-N_A ? 2 × 10¹⁴crmcm^?3.     

π−A1 interference in πN → ϱN

An estimate of the A₁NN coupling is made using axial vector meson dominance of weak form factors, PCAC and current algebra. We use this to predict a vanishingly small polarisation due to unnatural parity exchanges in πN → ?N near the forward direction. In contrast, the contribution to πN → ωN of the Z (the J^PC = 2^?? exchange degenerate partner of the A₁) is found to be significant as indeed indicated by experiment.     

Gain studies on a uranine-damc dye mixture laser under nitrogen laser pumping

The radiative and Forster type of energy transfer processes in a dye mixture laser of 7-diethylamino-4-methyl coumarin (donor) and fluorescein disodium salt (acceptor) under nitrogen laser pumping were investigated. The Forster transfer rate calculated from the absorption and emission spectra of acceptor and donor is 1.3 × 10¹¹ liter mole^?1sec^?1. The gain of acceptor at 550 nm was measured for acceptor concentrations N_A from 10^?3M to 3 × 10^?3M for a fixed ratio F = 1 of donor to acceptor concentrations at different pump powers. The results agreed with the rate equation model proposed for the dye mixture laser. The radiative rate constant calculated from these results is 3.1 × 10¹⁰ liter mole^?1sec^?1. Numerical simulation of the rate equations showed that the acceptor reaches peak emission with a time lag of 3 ns with respect to the donor peak emission for F = 0.998, N_A = 10^?5M. This time lag decreases with increasing N_A and becomes zero for N_A = 10^?1M, F = 0.048.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.     

Muon Capture on Light Nuclei

This work investigates the muon capture reactions ²H(?? ^?, ?? _?? )nn and ³He(?? ^?, ?? _?? )³H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A = 2 and 3 nuclear wave functions are obtained from the Argonne v ₁₈ two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A?=?3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^?1 for A = 2 and 1488(9) s^?1 for A?=?3, where the uncertainties arise from the adopted fitting procedure.     

Spectrum and energy levels of Cr3+ ions and exchange-coupled Cr3+ pairs in lanthanum aluminate

From the optical spectra the energy levels of the Cr³⁺ ion in LaAlO₃ were determined. In the cubic field approximation we obtained with the parametersDq=1750cm^-1,B=661 cm^-1, andC=2908 cm^-1 a good agreement between the calculated and measured energies. For higher Cr³⁺ concentrations the fluorescence spectrum of the exchange-coupled first nearest (1N) Cr³⁺ pairs was separated from the vibronic fluorescence spectrum of the single ions by selective excitation. From the experimental data the energy level scheme of the 1N pairs is constructed for the states ¦⁴ A ₂·⁴ A ₂〉 and ¦⁴ A ₂·² E〉. In the ground state the pairs are ordered antiferromagnetically due to an isotropic exchange interaction with an exchange integralJ=(?68 ± 1) cm^-1. From the fluorescence decay the intrinsic lifetimes of the fluorescent states of the single ions, the 1N and the 2N pairs were determined to be equal to (86± 4) msec, (1.75± 0.25) msec, and (31 ± 5) msec respectively. The fluorescence decay shows an energy transfer between the single ions and the pairs.     

Strong coupling 1/N c expansion in the gluonic sector of lattice quantum chromodynamics

The vacuum state of gluonic quantum chromodynamics on the lattice is determined up to fifth order in a 1/N _c expansion (N _c=number of colours). The vacuum expectation value of the gluon field squaredF _aμvF _a ^μv is deduced. The quark-antiquark and gluon-gluon potential is calculated in the same limit up to the 1/N _c ³ order.     

Diffractive production of vector mesons in lepton-nucleon reactions

We calculate cross sections for the production of vector mesons V in reactions if ? + N → ?' + V + N, ?, ?' = ν, e, μ, taking into account all presently known information from electroproduction of ?'s. This leads to considerable differences in results from previous calculations, often more than an order of magnitude. The results for the ? are then largely a translation of electroproduction data into ν predictions and they will provide a direct test of the relation of weak and electromagnetic currents. The y or Q² distributions for the ? are instructive. The prediction for the A₁ provides a direct test of the existence of the A₁ and of whether vector and axial vector currents materialize into particles in the same way. The detection of a B meson would provide direct evidence for second-class currents and a measurement of their strength. We estimate all F¹ production will account for at most 2% of the total ν cross section at FNAL energies, which must be multiplied by the muon semi-leptonic branching ratio (and possibly a factor of 2 for an axial vector F¹) to calculate its contribution to the dimuon event rate.     

New relations between ℓN-scattering cross sections and neutral current parameters

New relations which connect cross sections with neutral current parameters have been obtained in deep inelastic and (quasi-)elastic _v ^(?) N-,e ^±(μ^±)N-scattering; the relations are independent of the structure functions and formfactors of the nucleon. A known example is the Paschos-Wolfenstein relation in _v ^(?) N-scattering. The relations have been obtained with allowance for the contribution of the extraZ′-boson which makes it possible to use them both for extractions of the Standard Model parameters (ρ, sin²θ _w ) and for the search for some manifestations of new physics.     

Symmetry-restoring interactions for Kπ = 1+ isovector vibrations

The low-lying isovector 1⁺ states are studied by a symmetry-restoring RPA approach in some rare-earth nuclei. A new velocity-dependent residual interaction is proposed in order to restore the rotational invariance of the hamiltonian in the quasiparticle random-phase approximation with an axially-symmetric Woods-Saxon potential. A new quadrupole interaction is introduced with a self-consistently determined coupling strength. Calculations for six rare-earth nuclei (¹⁵⁴Sm, ^156,158Gd,¹⁶⁴Dy,¹⁶⁸Er,¹⁷⁴Yb) show a good agreement with the experimental energies and B(M1) values. The M1 transitions, corresponding to the experimental strong magnetic dipole states, have in all apart from one case a predominant orbital contribution. The largest orbital contribution (90%) is found in ¹⁵⁴Sm. About half of the low-energy (E < 5MeV, B(M1)↑>0.1μ_N²) states in each nucleus have an orbital character with a (10–40)% spin admixture. The M1 strength is concentrated in the region 2–9 MeV with a maximum around 5 MeV and corresponds to ΔN_osc = 0 transitions.     

“Crystal fields” for magnetic ions in metals from itinerant electrons

The interaction of conduction electrons with host ions are shown to give rise to “crystal fields”, V_C, which act on the magnetic ion in some dilute magnetic alloys. Crystal fields, V_N, arising directly from ions neighbouring the magnetic ion have been compared with V_C to show that the overall crystal field splitting from all 3d magnetic ions in axial symmetries is enhanced by the p-like character of V_C. A⁰₄〈r⁴〉 from V_N is also increased by the d-component of V_C. The angular properties of itinerant electron states give rise to the above results. For all rare-earth ions in fcc symmetry the radial and angular components of conduction-electron states with mainly d, but also f character, are shown to give rise to a reversal in sign of A⁰₄〈r⁴〉 from V_N. A⁰₆〈r⁶〉 is enhanced by the f component of the conduction electrons.     

Measurement of the average polarization of12B in the polarized-muon capture by12C: Magnitude of the induced pseudoscalar form factor

The average polarization of the nucleus¹²B (bound state) produced in the polarized-muon capture reaction¹²C(μ ^?,v _μ )¹²B was measured by the muon spin resonance method in a pulsed muon beam. The polarization of¹²B was maintained completely under a magnetic field of 3 kG in a Grafoil target. After the observed result was corrected for the contribution from the excited states of¹²B, P_av (ground state) was deduced to be 0.462±0.053. This result yieldsg _P /g _A =10.1 _?2.6 ^+2.4 , which is almost consistent with the PCAC prediction.