On the Determination of Spin-Parity of Elementary Particles Produced in Collisions of Polarized Particles

In this paper we adopt Peshkin's “maximum complexity method” for reactions 0 + 1/2 → j + s, γ + 0 → j + 0 with polarized initial particles. The produced particles undergo the decays s → 0 + 1/2, and j decays strongly into 0 + 0 + 0. Study of certain correlations in such processes allows to determine the spins of the produced particles. Because the spin of the X° (960) meson is not firmly established we apply the general results obtained to the reactions: K?p → X° Δ, πp → X°N^★, _γHe → X°He.     

Directional correlations in the decay of 1200y 166Ho

γγ-directional correlations have been measured between the ground state band transitions 6→4, 4→2 and 2→0 and the γ-rays depopulating the levels of the gamma vibrational band and the negative parity states of¹⁶⁶Er. Thereby angular momenta could be assigned to the latter states andM2/E1 multipole mixtures determined for the depopulating γ-transitions. TheE2/M1 mixing ratios were obtained for a series ofI _γ→I _g transitions up toI _γ=8⁺. These are used to investigate the angular momentum dependence of theE2/M1 admixtures.     

Rigorous spin tests from angular distribution of single two-body decays

We extend to the several-amplitude decays j→j₁+j₂, (j?j₁+j₂,j₁+j₂?2) the rigorous spin tests given by Doncel, Michel and Minnaert for the usual one-amplitude strong decays, in quadrupole and quadrupole-hexadecapole spaces. We also derive spin tests in dipole-quadrupole space for the parity violating decays $\text{j →}\text{1}\text{2}\text{0}\text{and}\text{j →}\text{1}\text{2}\text{1}\text{2}$.     

Exotic decays of the muon and heavy leptons in gauge theories

We have studied the decay ?₁ → ?₂ + γ for arbitrary like charged spin $\text{1}\text{2}$ leptons in a manner which is applicable to a large class of models. Our computations assume that this process is induced by one loop diagrams. When the leading effect is cancelled by a leptonic G.I.M. mechanism, we find an extremely large enhancement of O(M_W⁴/M_L⁴) in Λ(μ^?→e^?+e⁺e^?)/Λ(μ^?→e^?+γ) if the intermediate lepton is charged.     

Radiative decays of heavy vector mesons into paraquarkonia

The width for decays of the type 1^?→γ + 0^? is evaluated using the two gluon mechanism of QCD. In particular we compute Γ(Ψ → γ + η′), Γ(Ψ → γ + η) and Γ(? → γ + η_c). The first two are found to be in reasonable agreement with the experimental results, while the latter leads to a branching ratio of 2 × 10^?5.     

Finite-N fluctuation formulas for random matrices

For the Gaussian and Laguerre random matrix ensembles, the probability density function (p.d.f.) for the linear statistic Σ _j ^N =1 (x _j ? 〈x〉) is computed exactly and shown to satisfy a central limit theorem asN → ∞. For the circular random matrix ensemble the p.d.f.’s for the statistics ½Σ _j ^N =1 (θ _j ?π) and ? Σ _j ^N =1 log 2 |sinθ _j/2| are calculated exactly by using a constant term identity from the theory of the Selberg integral, and are also shown to satisfy a central limit theorem asN → ∞.     

Structure of even-even actinides in the interacting boson model and the N = 152 subshell closure

We show that a wide range of deformed actinides can be described in terms of an interacting boson model hamiltonian with three parameters, two of them [including the coefficient of the only SU(3) symmetry breaking term] remaining almost constant over the whole region. In addition to ground γ₁ and β₁ spectra, B(E2:0_g⁺ → 2_g⁺) values are well reproduced with no extra adjustable parameters for nuclei with 136⩽N⩽146, while for nuclei beyond N = 146 an effective boson number has to be considered in order to fit the observed in the B(E2:0⁺_g → 2⁺_g) values, which is due to the presensce of a subshell closure at N = 152. The sensitive dependence of the B(E2:0_g⁺→2_g⁺) values on the effective boson numbers is emphasized. β₁ → ground and β₁ → ground transitions are fitted by breaking the SU(3) symmetry of the E2 transition operator.     

The ground state energy of a Bose gas with Coulomb interaction

LetH _N be the 2N particle Hamiltonian $$\begin{array}{*{20}c} {H_N = \sum\limits_{i = 1}^{2N} {( - \Delta _\iota ) + \sum\limits_{i< j = 1}^N {\left| {x_i - x_j } \right|^{ - 1} + } \sum\limits_{i< j = 1}^N {\left| {x_{i + N} - x_{j + N} } \right|^{ - 1} } } } \\ { - \sum\limits_{i,j< j = 1}^N {\left| {x_i - x_{j + N} } \right|^{ - 1} ,} } \\ \end{array} $$ whereΔ _i is the Laplacian in the variablex _i ∈?³, 1≦i≦2N. The operatorH _N is assumed to act on wave functionsΨ(x ₁, ...,x _N ;x _N+1, ...,x _2N ) which are symmetric in the variables (x ₁, ...,x _N ) and (x _N+1, ...,x _2N ). SupposeΨ is supported in a setΛ ^2N , whereΛ is a cube in ?³. It is shown that if a normalized wave functionΨ can be written as a product of two wave functions $$\psi (x_1 ,...,x_N ;x_{N + 1} ,...,x_{2N} ) = \psi _1 (x_2 ,...,x_N )\psi _2 (x_{N + 1} ,...,x_{2N} ),$$ and the density of particles inΛ is constant, then 〈Ψ|H _N |Ψ〉≧?CN ^7/5 for some universal constantC.     

Improved lower limits on neutral fermion masses

Present lower limits on the mass of a neutral fermion N coupled with full strength to an electron via the right-handed weak current are set only by the absence of the decay K⁺→Ne⁺: m(N)?0.5 GeV/c². It is shown that searches for the decays τ→ν_τNe or F→Ne, followed by N→eπ, can raise the lower bound on m(N) to well over 1 G+-eV/c² if no signal is seen in present or soon-to-be-acquired data. Estimates for the branching ratios for these processes are given. If N couples to e cos φ + μ sin φ with full strength, reference to φ may be eliminated by summing over e and μ in all final states.     

New measurements of the radiative decay modes of the φ-meson

The radiative decay models of the φ-meson have been studied: e⁺e^?→φ→ηγ→3γ; e⁺e^?→φ→π^oγ→3γ. Cross sections σ_{φ→ηγ→3γ} and σ_{φ→π^oγ→3γ} have been measured at five energies in the φ-meson energy region and clearly show the φ-resonance in the ηγ → 3γ mode as well as in the π^oγ → 3γ mode. From a Breit-Wigner fit to the experimental data the values of the branching ratios are deduced: B_φ→ηγ = (1.5 ± 0.4) × 10^?2; B_φ→π^oγ = (1.4 ± 0.5) × 10^?3.     

One-electron relativistic molecules with Coulomb interaction

As an approximation to a relativistic one-electron molecule, we study the operator \(H = ( - \Delta + m^2 )^{1/2} - e^2 \sum\limits_{j = 1}^K {Z_j } |x - R_j |^{ - 1}\) withZ _j ≧0,e ^?2=137.04.H is bounded below if and only ife ² Z _j ≦2/π allj. Assuming this condition, the system is unstable whene ²∑Z _j >2/π in the sense thatE ₀=inf spec(H)→?∞ as the R _j →0, allj. We prove that the nuclear Coulomb repulsion more than restores stability; namely \(E_0 + 0.069e^2 \sum\limits_{i< j} {Z_i Z_j } |R_i - R_j |^{ - 1} \geqq 0\) . We also show thatE ₀ is an increasing function of the internuclear distances |R _i ?R _j |.     

Regge pole model for invariant functions. IV

TheNN→NN andγN→πN differential cross sections for polarized targets are discussed in terms of invariant functions. In former fits of high energy experimental data certain of these invariant functions came out to be small. Based on these fits thepn→np,p¯p→ n¯n, γp→ nπ ⁺ andγn→ pπ ^? differential cross sections are predicted to be independent of the target polarization.     

Half-life and configuration of the 1/2+ intruder state in203Bi

The decay properties of theJ ^π=1/2⁺,E _exc=1,098 keV state in²⁰³Bi were studied. The state was populated via the²⁰⁴Pb(p, 2n) reaction and the activity was studied with the ion guide isotope separator on-line system IGISOL. The half-life of the 1/2⁺ state was measured to beT _1/2=303 ±5 ms. From this value the partial half-lives of the three depopulating branches 1/2⁺ →7/2^? (E3), 1/2⁺→5/2^? (E3 +M2) and 1/2⁺→9/2 _g.s. ^? (M4) were deduced. Since all the transitions are configuration forbidden in first order, a detailed study of second-order shell-model configuration mixing could be performed.     

Etude spectrale d'une famille d'opérateurs non-symétriques intervenant dans la théorie des champs de reggeons

In this paper, we study a few spectral properties of a non-symmetrical operator arising in the Gribov theory. The first and second section are devoted to Bargmann's representation and the study of general spectral properties of the operator: $$\begin{gathered} H_{\lambda ',\mu ,\lambda ,\alpha } = \lambda '\sum\limits_{j = 1}^N {A_j^{ * 2} A_j^2 + \mu \sum\limits_{j = 1}^N {A_j^ * A_j + i\lambda \sum\limits_{j = 1}^N {A_j^ * (A_j + A_j^ * )A_j } } } \hfill \\ + \alpha \sum\limits_{j = 1}^{N - 1} {(A_{j + 1}^ * A_j + A_j^ * A_{j + 1} ),} \hfill \\ \end{gathered}$$ whereA* _j andA _j ,j∈[1,N] are the creation and annihilation operators. In the third section, we restrict our study to the case of nul transverse dimension (N=1). Following the study done in [1], we consider the operator: $$H_{\lambda ',\mu ,\lambda } = \lambda 'A^{ * 2} A^2 + \mu A^ * A + i\lambda A^ * (A + A^ * )A,$$ whereA* andA are the creation and annihilation operators. For λ′>0 and λ′²≦μλ′+λ². We prove that the solutions of the equationu′(t)+H _{λ′, μ,λ} u(t)=0 are expandable in series of the eigenvectors ofH _λ′,μ,λ fort>0. In the last section, we show that the smallest eigenvalue σ(α) of the operatorH _{λ′,μ,λ,α} is analytic in α, and thus admits an expansion: σ(α)=σ₀+ασ₁+α²σ₂+..., where σ₀ is the smallest eigenvalue of the operatorH _{λ′,μ,λ,0}.     

A measurement of the electromagnetic form factor of the eta meson and of the branching ratio for the eta Dalitz decay

In an optical spark chamber experiment we have obtained a sample of 80 eta Dalitz decays (η → e⁺e^?γ) and have measured the eta electromagnetic form factor to be F(X) = 1.0?(0.22 ±0.45)X, where X=M_ee²/M_η², and the branching ratio (η→e⁺e^?γ/(η→π⁺π^?π⁰)= (0.0082 ± 0.0020).     

The static multipole moments of Δ1236(3/2,3/2) from superconvergence inNγ → Δπ scattering

Saturating superconvergence sum rules inNγ→Δπ scattering byN andΔ, we are able to relate the (isoscalar) dipole magnetic moment \(\tilde \mu _\Delta\) and the quadrupole electric moment \(\tilde Q_\Delta\) of the isobarΔ to the electric charge \(\tilde Z_\Delta\) and the dipole magnetic momentμ _N of the nucleonN. The numerical results are: \(\tilde \mu _\Delta \equiv \mu _{\Delta ^ + } + \mu _{\Delta ^0 } = 3.26\) (in unitse/2M)=2.48 (in unitse/2m), and \(\tilde Q_\Delta \equiv Q_{\Delta ^ + } + Q_{\Delta ^0 } = 0.050\) (in unitse/M ²)=0.029 (in unitse/m ²), whereM(m) is the mass ofΔ(N). Neglecting the pion mass and takingM=m,μ _n /μ _p =?2/3, we get theSU ₆ result μ_Δ+=μ _p .     

Influence of the spatial rotation of a polarization plane on the radiative friction force in light fields with polarization gradients

Simple atomic models (1/2→1/2 and 1/2→3/2 transitions) were taken as an example to consider, in the sub-Doppler cooling approximation, influence of the spatial rotation of a polarization plane on the radiative friction force at arbitrary field configurations of dimensionality D<1. Spatial gradients of the angles determining this rotation additionally contribute to the friction force. This contribution is comparable in magnitude with other forces if the detuning δ is on the order of the radiative relaxation constant γ. For the j→j+1 transitions, the contribution promotes sub-Doppler cooling at δ<0, whereas for the j→j transitions (half-integer j) it induces anisotropic heating and cooling processes.     

Signatures for neutralinos at theZ 0

We calculate the visible and invisible width for production of neutralinos,Z ⁰→χ _i ⁰ χ _k ⁰ , and all possible decay rates of the neutralinos. We systematically study their dependence on the supersymmetry parameters and work out the domains where detectable signatures occur. These are the one-sided eventsZ ⁰→e ⁺ e ^?+p _miss,Z ⁰→jets+p _miss,Z ⁰→γ+p _miss andZ ⁰→H _2,3 ⁰ +p _miss, and the two-sided eventsZ ⁰→γ+γ+p _miss,Z ⁰→γ+l ⁺ l ^?+p _miss andZ ⁰→γ+jets+p _miss.     

Quantum percolation tunneling current 1/f~γ noise model for high-κ gate stacks Bi-layer breakdown

Based on the elastic trap-assisted tunneling mechanism in high-κgate stacks,a quantum percolation tunneling current 1/fγ noise model is proposed by incorporating quantum tunneling theory into the quantum percolation model.We conclude that the noise amplitude of the PSD(Power Spectral Density)for three stages,namely the fresh device,one-layer BD(breakdown),and two-layer BD,increases from 10-22→10-14→10-8 A2/Hz.Meanwhile,the noise exponent γ for the three stages,has the 1/f2type(γ→2),1/fγ type(γ→1~2),and 1/f type(γ→1),respectively.The simulation results are in good agreement with the experimental results.This model reasonably interprets the correlation between the bi-layer breakdown and the tunneling 1/fγ noise amplitude dependence and 1/fγ noise exponent dependence.These results provide a theoretical basis for the high-κ gate stacks bi-layer breakdown noise characterization methods.     

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.