Radiative decays as tests of the symmetries of the Ψ particles

The success of the Okubo-Iizuka-Zweig rule for decays of Ψ and Ψ′ suggests that the radiative decays Ψ → γ + hadrons should be dominated by intermediates like Ψ → Ψ′ hadrons. This mechanism is consistent with experimental data which show Γ(Ψ → ?⁰π⁰) and Γ(Ψ → ηγ) to be comparable. if all Ψ-like particles are isoscalar, $\text{Γ(Ψ →}{}^0\text{γ)}$ should be very small. If all Ψ-like particles are SU(3) singlets, Γ(Ψ → η′γ)/Γ(Ψ → ηγ) should be large. Substantial violation of our predictions would be circumstantial evidence for the existence of non-singlet new quarks.     

Unitarily invariant convex functions on the state space of type I and type III von Neumann algebras

Properties of unitarily invariant convex functions, defined on subsets of positive linear forms of type I and type III IV¹-algebras have been investigated. We especially characterize those pairs of positive linear forms f, g for which Ψ(f) ? Ψ(g) holds for every unitarily invariant convex function Ψ and in which case we call f “more chaotic” than g.     

Threshold singularities of theS-matrix and convergence of Haag-Ruelle approximations

We establish a one-to-one correspondence between the continuity properties of theS-matrix at the 2-particle threshold and the rate of convergence of the Haag-Ruelle approximations ψ(t) for asymptotic 2-particle states ψ with smooth wavefunctions. It turns out that the norm distance ∥ψ?ψ(t)∥ approaches 0 liktt ^?5/4 if theS-matrix has the normal threshold singularities and liket ^?3/4 in the exceptional case where the threshold has “absorbed” a bound state. These connections are valid both in relativistic quantum field theory and in non-relativistic models with short range interaction.     

A remark on transition probability

Uhlmann's transition probability P(ψ, φ) of two normal states of a von Neumann algebra M, which is the supremum of |(Ψ, Φ)|² for all possible choices of representative vectors Ψ and Φ of ψ and φ, is shown to be the infimum of (∫d(μ_{ψ, e})^1/2)² for the induced measures μ_{ω, e}(B)=ω(e(B)) (B: Borel set in ℝ, ω=ψ, φ) for all possible projection-valued measures e belonging to M.     

The semihard processes γγ→ΨX, γγ→ΨΨ, γγ→ϱΨ

The cross sections for Ψ-production in the semihard collisions are calculated at s ⪢ |t|, m_Ψ² and at not too large a jet effective mass m_X²≲m_Ψ² + |t| for the process γγ→ΨX. We found these cross sections in the lowest nontrivial QCD order (two-gluon exchange in the t-channel): σ(γγ→ΨX) ≈ 10³⁵ cm², σ(γγ→ΨΨ)=2×10⁻³⁶ cm². The polarization of Ψ in these processes is transversal (contrary to the longitudinal one of light mesons ϱ⁰, ω, ϕ in similar processes).     

Anregung gebundener Atomzustände durch die plötzliche Zentralfeldänderung beim β−-Zerfall des Kerns

By the sudden change of nuclear charge during β^?-decay the daughter-ion is ionized or excited with probabilities of the order of some percent; other processes in the electron shell may be neglected, therefore unperturbed excitations can be measured by detecting photons emitted from the decaying excited atomic states in delayed coincidence with β^?-particles as is shown in an earlier paper for the Kr 85-β^?-decay. More extensive measurements of the photonemission after this decay give results in good agreement with theoretical predictions. Mostly such photons are observed, which can be emitted after a monopol-excitation, for which the selectionrulesΔ J=0 andΔ l=0 are valid. The total excitationprobability into both 5p(J=0)-states of Rb II is found to be P(4p?5p)=5,6±1,0%. The lifetimes of these two states are measured (correspondingly) to be τ=7,6 ±0,5 nsec, from which the reduced matrixelements ¦〈5p∥D∥5s〉¦²=18,9±3,2 and ¦〈5p∥D∥4d〉¦²=10,4 ±1,8 a.u. are calculated.     

Steepest descent in the Hilbert space - A method for calculating state vectors of ground and excited states

A new method for calculating the ground state and the excited states of a hamiltonian is proposed. We derive differential equations describing the motion of a state vector z.sfnc;Ψ(θ)〉 towards the minima of 〈Ψz.sfnc;H²z.sfnc;Ψ〉-〈Ψz.sfnc;Hz.sfnc;Ψ 〉², corresponding to the stationary states of H. As an illustration of this general scheme we determine the few lowest stationary states of an anharmonic oscillator.     

Spin assignment to the 9.026 MeV resonance level of36Ar using35Cl(p, γ)36Ar triple angular correlation measurements forE p = 533 keV

Triple correlation experiments have been performed to study the³⁵Cl(p, γ)³⁶Ar resonance for a proton energyE _p = 533 keV. From the analysis of the measured gamma ray angular distributions, due to the gamma decay of the 9.026 MeV resonance level in³⁶Ar via the 9.026 MeV→1.97 MeV→0 MeV double cascade, a spin value ofJ ₁ =2⁺ for the 9.026 MeV level and a mixing ratio of ?1.97 MeV∥L′₁ = 2∥9.026 MeV?/?1.97 MeV∥ L₁ = 1∥9.026 MeV? = ?0.055 + 0.022 for the 9.026 MeV→ 1.97 MeV transition could be derived.     

A convergent expansion about mean field theory: I. The expansion

We give a convergent expansion for nearly Gaussian quantum field theory in the multiphase region. The expansion combines (1) an expansion in phase boundaries, (2) a cluster expansion, and (3) a perturbation expansion to isolate dominant behavior. We study in detail the ground state of the $\text{P}$(φ)₂ = (λφ⁴ ? φ² ? μφ)₂ model, with ∥ μ ∥ ? λ² ? 1. The ground state is close to the classical free field, obtained by replacing $\text{P}$(φ) by the quadratic mean field polynomial $\text{P}$_c(φ), tangent to $\text{P}$ at a global minimum. Selecting one minimum gives a pure phase (ergodic ground state) satisfying the Wightman-Osterwalder-Schrader axioms with a positive mass. We also establish analyticity in λ for μ = 0 in the sector ∥ Im λ ∥ < ? Re λ ? 1, for ? ? 1.     

On Bounding Entangling Rates and Mixing Rates in Some Special Cases

We derive bounds on mixing rates in a special case when the probabilistic ensemble of states is under certain restrictions. In this case we can prove the small incremental mixing conjecture with a constant c′ = 1, which is improved over the previous results of which the tightest is c′ = 2. Furthermore, we demonstrate a bound Γ(Ψ, H) ≤ 2∥H∥ log(d) for the small incremental entangling conjecture if d is sufficiently large.     

π+-electroproduction above the resonance region

The reaction e + p → e' + n + π⁺ was studied detecting e' and e' and π⁺ in coincidence at an invariant hadronic mass of 2.19 GeV. The measurements were performed at electron four-momentum transfers squared of Q² = 0.06, 0.28, 0.70, and 1.35 GeV² in the range of t = (γ_v?π)² between tmin and ?1.0 GeV². The cross section d²σ/dtd was found to be roughly independent of Q² for Q² > 0.7 GeV² and ∥t∥ > 0.2 GeV².     

The Itô-Clifford integral III. The Markov property of solutions to stochastic differential equations

It is shown that the solution to the Itô-Clifford stochastic differential equationdX _t =F(X _t ,t)dΨ _t +dΨ _t G(X _t ,t)+H(X _t ,t)dt, whereF, G, H are suitable Lipschitz functions andΨ _t is the fermion martingale, satisfies a Markov property.     

The microwave spectrum of a second N-gauche rotamer of allylamine

The microwave spectra of the ground and five excited states of a second gauche rotamer of allylamine have been measured and assigned. Three of the excited states belong to the same mode, most probably the CC torsion, the second and third vibrational states present a symmetrical splitting due to tunneling effect. The spectrum was conclusively identified as due to the N-gauche, lone-electron-pair trans form by means of the N-quadrupole coupling constants and dipole moment components. The variation observed for the quadrupole coupling constants in the different vibrationally excited states was explained by a suitable model. The ground state constants are (in MHz) A₀ = 23 957.05 ± 0.048, B₀ = 4 229.96 ± 0.025, C₀ = 4 154.91 ± 0.025, χ_aa = ? 1.48 ± 0.04, χ_bb - χ_cc = ? 1.42 ± 0.04, and (in D) ∥μ_a∥ = 0.766 ± 0.010, ∥μ_b∥ = 0.700 ± 0.005, ∥μ_c∥ = 0.290 ± 0.020.The excited states of the N-cis, lone-electron-pair trans form were also measured and assigned; two of these states appear to belong to the CC torsion as indicated by their intertial defects. The potential hindering the internal CC rotation was calculated using the relative intensity data of the N-cis and N-gauche forms as well as the tunneling splittings. A three-term cosine potential was fitted to the data yielding (in cm^?1) V₁ = ? 77 ± 85, V₂ = 170 ± 126, V₃ = 663 ± 95. The Dennison-Uhlenbeck potential was used for an approximate calculation of the N-trans barrier separating the two identical N-gauche forms. The barrier obtained was 1.9 ± 0.3 Kcal/mole.     

Microwave spectrum,dipole moment,and conformation of 3-methylcyclopentanone

The rotational spectrum of 3-methylcyclopentanone has been observed in the frequency region from 18.0 to 26.5 GHz. Both a-type and b-type transitions in the ground vibrational state and a-type transitions in five excited states have been assigned. The ground state rotational constants are determined to be A = 5423.32 ± 0.18, B = 1949.51 ± 0.01, and C = 1529.59 ± 0.01 MHz. Analysis of the measured quadratic Stark effects gives the dipole moment components ∥μ_a∥ = 2.97 ± 0.02, ∥μ_b∥ = 1.00 ± 0.03, ∥μ_c∥ = 0.18 ± 0.06, and the total dipole moment ∥μ_t∥ = 3.14 ± 0.03 D. These data are consistent with a twisted-ring conformation with a methyl group in the equatorial position.     

Surface photovoltage spectroscopy and surface piezoelectric effect in GaAs

“Real” (111) surfaces of n-type GaAs were investigated employing surface photovoltage spectroscopy and the surface piezoelectric effect. Surface states at the energy position E_c ? E_t ? 0.72 eV were found on both the Ga and the As surfaces. Both types of surfaces exhibited a barrier of about 0.55 V. No variations in the surface barrier or the energy position of the surface states were observed in various ambients at atmospheric pressure (dry air, wet air, ammonia and ozone). However, the capture cross-section of the surface states for electrons, as determined from the surface piezoelectric effect transients (of the order of 10^?13 cm²), was found to be sensitive to the ambient. It decreased in wet air and increased in ozone. This effect was more pronounced on the As than on the Ga surfaces. Additional surface states were found to be present in the energy region of 0.9 to 1.0 eV, below the bottom of the conduction band. However, their exact energy positions could not be determined due to interference caused by the carrier trapping of the surface states at E_c ? E_t ? 0.72 eV.     

A measurement of polarization in π−p→ K°Λ° at 5 GeV/c

We have measured the Λ° polarization in π^?p→ K°Λ° at 5 GeV/c, using a data sample of 3709 events. The polarization is positive for small t, passes through zero near t = ?0.3 (GeV/c)², and becomes large and negative at larger t, consistent with a value of ?1.0 for t between ?0.7 and ?1.6(GeV/c)².     

3 S 1−3 D 1 mixing and E1 radiative transitions in charmonium

The radiative transitions ψ′→γ+χ _J and χ _J →γ+ψ are studied in the quark model with the ψ and ψ′ interpreted conventionally as³ S ₁ \(c\bar c\) states and the χ _J as³ P _J \(c\bar c\) states. In particular, the effect of³ S ₁?³ D ₁ mixing on the decay widths is calculated. The photon angular distributions in these decays are also studied and are found to be a more sensitive test of³ D ₁ admixtures in the Ψ states. The³ D ₁ content of the Ψ is found to be large but the estimate is very sensitive to the photon angular distributions. More precise measurements could help to explain the large ψ″ leptonic width.     

Diffraction longitudinal multidomain structures in a layered nonlinearly absorbing medium

A method for measuring the composed phase parameter ?=Ψ₁+Ψ₂?2Ф₁ (where Ψ₁ and Ψ₂ are the phases of the mirror reflectances and Ψ₁ is the phase of the mirror transmittance) of dielectric mirrors with small absorption coefficients is proposed. This method is based on the use of the properties of a laser with a three-mirror cavity, and the mirror under study is the internal mirror of this cavity. It is shown that the value of the parameter Ψ, differing slightly from π, can be measured, and the results of the measurement are independent of the character of saturation of the laser active medium. The phase parameter was also measured for mirrors with reflectances below 0.8 by using an external method in which the interferometer with the mirror under study was placed outside of the laser cavity. It turned out that the intracavity laser method for measuring Ψ has a number of advantages and ensures an appreciably higher accuracy in measuring the parameter ε=Ψ?π than do extracavity techniques.     

Supermultiplet symmetry and near-threshold levels in systems featuring two or three extremely light clusters

On the basis of the supermultiplet potential model for the interaction of extremely light clusters (formalism of Young diagrams), it is explained why the d+t system does not feature a (1/2)⁺(L=0) level allied to (3/2)⁺(L=0) thermonuclear resonance. By using known data on the quasielastic knockout of nucleons from the inner1s shell of light nuclei, a systematics of near-threshold states in the t+d+d, t+t+d, and t+t+t systems is constructed in terms of excited Young diagrams like {f}={322}. The emergence of similar states in going over from the d+d and t+t systems (which feature no such states) to the α+d+d, α+t+d, and α+t+t systems (where they appear owing to the binding effect of the alpha particle) is discussed. The three-cluster states being considered may be important not only for nuclear physics proper but also for nuclear astrophysics.