Multi-\bar K configurations and the limit of kaon condensation

Our recent relativistic mean-field (RMF) calculations of multi?-? $\bar K$ nuclei are briefly reviewed. I discuss the saturation pattern of the $\bar K$ separation energy $B_{\bar K}$ and nuclear densities on increasing the number of antikaons embedded in the nuclear medium. Saturation appears to be a robust feature of multi- $\bar K$ nuclei. Because $B_{\bar K}$ generally does not exceed 200 MeV, it is unlikely that kaon condensation occurs in strong-interaction self-bound strange hadronic matter. Last, I present our calculations of self-bound strange systems made out of neutrons and ${\bar K}^0$ mesons.     

Probing of the Higgs-fermion coupling atγγ-colliders

Three possibilities to observe the Higgs-top interation at future γγ-colliders are discussed:

1. associated Higgs production via the \(\gamma \gamma \to t\bar tH\) reaction,
2. Higgs obliged radiative correction to the \(\gamma \gamma \to t\bar t\) channel,
3. Higgs resonance production via γγ→H→ZZ.

The results obtained show windows of the Higgs mass where the Yukawa interaction of the Higgs with the top quark can be studied at γγ-colliders.     

Unbounded derivations ofC*-algebras II

It is demonstrated that a closed symmetric derivation δ of aC?-algebra \(\mathfrak{A}\) generates a strongly continuous one-parameter group of automorphisms of aC?-algebra \(\mathfrak{A}\) if and only if, it satisfies one of the following three conditions

1. (αδ+1)(D(δ))= \(\mathfrak{A}\) , α∈?\{0}.
2. δ possesses a dense set of analytic elements.
3. δ possesses a dense set of geometric elements.

Together with one of the following two conditions

1. ∥(αδ+1)(A)∥≧∥A∥, α∈IR,A∈D(δ).
2. If α∈IR andA∈D(δ) then (αδ+1)(A)≧0 impliesA≧0.

Other characterizations are given in terms of invariant states and the invariance ofD(δ) under the square root operation of positive elements.     

The Dimension of Projections of Fractal Percolations

Fractal percolation or Mandelbrot percolation is one of the most well studied families of random fractals. In this paper we study some of the geometric measure theoretical properties (dimension of projections and structure of slices) of these random sets. Although random, the geometry of those sets is quite regular. Our results imply that, denoting by $E\subset\mathbb{R}^{2}$ a typical realization of the fractal percolation on the plane,

• If $\dim_{\rm H}E<1$ then for all lines ? the orthogonal projection E _? of E to ? has the same Hausdorff dimension as E,
• If $\dim_{\rm H}E>1$ then for any smooth real valued function f which is strictly increasing in both coordinates, the image f(E) contains an interval.

The second statement is quite interesting considering the fact that E is almost surely a Cantor set (a random dust) for a large part of the parameter domain, see Chayes et al. (Probab. Theory Relat. Fields, 77(3):307–324, 1988). Finally, we solve a related problem about the existence of an interval in the algebraic sum of d≥2 one-dimensional fractal percolations.     

Identification of \mathrm{\ensuremath J^{\pi} = 19/2^+} and \mathrm{\ensuremath 23/2^+} isomeric states in 127Sb

The nucleus $\ensuremath {\rm ^{127}Sb}$ , which is on the neutron-rich periphery of the $\ensuremath \beta$ -stability region, has been populated in complex nuclear reactions involving deep-inelastic and fusion-fission processes with $\ensuremath {\rm {}^{136}Xe}$ beams incident on thick targets. The previously known isomer at 2325 keV in $\ensuremath {\rm {}^{127}Sb}$ has been assigned spin and parity $\ensuremath 23/2^+$ , based on the measured $\ensuremath \gamma$ - $\ensuremath \gamma$ angular correlations and total internal conversion coefficients. The half-life has been determined to be 234(12) ns, somewhat longer than the value reported previously. The 2194 keV state has been assigned $\ensuremath J^{\pi} = 19/2^+$ and identified as an isomer with $\ensuremath T_{1/2} = 14(1) {\rm ns}$ , decaying by two $\ensuremath E2$ branches. The observed level energies and transition strengths are compared with the predictions of a shell model calculation. Two $\ensuremath 15/2^+$ states have been identified close in energy, and their properties are discussed in terms of mixing between vibrational and three-quasiparticle configurations.     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

Symmetrieeigenschaften achtkomponentiger Spinorfelder im Gitterraum

Starting from the four component Dirac equation for free particles without mass W.Heisenberg und W.Pauli have shown that the interaction term is uniquely defined, if one requires that all symmetries of free particles are preserved. Here we obtain similar results if we start from the eight component Dirac equation for free particles without mass:

1. The symmetry group of the eight component Dirac equation for free particles without mass has 16 parameters. It is isomorph to the direct product of the SU 4 and a one-parametric group: SU 4× (1).
2. The interaction operator is uniquely defined if one requires to preserve as many symmetries as possible of those given in (1).
3. But some of the symmetries in (1) are necessarily broken, in particular that of SU 3. The symmetry of the interaction operator is given by SO 4× (1)× (1).

These results mean:

1. The Heisenberg theory is uniquely defined, only if one assumes that the free particle part of the equation is well known.
2. The theory can be changed without modifying the fundamental idea ofHeisenberg andPauli to deduce an uniquely defined interaction operator if one starts with a modified free particle part.
3. A special kind of modification of the free particle part leads essentially to the SU 4-symmetry including that of SU 3, which is necessarily broken by the interaction term.
4. The question arises if this break of the SU 3-symmetry has something to do with the real break. This question is not yet touched in this paper.

     

Dynamical enhanced electron emission and discharges at contaminated surfaces

Broad-area electrodes show electron emission already at electric field strengthsF≈10⁷ V/m. This enhanced field emission (EFE) occurs only for contaminated surfaces. EFE is accompanied by photon emission and gas desorption yielding finally discharges. EFE is caused by dust and contaminants initiating the following effects:

an electron is stochastically emitted in a trigger zone

the electron gains energyΔE?eΔxF ^*

which excites electronic states

which relax by the emission of electrons, photons, and atoms

where the positive charges left behind enhanceF ^*=βF (β?1) initiating so an electron avalanche, i.e., a high conductivity channel. Because of charge migration and neutralization, this avalanche has a life time. This pulsating EFE is accompanied by light emission and gas desorption yielding finally a gas cloud and a discharge.

The pulsating, self-sustained EFE has the same root as:

the enhanced secondary emission found first by Malter

the conductivity switching exhibited by thin (≈ 1 μm) layers of semiconductors or insulators

the normal cathode fall and

the firing-wave instability in neurodynamics.

     

Energy dependence of {\bar{K}N} interaction in nuclear medium

When the $\bar{K}N$ system is submerged in nuclear medium the $\bar{K}N$ scattering amplitude and the final state branching ratios exhibit a strong energy dependence when going to energies below the $\bar{K}N$ threshold. A sharp increase of $\bar{K}N$ attraction below the $\bar{K}N$ threshold provides a link between shallow $\bar{K}$ -nuclear potentials based on the chiral $\bar{K}N$ amplitude evaluated at threshold and the deep phenomenological optical potentials obtained in fits to kaonic atoms data. We show the energy dependence of the in-medium K ^??? p amplitude and demonstrate the impact of energy dependent branching ratios on the Λ-hypernuclear production rates.     

Overview of \boldsymbol{\bar{K} N} and \boldsymbol{\bar{K}}-nucleus dynamics

The main features of coupled-channel ${\bar K}N$ dynamics near threshold and its repercussions in few-body $\bar K$ -nuclear systems are briefly reviewed highlighting the I?=?1/2 ${\bar K}NN$ system. For heavier nuclei, the extension of mean-field calculations to multi- $\bar K$ nuclear quasibound states is discussed focusing on kaon condensation.     

{\Xi} Hypernucler States Predicted by the New Interaction Model ESC08c

The features of the new interaction model ESC08c in ${\Lambda N}$ , ${\Sigma N}$ and ${\Xi N}$ channels are demonstrated single hyperon potentials ${U_Y(Y=\Lambda, \Sigma, \Xi)}$ in nuclear matter on the basis of the G-matrix theory. (K ^?, K ⁺) productions of ${\Xi}$ hypernuclei are studied with ${\Xi}$ -nucleus folding potentials.     

Spectroscopic properties of Ho 3 + -doped K–Sr–Al phosphate glasses

Trivalent holmium-doped K–Sr–Al phosphate glasses ( $\mathrm{P}_{2}\mathrm{O}_{5}$ – $\mathrm{K}_{2}\mathrm{O}$ –SrO– $\mathrm{Al}_{2}\mathrm{O}_{3}$ – $\mathrm{Ho}_{2}\mathrm{O}_{3}$ ) were prepared, and their spectroscopic properties have been evaluated using absorption, emission, and excitation measurements. The Judd–Ofelt theory has been used to derive spectral intensities of various absorption bands from measured absorption spectrum of 1.0 mol% $\mathrm{Ho}_{2}\mathrm{O}_{3}$ -doped K–Sr–Al phosphate glass. The Judd–Ofelt intensity parameters ( $\varOmega_{\lambda}$ , $\times10^{-20}~\mathrm{cm}^{2}$ ) have been determined of the order of $\varOmega_{2} = 11.39$ , $\varOmega_{4} = 3.59$ , and $\varOmega_{6} = 2.92$ , which in turn used to derive radiative properties such as radiative transition probability, radiative lifetime, branching ratios, etc. for excited states of $\mathrm{Ho}^{3+}$ ions. The radiative lifetimes for the ${}^{5}F_{4}$ , ${}^{5}S_{2}$ , and ${}^{5}F_{5}$ levels of $\mathrm{Ho}^{3+}$ ions are found to be 169, 296, and 317 μs, respectively. The stimulated emission cross-section for 2.05-μm emission was calculated by the McCumber theory and found to be $9.3\times10^{-2 1}~\mathrm{cm}^{2}$ . The wavelength-dependent gain coefficient with population inversion rate has been evaluated. The results obtained in the titled glasses are discussed systematically and compared with other $\mathrm{Ho}^{3+}$ -doped systems to assess the possibility for visible and infrared device applications.     

Influence of temperature on the electric,dielectric and AC conductivity properties of nano-crystalline zinc substituted cobalt ferrite synthesized by solution combustion technique

Cobalt–zinc nanoferrites with formulae Co $_{1-x}$ Zn $_{x}$ Fe $_{2}$ O $_{4}$ , where x = 0.0, 0.1, 0.2 and 0.3, have been synthesized by solution combustion technique. The variation of DC resistivity with temperature shows the semiconducting behavior of all nanoferrites. The dielectric properties such as dielectric constant ( $\varepsilon $ ’) and dielectric loss tangent (tan $\delta )$ are investigated as a function of temperature and frequency. Dielectric constant and loss tangent are found to be increasing with an increase in temperature while with an increase in frequency both, $\varepsilon $ ’ and tan $\delta $ , are found to be decreasing. The dielectric properties have been explained on the basis of space charge polarization according to Maxwell–Wagner’s two-layer model and the hopping of charge between Fe $^{2+}$ and Fe $^{3+}$ . Further, a very high value of dielectric constant and a low value of tan $\delta $ are the prime achievements of the present work. The AC electrical conductivity ( $\sigma _\mathrm{AC})$ is studied as a function of temperature as well as frequency and $\sigma _\mathrm{AC}$ is observed to be increasing with the increase in temperature and frequency.     

The unitary irreducible representations of\overline {SO} _0 (4,2)

An exhaustive classification of all irreducible Harish-Chandra \(\mathfrak{s}\mathfrak{o}\) (4,2)-modules, integrable to unitarizable projective representations of the conformal group, is established by infinitesimal methods: the classification is based

1. on the reduction upon the maximal compact subalgebra, associated with a lattice of points in ?³, and
2. on a set of additional parameters upon which the eigenvalues of central elements of the enveloping algebra depend polynomially.

     

Charmonium rescattering effects in \psi(2S) \rightarrow \gamma \eta_{c}^{} decay

Charmonium rescattering effects in the M1 transition of $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ are investigated by modeling a $ \chi_{{cJ}}^{}$ or J/ $ \psi$ rescattering into a $ \eta_{c}^{}$ final state. The absorptive and dispersive part of the transition amplitudes for the rescattering loops of $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) and $ \gamma$ $ \chi$ ( $ \psi$ ) are separately evaluated. The numerical results show that the contribution from the $ \gamma$ $ \chi$ ( $ \psi$ ) rescattering process is negligible. Compared with the virtual D $ \bar{{D}}$ (D ^*) rescattering processes, the $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) process may be regarded as the next-leading order of the hadronic loop mechanism, which only offers the partial decay width of ～ 0.045 keV to the $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ .     

Strange and non-strange (Anti-) baryon production at 200 A GeV/c

Rapidity distributions of net hyperons $\left( {\Lambda - \bar \Lambda } \right)$ are compared to distributions of participant protons $\left( {p - \bar p} \right)$ . Strangeness production (mean multiplicities of produced Λ/Σ⁰ hyperons and $\left\langle {K + \bar K} \right\rangle $ in central nucleusnucleus collisions is shown for different collision systems at different energies. An enhanced production of $\bar \Lambda $ compared to $\bar p$ is observed at 200 GeV per nucleon.     

Asymptotic Behavior for a Version of Directed Percolation on the Triangular Lattice

We consider a version of directed bond percolation on the triangular lattice such that vertical edges are directed upward with probability $y$ , diagonal edges are directed from lower-left to upper-right or lower-right to upper-left with probability $d$ , and horizontal edges are directed rightward with probabilities $x$ and one in alternate rows. Let $\tau (M,N)$ be the probability that there is at least one connected-directed path of occupied edges from $(0,0)$ to $(M,N)$ . For each $x \in [0,1]$ , $y \in [0,1)$ , $d \in [0,1)$ but $(1-y)(1-d) \ne 1$ and aspect ratio $\alpha =M/N$ fixed for the triangular lattice with diagonal edges from lower-left to upper-right, we show that there is an $\alpha _c = (d-y-dy)/[2(d+y-dy)] + [1-(1-d)^2(1-y)^2x]/[2(d+y-dy)^2]$ such that as $N \rightarrow \infty $ , $\tau (M,N)$ is $1$ , $0$ and $1/2$ for $\alpha > \alpha _c$ , $\alpha < \alpha _c$ and $\alpha =\alpha _c$ , respectively. A corresponding result is obtained for the triangular lattice with diagonal edges from lower-right to upper-left. We also investigate the rate of convergence of $\tau (M,N)$ and the asymptotic behavior of $\tau (M_N^-,N)$ and $\tau (M_N^+ ,N)$ where $M_N^-/N\uparrow \alpha _c$ and $M_N^+/N\downarrow \alpha _c$ as $N\uparrow \infty $ .     

Analysis of the vertexes \Xi_{Q}^{*}′QV , \Sigma_{Q}^{*} \Sigma_{Q}^{}V and radiative decays \Xi_{Q}^{*} \rightarrow ′Q \gamma , \Sigma_{Q}^{*} \rightarrow \Sigma_{Q}^{} \gamma

In this article, we study the vertexes $ \Xi_{Q}^{*}$ ′_Q V and $ \Sigma_{Q}^{*}$ $ \Sigma_{Q}^{}$ V with the light-cone QCD sum rules, then assume the vector meson dominance of the intermediate $ \phi$ (1020) , $ \rho$ (770) and $ \omega$ (782) , and calculate the radiative decays $ \Xi_{Q}^{*}$ $ \rightarrow$ ′_Q $ \gamma$ and $ \Sigma_{Q}^{*}$ $ \rightarrow$ $ \Sigma_{Q}^{}$ $ \gamma$ .