arXiv subjects

G. Zhang

Publications and source records attributed to G. Zhang.

81 records · Page 5Linked to original sources

arXiv2009

On the Production of $π^+π^+$ Pairs in pp Collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the $pp\to ppπ^+π^-$ reaction at a beam energy of 0.793 GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the $pp \to nnπ^+π^+$ reaction channel. The latter is expected to be the only $ππ$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $ππ$ production process. No single event has been found, which meets all conditions for being a candidate for the $pp \to nn π^+π^+$ reaction. This gives an upper limit for the cross section of 0.16 $μ$b (90% C.L.), which is more than an order of magnitude smaller than the cross sections of the other two-pion production channels at the same incident energy.

nucl-ex↗

arXiv2009

Existence of a degenerate singularity in the high activation energy limit of a reaction-diffusion equation

We consider the singular perturbation problem $$ Δu_ε=β_ε(u_ε), $$ where $β_ε(s)=\frac{1}εβ(\frac{s}ε)$, $β$ is a Lipschitz continuous function such that $β>0$ in $(0, 1)$, $β\equiv 0$ outside $(0, 1)$ and $\int_0^1β(s) ds={1/2}$. We construct an example exhibiting a {\em degenerate singularity} as $ε_k\searrow 0$. More precisely, there is a sequence of solutions $u_{ε_k}\to u$ as $k\to \infty$, and there exists $x^0\in\partial\{u>0\}$ such that $$ \frac{u(x^0+r\cdot)}{r} \to 0 \textrm{as} r\to 0.$$ Known results suggest that this singularity must be {\em unstable}, which makes it hard to capture analytically and numerically. Our result answers a question raised by Jean-Michel Roquejoffre at the FBP'08 in Stockholm.

math.AP↗

arXiv2009

Single-Pion Production in pp Collisions at 0.95 GeV/c (II)

The single-pion production reactions $pp\to dπ^+$, $pp\to npπ^+$ and $pp\to ppπ^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements from other detector parts. Thus all pion production channels were recorded with 1-4 overconstraints. Main emphasis is put on the presentation and discussion of the $npπ^+$ channel, since the results on the other channels have already been published previously. The total and differential cross sections obtained are compared to theoretical calculations. In contrast to the $ppπ^0$ channel we find in the $npπ^+$ channel a strong influence of the $Δ$ excitation already at this energy close to threshold. In particular we find a $(3 cos^2Θ+ 1)$ dependence in the pion angular distribution, typical for a pure s-channel $Δ$ excitation and identical to that observed in the $dπ^+$ channel. Since the latter is understood by a s-channel resonance in the $^1D_2$ $pn$ partial wave, we discuss an analogous scenario for the $pnπ^+$ channel.

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arXiv2008

Two-Pion Production in Proton-Proton Collisions with Polarized Beam

The two-pion production reaction $\vec{p}p\to ppπ^+π^-$ was measured with a polarized proton beam at $T_p \approx$ 750 and 800 MeV using the short version of the COSY-TOF spectrometer. The implementation of a delayed pulse technique for Quirl and central calorimeter provided positive $π^+$ identification in addition to the standard particle identification, energy determination as well as time-of-flight and angle measurements. Thus all four-momenta of the emerging particles could be determined with 1-4 overconstraints. Total and differential cross sections as well as angular distributions of the vector analyzing power have been obtained. They are compared to previous data and theoretical calculations. In contrast to predictions we find significant analyzing power values up to $A_y$ = 0.3.

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arXiv2007

Toeplitz and Hankel operators and Dixmier traces on the unit ball of \mathbb C^n

We compute the Dixmier trace of pseudo-Toeplitz operators on the Fock space. As an application we find a formula for the Dixmier trace of the product of commutators of Toeplitz operators on the Hardy and weighted Bergman spaces on the unit ball of \mathbb C^d. This generalizes an earlier work of Helton-Howe for the usual trace of the anti-symmetrization of Toeplitz operators.

math.CV↗

arXiv2006

Single-Pion Production in pp Collisions at =.95 GeV/c (I)

The single-pion production reactions $pp\to dπ^+$, $pp\to npπ^+$ and $pp\to ppπ^0$ were measured at a beam momentum of 0.95 GeV/c ($T_p \approx$ 400 MeV) using the short version of the COSY-TOF spectrometer. The implementation of a central calorimeter provided particle identification, energy determination and neutron detection in addition to time-of-flight and angle measurements. Thus all pion production channels were recorded with 1-4 overconstraints. The total and differential cross sections obtained are compared to previous data and theoretical calculations. Main emphasis is put on the discussion of the $ppπ^0$ channel, where we obtain angular distributions different from previous experimental results, however, partly in good agreement with recent phenomenological and theoretical predictions. In particular we observe very large anisotropies for the $π^0$ angular distributions in the kinematical region of small relative proton momenta revealing there a dominance of proton spinflip transitions associated with $π^0$ $s$- and $d$-partial waves and emphasizing the important role of $π^0$ d-waves.

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arXiv2005

Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.

math.QA↗

arXiv2003

Berezin transform on the quantum unit ball

We introduce and study, in the framework of a theory of quantum Cartan domains, a q-analogue of the Berezin transform on the unit ball. We construct q-analogues of weighted Bergman spaces, Toeplitz operators and covariant symbol calculus. In studying the analytical properties of the Berezin transform we introduce also the q-analogue of the SU(n,1)-invariant Laplace operator (the Laplace-Beltrami operator) and present related results on harmonic analysis on the quantum ball. These are applied to obtain an analogue of one result by A.Unterberger and H.Upmeier. An explicit asymptotic formula expressing the q-Berezin transform via the q-Laplace-Beltrami operator is also derived. At the end of the paper, we give an application of our results to basic hypergeometric q-orthogonal polynomials.

math.QA↗

arXiv2002

Measurements of the 64Zn(n,a)61Ni cross section at En=5.0-6.75 MeV

The experiment of determination of the 64Zn(n,a)61Ni reaction cross section in the 5.0-6.75 MeV neutron energy range was performed at the 4.5 MV Van de Graaf accelerator at the Institute of Heavy Ion Physics, Peking University, Beijing. Double section ionization chamber with grid was used for direct registration of the reaction products. The cross sections and angular distributions were extracted from the experimental data. The obtained values were compared with the results of other authors and theoretical estimations. The analysis of the experimental data and model calculations were carried out.

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