Non-resonant kaon pair production and medium effects in proton-nucleus collisions

We study the non-resonant (non-$\phi$) production of $K^+K^-$ pairs by protons of 2.83 GeV kinetic energy on C, Cu, Ag, and Au targets within the collision model, based on the nuclear spectral function, for incoherent primary proton--nucleon and secondary pion--nucleon creation processes. The model takes into account the initial proton and final kaon absorption, target nucleon binding and Fermi motion as well as nuclear mean-field potential effects on these processes. We calculate the antikaon momentum dependences of the exclusive absolute and relative $K^+K^-$ pair yields in the acceptance window of the ANKE magnetic spectrometer, used in a recent experiment performed at COSY, within the different scenarios for the antikaon-nucleus optical potential. We demonstrate that the above observables are strongly sensitive to this potential. Therefore, they can be useful to help determine the $K^-$ optical potential from the direct comparison of the results of our calculations with the data from the respective ANKE-at-COSY experiment. We also show that the pion--nucleon production channels dominate in the low-momentum $K^-$, $K^+$ production in the considered kinematics and, hence, they have to be accounted for in the analysis of these data.Comment: 19 page

Medium effects in ΛK+{\Lambda}K^+ pair production by 2.83 GeV protons on nuclei

We study ${\Lambda}K^+$ pair production in the interaction of protons of 2.83 GeV kinetic energy with C, Cu, Ag, and Au target nuclei in the framework of the nuclear spectral function approach for incoherent primary proton--nucleon and secondary pion--nucleon production processes, and processes associated with the creation of intermediate ${\Sigma^0}K^+$ pairs. The approach accounts for the initial proton and final $\Lambda$ hyperon absorption, final $K^+$ meson distortion in nuclei, target nucleon binding, and Fermi motion, as well as nuclear mean-field potential effects on these processes. We calculate the $\Lambda$ momentum dependence of the absolute ${\Lambda}K^+$ yield from the target nuclei considered, in the kinematical conditions of the ANKE experiment, performed at COSY, within the different scenarios for the $\Lambda$-nucleus effective scalar potential. We show that the above observable is appreciably sensitive to this potential in the low-momentum region. Therefore, direct comparison of the results of our calculations with the data from the ANKE-at-COSY experiment can help to determine the above potential at finite momenta. We also demonstrate that the two-step pion--nucleon production channels dominate in the low-momentum ${\Lambda}K^+$ production in the chosen kinematics and, therefore, they have to be taken into account in the analysis of these data.Comment: 29 page

Bimodule structure of the mixed tensor product over Uqsℓ(2∣1)U_{q} s\ell(2|1) and quantum walled Brauer algebra

We study a mixed tensor product $\mathbf{3}^{\otimes m} \otimes \mathbf{\overline{3}}^{\otimes n}$ of the three-dimensional fundamental representations of the Hopf algebra $U_{q} s\ell(2|1)$, whenever $q$ is not a root of unity. Formulas for the decomposition of tensor products of any simple and projective $U_{q} s\ell(2|1)$-module with the generating modules $\mathbf{3}$ and $\mathbf{\overline{3}}$ are obtained. The centralizer of $U_{q} s\ell(2|1)$ on the chain is calculated. It is shown to be the quotient $\mathscr{X}_{m,n}$ of the quantum walled Brauer algebra. The structure of projective modules over $\mathscr{X}_{m,n}$ is written down explicitly. It is known that the walled Brauer algebras form an infinite tower. We have calculated the corresponding restriction functors on simple and projective modules over $\mathscr{X}_{m,n}$. This result forms a crucial step in decomposition of the mixed tensor product as a bimodule over $\mathscr{X}_{m,n}\boxtimes U_{q} s\ell(2|1)$. We give an explicit bimodule structure for all $m,n$.Comment: 43 pages, 5 figure

Light scattering by optically anisotropic scatterers II: T--matrix computations for radially and uniformly anisotropic droplets

This is the second paper in a series on light scattering from optically anisotropic scatterers embedded in an isotropic medium. The apparently complex T-matrix theory involving mixing of angular momentum components turns out to be an efficient approach to calculating scattering in these systems. We present preliminary results of numerical calculations of the scattering by spherical droplets in some simple cases. The droplets contain optically anisotropic material with local radial or uniform anisotropy. We concentrate on cases in which the scattering is due only to the local optical anisotropy within the scatterer. For radial anisotropy we find non-monotonic dependence of the scattering cross-section on the degree of anisotropy can occur in a regime for which both the Rayleigh and semi-classical theories are inapplicable. For uniform anisotropy the cross-section is strongly dependent on the angle between the incident light and the optical axis, and for larger droplets this dependence is non-monotonic.Comment: 14 pages, 6 figures, uses RevTex