Geometric scaling for the total gamma(*)p cross section in the low x region

We observe that the saturation model of deep inelastic scattering predicts a geometric scaling of the total gamma(*)p cross section in the region of small Bjorken variable x. The geometric scaling in this case means that the cross section is a function of only one dimensionless variable tau = Q(2)R(2)(0)(x), where the function R(0)(x) decreases with decreasing x. We show that the experimental data from HERA in the region x<0.01 confirm the expectations of this scaling over a very broad region of Q(2). We suggest that the geometric scaling is more general than the saturation model.     

Production of charged pions, kaons and antikaons in relativistic C + C and C + Au collisions

Production cross-sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(π⁺)/<A _part> is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K⁺ multiplicities per participating nucleon M(K⁺)/ <A _part> are independent of the target size at 1 AGeV and at 1.8 AGeV. The K^- multiplicity per participating nucleon M(K^-)/ <A _part> is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K^-/K⁺ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K-mesons are neglected. Received: 10 December 1999 / Accepted: 14 November 2000     

Some aspects of deformation in Al-Zn alloys

Creep resistance investigations of the Al-40 wt % Zn alloy at room temperature have been performed and revealed some creep compliance. Additions of Cu and Si decrease considerably the preliminary creep compliance in the alloy which then turn to be dimensionally stable and resistant to creep. Tensile test investigations performed at different deformation rates have not revealed the existance of the superplastic deformation mechanism.Presented at the 4^th International Symposium on Plasticity of Metals and Alloys, September 711, 1987, Srni, Czechoslovakia.     

Kinetic Carbon Isotope Effects in the Decarbonylation of Lactic Acid of Natural Isotopic Composition and of [1-14C] Lactic Acid

Studies of carbon-13 and carbon-14 kinetic isotope effects (K. I. E.) in the decarbonylation of lactic acid (L. A.) in sulphuric acid and in phosphoric acids media have been summarized and compared with earlier studies of ¹⁴C and ¹³C K. I. E. in the decarbonylation of formic and oxalic acids in concentrated sulphuric acid. Supplementary data concerning the decarbonylation of L. A. in sulphuric acid diluted with water and in pyrophosphoric acid are presented and discussed. The observed temperature dependences of ¹³C and ¹⁴C K. I. E. in concentrated H₂SO₄ and in concentrated phosphoric acids media have been rationalized by invoking a change of the mechanism of decarbonylation of L. A. in concentrated sulphuric and phosphoric acids with temperature. Preliminary calculational results concerning ¹³C and ^1??C K. I. E. in decarbonylation processes are also presented. In H₂SO₄ diluted with water and in H₃PO₄ diluted with water the temperature dependence of ¹³C and ¹⁴C K. I. E. is normal and well reproduced by one frequency approximation. In concentrated sulphuric acid and in concentrated phosphoric acids besides the C—OH bond rupture the rupture of a C—C bond had to be considered also to reproduce the observed ¹³C K. I. E. in selected temperature regions.     

The Exact Three-Dimensional Half-Shell t-Matrix for a Sharply Cut-off Coulomb Potential in the Screening Limit

The screening limit of the three-dimensional half-shell t-matrix for a sharply cut-off Coulomb potential is analytically derived without reference to partial wave expansion. The numerical solutions of the three-dimensional Lippmann–Schwinger equation for increasing cut-off radii provide half-shell t-matrices which are in quite a good agreement with the asymptotic values.     

Assessment of undesirable dose to eye-melanoma patients after proton radiotherapy

Radiotherapy with a proton beam of initial energy 55–80 MeV is presently the clinically recommended therapy for some cases of intraocular melanoma such as large melanomas or tumours adjacent to critical organs. Evaluation and optimization of radiation doses outside the treatment volume may contribute to reducing undesirable side-effects and decreasing the risk of occurrence of secondary cancers, particularly for paediatric patients. In this work the undesired doses to organs were assessed basing on Monte Carlo calculation of secondary radiation transport and on results of measurements of neutron and γ-ray doses at the proton therapy facility of the Institute of Nuclear Physics at Kraków. Dosimetry was performed using a He-3-based FHT 762 neutron monitor (Wendi II), a FH40G proportional counter (for γ-rays), and MTS-7 (LiF:Mg,Ti) thermoluminescence detectors (TLDs). Organ doses were calculated in the ADAM anthropomorphic phantom using the MCNPX Monte Carlo transport code and partly verified, for γ-ray doses, with TLD measurements in the RANDO Anderson anthropomorphic phantom. The effective dose due to undesired radiation, including exposure from scattered radiation during the entire process of proton radiotherapy and patient positioning using X-rays, does not exceed 1 mSv.     

Two-electron entanglement in elliptically deformed quantum dots

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.     

De Sitter Quasigroups

The Cayley–Klein parameters for the de Sitter groups SO(4, 1) and SO(3, 2) are introduced, and in an extension of the earlier investigation of quasigroups connected with Clifford groups, quasigroups connected with the SO(4, 1) and SO(3, 2) groups are determined. It is shown that these quasigroups have eight-dimensional, double-valued irreducible cracovian representations. The covariance of a five-dimensional form of the Dirac equation with respect to the quasi-rotations forming quasigroups connected with the groups SO(4, 1) and SO(3, 2) is demonstrated. An analogy is drawn between Weyl's hidden symmetry group and a quasigroup.     

Rotationally invariant bipartite states and bound entanglement

We consider rotationally invariant states in CN₁⊗CN₂${\mathbb{C}}^{N_1}\otimes {\mathbb{C}}^{N_2}$ Hilbert space with even N₁?4$N_1?4$ and arbitrary N₂?N₁$N_2?N_1$, and show that in such case there always exist states which are inseparable and remain positive after partial transposition, and thus the PPT criterion does not suffice to prove separability in such systems. We demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys. Rev. Lett. 97 (2006) 080501] to states that remain invariant after partial time reversal.