The π N → e +e−N reaction close to the vector-meson production threshold

The π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections are calculated below and in the vicinity of the vector-meson (?⁰,ω) production threshold. These processes are largely responsible for the emission of e ⁺e^? pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector-meson-nucleon channels. The vector mesons materialize subsequently into e ⁺ e^? pairs. Using πN→?⁰ N and πN→ωN, amplitudes calculated in the center of mass energy interval 1.4 < √s<1.8 GeV, we compute the π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections in these kinematics. Below the vector-meson production threshold, the π⁰?ω interference in the e ⁺ e^? channel appears largely destructive for the π^? p→e ⁺ e ^? n cross section and constructive for the π⁺ n→e ⁺ e ^? p cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector-meson-nucleon channels to low-lying baryon resonances.     

A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.     

Über Sesquiselenide der Lanthanoide: Einkristalle von Ce2Se3 im C‐, Gd2Se3 im U‐ und Lu2Se3 im Z‐Typ

On Sesquiselenides of the Lanthanoids: Single Crystals of C‐type Ce₂Se₃, U‐type Gd₂Se₃, and Z‐type Lu₂Se₃ Single crystals of lanthanoid sesquiselenides (M₂Se₃; here: M = Ce, Gd, Lu) are accessible through conversion of the elements (lanthanoid and selenium) in molar ratios of 2:3 within seven days at 850 °C from evacuated silica ampoules if equimolar amounts of NaCl serve as a flux. In the case of Ce₂Se₃ (a = 897.74(6) pm) und Gd₂Se₃ (a = 872.56(5) pm) the cubic C‐type (I4¯3d, Z = 5.333) forms as dark red beads, whereas the orthorhombic Z‐type (Fddd, Z = 16) emerges for Lu₂Se₃ (a = 1125.1(1), b = 798.06(8), c = 2387.7(2) pm) as orange‐yellow bricks. Upon oxidation of monochloride hydrides (MClH_x or A_yMClH_x; M = Ce, Gd, Lu; x = 1; A = Li, Na; y = 0.5) with selenium in arc‐welded tantalum ampoules the same main products appear with C‐Ce₂Se₃ and Z‐Lu₂Se₃, even with a surplus of NaCl or LiCl as fluxing agent. In the case of Gd₂Se₃, however, black‐red needles of the orthorhombic U‐type (Pnma, Z = 4; a = 1118.2(1), b = 403.48(4); c = 1097.1(1) pm) are yielded instead of C‐Gd₂Se₃. C‐Ce₂Se₃ crystallizes in a cation‐deficient Th₃P₄‐type structure (Ce₂S₃ type) according to Ce_2.667□_0.333Se₄ (Z = 4) or with Z = 5.333 for the empirical formula Ce₂Se₃. Here, Ce³⁺ is coordinated by eight Se^2— anions trigon‐dodecahedrally. In U‐Gd₂Se₃ (U₂S₃ type) two crystallographically independent Gd³⁺ cations with coordination numbers of 7 (Gd1) and 7+1 (Gd2), respectively, are present, exhibiting mono‐ or bicapped trigonal prisms as coordination polyhedra. The crystal structure of Z‐Lu₂Se₃ (Sc₂S₃ type) shows two different Lu³⁺ cations as well, which now both reside in octahedral coordination of six Se^2— anions each.