Stretched helium

We model stretched helium configurations using two-electron product states built from the extremal Stark states 5l ) defined in (7.2.7). As shown in Fig. 7.4 these states are quasi-one-dimensional states highly elongated in the direction. But a trivial rotation of the coordinate system results in a coordinate system E in which the states and... 

The stretched helium model can be interpreted as a chaotic scattering system. In order to establish the connection, we first consider the potential (10.2.5) of the Hamiltonian (10.2.4). Some equi-potential lines for V(e xi,X2) are shown in Fig. 10.5 for e = 1/2. This potential is very similar to the potential of elbow scattering systems investigated... 

Fig. 10.6. Distribution of lifetimes for a chaotic scattering experiment with the one-dimensional model. Irregular behaviour and dynamic scattering singularities in the interval 4.7 < 6i < 5.7 indicate the presence of chaotic scattering in the stretched helium atom. (Adapted from Bliimel and Reinhardt (1995).)...

Bliimel, R. and Reinhardt, W.P. (1995). Stretched helium a model for quantmu chaos in two-electron atoms, in Quantum Chaos, eds. G. Casati and B.V. Chirikov (Cambridge University Press, Cambridge). 

Another well-defined configuration of the classical three body Coulomb problem with unambiguous quantum correspondence is the collinear antisymmetric stretch configuration, where the electrons are located on opposite sides of the nucleus. In contrast to the frozen planet orbit, the antisymmetric stretch is unstable in the axial direction (G.S. Ezra et.al., 1991 P. Schlagheck et.al., 2003), with the two electrons colliding with the nucleus in a perfectly alternating way (Fig. 3 (left)). Hence, already the one dimensional treatment accounts for the dominant classical decay channel of this configuration. As for the frozen planet, there are doubly excited states of helium associated to the periodic orbit of the ASC as illustrated in Fig. 3 (left). 

Figure 3. Contour piot of the eiectronic density of a (tripiet) eigenstate strongly scarred by the antisymmetric stretch orbit (left), in 2D configuration space (spanned by the electrons distances ri and r-2 from the nucleus, in the collinear configurations considered here). This eigenstate belong to the N = 9 series. The solid lines depict the associated classical periodic orbit. Autoionization rates of antisymmetric stretch singlet states (right) of the Nth autoionizing series of the helium spectrum, in ID (squares), 2D (circles), and 3D (diamonds) configuration space.

Polyethylene. The Raman spectrum of polyethylene has been known for some years and all the bands have been identified seemingly unambiguously. Recently the spectrum has been recorded using stretched large-diameter fibres as a sample. The spectra were recorded with the fibre bundled vertically, horizontally and end-on in a Cary 81 spectrometer. The arrangements are illustrated in Fig. 3. The electric vector of the helium-neon laser is set vertically and therefore in the first orientation (a), the fibre axis and electric vector are parallel. 

Helium is produced primarily by separating it from natural gas. Natural gas as delivered by utilities may also include propane and air added to stretch the supply of natural gas during periods of high demand, typically during winter months. 

Thermodynamically, it can be reasoned that the major contribution of heat generation or absorption must have come from source other than the lattice, i.e., such as electrons and changes in their thermodynamic state. Similar phenomena exist in stretching a piece of rubber or other cooperative phenomenon such as the transition between ordinary helium to helium-11. 

Shortly after these elements were first characterized near the beginning of this century, chemists began their efforts to force them into some type of chemical combination. The elements have yielded grudgingly and, in almost all cases, equivocally. Compounds of helium reported formed in discharge tubes have, at best, only momentary survival, whereas the absorption of helium and argon on metals may be called chemical interaction only if the word chemical is severely stretched. The existence of acid-base compounds of argon with boron trifluoride has been reported but is still in question. 

At liquid-helium temperatures, hydrogenated ZnO samples exhibit an 0-H stretch mode at a frequency of 3326 cm at liquid-helium temperatures (Fig 1). The IR peak corresponding to this mode broadens and shifts to higher frequency when the sample is warmed to room temperature. Deuterated ZnO samples, at liquid-helium temperatures, have an 0-D stretch mode at 2470 cm . The ratio of the 0-H and 0-D frequencies are in good agreement with a simple diatomic model. More importantly, the frequency ratio is nearly identical to that of 0-H and 0-D complexes in GaP. ° Our observed 0-H mode is different from those observed by Lavrov et al. and Nickel and Fleischer. ... 

Figure 7 Experimental signal recorded for photolyzed MbCO. Fe-ligand vibrations dominate the cluster of modes observed in the 230-270 cm region. The clearly resolved frequency separation between the in-plane Fe-N, yr frequencies at 251 and 267 cm reflects the asymmetric interactions with the histidine ligand. The Fe-histidine stretching frequency appears at 234cm L Data were recorded under continuous illumination by a 15 mW helium neon laser with k = 633 nm. The temperature of a sensor mounted in the sapphire sample block was 15 K...

In association with infrared data, Raman spectra are invaluable in assigning CO-stretching frequencies. Few Raman data for carbonyl compounds are available, however, because of the experimental difficulties involved. Solutions of the compounds at high concentrations are required to obtain acceptable Raman data unfortunately, many carbonyl compounds are insufficiently soluble in the appropriate solvents. There are a few examples, however, where this problem of solubility has been circumvented by employing another phase. Thus, Raman data have been reported for the compounds, M(CO)5 (M = Mo, Cr, or W) (8), M2(CO)io [M = Re (104, 122, 179, 220) or Mn (122)] -, Mn(CO)sBr (122), Re(CO)6l (179), and Re3(CO)i2H3 (277) in the solid state and Ni(CO)4 in the gas phase (39). Another limitation is that decomposition or isomerism of the compound may occur on irradiation. The fact that all colored compounds absorb the mercury excitation line at 4358 A poses an additional problem. However, it is possible to use the helium lines at 5876, 6678, and 7065 A to obtain Raman spectra, as has been done for the compounds Fe(CO)s (283), HFe(CO)4-, Fe(CO) -, Co(CO)4- (282), M[Co(CO)4]2 (M = Cd or Hg) (281), and Ni(CO)4 (280). Further, the use of laser sources in the measurement of Raman spectra overcomes many of these difficulties this technique is now being applied extensively (122, 179, 198). 

A weather balloon filled with helium (He) has a volume of 1.0 X 10" L at 1.00 atm and 30°C. It rises to an altitude at which the pressure is 0.60 atm and the temperature is —20°C. What is the volume of the balloon then Assume that the balloon stretches in such a way that the pressure inside stays close to the pressure outside. 

FIGURE 6.8 Photoelectron spectrum of 20 produced by laser vaporization of graphite in helium gas (spectrum reproduced from Reference 37). Inset the totally symmetric tangential stretching mode of the acetylenic structure. 

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