A hybrid mass spectrometer consisting of a magnetic sector, two electric sectors, and a quadrupole mass filter (BEEQ) has been built for the study of polyatomic ion/surface collision phenomena over the energy range of a few electron volts to several keV. Primary ions are generated by electron ionization or by chemical ionization, and the first two sectors are used to deliver a monoenergetic beam of ions, of a selected mass-to-charge m/z ratio, to a decelerator which sets the desired collision energy. The target, which can be introduced into the system without breaking vacuum, is mounted on a goniometer and situated in an electrically shielded region in the center of a large scattering chamber which contains an electric sector and a quadrupole mass analyzer used for kinetic energy and mass measurements on the ejected ions. These analyzers rotate around the scattering center to allow selection of the scattering angle of ions leaving the surface. Ultimate pressures attainable in the main scattering chamber are below 10v9 Torr allowing molecular targets, such as self-assembled monolayers of alkyl thiols on gold, to be examined without surface contamination. Low-energy (20-100 eV) collisions of polyatomic ions are reported, and examples are given of the effects of collision energy and scattering angle on surface induced dissociation mass spectra, The kinetic energy of the inelastically scattered ions is also measured, and in some cases, the internal energy can be estimated, the two measurements together providing information on energy partitioning associated with surface collisions. For example, it is shown that n-butylbenzene molecular ions of 25 eV colliding with ferrocenyl-terminated self-assembled monolayer surfaces, rebound with 10 eV of recoil energy and 3 eV of internal energy. The remainder of the energy goes into the surface. The capability of the BEEQ instrument to provide data on ion/surface reactive collisions is also illustrated with reactions such as alkyl group transfer at self-assembled monolayer surfaces. In addition, data are given showing the ability of the system to provide information on the kinetic energy distributions of ions generated in the course of high-energy collisions at the surface. Mass analysis of the sputtered products provides the instrument with secondary-ion mass spectrometry capabilities.
We discuss the maximal analytic extension along an axis where O,+ = constant of the solution to Einstein's field equations with cosmological constant with a charged point-mass source.Einstein's field equations with cosmological conthe cosmological constant may well be important stant, in understanding the global properties of our actual space-time, and (c) because metric (3) provides Rub -% g a p + Agab = -K T ,~ , another example which illustrates that the global have solutions with line elements nature of solutions to nonlinear field equations Taking for Tub the energy-momentum tensor a s s ociated with the electric field surrounding a charged point m a s s , one obtains for @ ( r ) in Eq. (2) Here w i and e a r e the m a s s and charge of the central body. The solution (3) can be obtained by anintegrationprocedure illustrated in textbooksfor the Reissner-Nordstram solution [A = 0 in Eq. (3)11 o r the Schwarzschild solution with o r without cosmological constant [e = 0 in Eq. (3)].2 Solution (3) i s containedin a more general solution mentionedby Carter.3 A metric of the f o r m (2) h a s singularities where @ vanishes o r becomes infinite. However, s o m e of these singularities a r e pseudosingularities, caused by a n inappropriate coordinate system. Graves and rill^ have shown how to extend a metric of the f o r m (2) a c r o s s a pseudosingularity by means of a coordinate transformation of the Kruskal type. They illustrated the procedure f o r the Reissner-, Nordstrijm c a s e with e 2 < m 2 . The resulting maximally extended analytic manifold turned out to be a world infinitely repeated in a timelike direction with a timelike singularity a t r = 0. It is best r e presented by means of a P e n r o s e diagram a s in some m o r e recent t e~t b o o k s .~~' The method was also used by c a r t e r 7 to find the maximal analytic extension of the K e r r solution a s well a s that of the Reissner-Nordstrijm solution f o r the special c a s e of e2=wz2. Here we do the s a m e for the metric (3). This i s an interesting exercise (a) because it i s important, in trying to understand the physical significance of Eq. (1) to study the qualitative properties of all exact solutions in idealized situations, (b) because may depend drastically on s m a l l perturbations of the equations. Since the technique of analytic extension a c r o s s pseudosingularities is well understood,' we quote h e r e only the results. It is convenient and interesting in itself to consider first the c a s e when e = 0 in metric (3), i.e., the c a s e of the Schwarzschild solution with cosmological constant. It will be easy a t the end to piece together the result f o r e = 0 with the result for A = 0 (~e i s s n e r -N o r d s t r i j m ) to obtain the result f o r the general c a s e (3).F o r e = 0, O < A < l/9tn2, @(Y) has two positive roots r, > r,, and one negative root r,. The two positive roots a r e pseudosingularities. The negative unphysical root cannot be reached because of the singularity a t r = 0 and will not concern us further...
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