A theoretical analysis of the collisions of particles with deuterons is carried out in the high-energy approximation. This approximation, which corresponds to a generalized form of diffraction theory, takes explicit account of double collision processes as well as single ones. It is used to express the amplitudes for elastic and inelastic scattering by deuterons in terms of the elastic-scattering amplitudes of the neutron and proton and the deuteron wave functions, The resulting expressions are used to evaluate the differential cross section for elastic scattering, and the angular distribution of inelastic scattering (i.e. , the differential cross section for deuteron breakup integrated over 6nal energies of the incident particle). The contributions to these cross sections of the various single and double scattering processes and the terms which represent their interference are exhibited individually. Expressions are derived for the total cross section of the deuteron and for its elastic and inelastic total scattering and absorption cross sections. The difference between the various types of deuteron cross sections and the sum of the corresponding cross sections for the free neutron and proton is explained in some detail. Spin-dependent interactions are treated, and for incident particles of spin 2 an expression is given for the deuteron total cross section in terms of the general spindependent scattering amplitudes of the neutron and proton. The theory is applied to antiproton-deuteron collisions in the energy range from 0.13 to 17.1 BeV. The results for the total and absorption cross sections which are calculated for a variety of models of the deuteron wave function are found to be in good agreement with the measurements. The magnitudes of such effects as double scattering and the interference of singleand double-scattering amplitudes are seen to be appreciable. , Phys. Rev. 123, 320 (1961. ).' V. Franco, thesis, Harvard University, 1963 (unpublished).

Pt on mesostructured CeO(2) nanoparticles embedded within ultrathin layers of highly structured SiO(2) binder shows highest activity reported with 80% selectivity for the chemoselective hydrogenation of crotonaldehyde. Characterization by transmission electron microscopy (TEM), CO adsorption, and X-ray photoelectron spectroscopy (XPS) show the presence of small Pt metal particles, preferentially located on CeO(2) (70%) together with the formation of Pt-CeO(2-x) sites at the interface between Pt and CeO(2) (4 nm) nanoparticles. These sites are able to polarize the carbonyl group and facilitate the selective hydrogenation of this with respect to the double bond.

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Glauber theory can describe elastic scattering of a. particles by 4 He, 3 He, 2 H, and *H at 7 GeV/c if the phase of the nucleon-nucleon elastic-scattering amplitude varies with momentum transfer. The phase variation leads to diffraction patterns differing markedly from those typical of constant-phase calculations and greatly affects the magnitudes of the intensities. These changes are mainly due to changes in the interference between amplitudes for different orders of multiple scattering and to a decrease in their moduli. PACS numbers: 25.55.Ci, 21.30. + y, 24.10.Ht During the past twenty years the Glauber theory has been extremely successful in describing hadronnucleus elastic scattering at energies of approximately 1 GeV or higher. This success has not been shared to the same degree in nucleus-nucleus ("heavy-ion") elastic scattering at corresponding energies of 1 GeV/nucleon or higher for several reasons. First, there has been a relative paucity of such measurements. Second, the extension of the theory to nucleus-nucleus collisions is significantly more complex and the computations are more difficult and lengthy so that fewer of these types of calculations exist. 1 Recently a comprehensive set of measurements of elastic scattering of a particles by four very light nuclei ( 4 He, 3 He, 2 H, *H) was made at an incident a-particle momentum of 7 GeV/c over a range of |r| values from -0.07 to -4 (GeV/c) 2 . The cross sections fell from the barn to the nanobarn level. Such data, in which the intensities vary through so many orders of magnitude and over such a large range of momentum transfers, are extremely useful because they put enormous constraints on any theory. It is no longer sufficient to show that the theory describes measurements of collisions between just one given pair of nuclei. Now the theory must describe measurements between four different pairs of nuclei, and it must do so consistently. Whatever nucleon-nucleon (AW) elasticscattering amplitude is used for one calculation should be used for the others as well. In addition, since these measurements have gone out to rather large momentum transfers, the calculated intensities will be much more sensitive to the AW elastic scattering amplitudes used as input.The measurements for elastic scattering of a particles by the four light nuclei were accompanied 2 by theoretical analyses for the a-2 H, «-3 He, and «-4 He cross sections. These analyses were both by means of the so-called "rigid projectile approximation" and by means of the Glauber theory, with Gaussian densities for the nuclear ground states. The rigid-projectile approximation failed even qualitatively except at very small momentum transfers. 2 In the Glauber-theory calculations shown, 2 the broad qualitative trends of the data were to some extent roughly described. Quantitatively the results were in strong disagreement with the data, often being as much as an order of magnitude too low.In the present analysis we have calculated the elastic-scattering differential cross sections for all four p...

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14we have used the normalization as iiu = mZs/h' for 1 5~. Gottfried and J. D. Jackson, Nuovo Cimento 33, any spin in Refs. 3 and 4 and Cxu = rn1'/2 E' . The 309 (1964). differential cross section which appeared in Refs. 3 and H. Albright and L. S. Liu, Phys. Rev. 140, B1611 4 should be divided by (1965).The general expression for the electron-deuteron scattering amplitude is derived within the framework of Glauber theory. An approximation to this expression, used earlier, is shown to be valid at large, but not at small, momentum transfers. Two-photon exchange effects are somewhat smaller than previously thought. A simple extrapolation of the data does not indicate two-photon exchange dominance at large momentum transfers. Existing data indicate that because of interferences, two-photon exchange effects can change the cross section by -10% fort --1 (G~V/C)~.It has been known f o r s o m e time that double scatterings dorninate in collisions of high-energy hadrons with deuterons a t large momentum transfers.' The methods used t o analyze such collisions a r e usually based upon Glauber theory.' The a mplitude F, for double scattering i s a two-dimensional integral, over momentum transfers Eh, involving the hadron-proton and hadron-neutron strong-interaction elastic scattering amplitudes f,(G) and fn(4) and the deuteron wave function. It takes the form3 where ~( 3 )is the deuteron f o r m factor and t i E i s the incident momentum. Since the deuteron i s considerably l a r g e r than the range of the hadron-nucleon strong interaction, S (qf)decreases much m o r e rapidly wifh increasing q' near q'=O than do f,,,(+: f 6'). Hence it i s usually a good approximation to replace the amplitudes f, and f, in Eq. (1) by their values a t q' = 0. This leads t o a n approximation to Fz given by where ( F 2 ) is the expectation value, in the deuteron ground state, of the inverse-square neutronproton separation. The intensity f o r double scattering is then given by Double scattering i s typically s m a l l e r than single scattering near the forward direction. However the single-scattering intensity contains a factor s 2 ( i q ) which d e c r e a s e s rapidly with q near q = O . We s e e that in Eq. (3) the structure of the deuteron appears only via (r-'), a constant. Consequently, double scattering does not d e c r e a s e s o rapidly with q, and eventually dominates single scattering. Its q dependence i s insensitive to the structure of the deuteron.Equation (3) has been recently used by Gunion and Stodolsky4 to describe electron-deuteron scattering, a n electromagnetic interaction. Since Eqs.(1)-(3) were derived f o r strong interactions, it is necessary to derive a n equivalent expression f o r the electromagnetic case. We s e e , f o r example, that for e-d scattering the integral in Eq. (1) diverges since f,(q) mq-' for small g. Hence Eqs.(2) and (3) will clearly not be valid for small q. The need for a special derivation was recognized in Ref. 4. Let the e-p and e-n scattering amplitudes, f, and f,, be written a ...

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The Glauber approximation is applied to elastic scattering of protons by hydrogen atoms and to excitation of the 2s, 2p, 3s, and 3p levels of the hydrogen atom by proton impact. The predicted differential and integrated elastic and excitation cross sections are compared with other calculations and with the available experimental data. A minimum appears in both the 1s-2s and ls-3s integrated cross sections near 15keV. The corresponding differential cross sections near 15 keV exhibit a minimum and a maximum at very small scattering angles. The Glauber approximation is a considerable improvement over the Born approximation at energies &-200keV and the distortion approximation at energies &-100keV. At energies &-200keV, our calculated total excitation cross sections are close to the Born approximation.Nevertheless, over most of the angular range our calculated differential cross sections are very different from the Born-approximation values. Above 10keV our results are in good agreement with the only available experimental data (1s-2p), indicating that above 10keV the Glauber approximation should yield reasonable estimates for proton-hydrogen-atom collision cross sections.