Primjenljivost Comptonovog raspršenja za određivanje impulsne raspodjele elektrona

We present new insights regarding the validity of the impulse approximation (IA) in determining electron momentum density (EMD) from Compton scattering. These insights are obtained utilizing the code we have recently developed for the full calculation of the triple differential cross-section (TDCS) for Compton scattering. We find that, due to the averaging, at lower energies IA is more accurate for the double differential cross-section (DDCS) than for TDCS. We conclude that at such energies an EMD determination from the DDCS is more accurate than its direct determination through the measurement of the TDCS at the same energy. We also discuss the validity of IA for calculations of other less averaged Compton observables.Predstavljamo nove poglede o valjanosti impulsne aproksimacije (IA) za određivanje impulsne raspodjele elektrona (EMD) Comptonovim raspršenjem. Ti se pogledi osnivaju na primjeni nedavno razvijenog programa za računanje trostrukog diferencijalnog udarnog presjeka (TDCS) za Comptonovo raspršenje. Nalazimo da zbog računanja prosjeka, IA je na niskim energijama točnija za dvostruke diferencijalne presjeke (DDCS) nego za TDCS. Zaključujemo kako je na tim energijama određivanje EMD na osnovi DDCS točnije nego mjerenjem TDCS na istoj energiji. Raspravljamo također valjanost IA za određivanje drugih Comptonovih manje usrednjenih veličina

Primjenljivost Comptonovog raspršenja za određivanje impulsne raspodjele elektrona

We present new insights regarding the validity of the impulse approximation (IA) in determining electron momentum density (EMD) from Compton scattering. These insights are obtained utilizing the code we have recently developed for the full calculation of the triple differential cross-section (TDCS) for Compton scattering. We find that, due to the averaging, at lower energies IA is more accurate for the double differential cross-section (DDCS) than for TDCS. We conclude that at such energies an EMD determination from the DDCS is more accurate than its direct determination through the measurement of the TDCS at the same energy. We also discuss the validity of IA for calculations of other less averaged Compton observables.Predstavljamo nove poglede o valjanosti impulsne aproksimacije (IA) za određivanje impulsne raspodjele elektrona (EMD) Comptonovim raspršenjem. Ti se pogledi osnivaju na primjeni nedavno razvijenog programa za računanje trostrukog diferencijalnog udarnog presjeka (TDCS) za Comptonovo raspršenje. Nalazimo da zbog računanja prosjeka, IA je na niskim energijama točnija za dvostruke diferencijalne presjeke (DDCS) nego za TDCS. Zaključujemo kako je na tim energijama određivanje EMD na osnovi DDCS točnije nego mjerenjem TDCS na istoj energiji. Raspravljamo također valjanost IA za određivanje drugih Comptonovih manje usrednjenih veličina

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Compton scattering beyond the impulse approximation

We treat the non-relativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation (IA) or the independent particle model (IPM). An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the (N-1) electron singly ionized quantum states of the target. We show how in the high energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground state electron momentum density (EMD) of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering (IXS) spectroscopy beyond the constraints of the IA and the IPM.Comment: 7 pages, 1 figur

Analytical Derivation of the Fuss Relations for Bicentric Hendecagon and Dodecagon

In this article we present analytical derivation of the Fuss relations for n=11 (hendecagon) and n=12 (dodecagon). We base our derivation on the Poncelet closure theorem for bicentric polygons, which states that if a bicentric n-gon exists on two circles then every point on the outer circle is the vertex of same bicentric n-gon. We have used Wolfram Mathematica for the analytical computation. We verified results by comparison with earlier obtained results as well as by numerical calculations

Perturbative calculation of the cross section in double ionization by high-energy Compton scattering

In this paper we investigate double ionization in high-energy Compton scattering from the He-atom including both the shake-off mechanism and a perturbative correction to that mechanism. The correction is calculated in second-order perturbation theory and includes Coulomb electron-electron interaction in addition to the correlation in the ground state of the He-atom. Our calculations for the ratio of double to single cross section cover the range from 30 to 300 keV of impact photon energy and explain the slow convergence of the ratio towards the asymptotic value

Orientation dependence of multiple ionization of diatomic molecules in collisions with fast highly charged ions

Siegmann B, Werner U, Mann R, Kaliman Z, Kabachnik NM, Lutz HO. Orientation dependence of multiple ionization of diatomic molecules in collisions with fast highly charged ions. Physical Review A. 2002;65(1): 010704.We report an observation of the strong dependence of the multiple (6<q&LE;10) ionization cross section on the alignment of the molecular axis in collisions of highly charged Xe ions with N-2 molecules at an impact energy of 5.9 MeV/amu. Theoretical calculations based on the statistical-energy-deposition model well describe the experimental data