Mechanisms of inner-shell vacancy production in slow ion-atom collisions

Wille, U.; Hippler, R.

doi:10.1016/0370-1573(86)90045-1

Cited by 147 publications

(24 citation statements)

References 183 publications

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“…In [240,241] the ME is applied to study the time-evolution of rotationally induced inner-shell excitation in atomic collisions. In this context the internuclear motion can be treated classically and the remaining quantum-mechanical problem for the electronic motion is then time-dependent.…”

Section: Nuclear Atomic and Molecular Physicsmentioning

confidence: 99%

The Magnus expansion and some of its applications

Blanes¹,

Casas²,

Oteo³

et al. 2009

Physics Reports

1,064

1,300

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Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to built up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving at any order certain symmetries of the exact solution.The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature.

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Section: Nuclear Atomic and Molecular Physicsmentioning

confidence: 99%

The Magnus expansion and some of its applications

Blanes¹,

Casas²,

Oteo³

et al. 2009

Physics Reports

1,064

1,300

View full text Add to dashboard Cite

show abstract

“…For specific orbitals, however, quasi-molecular promotion and rotational coupling may still lead to exceptional high transition probabilities. In this energy range the collision dynamics depends significantly on the projectile charge state, impact parameter and on the specific projectile-target combination [27].…”

Section: Inside Solids There Is a Dynamicmentioning

confidence: 99%

Femtosecond dynamics – snapshots of the early ion-track evolution

Schiwietz¹,

Czerski²,

Roth³

et al. 2004

Nuclear Instruments and Methods in Physics Research Section B:

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The energy dissipation and femtosecond dynamics due to fast heavy ions in matter is critically reviewed with emphasis on possible mechanisms that lead to materials modifications. Starting from a discussion of the initial electronic energy-deposition processes, three basic mechanisms for the conversion of electronic into atomic energy are investigated by means of Auger-electron spectroscopy. Results for amorphous Si, amorphous C and polypropylene are presented and discussed. Experimental evidence for a highly charged track region as well as for hot electrons inside tracks is shown. As follows mainly from Auger-electron spectroscopy, there are strong indications for different track-production mechanisms in different materials.

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“…Since then, the Magnus Expansion became rapidly popular. It has been used in quantum mechanics to study time-dependent problems (Pechukas & Light 1966), semiclassical atomic collisions theory (Baye & Heenen 1973), the behaviour of molecular systems in intense laser fields (Milfeld & Wyatt 1983), multiphoton excitation of molecules (Schek, Jortner & Sage 1981), pulsed magnetic resonance spectra (Evans 1968), spectral line broadening (Cady 1974), infrared divergences in QED (Dahmen, Scholz & Steiner 1982), the solar neutrino problem (MSW effect) (D'Olivo & Oteo 1990) and a trajectories solution of the Hamilton equations in classical mechanics (Oteo & Ros 1991), transition amplitude and the cross section for K-shell ionization of atoms by heavy-ion impact (Eichler 1977), the time-evolution of rotationally induced inner-shell excitation in atomic collisions (Wille 1981; Wille & Hippler 1986), the theoretical study c ⃝ 2016 BISKA Bilisim Technology of electron-atom collisions, involving many channels coupled by strong, long-range forces (Hyman 1985), the theory of the pressure broadening of rotational spectra (Cady 1974), computing propagation in optical waveguides (Lu 2006), Helmholtz equation in waveguides (Lu 2005;2007), non-holonomic motion planning of systems without drift (Duleba 1997;, among non-holonomic systems there are free-floating robots, mobile robots and underwater vehicles (Murray, Li & Satry 1994). Also new ideas emerged for the algorithm used as an efficient numerical integrator (Iserles & Nørsett 1997;.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of a mass on a spring by means of magnus expansion method

Eryılmaz¹,

Atay²,

Başbük³

2016

ntmsci

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In this paper, the differential equation for the motion of a mass on a spring is investigated, solutions of six different cases were analyzed and numerical solutions are obtained by means of Magnus Expansion Method. Any truncation of the Magnus series preserves qualitative geometric properties of the exact solution (Castellano et al. 2014). This is an important advantage of the Magnus expansion method. Therefore Magnus expansion method provides more accurate solutions than other frequently used numerical schemes. Finally the numerical results obtained by the present method and the analytical results were compared.

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Mechanisms of inner-shell vacancy production in slow ion-atom collisions

Cited by 147 publications

References 183 publications

The Magnus expansion and some of its applications

The Magnus expansion and some of its applications

Femtosecond dynamics – snapshots of the early ion-track evolution

Vibration analysis of a mass on a spring by means of magnus expansion method

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