Discrete sets of many‐body Sturmians

Randazzo, J M; Frapiccini, Ana Laura; Colavecchia, F. D.; Gasaneo, Gustavo

doi:10.1002/qua.21686

Cited by 16 publications

(17 citation statements)

References 19 publications

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“…Equation 23 can be solved by using standard matrix diagonalization subroutines, such as Lapack package. 25 The eigenfunctions of eq 23 constitute an orthogonal set with respect to both R i and n These equations define the discrete analogues of the orthogonality and completeness relations (10) and (11).…”

Section: A Numerical Approach To Solve the Sturmian Equations 3a Fimentioning

confidence: 99%

“…This produces a very substantial reduction of the amount of computational resources needed to solve a given problem. 9,11,12 The method described before has been implemented for systems having two light and one heavy particle. 11,12 In this report we extend it to general systems, by using mass weighted hyperspherical coordinates suitable for a variety of systems with different masses and interactions.…”

Section: Introductionmentioning

confidence: 99%

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Theory of Hyperspherical Sturmians for Three-Body Reactions

et al. 2009

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In this paper we present a theory to describe three-body reactions. Fragmentation processes are studied by means of the Schrodinger equation in hyperspherical coordinates. The three-body wave function is written as a sum of two terms. The first one defines the initial channel of the collision while the second one describes the scattered wave, which contains all the information about the collision process. The dynamics is ruled by an nonhomogeneous equation with a driven term related to the initial channel and to the three-body interactions. A basis set of functions with outgoing behavior at large values of hyperradius is introduced as products of angular and radial hyperspherical Sturmian functions. The scattered wave is expanded on this basis and the nonhomogeneous equation is transformed into an algebraic problem that can be solved by standard matrix methods. To be able to deal with general systems, discretization schemes are proposed to solve the angular and radial Sturmian equations. This procedure allows these discrete functions to be connected with the hyperquatization algorithm. Finally, the fragmentation transition amplitude is derived from the asymptotic limit of the scattered wave function.

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Section: A Numerical Approach To Solve the Sturmian Equations 3a Fimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Theory of Hyperspherical Sturmians for Three-Body Reactions

et al. 2009

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“…Since Sturmians are orthogonal with respect to the generating potential [29] the orthogonality relation is similar to that of energy eigenfunctions in the SW case. However, those energy eigenfunctions belong to a continuum spectrum and have no net flux.…”

Section: Generalized Sturmian Functions Generated By a Square-well (Smentioning

confidence: 95%

Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

2014

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In a recent contribution our group proposed a perturbative approach to deal with the open problem of double ionization of helium by electron impact. The goal of this work is to delve into the physics of the scattering function, and provide evidence of the nature of the single-ionization channels present in the three-body wave function. We show that the fast oscillating parts of the wave function are indeed the single-ionization channels, which appear coupled with the double continuum ones. We found a particular type of basis set within the Generalized Sturmian method that is better suited to isolate single from double-ionization channels.

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“…For convenience, as explained in [17,18], the helium ground state is also constructed within the GSF formalism. GSF basis sets with negative energy were shown to be very efficient in obtaining two-electron bound states [22,32,33]. In order to calculate the scattering function, we proceed as outlined in Ref.…”

Section: Fast Projectile Formulation and Gsf Approachmentioning

confidence: 99%

Double ionization of helium by proton impact: A generalized-Sturmian approach

et al. 2015

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We present ab initio calculations for the double ionization of helium by fast proton impact, using the generalized-Sturmian-functions methodology and within a perturbative treatment of the projectile-target interaction. The cross-section information is extracted from the asymptotic behavior of the numerical three-body function that describes the emission process. Our goal is to provide benchmark first-order Born fully differential cross sections with which one may investigate the suitability of transition matrices calculated using approximate analytic-type solutions for the double continuum (the choice of effective charges or effective momenta to partially account for the internal target interactions being, to some extent, arbitrary). We also provide fully differential cross sections for the low-ejection-energy regime, which is beyond the suitable range of such perturbative methods. We find, however, that the effective momentum approach allows one to get at least a rough characterization of the most dominant physical process involved. We also compare our calculations with the only available relative experimental set, showing an agreement in shape that can be well understood within the given momentum transfer regime.

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Discrete sets of many‐body Sturmians

Cited by 16 publications

References 19 publications

Theory of Hyperspherical Sturmians for Three-Body Reactions

Theory of Hyperspherical Sturmians for Three-Body Reactions

Insights from the zero-angular-momentum wave in single and double ionization of He by fast electrons

Double ionization of helium by proton impact: A generalized-Sturmian approach

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