<i>L</i><sup>2</sup> discretization of Sturmian wave functions for Coulomb‐like potentials

ABSTRACT:In this work, we present a method to obtain two-particle Coulomb Sturmians Functions (CSF) with an expansion in a set of L 2 basis functions. In the two-body case, we recover the exact (discrete) spectrum of the CSFs for negative energies and a discretized approximation for positive ones. Besides, we make use of this method to analyze the two-independent electron problem as a Generalized Sturmian problem. We propose a discretized version of the wave function in terms of the CSF states, and show that the problem reduces to find numerical coincidences between energy-dependent eigencharges of the mutually independent one-electron systems. This expansion methodology includes the continuum information which is lost in the sets used previously in the literature, and is complete when the size of the basis goes to infinity.

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“…It has been shown that the coefficients (9) are polynomials in β ν , and these eigenvalues are the N solutions of [12] …”

Section: A Quadrature Schemementioning

confidence: 99%

“…We first discuss the general theory in Section 2.1. In Section 2.2 and 2.3 we review the quadrature and finite differences scheme used to obtain a discrete charge spectrum for any (negative or positive) energy [12]. The extension to the problem of two-electron atoms is discussed in Section 3.…”

Section: Introductionmentioning

confidence: 99%

Discrete sets of many‐body Sturmians

Randazzo

Frapiccini

Colavecchia

et al. 2008

Int J of Quantum Chemistry

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“…The three-body solutions that are obtained with them are equivalent, although the basis functions they produce differ considerably. In the three-body context, the SW basis was used in [23], and both types were used in [24], where they were generated with two different methodologies [15,20].…”

Section: B Basis Set Typesmentioning

confidence: 99%

“…where H TP is the matrix representation of the operators in (15), separating the overlapping term, whose elements are O | n a ,n b . Similarly, the F vector is the projection of the RHS of Eq.…”

Section: Fast Electron Regime Modelmentioning

confidence: 99%

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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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Application of a water jet system to the pretreatment of cellulose

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Plant cellulose is the most abundant organic compound on earth. Technologies for producing cellulose fiber or improving the enzymatic saccharification of cellulose hold the key to biomass applications. A technology for atomizing biomass without strong acid catalysis remains to be developed. The water jet is a well-known device used in machines (e.g., washing machines, cutters, and mills) that use high-pressure water. In this study, we examined whether a water jet system could be used to atomize crystalline cellulose, which comprises approximately 50% of plant biomass. The Star Burst System manufactured by Sugino Machine Limited (Sugino Machine; Toyama, Japan) is a unique atomization machine that uses a water jet to atomize materials and thereby places lower stress on the environment. After treatment with this system, the crystalline cellulose was converted into a gel-like form. High-angular annular dark-field scanning transmission electron microscopy showed that the cellulose fibers had been converted from a solid crystalline into a matrix of cellulose nanofibers. In addition, our results show that this system can improve the saccharification efficiency of cellulases by more than three-fold. Hence, the Star Burst System provides a new and mild pretreatment system for processing biomass materials.

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L² discretization of Sturmian wave functions for Coulomb‐like potentials

Cited by 17 publications

References 31 publications

Discrete sets of many‐body Sturmians

Discrete sets of many‐body Sturmians

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

Application of a water jet system to the pretreatment of cellulose

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L2 discretization of Sturmian wave functions for Coulomb‐like potentials

Cited by 17 publications

References 31 publications

Discrete sets of many‐body Sturmians

Discrete sets of many‐body Sturmians

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

Application of a water jet system to the pretreatment of cellulose

Contact Info

Product

Resources

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L² discretization of Sturmian wave functions for Coulomb‐like potentials