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This study examines inelastic electron scattering form factors for the 17O and 26Mg nuclei within the sd model space, accounting for excitations outside the 16O core. Shell model computations were conducted utilising the NuShellX@MSU software, applying an effective interaction w to ascertain energy eigenvalues and eigenstates. The eigenstates were utilised to compute one-body transition densities (OBTD) for further computations of inelastic electron scattering form factors. Core polarisation (CP) effects were incorporated into the computations using the Michigan three-range Yukawa interaction as the residual interaction for core polarisation matrix elements. The computed form factors were juxtaposed with empirical data acquired from nuclear data archives. We plotted theoretical and experimental form factors as functions of momentum transfer (q) in our analysis. The incorporation of core polarisation effects markedly enhanced the concordance between theoretical predictions and experimental results.

In this work, the Whittaker wave functions were used to study the nuclear density distributions and elastic electron scattering charge form factors for proton-rich nuclei and their corresponding stable nuclei ( 10,8 B, 13,9 C, 14,12 N and 19,17 F). The parameters of Whittaker’s basis were fixed to generate the experimental values of available size radii. The Whittaker basis was connected to harmonic-oscillator basis through boundary condition at match point. The nuclear shell model was opted with pure configuration for all studied nuclei to compute aforementioned studied quantities except 10 B. For 10 B, the total spin is 3 + , therefore, there is a C2 component in empirical Coulomb form factor in addition to C0 component. The theory of core-polarization was applied to account such C2 contribution using Tassie, Bohr-Mottelson and valence models. The contribution of model space to C2 component was computed using Cohen-Kurath interaction. For exotic 8 B, 9 C, 12 N and 17 F nuclei, the Whittaker’s basis was applied only to the last exotic valence proton, on contrary to stable 10 B, 13 C, 14 N and 19 F which the Whittaker’s basis was applied to both last stable valence proton and neutron . It was seen that such treatment highly improved the calculated quantities in comparison with empirical data.

We present a comprehensive set of theoretical results for differential, integrated, and momentum transfer cross sections for the elastic scattering of electrons by beryllium, magnesium, and calcium at energies below 1 keV. In addition, we provide Sherman function values for elastic electron scattering from calcium in the same energy range. This study extends the application of our method of calculations, already employed for barium and strontium, to all stable alkaline-earth-metal atoms. Our semi-empirical approach to treating target polarization has produced in our earlier work a satisfactory agreement with experimental values and precise theoretical results such as convergent close-coupling calculations for barium. The present data are expected to be of similar high accuracy, based on our previous success in similar calculations for barium and all inert gases.

A novel scattering formalism, the multi-configuration Dirac–Fock partial wave analysis (MCDF-PWA), is presented in this study. This approach extends the conventional Dirac partial wave analysis by incorporating multiple atomic configurations of the target scatterer. The newly formulated methodology is employed to compute the cross-sections in elastic e-atom scattering. The analysis is performed for a few atomic targets like Mg, Ca, and Ba.

We report on an extensive semi-empirical analysis of scattering cross-sections for electron elastic collision with noble gases via the Markov Chain Monte Carlo-Modified Effective Range Theory (MCMC−MERT). In this approach, the contribution of the long-range polarization potential (∼r−4) to the scattering phase shifts is precisely expressed, while the effect of the complex short-range interaction is modeled by simple quadratic expression (the so-called effective range expansion with several adjustable parameters). Additionally, we test a simple potential model of a rigid sphere combined with r−4 interaction. Both models, the MERT and the rigid sphere are based on the analytical properties of Mathieu functions, i.e., the solutions of radial Schrödinger equation with pure polarization potential. However, in contrast to MERT, the rigid sphere model depends entirely upon one adjustable parameter—the radius of a hard-core. The model’s validity is assessed by a comparative study against numerous experimental cross-sections and theoretical phase shifts. We show that this simple approach can successfully describe the electron elastic collisions with helium and neon for energies below 1 eV. The purpose of the present analysis is to give insight into the relations between the parameters of both models (that translate into the cross-sections in the very low energy range) and some “macroscopic” features of atoms such as the polarizability and atomic “radii”.

This article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic centers is modified if we abandon the assumption, standard in molecular physics, that outside of some molecular sphere surrounding the centers, the wave function of the molecular continuum is atomic-like, being a linear combination of the regular and irregular solutions of the wave equation. For this purpose, the elastic scattering of slow particles by a pair of non- overlapping short-range potentials has been studied. The continuum wave function of the particle is represented as a combination of a plane wave and two spherical s-waves propagating freely throughout space. The asymptotic behavior of this function determines the amplitude of elastic particle scattering in closed form. It is demonstrated that this amplitude can be represented as a partial expansion in a set of the orthonormal functions Zλ(r) other than spherical harmonics Ylm(r). General formulas for these functions are obtained. The coefficients of the scattering amplitude expansion into a series of functions Zλ(r) and determine the scattering phases ηλ(k) for the considered two- atomic target. The special features of the S-matrix method for the case of arbitrary non-spherical potentials are discussed.

Precise knowledge of such fundamental quantity as the proton charge radius rp is extremely important both for the quantum chromodynamics (for quark-gluon structure) and for atomic physics (for atomic hydrogen spectroscopy). Yet the ambiguity in measuring rp persists for over a dozen of years by now—from the time when in 2010 the muonic hydrogen spectroscopy experiment yielded rp ≈ 0.84 fm in contrast to the form factor experiment by the Mainz group that produced rp ≈ 0.88 fm. Important was that this difference corresponded to about seven standard deviations and therefore was inexplicable. In the intervening dozen of years, more experiments of various kinds were performed in this regard. Nevertheless, the controversy remains, which is why several different types of new experiments are being prepared for measuring rp. In one of our previous papers, we pointed out the factor that was never taken into account by the corresponding research community: the flavor symmetry of electronic hydrogen atoms, whose existence was confirmed by four kinds of atomic or molecular experiments and also evidenced by two kinds of astrophysical observations. Specifically, in that paper there was discussed the possible presence of the second flavor of muonic hydrogen atoms (in the corresponding experimental gas) and its effect on the shift of the ground state of muonic hydrogen atoms due to the proton finite size. In the present paper we analyze the effect of the flavor symmetry of electronic hydrogen atoms on the corresponding elastic scattering cross-section and on the proton charge radius rp deduced from the cross-section. As an example, we use our analytical results for reconciling two distinct values of rp obtained in different elastic scattering experiments: 0.88 fm and 0.84 fm (which is by about 4.5% smaller than 0.88 fm). We show that if the ratio of the second flavor of hydrogen atoms to the usual hydrogen atoms in the experimental gas would be about 0.3, then the extraction of rp from the corresponding cross-section would yield by about 4.5% smaller value of rp compared to its true value. We also derive the corresponding general formulas that can be used for interpreting the future electronic and muonic experiments.

Low-energy electron diffraction (LEED) is considered as elastic electron-atom scattering (EEAS) operating in a target crystal waveguide, where a signal electron carrier wave is wavenumber modulated by signal exchange-correlation (XC) interaction. A carrier potential is designed using a KKR (Korringa-Kohn-Rostoker) muffin-tin (MT) model built on overlapping MT spheres that implement atoms with double degree of freedom, radius and potential level. An XC potential is constructed using Sernelius’s many-particle theory on electron self-energy. EEAS phase shifts are derived from Dirac’s differential equations, and four recent LEED investigations are recalculated: Cu(111) + (3 √ 3 × √ 3)R30° -TMB, TMB = 1,3,5-tris(4-mercaptophenyl)-benzene with chemical formula C24H15S3; Ag(111) + (4 × 4)-O; Ag(111) + (7 × √ 3)rect-SO4; and Ru(0001) + ( √ 3 × √ 3)R30° -Cl. Our EEAS phase shifts generate substantially improved reliability factors, and we report the first confirmation of electron self-energy by LEED experiment.

Electron Rutherford backscattering (ERBS) is a new technique that could be developed into a tool for materials analysis. Here we try to establish a methodology for the use of ERBS for materials analysis of more complex samples using bone minerals as a test case. For this purpose, we also studied several reference samples containing Ca: calcium carbonate (CaCO3) and hydroxyapatite and mouse bone powder. A very good understanding of the spectra of CaCO3 and hydroxyapatite was obtained. Quantitative interpretation of the bone spectrum is more challenging. A good fit of these spectra is only obtained with the same peak widths as used for the hydroxyapatite sample, if one allows for the presence of impurity atoms with a mass close to that of Na and Mg. Our conclusion is that a meaningful interpretation of spectra of more complex samples in terms of composition is indeed possible, but only if widths of the peaks contributing to the spectra are known. Knowledge of the peak widths can either be developed by the study of reference samples (as was done here) or potentially be derived from theory.