Screening Constants Research Articles

Determination of the Ion—Solid Interaction Potential from the Experiment and Its Influence on the Profiles of Implanted Particles

Based on the analysis of the angular distributions of particles passing through thin gold films, the parameters of the potential that best describes the experiment are obtained. The resulting potential differs from the potential describing collisions in the gaseous phase by a noticeable change in the screening constant. The influence of the collision energy, the choice of potential, and the model of electron bremsstrahlung on the depth distribution of implanted particles is analyzed.

Effective interactions, structure, and pressure in charge-stabilized colloidal suspensions: Critical assessment of charge renormalization methods.

Charge-stabilized colloidal suspensions display a rich variety of microstructural and thermodynamic properties, which are determined by electro-steric interactions between all ionic species. The large size asymmetry between molecular-scale microions and colloidal macroions allows the microion degrees of freedom to be integrated out, leading to an effective one-component model of microion-dressed colloidal quasi-particles. For highly charged colloids with strong macroion-microion correlations, nonlinear effects can be incorporated into effective interactions by means of charge renormalization methods. Here, we compare and partially extend several practical mean-field methods of calculating renormalized colloidal interaction parameters, including effective charges and screening constants, as functions of concentration and ionic strength. Within the one-component description, we compute structural and thermodynamic properties from the effective interactions and assess the accuracy of the different methods by comparing predictions with elaborate primitive-model simulations [P. Linse, J. Chem. Phys. 113, 4359 (2000)]. We also compare various prescriptions for the osmotic pressure of suspensions in Donnan equilibrium with a salt ion reservoir and analyze instances where the macroion effective charge becomes larger than the bare one. The methods assessed include single-center cell, jellium, and multi-center mean-field theories. The strengths and weaknesses of the various methods are critically assessed, with the aim of guiding optimal and accurate implementations.

Comparison between PBE-D3, B3LYP, B3LYP-D3 and MP2 Methods for quantum mechanical calculations of polarizability and IR-NMR spectra in C24 isomers, including a novel isomer with D2d symmetry

In this study, we have performed a comprehensive theoretical analysis of C24 isomers in the gaseous phase using the PBE-D3/cc-pVTZ, B3LYP/cc-pVTZ, B3LYP-D3/cc-pVTZ and MP2/6-31G methods. We have also considered the basis set cc-pVTZ for the MP2 method, and carried out optimized (single point) calculations in three isomers (in the remaining two isomers where the convergence was too time consuming) in order to reveal the potentiality of the method. Our investigation covered a wide range of properties, including geometry optimizations, chemical stability, polarizabilities, nuclear screening constants, Fermi (FE), gap (GE) and atomization energies (AE), thermodynamic analysis, reactivity index, as well as IR and NMR spectra. These calculations were performed for the ring (D12h), sheet (D6h) and two cage (D6d and Oh) configurations. Interestingly, we also proposed a new structure, the bracelet (D2d) arrangement, which appeared to be stable according to the PBE, B3LYP and B3LYP-D3 methods, but was classified as a transition state by the MP2 method. The results consistently indicated that the D6h isomer is the most stable one among the C24 isomers studied, while the D2d isomer was found to be the least stable. Regarding the gap energy (GE), the B3LYP and B3LYP-D3 methods consistently yielded higher values compared to the PBE’s, with an average DFT (PBE and B3LYP) GE of 1.89 eV, whereas the MP2 method showed a substantially higher GE value of 7.6 eV, representing an increase of approximately 75%. Additionally, the polarizabilities of the C24 isomers were found to be overestimated by the PBE, B3LYP and B3LYP-D3 methods when compared to the corresponding MP2 values. The PBE-D3 method consistently produced higher polarizabilities for the C24 isomers in comparison to the B3LYP, B3LYP-D3 and MP2 methods. The investigation confirms that the Oh (D12h) isomer has the smallest (largest) polarizability, as agreed upon by all methods. Moreover, the polarizability of D12h is notably affected by the selected DFT method, while that of Oh displays lower sensitivity but shares similarities with D6d. However, for the newly proposed D2d isomer, the polarizability is ranked third (fourth) in ascending order with the PBE-D3 (B3LYP-D3) method. This highlights the importance of considering the electronic correlation and dispersion effects in accurately predicting polarizabilities. The results obtained from the different methods shed light on the impact of the methodology choice on the predicted properties, emphasizing the need for careful consideration when analyzing and interpreting theoretical results for such various geometries.

Hydrogen-like Plasmas under Endohedral Cavity

Over the past few decades, confined quantum systems have emerged to be a subject of considerable importance in physical, chemical and biological sciences. Under such stressed conditions, they display many fascinating and notable physical and chemical properties. Here we address this situation by using two plasma models, namely a weakly coupled plasma environment mimicked by a Debye-Hückel potential (DHP) and an exponential cosine screened Coulomb potential (ECSCP). On the other hand, the endohedral confinement is achieved via a Woods-Saxon (WS) potential. The critical screening constant, dipole oscillator strength (OS) and polarizability are investigated for an arbitrary state. A Shannon entropy-based strategy has been invoked to study the phase transition here. An increase in Z leads to larger critical screening. Moreover, a detailed investigation reveals that there exists at least one bound state in such plasmas. Pilot calculations are conducted for some low-lying states (ℓ=1−5) using a generalized pseudo spectral scheme, providing optimal, non-uniform radial discretization.

Scattering of low energy neutrinos and antineutrinos by neon and argon

The theory of scattering of low energy neutrinos and antineutrinos by atomic electrons has recently been developed [ I. B. Whittingham, Phys. Rev. D 105, 013008 (2022)] using the bound interaction picture in configuration space to fully implement the relationship between the neutrino helicities and the orbital and spin angular momenta of the atomic electrons. The energy spectra of ionization electrons produced by scattering of neutrinos and antineutrinos with energies of 5, 10, 20, and 30 keV by hydrogen, helium and neon were calculated using Dirac screened Coulombic eigenfunctions. This paper reports further applications of this theory, to a new calculation of the energy spectra for neon, as the original calculation used some screening constants which underestimated the effects of screening in the inner subshells, and to scattering by argon. The results are presented as ratios to the corresponding quantities for scattering by $Z$ free electrons. The new spectra ratios for neon are larger than the original ratios by $\ensuremath{\approx}0.03$--$\ensuremath{\approx}0.14$, with the greatest increases occurring for 10 keV neutrinos and antineutrinos. Integrated spectra ratios range from 0.16 to 0.59 for neon, and from 0.15 to 0.48 for argon, as the neutrino energy increases from 5 to 30 keV.

Electron shake probability for arbitrary shell

AbstractGeneral expressions for electron shakeup and shakeoff probabilities of arbitrary atomic shells under the sudden change in central potential have been obtained in the sudden approximation by the use of non‐relativistic hydrogenic wave functions. The matrix elements for the shakeup and shakeoff processes are expressed analytically in the similar form in terms of the Gauss‐type hypergeometric functions. Many‐electron effect is taken into account through the screened hydrogenic model and the effect of the screening constants is examined. It is found that the shakeup and total shakeoff probabilities can be written in universal form by the use of a single parameter. The dependence of the shake probabilities on this parameter is discussed.

Molecular structure, spectral and theoretical study of new type bile acid–sterol conjugates linked via 1,2,3-triazole ring

New six steroid conjugates have been prepared from bile acids (tail part)and sterol (head part) derivatives using click chemistry method. The azide-alkyne Huisgen cycloaddition (intermolecular 1,3-dipolar cycloaddition) of the azide derivatives of lithocholic, deoxycholic, cholic acid and propiolate ester of cholesterol and cholestanol gave a new bile acid–sterol conjugates linked with a 1,2,3-triazole ring. Previously, bile acids were converted into bromoacetyl substituted derivatives by the reaction of propargyl esters of lithocholic, deoxycholic, cholic with bromoacetic acid bromide in toluene with TEBA and sodium hydride. Additionally, five of the reagents: bromoacetyl and azidoacetyl substituted derivatives of propargyl esters of deoxycholic and cholic acids as well as 5α-cholestan-3-yl-propynoatewere also obtained and characterized for the first time. All conjugates were obtained in good yields using an efficient synthesis method. The structures of all conjugates as well as four substrates were confirmed by spectral (1H- and 13C NMR, and FT-IR) analysis, mass spectrometry (ESI-MS), as well as PM5 semiempirical methods. Also B3LYP calculations have been carried out. The screening constants for 13C and 1H atoms have been calculated by the GIAO/B3LYP/6–311G(d,p) approach and analyzed. Theoretical vibrational parameters are compared with obtained experimental parameters. Estimation of the pharmacotherapeutic potential has been accomplished for the synthesized compounds on the basis of Prediction of Activity Spectra for Substances (PASS). Additionally molecular docking was performed for the selected conjugate.

Metallization in hydrogenlike systems under high pressure

Almost a century ago, it was proposed that solid hydrogen could become metallic at sufficiently high pressure. Five years back, scientists observed an insulator to metal transition in liquid deuterium experimentally, at around 300 $\mathrm{GPa}$. The present work discusses and demonstrates the metal-like behavior in elemental hydrogen under various plasma environments. At the onset, the Herzfeld criterion is invoked to examine such characteristics in such plasmas under multimegabar pressure. However, a thorough study using this condition can only explain the metal-like pattern in $s$-wave states under a shell-confined condition (the system is trapped inside two concentric spheres with inner and outer radii ${R}_{a},{R}_{b}$). Moreover, using this criterion, it is not possible to explain such phenomena in (i) confined systems (involving all $\ensuremath{\ell}$) and (ii) for $\ensuremath{\ell}\ensuremath{\ne}0$ states in a shell-confined environment. Here this criterion is modified to incorporate the environmental conditions (nuclear charge, screening constant, boundary conditions) by utilizing several independent and generalized scaling concepts. The present condition can interpret a metallic pattern in confined and shell-confined plasmas connecting $\ensuremath{\ell}\ensuremath{\ge}0$ states. Further, a different descriptor is proposed therefrom. The role of pressure in defining such a descriptor is also examined. Pilot calculations are performed using Debye H\"uckel, exponential screen Coulomb potential, and ion-sphere plasmas. The relevance of the shell-confined model in the context of plasmas is elaborated. Additionally, an attempt is made to investigate the metallic character in H-like systems embedded in fullerene under high pressure.

Z-dependence of forward scattering peak intensity of electron by atoms

The dependence of the forward scattering peak intensity I on Z was considered as the power law I ̴ Zα, and the value of α was discussed. Using the Yukawa potential and the first Born approximation α = 2 is obtained as in the Z2 contrast of the HAADF-STEM. The simulation shows α at Ek = 600 eV and 30 keV are about 1/2 and 1, respectively. Z-dependence of the screening constant could explain α = 1 at Ek = 30 keV. This knowledge of Z dependence will help elemental analysis in photoelectron holography.

Forecasting football injuries by combining screening, monitoring and machine learning

Identifying players or circumstances associated with an increased risk of injury is fundamental for successful risk management in football. So far, time-constant and volatile risk factors are generally considered separately in either a screening (constant) or a monitoring (volatile) approach each resulting in a restricted set of explanatory variables. Consequently, improvements in predictive accuracy may be expected when screening and monitoring data are combined, especially when analysed with current machine learning (ML) techniques. This trial was designed as a prospective observational cohort study aiming to forecast non-contact time-loss injuries in male professional football (soccer). Injuries were registered according to the Fuller consensus. Gradient boosting with ROSE upsampling within a leave-one-out cross-validation was used for data analysis. The hierarchical data structure was considered throughout. Different splits of the original dataset were used to probe the robustness of results. Data of 88 players from 4 teams and 51 injuries could be analysed. The cross-validated performance of the gradient boosted model (ROC area under the curve 0.61) was promising and higher compared to models without integration of screening data. Importantly, holdout test set performance was similar (ROC area under the curve 0.62) indicating prospect of generalizability to new cases. However, the variation of predictive accuracy and feature importance with different splits of the original dataset reflects the relatively low number of events. It is concluded that ML-based injury forecasting based on the integration of screening and monitoring data is promising. However, external prospective verification and continued model development are required.

Energies of Doubly Excited <sup>1,3</sup>P° Resonances in He-like Systems Below the N = 2–14 Hydrogenic Threshold

In this present work, resonance energies and excitation energies of doubly ^1,3P° excited states of the helium isoelectronic sequence are calculated. The doubly excited states investigated are labelled in the (K, T, A) classification scheme. The energies are calculated in the framework of the variationnal procedure of the Screening constant by unit nuclear charge (SCUNC) formalism. The results obtained compared very well with theoretical and experimental literature values. The possibility to use the SCUNC formalism report rapidly with an excellent accuracy the position of the excitation resonances as well as their width within simple analytical formulae is demonstrated. It is demonstrated that the SCUNC-method can be used to assist fruitfully experiments for identifying narrow resonance energies. Thus, our results can be used as reference data for the interpretation of atomic spectra for the diagnosis of astrophysical and laboratory plasma. In the present work, a new correlated wave function is presented to express analytically the resonance energies and excitation energies of doubly ^1,3P° excited states in the He-like systems.

Pressure Ionization, Polarizability and Screening Constants in Confined Hydrogen Like Ions of Astrophysical Importance

Pressure Ionization, Polarizability and Screening Constants in Confined Hydrogen Like Ions of Astrophysical Importance

Confined hydrogenlike ions in plasma environments

The behavior of H-like ions embedded in astrophysical plasmas in the form of \emph{dense, strongly and weakly coupled} plasmas are investigated. In these, the increase and decrease in temperature is impacted with a change in confinement radius $(r_{c})$. Two independent and generalized scaling ideas have been applied to modulate the effect of plasma screening constant ($\lambda$) and charge of ion ($Z$) on such systems. Several new relations are derived to interconnect the original Hamiltonian and two scaled Hamiltonians. In exponential cosine screened Coulomb potential (ECSCP) (dense) and weakly coupled plasma (WCP) these scaling relations have provided a linear equation connecting the critical screening constant $(\lambda^{(c)})$ and $Z$. Their ratio offers a state-dependent constant, beyond which, a particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. With increase in $\lambda$, the accumulation of opposite charge surrounding the ion increases leading to a reduction in number of bound states. However, with rise in ionic charge $Z$, this effect can be delayed. The competing effect of plasma charge density ($n_e$) and temperature in WCP and ECSCP is investigated. A recently proposed simple virial-like theorem has been established for these systems. Multipole ($k=1-4$) oscillator strength (OS) and polarizabilities for these are studied considering $1s, 2s$ states. As a bonus, analytical closed-form expressions are derived for $f^{(k)}$ and $\alpha^{(k)} (k=1-4)$ involving $1s$ and $2s$ state, for \emph{free H-like ion}.

Influence of binding effects in cerium materials for Lq (q = l, ƞ and α1,2) X-ray emission spectra

The current investigation illustrates the systematic interrogation of the energy changes in the Lq (q = l, ƞ and α1,2) X-ray peaks of distinct cerium (Ce) materials by employing a wavelength-dispersive spectrometer. The present work counsel’s valuable information for deep insight about the local structure and binding energy effects in distinct cerium materials viz., CeX [X = Cl3, F3 and O2] and Ce2S3O12 on the Lq (q = l, ƞ and α1,2) X-ray lines. The present finding reveals that the Lq (q = l, ƞ and α1,2) X-ray lines emanated from different Ce materials show energy shifts of ~1.67–7.62 eV concerning the pure Ce target. A procedure for estimating measured and calculated radiative L3M transition probabilities for distinct Ce materials has been incorporated at present assessment, assuming the different sets of natural line widths for the L-shell hole states, prominent to statistical dissemination of particular initial states. Additionally, the measured values of relative intensity ratios IQ [Q = Ll/Lα1,2 and Lƞ/Lα1,2] for Ce materials show higher discrepancies relative to pure Ce which can be imitated in the perspective of change in the crystal structures, different electronegativity of the adjacent ligands attached to Ce+3 or Ce+4 ions and influence of outermost screening constants. The promising connection among energy shifts in Ce Lq (q = l, ƞ and α1,2) X-ray lines of different materials and influencing parameters are also explored in this work.

Ionization of many-electron atoms by the action of two plasma models

The Hartree-Fock equations for many-electron atoms embedded in a plasma medium are solved using two different plasma models: (a) Debye-Hückel screening (DHS) potential and (b) exponential cosine screened Coulomb (ECSC) potential. Roothaan's approach is implemented for these models after solving the inherent difficulties to evaluate integrals where screening appears explicitly. A corresponding computer code was developed using the method of global basis sets (GBS). The reliability of this approach was verified by solving the Hartree-Fock equations through implementation of the finite-differences and finite-element grid methods and applied to two-electron atoms, yielding excellent agreement with the Roothaan-GBS (RGBS) method. The RGBS method was used to study the energy evolution and ionization threshold of several closed- and open-shell many-electron atoms embedded either in weak or strong DHS or ECSC plasma conditions. In all cases, a critical value of the screening length is obtained for which ionization is achieved, being systematically larger for DHS conditions, indicating the effect of a more repulsive ECSC potential. For He-like atoms in the ground state, we report a comprehensive set of accurate total energy data as a function of the screening constant using the Lagrange mesh method, which includes the electron correlation effects. The electron correlation energy is estimated using this data with reference to the RGBS estimates of energy as the Hartree-Fock energy. The variation of correlation energy as a function of screening constant under the different plasma potentials is rationalized in terms of a conjectured comparison theorem. Finally, a discussion on the effect of plasma strength on localization or delocalization of the electronic density derived from the RGBS method is presented in terms of changes in the Shannon entropy, yielding consistent results for delocalization close to the ionization threshold.

Construction of Оne-Range Addition Theorems for Noninteger Slater Functions Using Self-Friction Exponential Type Orbitals and Polynomials

The addition theorems of Slater type orbitals (STOs) presented in literature are generally complicated to theoretically examine the electronic structure of atoms and molecules. The computational deficiencies in use of these theorems arise from the separation of integral variables. In this work, to eliminate these calculation efforts, a large number of independent one-range addition theorems for $$\chi $$ -noninteger Slater type orbitals ( $$\chi $$ -NISTOs) in terms of $$\chi $$ -integer STOs ( $$\chi $$ -ISTOs) is presented by using complete orthogonal basis sets of $${{L}^{{(p_{l}^{*})}}}$$ -self-friction (SF) polynomials ( $${{L}^{{(p_{l}^{*})}}}$$ -SFPs), $${{\psi }^{{(p_{l}^{*})}}}$$ -SF exponential type orbitals ( $${{\psi }^{{(p_{l}^{*})}}}$$ -SFETOs), $${{L}^{{(\alpha \text{*})}}}$$ -modified SFPs ( $${{L}^{{(\alpha \text{*})}}}$$ -MSFPs), and $${{\psi }^{{(\alpha \text{*})}}}$$ -modified SFETOs ( $${{\psi }^{{(\alpha \text{*})}}}$$ -MSFETOs) introduced by one of the authors. Here, $$p_{l}^{*} = 2l + 2 - \alpha \text{*}$$ and $$\alpha \text{*}$$ are the integer $$(\alpha \text{*} = \alpha ,\; - {\kern 1pt} \infty < \alpha \leqslant 2)$$ or noninteger ( $$\alpha \text{*} \ne \alpha ,$$ $$ - \infty < \alpha < 3$$ ) SF quantum numbers based on the Lorentz damping theory. The expansion coefficients of series for the one-range addition theorems are expressed through the analytical relations for the overlap integrals of $$\chi $$ -NISTOs with the same screening parameters. As an application, the calculations of overlap integrals with the different screening constants of $$\chi $$ -NISTOs are performed.

Critical stability and quantum phase transition of two-electron system under exponential-cosine-screened-Coulomb interaction

The stability of two electron system under the influence of the exponential-cosine-screened-Coulomb (ECSC) potential has been studied as a function of continuously varying nuclear charge (Z) and screening constant (μ). Inter-electronic correlation has explicitly been considered by adopting Hylleraas type basis set under Ritz variational framework. The correlated basis integrals originating from the elements of Hamiltonian and overlap matrices are evaluated analytically. Critical nuclear charges (Zc), the minimum amount of nuclear charge required to form at least one bound state, corresponding to different μ values have been predicted. Different structural properties along with two-particle densities (TPD) for all possible orientations of the electrons have been estimated using the optimized wave function. Prominent signature of quantum phase transition (QPT) of the system around the Zc values has been reported. A comparative study has been done on the critical stability of the system under the influence of ECSC potential, screened Coulomb (SC) potential and pure Coulomb (PC) potential.

Energy and Screening Constants of the Two-Dimensional Helium Atom

Following the calculational technique proposed in our previous works, the energy and screening constants of the helium atom with a two-dimensional spatial configuration of its electron distribution have been calculated for the case when one electron is found in the ground state with energy quantum number N′ =0 , and the second in an excited state with values of the quantum number N =1, 2, ..., 10 . Graphs are presented of the dependence of these quantities on the discrete variable N with elucidation of their characteristic asymptotic behavior.

Energy and Screening Constants of a One-Dimensional Helium Atom in Excited States

In analogy with earlier calculations by the authors of screening constants and the energy of the ordinary threedimensional helium atom, this same program has now been used for the first time for the one-dimensional atom. For one of the electrons with energy quantum number n′ = 1, found in the ground state, and for the second electron with quantum number n = 2,3,...9 , found in an excited state, we find that in this range the screening constant σn falls monotonically with growth of n, tending to zero in the formal limit n → ∞ , and the absolute value of the energy En in this limit tends to a constant value in complete analogy with the threedimensional atom. Results of numerical calculations of σn and |En| in this range are presented in the form of tables and graphs. The conclusions of this work can in principle be verified since, for example, onedimensional Na atoms in the Bose condensate phase were previously obtained experimentally, and it appears to be entirely possible to also obtain one-dimensional He atoms.

Энергия и постоянные экранирования двумерного атома гелия

Энергия и постоянные экранирования двумерного атома гелия