Effective Charge Approach Research Articles

Use of Gaussian-type functions for flux-based dose calculations in carbon ion therapy.

In radiation therapy, it is very important to ensure that the radiation dose is correctly delivered to the patient. This is achieved by obtaining quantitative dose measurements for beam calibration in the treatment planning system. Dose calculations should be performed with the required accuracy to a degree of uncertainty of less than 1%. The measurement of the absorbed dose in and around body tissues irradiated with carbon ions requires careful use of materials selected from established phantom and radiation detectors. The main advantage of such materials is that when information on the energy and nature of charged particles at the desired point is incomplete or inaccurate, they can allow determination of the absorbed dose. In general, radiation interactions in a tissue representation caused by carbon ions can be characterized by calculating the linear stopping power. Carbon ions have a limited penetration depth within human tissues that depends on the energy and stopping power of these ions as they penetrate into the body. The purpose of the present study was to calculate the stopping power, range and dose to intestinal and prostate tissues of carbon ions. The stopping power values of these tissues were specified by the effective charge approach method. The 5ZaPa-NR-CV, pcemd-4 and pcSseg-4 sets of Gaussian-type functions were employed for the calculation of electronic charge density. Range calculations were made by means of the Gaussian quadrature method, making use of the continuous slowing down approximation. Flux-based dose calculations were also carried out in accordance with the Bragg-Gray theorem using the Geant4 and FLUKA simulation toolkits. The results were compared with each other and with the SRIM and CasP datasets. Then, depth-dose distributions and range values were verified by positron emission activity using the GATE toolkit. Among the different types of Gaussian functions used here, the best semi-analytical result was found for the 5ZaPa-NR-CV set. The results obtained in the present study can be used for dose verification and dose reconstruction in charged particle radiotherapy and for radiation research on the interaction of radiation with matter. The results calculated here will be useful for quantifying uncertainties associated with stopping power, range, and reconstruction of dose in charged particle therapy.

Room-temperature ferroelectricity in A-site ordered Ruddlesden-Popper Li2CaTa2O7 ceramics

In the present work, the crystal structure, ferroelectric and dielectric properties of the dense single-phase Li2CaTa2O7 ceramics with A-site ordered double-layer Ruddlesden-Popper structures have been investigated by the experiments and first-principles calculations. A polar Pna21 phase was determined by the Rietveld refinement against the X-ray diffraction pattern at room temperature, and it was confirmed by its lowest calculated energy and rigid phonon modes. The ferroelectricity was found by observing the ferroelectric hysteresis loop at room temperature, and its remanent polarization was similar to the value calculated from the Berry phase and Born effective charge approaches. The ferroelectricity is a non-conventional proper one since its polarization is induced from the displacement of oxygen anions instead of tantalum cations based on the individual atomic polarization. A first-order transition from an antiferroelectric to paraelectric phase around 900 K was found by the DSC and variable-temperature dielectric measurements. From the present work, the room-temperature ferroelectricity is experimental confirmed in the present ceramics, inspiring the search for new ferroelectricity in the ceramics with A-site ordered Ruddlesden-Popper structures.

İnce Cu2ZnSnS4 (CZTS) filmin RBS spektrumundan enerji kaybı analizi

The goal of this work is to offer an alternative method to the available literature on determining the energy loss of CZTS thin films. For this purpose, thin CZTS film structures were first produced by sol-gel method and then the RBS spectrum was received with RBS detector irradiating this structure with 3.034 MeV proton beams in a microbeam chamber. The energy calibration was implemented to this spectrum, where the it was fitted with SIMNRA program. In the RBS spectrum of the thin film generated, a method for the calculation of energy loss was used for the position and energy width analysis of the corresponding peaks and a polynomial fit was obtained from the stopping power of the CZTS thin film by making certain approaches. Also, the effective charge approach that we used in our previous studies for the stopping power was employed with atomic natural orbitals and it was founded that the results were close to each other at certain error rates. The data obtained from this study will inspire the future studies on the interaction of radiation with matter.

The calculation of stopping power and range for radium, thorium and uranium using new electronic potential energy function

In this paper, the electronic stopping power and range calculations of radium-226, thorium-229 and uranium-236 isotopes, which are natural alpha emitters, were performed for the alpha particles in the 200 keV-10 MeV energy range. The effective charge approach based on the Bethe-Bloch theory for the stopping power, the continuous slowing down approach and the Simpson 1/3 method were used for calculation of the range. To this end, new electronic potential energy functions were primarily obtained by using the Lie group method for the target elements. For electronic charge density, relativistic atomic natural orbitals based on Gaussian type orbitals were selected. The results were compared with the existing data sets in the literature. The potential energy curves obtained were irregular at certain distances, but were quite close to that of the multi-atomic target systems. The stripping distances of the target atoms and the corresponding potential energy values were determined from the potential energy functions. It was observed that the stopping power and range values were generally compatible with the SRIM and ICRU 49 data at specific error rates. By adding some correction factors to the calculations, it is predicted that the discrepancies and the error rates may be reduced. The results acquired with this innovative work can be used in the interaction of charged particles with matter, applications related to alpha decay and shielding.

Stopping power and dose calculations with analytical and Monte Carlo methods for protons and prompt gamma range verification

In this study, we have performed the calculations stopping power, depth dose, and range verification for proton beams using dielectric and Bethe–Bloch theories and FLUKA, Geant4 and MCNPX Monte Carlo codes. In the framework, as analytical studies, Drude model was applied for dielectric theory and effective charge approach with Roothaan–Hartree–Fock charge densities was used in Bethe theory. In the simulations different setup parameters were selected to evaluate the performance of three distinct Monte Carlo codes. The lung and breast tissues were investigated are considered to be related to the most common types of cancer throughout the world. The results were compared with each other and the available data in literature. In addition, the obtained results were verified with prompt gamma range data. In both stopping power values and depth-dose distributions, it was found that the Monte Carlo values give better results compared with the analytical ones while the results that agree best with ICRU data in terms of stopping power are those of the effective charge approach between the analytical methods and of the FLUKA code among the MC packages. In the depth dose distributions of the examined tissues, although the Bragg curves for Monte Carlo almost overlap, the analytical ones show significant deviations that become more pronounce with increasing energy. Verifications with the results of prompt gamma photons were attempted for 100–200 MeV protons which are regarded important for proton therapy. The analytical results are within 2%–5% and the Monte Carlo values are within 0%–2% as compared with those of the prompt gammas.

Monitoring of saline tracer movement with vertically distributed self-potential measurements at the HOBE agricultural test site, Voulund, Denmark

The self-potential (SP) method is sensitive to water fluxes in saturated and partially saturated porous media, such as those associated with rainwater infiltration and groundwater recharge. We present a field-based study at the Voulund agricultural test site, Denmark, that is, to the best of our knowledge, the first to focus on the vertical self-potential distribution prior to and during a saline tracer test. A coupled hydrogeophysical modeling framework is used to simulate the SP response to precipitation and saline tracer infiltration. A layered hydrological model is first obtained by inverting dielectric and matric potential data. The resulting model that compares favorably with electrical resistance tomography models is subsequently used to predict the SP response. The electrokinetic contribution (caused by water fluxes in a charged porous soil) is modeled by an effective excess charge approach that considers both water saturation and pore water salinity. Our results suggest that the effective excess charge evolution prior to the tracer injection is better described by a recent flux-averaged model based on soil water retention functions than by a previously proposed volume-averaging model. This is the first time that raw vertically distributed SP measurements have been explained by a physically based model. The electrokinetic contribution cannot alone reproduce the SP data during the tracer test and an electro-diffusive contribution (caused by concentration gradients) is needed. The predicted amplitude of this contribution is too small to perfectly explain the data, but the shape is in accordance with the field data. This discrepancy is attributed to imperfect descriptions of electro-diffusive phenomena in partially saturated soils, unaccounted soil heterogeneity, and discrepancies between the measured and predicted electrical conductivities in the tracer infiltration area.

Two pyrazolylborate dysprosium(III) and neodymium(III) single ion magnets modeled by a Radial Effective Charge approach

A Radial Effective Charge model based on a point charge approach is applied in order to study the magnetic behavior of two lanthanoid single ion magnets coordinated by pyrazole-based ligands that produce a D3h crystal field. We obtain the lowest-lying magnetic levels and the associated wave functions of Dy(H2BPzMe22)3 (1), and the tricapped NdTp3 (2), where H2BPzMe22=dihydrobis(dimenthylpyrazolyl)borate and Tp=trispyrazolylborate. Results support the observed SMM behavior.

Effective charge and the mean charge of swift ions in solids

We perform a nonlinear study of the energy loss of light and heavy ions in solids using the quantum transport-cross-section method based on numerical solution of the Schr\"odinger equation. The charge of the ion---the relevant parameter in this calculation---is considered equal to the average ion charge measured after emergence from solid foils. When the calculated energy loss values are analyzed within the framework of the effective charge approach, the results of the present calculations are in excellent agreement with the empirical values and also show the expected scaling properties. Through this analysis, we find a relationship between the charge state inside the solid and the effective charge related to energy loss studies, which solves a seaming contradiction between these values. The implications of this study with respect to the Bohr-Lindhard and Betz-Grodzins models are discussed.

Vibrational Properties of Cubic AlxGa1?xN and InxGa1?xN Ternary Alloys

The phonon dispersion curves and phonon density of states of the cubic AlxGa1—xN and InxGa1—xN alloys were calculated within the framework of a valence force field method and an effective charge approach for the long-range Coulomb interaction. The valence-force parameters and effective charges for the cubic GaN, AlN and InN binary compounds were fitted to the phonon frequencies at high-symmetry points in the Brillouin zone measured by Raman spectroscopy and calculated by ab initio methods. The scaling factor approximation was used to obtain the valence-force parameters and effective charges for the alloys. A good agreement between our calculations and recent Raman data for the alloys is achieved.

Renormalons and multi-loop estimates in scalar correlators, Higgs decay and quark-mass sum rules

Abstract The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the MS -scheme in the limit of a large number of fermions, N f . At n -loop order we find that in the MS -scheme the factorial growth of the perturbative coefficients due to renormalons takes over almost immediately in the Euclidean region. The essential differences between the large-order growth of perturbative coefficients in the present scalar case, and in the previously-studied vector case are analysed. In the timelike region a stabilization of the corresponding perturbative series for the imaginary part, with n -loop behaviour S n /[ log (s/Λ 2 )] n−1 , where S n is essentially constant for n≤6 , is observed. Only for n≥7 does one discern the factorial growth and alternations of sign. We use the new all-orders results to scrutinize the performance of multi-loop estimates, using a large- β 0 =(11N c −2N f )/12 approximation, the so-called “naive nonabelianization” procedure, and within the effective charges approach. The asymptotic behaviour of perturbative coefficients, in both large- N f and large- N c limits, is analysed both in the spacelike and timelike regions. A contour-improved resummation technique in the timelike region is developed. Some subtleties connected with scheme-dependence are analysed, and illustrated using results in the MS - and V -schemes. The all-orders series under investigation are summed up with the help of the Borel resummation method. The results obtained are relevant to the analysis of the theoretical uncertainties in the 4-loop extractions of the running and invariant s -quark masses from QCD sum rules, and in calculations of the Higgs boson decay width into a quark–antiquark pair.

Critical comparison of retention models for the optimisation of the separation of anions in ion chromatography: II. Suppressed anion chromatography using carbonate eluents

Seven theoretical retention models, namely the linear solvent strength model (using the dominant equilibrium approach and competing ion effective charge approach), the dual eluent species model, the Kuwamoto model, the extended dual eluent species model, the multiple species eluent/analyte model and the empirical end-points model, were used to describe the retention behaviour of anions in suppressed ion chromatography (IC). An extensive set of experimental retention data was gathered for 24 anions (fluoride, formate, bromate, chloride, hexanesulfonate, bromide, chlorate, nitrate, iodide, thiocyanate, perchlorate, sulfite, succinate, sulfate, tartrate, selenate, oxalate, tungstate, phthalate, molybdate, chromate, thiosulfate and phosphate) on a Dionex AS4A-SC column using carbonate eluents of varying concentration and HCO 3 −:CO 3 2− ratios. Statistical comparison of the predicted and experimentally obtained retention factors showed that the performance of the theoretical models improved with the complexity of the model. However the empirical model (in which a linear relationship is assumed between the logarithm of retention factor and the logarithm of eluent strength, but the slope is determined empirically) gave the most consistent performance across the widest range of anions. The empirical end-points model was also shown to be the most satisfactory model due to its low knowledge requirements and easy solution. Compared with non-suppressed IC (see Part I), the retention behaviour in suppressed IC was found to be easier to model by all retention models.

Critical comparison of retention models for optimisation of the separation of anions in ion chromatography: I. Non-suppressed anion chromatography using phthalate eluents and three different stationary phases

A series of mathematical models describing analyte retention behaviour in non-suppressed ion chromatography of anions has been compared in order to assess their suitability for inclusion in computer optimisation software for determining the optimal eluent composition for a desired separation. The series of models comprised the linear solvent strength model (using both the dominant equilibrium approach and the competing ion effective charge approach), the dual eluent species model, the Kuwamoto model, the extended dual eluent species model and the multiple species eluent/analyte model, together with a new empirical model, the end points model. An extensive set of experimental retention data obtained for 15 anions (acetate, fluoride, iodate, bromate, chloride, nitrite, bromide, chlorate, nitrate, iodide, oxalate, sulfate, sulfite, thiosulfate and phosphate) on three columns (Waters IC Pak A, Hamilton PRP-X100 and Vydac 302 IC) using phthalate eluents of varying concentration and pH was used to evaluate the ability of each model to predict retention factors. Statistical comparison of the predicted retention factors with those obtained experimentally showed that the performance of the theoretical models improved with the complexity of the model, but none of the theoretical models could give sufficiently reliable prediction of retention factors (especially for divalent analyte ions) for the model to be used in optimisation software. However, the empirical end points model (in which a linear relationship is assumed between log k′ and log [eluent], but the slope of the relationship is determined empirically) gave satisfactory performance, with correlation coefficients for all analytes of 0.9953, 0.9840 and 0.9919 for the Hamilton PRP-X100, Vydac 302 IC and Waters IC Pak A columns, respectively.

Relations between observables and the infrared fixed point in QCD

We investigate the possibility that α s freezes as function of N f within perturbation theory. We use two approaches — direct search for a zero in the effective-charge (ECH) β function, and the Banks-Zaks (BZ) expansion. We emphasize the fundamental difference between quantities with space-like vs. those with time-like momentum. We show that within the ECH approach several space-like quantities exhibit similar behavior. In general the three-loop ECH β functions can lead to freezing for N f ⪆ 5 , but higher-order calculations are essential for a conclusive answer. The BZ expansion behaves differently for different observables. Assuming that the existence of a fixed point requires convergence of the BZ expansion for any observable, we can be pretty sure that there is no fixed point for N f ⪅ 12. The consequences of the Crewther relation concerning perturbative freezing are analyzed. We also emphasize that time-like quantities have a consistent infrared limit only when the corresponding space-like effective charge has one. We show that perturbative freezing can lead to an analyticity structure in the complex momentum-squared plane that is consistent with causality.

Corrections to the wave function and the hyperfine structure in exotic atoms

We present an analytical evaluation of radiative corrections in exotic atoms induced by the one-loop electronic vacuum polarization. We evaluate corrections to the energy levels, to the wave function (at the origin) and to the hyperfine structure. We treat all corrections analytically within a non-relativistic approximation. Agreement is found with a few available numerical results. The analytical treatment allows to determine the asymptotic forms of the corrections in the limit of a small atomic radius, which for the atomic systems considered corresponds to a large mass of the constituent particle as compared to the electron mass. The asymptotics can be verified using the effective charge approach.

Wave function correction to the decay of pionium and heavy fermionium

Abstract The decay rates of heavy atomic systems consisting of a particle and its own antiparticle are influenced by the probability density (“charge density”, square of the wave function) at the origin. In heavy systems, the one-loop electronic vacuum polarization induces a correction to the charge density (at the origin) of relative order α π . The correction is analyzed in this Letter, and results are provided for dimuonium ( μ + μ − atom), pionium ( π + π − atom), and the hypothetical heavy tauonium ( τ + τ − atom). We investigate the correction in the limit of strong binding and discuss the applicability of the effective charge approach to derive leading logarithmic asymptotics.

Renormalization-scheme dependence of Padé summation in QCD

We study the renormalization-scheme (RS) dependence of Pade Approximants (PA's), and compare them with the Principle of Minimal Sensitivity (PMS) and the Effective Charge (ECH) approaches. Although the formulae provided by the PA, PMS and ECH predictions for higher-order terms in a QCD perturbation expansion differ in general, their predictions can be very close numerically for a wide range of renormalization schemes. Using the Bjorken sum rule as a test case, we find that Pade Summation (PS) reduces drastically the RS dependence of the Bjorken effective charge. We use these results to estimate the theoretical error due to the choice of RS in the extraction of $\alpha_s$ from the Bjorken sum rule, and use the available data at $Q^2=3 GeV^2$ to estimate $\alpha_s(M_Z) = 0.117^{+0.004}_{-0.007} \pm 0.002$, where the first error is experimental, and the second is theoretical.

Estimates of the higher-order QCD corrections: theory and applications

We consider the further development of the formalism of the estimates of higher-order perturbative corrections in the Euclidean region, which is based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We present the estimates of the order $O(\alpha^{4}_{s})$ QCD corrections to the Euclidean quantities: the $e^+e^-$-annihilation $D$-function and the deep inelastic scattering sum rules, namely the non-polarized and polarized Bjorken sum rules and to the Gross--Llewellyn Smith sum rule. The results for the $D$-function are further applied to estimate the $O(\alpha_s^4)$ QCD corrections to the Minkowskian quantities $R(s) = \sigma_{tot} (e^{+}e^{-} \to {\rm hadrons}) / \sigma (e^{+}e^{-} \to \mu^{+} \mu^{-})$ and $R_{\tau} = \Gamma (\tau \to \nu_{\tau} + {\rm hadrons}) / \Gamma (\tau \to \nu_{\tau} \overline{\nu}_{e} e)$. The problem of the fixation of the uncertainties due to the $O(\alpha_s^5)$ corrections to the considered quantities is also discussed.

ESTIMATES OF THE HIGHER ORDER QCD CORRECTIONS TO R(s), Rτ AND DEEP INELASTIC SCATTERING SUM RULES

We present the attempt to study the problem of the estimates of higher order perturbative corrections to physical quantities in the Euclidean region. Our considerations are based on the application of the scheme-invariant methods, namely the principle of minimal sensitivity and the effective charges approach. We emphasize that in order to obtain the concrete results for the physical quantities in the Minkowskian region the results of application of this formalism should be supplemented by the explicit calculations of the effects of the analytical continuation. We present the estimates of the order [Formula: see text] QCD corrections to the Euclidean quantities: the e+e−-annihilation D-function and the deep inelastic scattering sum rules, namely the nonpolarized and polarized Bjorken sum rules and to the Gross–Llewellyn Smith sum rule. The results for the D-function are further applied to estimate the [Formula: see text] QCD corrections to the Minkowskian quantities R(s) = σ tot (e+e− → hadrons )/σ(e+e− → µ+µ−) and [Formula: see text]. The problem of the fixation of the uncertainties due to the [Formula: see text] corrections to the considered quantities is also discussed.

Extracting Lambda MS-bar from experiment.

We show that standard next-to-leading order (NLO) perturbative QCD analyses used to extract [alpha][sub [ital s]] from [ital e][sup +][ital e[minus]] annihilation data do not serve to disentangle the completely unknown renormalization scheme (RS) invariant next-NLO (NNLO) and higher-order uncalculated corrections from those dependent on the renormalization scale in a predictable manner. The resulting quoted values of [alpha][sub [ital s]]([ital M][sub [ital Z]])([tilde [Lambda]][sub M[bar S]]) with attendant scheme dependence uncertainties, therefore, reflect the [ital ad] [ital hoc] way in which they were extracted, rather than the actual values of these parameters. Choosing the scale so that the NLO coefficient vanishes (effective charge scheme) exposes the relative size of these unknown RS invariant higher-order terms. They are seen to be sizable for some of the [ital e][sup +][ital e[minus]] observables, indicating that they must be estimated if [tilde [Lambda]][sub M[bar S]] is to be determined reliably. This can be accomplished either from NNLO calculations, at present only available for the hadronic width of the [ital Z][sup 0] ([ital R][sub [ital Z]]), or nonperturbatively by writing the RS-invariant uncertainty in [tilde [Lambda]] in terms of the running [ital dR]([ital Q])/[ital d] ln[ital Q] of the observable [ital R]([ital Q]) with energymore » using an effective charge formalism. The NNLO calculations for [ital R][sub [ital Z]] and CERN LEP data supplemented by lower energy DESY PETRA data lead to [tilde [Lambda]][sub M[bar S]][sup (5)]=287[plus minus]100 MeV. We also discuss how the effective charge approach can be used to remove scale dependence from next-to-leading logarithm resummations of some [ital e][sup +][ital e[minus]] observables.« less

On some possible extensions of the Brodsky-Lepage-Mackenzie approach beyond the next-to-leading order

Noting that the choice of renormalization point advocated by Brodsky, Lepage and Mackenzie (BLM) is the flavor independent prescription which removes all f-dependence from the next-to-leading order coefficients, we consider the possible generalization which requires all higher order coefficients r i to be f-independent constants r i ∗ . We point out that in QCD, setting r i = r i ∗ is always possible, but leaves us with an ambiguous prescription. We consider an alternative possibility within the framework of the BLM approach and apply the corresponding prescription to the next-to-next-to-leading approximation of σ tot( e + e −→hadrons) in QCD. The analogous questions and the special features of the BLM and effective charge approaches in QED are also discussed.