Effective Charge Parameter Research Articles

Stopping power of 16O, 48Ti and 108Ag ions in C and Al between 0.5 and 3. MeV/u

Stopping powers for 16O, 48Ti and 108Ag ions have been measured in C and AI targets in the energy range 0.5 to 3. MeV/u. The results are compared with available experimental data and semiempirical values. Calculations based on the Lindhard theory within the local density approximation are made from 0.2 MeV/u to 20 MeV/u with polynomial fits derived from numerical integration of the stopping. Within the energy range where our stopping interaction polynomial fits apply, good agreement with experimental results is found. The magnitude of the z 3 correction is calculated in the framework of the dielectric theory and compared with other calculations and with experimental values. Two different methods used to deduce the effective charge parameter are compared: one using the scaling of proton stopping and the other based on the theoretical treatment with higher-order corrections.

Cu, I and Au stopping powers in solid targets

We have measured the energy loss of Cu, I and Au ions in six elemental solids targets (C, Al, Cu, Ag, Ta and Au) at energies near and below the maximum of the stopping power curve. The low-velocity Barkas and Bloch correction terms are calculated and compared with values from four different formalisms applied to several projectiles (p, C, Al, Cu, I and Au) in various targets. The effective charge parameters deduced from stopping powers by using high-order approximations are found to be very sensitive to the model serving to determine the Barkas and Bloch effects. Finally, the formalism giving the best agreement is used to deduce from our measurements the effective charge parameter and to study its dependence on the stopping medium. Our results are compared with previous calculations that include z 3 and z 4 effects.

Compilation, measurements and tabulation of heavy ion stopping data

In 1978 and 1980, two series of measurements, performed with 3–6 MeV/u heavy ions, indicated without ambiguity that the commonly used stopping power tabulations failed in reproducing the data. After analysis, this was attributed to the fact that the effective charge parametrization, which is the basis of such tabulations, was oversimplified. A new tabulation of stopping powers and ranges of heavy ions in solids, covering the energy range from 2.5 to 100 MeV/u was proposed in 1980. The basis of this tabulation was a Q 1 2 scaling of the stopping powers relative to those of 4He at the same velocity in the same media, the effective charge parameter being adjusted according to experimental data. From 1983 to 1990, a new series of measurements performed with 20–100 MeV/u heavy ions at GANIL revealed some defects in this parametrization when the ions tend to be fully stripped. These defects were corrected for in a new tabulation (1990) based on a set of 600 stopping power measurements, and covering the energy range from 2.5 to 500 MeV/u. In 1982, at Darmstadt, a systematic difference was observed between the stopping powers of very heavy ions in gases and in solids. It was therefore impossible to apply to gases the effective charge parametrization valid for solids. This gas-solid effect was confirmed by an extensive experimental study, carried out at Orsay in the energy range 2–13 MeV/u (1985), and its vanishing at high energy was observed at GANIL in a recent series of experiments (1988–1990).

Volume Dependence of Effective Charge Parameter and Photoelastic Behaviour of Alkali Halide Crystals

AbstractAn analysis of the volume dependence of effective charge parameter and electronic strain polarizability parameter is presented for alkali halide crystals. The deformation dipole model due to Hardy is used along with the seven different potential forms for the short‐range overlap repulsive energy and the modified form of the additivity rule for the crystalline state polarizabilities as proposed by Raghurama and Narayan. The effective charge model due to Hanlon and Lawson is adopted to obtain the strain polarizability parameter within the framework of Coker's theory. The results are compared with the available experimental data. It is found that the results are fairly insensitive to the form of the overlap repulsive potential used whereas they depend sensitively upon the choice of polarizability.

Analysis of dielectric properties of I–VII, II–VI and III–V crystals with ZnS structure

An analysis of dielectric properties such as polarizabilities, effective charge parameters and dielectric constants is presented for I-VIII (CuCl, CuBr, CuI), II-VI (ZnSe, ZnTe, CdS, CdTe) and III-V (AlSb, GaP, GaAs, GaSb, InP, InAs, InSb) crystals with the zincblende structure. Calculations were performed with and without using full local field corrections. The analysis has been extended to evaluate the volume derivatives of the polarizabilities and effective charge parameters for GaAs, GaP, ZnS and CdS crystals. The transverse optic model Grüneisen parameters and anharmonic contributions to dielectric constants are also calculated for these crystals. The results are discussed and compared with available experimental data.

Dielectric Properties of Mixed Alkali and Silver Halide Crystals

AbstractThe static and optical dielectric constants are calculated for the entire range of composition in twelve systems of mixed crystals of alkali halides and silver halides with NaCl‐type structure, by adopting the method developed by Kamiyoshi and Nigara (KN). Transverse and longitudinal optical mode frequencies are also evaluated using the Lyddane‐Sachs‐Teller relation. Calculated values of static dielectric constants are found to exhibit a sharp non‐linear dependence on composition near the equi‐molar region in KClKBr, KClRbCl, KBrRbBr, KIRbI, RbClRbBr, and AgClAgBr mixed crystals and a slight non‐linear dependence on composition near the NaBr end in NaCl‐NaBr mixed crystals, which is in agreement with experimental data. The usefulness of dielectric constants and optical mode frequencies is demonstrated by investigating the composition dependence of the Szigeti effective charge parameter.

Recombination Rates for Ti, Cr, Fe and Ni Ions

Current status of the theoretical effort to evaluate the radiative recombination (RR) and dielectronic recombination (DR) rates for the Ti, Cr, Fe and Ni ions is reviewed. (i) A complete set of RR rates for all ions is given in the Z-scaled Coulombic representation, with improved formulas for the effective charge parameter. Using this result, sample RR rates are presented for Ti and Fe ions in several initial charge states. (ii) The DR data for ions with the number of electrons N = 1, 2, 4 and 10, before capture, are summarized. Only partial data are available for ions with N = 3, 5, 9, 11 and 12. There are serious gaps in the DR data for ions with N in the regions 5 < N < 9 and N > 12. The DR rates for ions in the gaps may be estimated using an approximate empirical rate formula, which is derived by fitting all the currently available results. The general trends of the rates as functions of temperature, core charge and the number of electrons are predicted by the rate formula. The effects of plasma environment on the rates, in terms of plasma microfield and density, are important but not incorporated into the rates presented here.

Moments of dipole oscillator-strength distribution for the helium sequence

The moments S( mu ) for -6<or= mu <or=2 and L( mu ) for mu =0, 1 and 2 are calculated for the helium sequence for atomic numbers Z up to 30 under a screened hydrogenic model. In this model, one describes the atom by single-particle hydrogenic wavefunctions and treats the initial and the final state as characterised by two different effective charge parameters Zi and Zf, respectively. An asymptotic expansion is made of the differential oscillator strength of the screened hydrogenic model. Assuming the value 287.6 for the coefficient of the term in -7/2 for helium atom as given by Salpeter et al. (1962), the parameter Zf is determined for the helium sequence. This approach has resulted in values which are in reasonable agreement with the various moment values of other authors.

Stopping powers of solids for 84,86Kr, 100Mo and 129,132Xe ions at intermediate energies (20–45 MeV/u) and the charge state distributions at equilibrium

The stopping powers of ten solid media (nine elements from Be to Au and mylar) have been measured for 25–45 MeV/u Kr and 25 MeV/u Mo and Xe ions. The accuracy in stopping power determinations is ± 1–2%. In addition, the charge state distributions at equilibrium of Kr, Mo, Xe ions exiting Be, Al and Au targets have been determined. Average charge states Q ̄ have been deduced. For Kr ions exiting any target, a semi-empirical expression has been obtained to predict the mean charge Q ̄ in a large energy domain (4–50 MeVu). The stopping power data have been compared with a scaling relative to He 2+ ion stopping powers, assuming fully stripped ions inside the degraders. Effective charge parameters γ have been derived and compared with the ionization degree Q ̄ /Z 1 . Information concerning the emission of Auger electrons by ions exiting targets has been obtained. The stopping power data have also been compared with values from Ziegler (1980). Discrepancies are observed for light (Be) and heavy media (Ta-Au). A comparison has been made with the very recent semi-empirical calculations from Hubert et al. (1989). Excellent agreement is found with experimental data for all projectiles and media.

Screened hydrogenic radial integrals

The screened hydrogenic radial integral both for discrete-discrete and discrete-continuum transitions is expressed in forms suitable for obtaining closed-form expressions for specific transitions. Two effective charge parameters Zi and Zf, respectively, for the initial state and for the final state are retained in these formulas. As examples, explicit expressions for a few transitions are derived and a method for obtaining a series for a discrete-discrete radial integral, suitable for large final-state principal quantum numbers, is indicated.

Differential oscillator strengths and dipole polarizabilities for transitions of the helium sequence

The dipole radial integral for an initial discrete 1s state and a final continuum state has been calculated under the screened hydrogenic model. In this model, single-electron hydrogenic wave functions are employed and the initial and the final states are treated by two different effective-charge parameters. Numerical values of differential oscillator strengths for transitions from 1s 21S to the continuum for the helium sequence ions are obtained. Also calculated are the dipole polarizabilities, which are found to be in excellent agreement with the results of other authors.

1s2 1S-1s np 1P transitions of the helium isoelectronic sequence members up to Z = 30.

Radial integrals have been calculated under the one-electron hydrogenic model. Two different values of the effective charge parameter, one for the initial state and the other for the final state, are retained in these formulae. The model is able to reasonably reproduce the existing dipole oscillator strength values with little effort. The dipole oscillator strength values are given for many ions for the first time.

Dielectric properties of NaCl1−xBr and KCl1−xBrx mixed ionic solution

In the present paper a three-body potential model (TBPM) has been employed for the analysis of dielectric behaviour of NaCl-NaBr and and KCl-KBr mixed crystals with varying compositions. The physical properties like dielectric constants (ɛ0 andɛ∞), optic mode frequencies (ΩOLO andΩTO), effective charge parameter (es*), optic mode Gruneisen parameters and strain derivatives ofɛ0 andɛ∞ dielectric constants have been calculated. The results achieved in the present study are found in fairly good agreement with the available experimental data. The results obtained by previous investigators are also shown for the sake of comparison.

Volume Dependence of Dielectric Properties of Some Fluorite‐Structure Crystals

AbstractThe experimental data on first and second order pressure derivatives of dielectric constants are used to make an analysis of the volume dependence of polarizabilities, effective charge parameter, and transverse‐optic‐mode frequencies in CaF2, SrF2, BaF2, PbF2, Sr(NO3)2, Ba(NO3)2, and Pb(NO3)2. The short range force constant responsible for the ion‐displacement polarizability is calculated with the help of Lundqvist's three‐body interaction model. Reasonable values for the volume derivatives of various dielectric parameters are obtained. Values of optic‐mode‐Grüneisen parameters and their volume derivatives are also calculated and compared with available experimental data.

Measurement of specific energy losses of individual fission fragments with a back-to-back δE− E detector system

The specific ionization of fission fragments of specified charge and E M values in thermal neutron induced fission of 235U have been measured employing a back-to-back gridded ionization chamber ΔE-semiconductor detector E setup. The measurements were carried out for the case of a mixture of argon (95%) and methane (5%) gases at two gas pressures, 44 Torr and 270 Torr. The experimental data for the lower gas pressure were used to determine the effective charge parameter γ for the fragments at various velocities. These γ-values have been used to compute the fragment energy losses at the higher gas pressure and are compared with the measured energy loss values.

Nonlinear-optical properties and signs of the Raman tensor for LiGaO2

A detailed experimental and theoretical study of the Raman spectrum of the orthorhombic piezoelectric crystal LiGa${\mathrm{O}}_{2}$ is presented. The 45 fundamental modes were analyzed with respect to their frequency and intensity and a classification into symmetry species and LO-TO splitting is obtained. From these results the angular dispersion and the infrared absorption spectra were calculated and found to be in very good agreement with experimental results. It is shown that from a complete set of classified modes the effective charge parameters, the Raman tensor components including their signs, the nonlinear-optical tensor, and the electro-optical tensor can be derived. In addition a relation for the nonlinear susceptibility as a function of the frequency was obtained which exhibits characteristic resonances at the fundamental phonon frequencies. Results evaluated for LiGa${\mathrm{O}}_{2}$ showed that the nonlinear-optical tensor for this crystal is very small.

Coupling impedances in synchronous fast-wave devices†

Abstract The coupling impedances for TE and TM gyrotron-type interactions occurring in rectangular and cylindrical waveguides are determined and found to be proportional to a functional impedance which decreases inversely proportional to' the fourth power of the propagation constant β, leading to a gain per unit length inversely proportional to the cube root of β, and proportional to the cube root of the current. Farther away from waveguide cut-off, the functional coupling impedance for TM-gyrotrons is found to be larger than the corresponding impedance for TE-gyrotrons, and decreases only inversely proportional to the square of β, leading to a gain per unit length which increases with frequency. However, under grazing-angle conditions, the coupling impedance for TM-gyrotrons vanishes, second order effects must be taken into account, and the gain per unit length becomes proportional to the square root of the current. Beam velocity spreads lead to an effective space charge parameter QC.

Analysis of the dielectric properties of mixed alkali halide crystals

AbstractThe electronic and static dielectric constants, longitudinal and transverse optic mode frequencies, effective charge parameters, optic mode Gruneisen parameters, and volume derivatives of dielectric constants are calculated for the entire range of composition of mixed NaCl—NaBr, KCl—KBr‐and KBr—KI crystals. The calculations are performed using the knowledge of interionic potentials. The results are discussed and compared with available experimental data.

Dielectric and anharmonic behaviour of alkali halide crystals

AbstractThe dielectric and anharmonic behaviour of alkali halide crystals is studied by determining the volume derivatives of low frequency dielectric constant and polarizability. An interionic force model which takes into account the contributions arising from the short range overlap repulsion and the van der Waals interactions is used in calculations. The implicit and explicit temperature derivatives of low frequency and high frequency dielectric constants are obtained separately for all the alkali halide crystals with NaCl and CsCl structures. The anharmonic contribution to the dielectric constant is calculated using theoretical models due to Szigeti and Havinga. The recent analysis of pressure dependence of effective charge parameter and dielectric constant of ionic crystals performed by Varotsos is shown to be invalid.

IsovectorE2matrix elements from electromagnetic transitions in thes−dshell: Experiment and shell-model calculations

All available $B(E2)$ values in the mass region $8\ensuremath{\le}Z$, $N\ensuremath{\le}20$ relevant to the isovector electric quadrupole operator are compared to the theoretical $B(E2)$ values based on Chung-Wildenthal $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ shell-model wave functions with harmonic oscillator radial wave functions, and some selected cases are compared with local and energy dependent Woods-Saxon potential wave functions. The empirical effective charges deduced from these comparisons are insensitive to differences in mass, state, and dominant single-nucleon orbit. The value for the effective charge parameter ${e}_{p}\ensuremath{-}{e}_{n}$ extracted in the harmonic oscillator approximation is consistent with $1.0e$. The values extracted with local and energy-dependent Woods-Saxon potentials, which are more meaningfully related to the underlying structure of the isovector polarizability, are consistent with $0.7e$ and $0.6e$, respectively. Some inadequacies in the experimental data and theoretical models are discussed and improvements are suggested.NUCLEAR STRUCTURE $17\ensuremath{\le}A\ensuremath{\le}39$ nuclei: comparison of experimental $E2$ isovector matrix elements with shell-model predictions; extraction of the isovector effective charge; full basis $0{d}_{\frac{5}{2}}\ensuremath{-}1{s}_{\frac{1}{2}}\ensuremath{-}0{d}_{\frac{3}{2}}$ shell-model wave functions; Chung-Wildenthal Hamiltonians.