Equilibrium Charge State Research Articles

Average charges of superheavy Fl (Z[formula omitted]114), Mc (Z[formula omitted]115), Lv (Z[formula omitted]116) and Ts (Z[formula omitted]117) ions passing through He-gas target at ion energies [formula omitted] 0.25 – 300 keV/u

Equilibrium charge-state fractions Fq and average charges 〈q〉 are calculated for ion beams of superheavy Flq+, Mcq+, Lvq+ and Tsq+ ions with charges q= 0 – 11 colliding with He atoms at ion energies E= 0.25 – 300 keV/u. The data are obtained using electron-loss and capture cross sections, calculated for He-gas pressures P= 0 and P=0.8 mbar with account for the target-density effect. At energies E≈ 0.25 – 10 keV/u, the influence of the effect is found small, but at higher energies E≥ 10 keV/u, it becomes important and leads to increase of 〈q〉 values by 3 – 5 times.Calculated average charges are in a good agreement with experimental data and semi-empirical estimates available at E= 132 keV/u and P=0.8 mbar. The 〈q〉 values are also compared with experimental data and other calculations for heavy and superheavy ions with atomic numbers Z= 38 – 114 as a function of the Bohr scaling parameter vZ1/3, where v is the ion velocity.

Reaction 55Mn + 159Tb : preparation for the synthesis of new elements* *Supported by the Strategic Priority Research Program of Chinese Academy of Sciences (XDB34010000), the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006), the National Key R&D Program of China (2018YFA0404402), the CAS Project for Young Scientists in Basic Research (YSBR-002), the Youth Innovation Promotion Association CAS

The complete fusion reaction of Mn + Tb was studied on the gas-filled recoil separator SHANS2. Nineteen ER - α - α decay chains from Th produced from the 4n evaporation channel were observed. The α-particle energy and half-life of Th were determined as 7922(14) keV and 14(4) ms, respectively. In addition, the decay properties of = 7788(14) keV and = 36 ms were obtained for Th. The measured α decay properties of Th and Th were consistent with literature data. The cross sections were measured to be 0.59 nb and 0.19 nb for Th and Th, respectively. The equilibrium charge state of the recoiled nucleus Th was determined experimentally. The new data were helpful for estimating the equilibrium charge states of elements 119 and 120, which could be produced via the Pu(Mn, 3n)119 and Am(Mn, 3n)120 reactions, respectively.

Surface characterization of CaF2 crystals irradiated with MeV ions below charge state equilibrium

Single crystals of CaF2, cleaved along the (111) plane, were irradiated by 35Cl, 39K, 52Cr, 58Ni, 79Br and 197Au ions with energies from 2 to 48 MeV, charge states from 1+ to 11+ and ion fluences from 2 × 1010 to 1 × 1013 ions/cm2. The surface properties of the irradiated samples were studied using Atomic Force Microscopy in contact mode. Nanoscale surface structures were observed for some surfaces irradiated by Cl, K, Cr, Ni, Br and Au ions. Thresholds for nanostructure formation were found in terms of projectile ion velocity and electronic stopping power (Se). Clear surface modification was observed for projectiles with specific energies above approximately 0.04 MeV/u. The threshold in Se for the generation of distinct triangular structures was observed to be velocity-dependent. The average formation efficiency, referring to the ratio of the number of distinct nanostructures observed on the surface to the number of incident ions, as well as the average height of nanostructures increases with Se.

Optimization of 10Be measurements at the 6 MV AMS facility DREAMS

We investigated benefits from raising the ion beam energy during measurements of 10Be with Accelerator Mass Spectrometry (AMS) at the 6MV DREAMS (DREsden AMS) facility. Increasing the terminal voltage to ≥5MV hardly reduces the yield of the Be2+ charge state after the accelerator if one applies only a thin Ar gas stripper and makes use of an overpopulation of the 2+ charge state with respect to the expected equilibrium charge state yield. As a further stripping to the 4+ charge state is conducted in a degrader foil after the analysing magnet, it is desirable to hit the foil with the highest available velocity in order to have optimal stripping of Be2+ to the fully stripped ion. At DREAMS the 10Be yield can be improved by a factor of 1.36. Applying a terminal voltage of 5.8MV the transport efficiency of 10Be from the ion source to the detector is ca. 32.5%.

Partial-ionization deconfinement effect in magnetized plasma

In partially ionized plasma, where ions can be in different ionization states, each charge state can be described as a different fluid for the purpose of multi-ion collisional transport. In the case of two charge states, transport pushes plasma toward equilibrium, which is found to be a combination of local charge-state equilibrium and generalized pinch relations between ion fluids representing different charge states. Combined, these conditions lead to a dramatic deconfinement of ions. This deconfinement happens on the timescale similar but not identical to the multi-ion cross-field transport timescale, as opposed to electron–ion transport timescale in fully ionized plasma. Deconfinement occurs because local charge-state equilibration enforces the disparity in diamagnetic drift velocities of ion fluid components, which in turn leads to the cross-field transport due to ion–ion friction.

Prediction of charge-changing cross sections of low-charged 88Sr, 138Ba and 142Nd ions in a He-gas target at collision energies 50 eV/u–10 GeV/u

Electron-loss (EL) and electron-capture (EC) cross sections of neutral and low-charged heavy Srq+, Baq+ and Ndq+ ions with charges q = 0, 1 and 2 in collisions with He atoms are predicted in the energy range E = 50 eV/u–10 GeV/u. Experimental data on EL and EC cross sections of these particles colliding with He atoms are practically absent. At relatively low energies E = 8–30 keV, EL cross sections σ12 of Sr1+, Ba1+ and Nd1+ ions are predicted from new experimental equilibrium charge-state fractions F1 and F2 and calculated EC cross sections. Predicted value for Ba1+ ions, σ12=6.8⋅10−18cm2, is in a good agreement with the one available experimental point σ12exp=5.7⋅10−18cm2 at E = 20 keV (Fedorenko, 1954). Calculations of EL and EC cross sections are performed by available computer codes shortly described in the paper. Theoretically estimated neutral-atom fractions F0 are found much smaller than the measured F1, F2, and F3 charge-state fractions.

Calculated energy loss of swift light ions in platinum and gold: importance of the target electronic excitation spectrum

Understanding and predicting the energy loss of swift ions in metals is important for many applications of charged particle beams, such as analysis and modification of materials, and recently for modelling metal nanoparticle radiosensitisation in ion beam cancer therapy. We have calculated the stopping power of the transition metals Pt and Au for protons and alpha particles in a wide energy range, using the dielectric formalism, which realistically accounts for the excitation spectrum of each metal through the Mermin Energy Loss Function - Generalised Oscillator Strength methodology. For each combination of projectile, energy and target, we have considered: (i) the equilibrium charge state of the projectile through the target, (ii) the energy-loss due to electron capture and loss processes, and (iii) the energy loss resulting from the polarisation of the projectile’s electronic cloud due to the self-induced electric field. Our calculated stopping powers show a fairly good agreement with the available experimental data for platinum and gold, particularly the most recent ones around the stopping power maximum, which validates the methodology we have used to be further extended to other transition metals. For the materials studied (platinum and gold), two commonly used and different sources of the experimental excitation spectrum yield comparable calculated stopping powers and mean excitation energies, the latter being closer to the most recent data provided in a recent ICRU Report than to previous compilations. Despite the small differences in the sources of excitation spectra of these metals, they lead to practically the same stopping power results as far as they reproduce the main excitation features of the material and fulfil physically motivated sum rules.

Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.

Stripping features of 2-MeV/u sulfur-ion beams penetrating carbon foils

The dynamics of charge-state fractions of sulfur-ion beams stripped by carbon foils at 2.0 MeV/u is investigated as a function of the initial-ion charge state q0 of the incident beam using experimental data and theoretical calculations. Experimental dependencies of the ion fractions, mean charges and equilibrium foil thicknesses on q0 are explained using the BREIT code, based on the analytical solution of the balance rate equations, as well as the ETACHA code. Experimental equilibrium charge-state distribution is qualitatively reproduced by both codes, demonstrating the capability of their approaches to the density effect. It is shown experimentally and theoretically that the non-equilibrium charge-state fractions and equilibrium foil thicknesses strongly depend on the initial ion charge q0.

Equilibrium charge state of NV centers in diamond

We investigated charge states of nitrogen vacancy (NV) centers in diamond single crystals. The charge states were evaluated using concentrations of both negatively charged (NV−) and neutral-state (NV0) NV centers. This study specifically examines diamond crystals containing mainly neutral substitutional nitrogen (N0s), NV− centers, and NV0 centers. Results show that the charged states of NV centers evaluated for this study depended on concentrations of both neutral substitutional nitrogen (N0s) and NVT centers, which is a sum of [NV−] and [NV0]. The NV centers were fully negatively charged when the ratio of [NVT] to [N0s] was 1%–20% in our diamond crystals. When [NVT]/[N0s] is larger than 20%–30%, NV0 centers appeared gradually. The concentration ratio between NV− centers and NV0 centers was described using an equilibrium equation.

Peeling graphite layer by layer reveals the charge exchange dynamics of ions inside a solid

Over seventy years ago, Niels Bohr described how the charge state of an atomic ion moving through a solid changes dynamically as a result of electron capture and loss processes, eventually resulting in an equilibrium charge state. Although obvious, this process has so far eluded direct experimental observation. By peeling a solid, such as graphite, layer by layer, and studying the transmission of highly charged ions through single-, bi- and trilayer graphene, we can now observe dynamical changes in ion charge states with monolayer precision. In addition we present a first-principles approach based on the virtual photon model for interparticle energy transfer to corroborate our findings. Our model that uses a Gaussian shaped dynamic polarisability rather than a spatial delta function is a major step in providing a self-consistent description for interparticle de-excitation processes at the limit of small separations.

Impact Features Induced by Single Fast Ions of Different Charge-State on Muscovite Mica

The influence of the charge state q on surface modifications induced by the impact of individual fast, heavy ions on muscovite mica was investigated. Beams of 593 MeV 197Auq+ with well-defined initial charge states over a relatively broad range of values (30 to 51) and at different irradiation geometries were used. At normal incidence, the impact features are rounded protrusions (hillocks) with ≳20 nm in diameter. At grazing angles, besides the hillocks, craters and elongated tails (up to 350 nm-long) extending along the direction of ion penetration are produced. It is shown that the impact features at normal incidence depend strongly on the initial charge state of the projectiles. This dependence is very weak at grazing angles as the ion reaches the equilibrium charge state closer to the surface. At normal ion incidence, the hillock volume scales with q3.3 ± 0.6. This dependence stems largely from the increase in the hillock height, as a weak dependence of the diameter was observed.

Nonlinear Problems of Equilibrium Charge State Transport in Hot Plasmas

The general coupling between particle transport and ionization-recombination processes in hot plasma is considered on the key concept of equilibrium charge state (CS) transport. A theoretical interpretation of particle and CS transport is gained in terms of a two-dimensional (2D) Markovian stochastic (random) processes, a discrete 2D Fokker-Plank-Kolmogorov equation (in charge and space variables) and generalized 2D coronal equilibrium between atomic processes and particle transport. The basic tool for analysis of CS equilibrium and transport is the equilibrium cell (EC) (two states on charge and two on space), which presents simultaneously a unit phase volume, the characteristic scales (in space and time) of local equilibrium, and a comprehensive solution for the simplest nonlinear relations between transport and atomic processes. The space-time relationships between the equilibrium constant, transport rates, density distributions, and impurity confinement time are found. The subsequent direct calculation of the total and partial density profiles and the transport coefficients of argon impurity showed a strong dependence of the 2D CS equilibrium and transport on the atomic structure of ions. A model for recovering the recombination rate profiles of carbon impurity was developed basing on the CS equilibrium conditions, the derived relationships, the data about density profiles, plasma parameters and ionization rates.

Energy deposition by nonequilibrium charge states of MeV I127 in Au

The energy loss of iodine ions at initial charge states up to 25+ and energies up to 36 MeV in self-supporting gold foils between 37 and 107 nm of thickness was measured with an electron mirror type time-of-flight detector. An excess energy loss of 130 keV was observed at 36 MeV for charge state 25+ compared to 16+, and an energy loss deficit of 100 keV was observed for charge state 8+. The charge state equilibration length for 36-MeV iodine was estimated to lie between 3 and 7 nm, corresponding to an equilibration time between 0.4 and 0.9 fs. This result is relevant both for nanostructure fabrication with MeV ion beams and for depth profiling based on ion beam analysis data in cases where the charge state of the primary ion is far from the equilibrium value in the sample under study. A comparison to published data on charge state equilibration for various projectile-target combinations and energies from 10 keV to 6 GeV indicated that the energy scaling of the equilibration length observed at high energy is invalid for projectile velocities on the order of the Bohr velocity and below. The measurement further provided equilibrium values of the electronic stopping power for iodine in gold at ten energies between 10 and 36 MeV.

Cosmic radiation does not prevent collisional charging in (pre)-planetary atmospheres

In (pre)-planetary environments, dust and sand grains regularly collide. They electrically charge and discharge during these events. In this work, we study if cosmic radiation has any influence on the equilibrium charge state on timescales of minutes. We developed an experiment that was carried out during the ascent of a stratospheric balloon. With increasing altitude, the radiation activity increases by a factor of 54. However, we found only a very minor decrease in grain charges of up to 30%. This implies that charge-moderated processes from thunderstorms on Earth, over early phases of planet formation to particle motion on the Martian surface on short timescales essentially proceed unhindered from a direct influence of cosmic radiation.

Critical behavior of charge-regulated macro-ions

Based on a collective description of electrolytes composed of charge-regulated macro-ions and simple salt ions, we analyze their equilibrium charge state in the bulk and their behavior in the vicinity of an external electrified surface. The mean-field formulation of mobile macro-ions in an electrolyte bathing solution is extended to include interactions between association and dissociation sites. We demonstrate that above a critical concentration of salt, similar to the critical micelle concentration, a non-trivial distribution of charge states sets in. Such a charge state can eventually lead to a liquid-liquid phase separation based on charge regulation.

Observation of the magneto-optic Voigt effect in a paramagnetic diamond membrane

The magneto-optic Voigt effect is observed in a synthetic diamond membrane with a substitutional nitrogen defect concentration in the order of 200 ppm and a nitrogen-vacancy defect sub-ensemble generated through neutron irradiation and annealing. The measured polarisation rotation in the reflected light is observed to be quadratically proportional to the applied magnetic field and to the incident reflection angle. Additionally, it is observed to be modifiable by illuminating the diamond with a 532 nm laser. Spectral analysis of the reflected light under 532 nm illumination shows a slow narrowing of the spectral distribution, indicating a small increase in the overall magnetisation, as opposed to magnetisation degradation caused by heating. Further analysis of the optical power dependence suggest this may be related to a shift in the spin ensembles charge state equilibrium and, by extension, the resulting ensemble magnetisation.

Charge-state distributions and charge-changing cross sections and their impact on the performance of AMS facilities

The charge state distributions of ions passing through gases or foils have a significant influence on the performance of AMS facilities. Most important is the stripping process in the terminal of the accelerator. Published data on charge state distributions have been collected as well as associated charge-changing cross sections for various projectiles and targets relevant to AMS. Based on these data, the stripping yields as function of the stripper thickness and ion energy are calculated. This allows to evaluate the stripping thickness required for reaching charge state equilibrium, as well as mass fractionation effects depending on energy and stripper thickness. The significantly different behavior of helium compared to other gases leads to very high stripping yields for specific charge states at low energies. The cross sections for electron detachment of negative ions give a tool for estimating beam losses in the low energy acceleration tube. Further, electron capture and loss cross sections allow the estimation of backgrounds caused by charge exchange processes in the acceleration tubes. The effects discussed here are illustrated with calculations and simulations for Carbon beams. The data are useful for the design of new AMS facilities or improving existing ones.

Charge-state dynamics of 1.4- and 11-MeV/u uranium ions penetrating H2 and He gas targets

Abstract Theoretical description and interpretation are presented of the recent experimental data on stripping of fast 238U ions, penetrating H2 and He gaseous targets: obtained in GSI, Darmstadt, Germany at 1.4 MeV/u with a H2 stripper, and in RIKEN, Saitama, Japan at 11 MeV/u with H2 and He strippers. Electron-loss and capture cross sections for uranium ions, interacting with H2 and He targets are calculated and used as input data in the BREIT code to obtain dynamic characteristics of uranium-ion beams: non-equilibrium and equilibrium charge-state fractions, mean and equilibrium charges, and equilibrium thicknesses. Special attention is paid for the calculation of the dynamic characteristics of 1.4-MeV/u uranium ions stripped by a H2 in a windowless gas target at GSI, using a newly designed pulsed gas cell with a pressure changing from ∼ 0.1 to ∼ 100 mbar along the ion beam. To explain the experimental data, a Gaussian pressure model for the H stripper is applied with account for the target-density effect. A possible deviation of the Bragg’s additivity rule for electron-capture cross sections for a H2 target is also considered and we predict that the equilibrium charge of a 1.4-MeV/u uranium beam in atomic hydrogen is larger than in molecular hydrogen, i.e., it is indicated that atomic hydrogen can be a more effective stripper than molecular hydrogen. Charge-changing cross sections and dynamic characteristics of 11-MeV/u uranium ions passing through He and H2 targets are calculated as well. Calculated equilibrium mean charge states q ¯ ( He ) = 67.8 and q ¯ ( H 2 ) = 75.7 are in agreement with RIKEN experimental data within 10%.

Accelerator mass spectrometry of 236U with He stripping at the Centro Nacional de Aceleradores

In January 2015, the 1 MV AMS facility at the Centro Nacional de Aceleradores (CNA, Seville, Spain) was upgraded with He stripping. In this work, we present a comprehensive study of the uranium transmission through the accelerator together with the background sources that limit the current sensitivity of our system to measure the 236U/238U atom ratio. In addition to the well-known background caused by scattered 235U3+ molecular fragments, we identify an additional component, not observed with Ar gas, that we relate to scattered 238U3+ molecular fragments. Stripper gas pressures below the one corresponding to the equilibrium charge state distribution are used to minimize the resulting overall background, which is in the (0.8–1.3) × 10−10 range. This is at least a factor of 3 higher than the background obtained with Ar gas. On the other hand, new information on the stripping process of U on He gas at the 400–1000 keV stripping energy range is presented. A maximum transmission of 45% for U3+ is achieved at about 650 keV, which correspond to a stripping yield of about 50%. This is the maximum yield that can be actually obtained working with He gas at low energies according to previous results.