Electronic stopping power calculation method for molecular dynamics simulations using local Firsov and free electron-gas models

Molecular dynamics simulations have proven to be accurate in predicting depth distributions of low-energy ions implanted in materials. Free parameters adjusted for every ion-target combination are conventionally used to obtain depth profiles in accordance with the experimental ones. We have previously developed a model for predicting depth profiles in crystalline Si without free parameters. The electronic stopping power was calculated using local total electron density. The model underestimated the stopping in the ?1 1 0? channeling direction. We have now taken a new approach to calculate the electronic stopping power. We use the local valence (3p²) electron density to account for the electronic energy loss between collisions and the Firsov model to account for the electronic energy loss during collision. The lowest electron densities are adjusted with a parametrization that is same for all ions in all implanting directions to correct the problems in the ?1 1 0? channeling direction.     

Binary stopping theory for swift heavy ions

The Bohr theory treats charged-particle stopping as a sequence of interactions with classical target electrons bound harmonically to their equilibrium positions. We demonstrate that equivalent results can be derived on the assumption of free binary collisions governed by a suitable effective potential. This kind of mapping is rigorous in the limits of distant and close collisions and therefore provides a tool to evaluate energy losses via binary-scattering theory. This model was developed with the aim of calculating stopping forces for heavy ions at moderately high velocities, where a classical-orbital calculation is typically superior to the Born approximation. The effective potential employed holds equally well for dressed as for stripped ions. Unlike the Bohr theory, the present evaluation avoids a formal division into regimes of close and distant collisions that do not necessarily join smoothly. Moreover, no perturbation expansion is necessary. For these reasons the overall accuracy as well as the range of validity of the Bohr model are significantly enhanced. Extensive tests have been performed, including comparisons with rigorous evaluations of the Z ₁ ³ effect, with excellent agreement even where such was not necessarily expected. Moreover, credible results have been obtained under conditions where the perturbation expansion shows poor convergence. A comparison with experimental data on O–Al is encouraging, even though shell corrections and projectile excitation/ionization have not yet been incorporated and input has not yet been optimized. Received 21 April 2000 and Received in final form 16 June 2000 An erratum to this article is available at .     

Stopping of slow ions

The 50th anniversary of the appearance of a series of seminal papers by O.B. Firsov is taken as an occasion to have a look at some central aspects of the stopping of slow ions in matter. A brief characterization of Firsov’s model of electronic energy loss is given in comparison with alternative views. The main part of the paper is devoted to central problems such as scaling behavior, Z ₁ and Z ₂ structure, deviations from velocity proportionality, threshold behavior, metal-insulator and gas-solid differences, and correlation between nuclear and electronic stopping.     

Analysis of deep inelastic collisions between16O and27Al

Deep inelastic collisions in light systems formed with¹²C,¹⁴N and¹⁶O projectiles and different target nuclei have been studied at incident energies between 5 and 7 MeV/u. A detailed analysis is presented for the results of the¹⁶O+²⁷Al reaction at 80.6 MeV incident energy which is based on trajectory calculations and the transport theory. The questions of angular distributions and the interaction time, the energy dissipation and the fragment deformation as well as the element-distribution and the effect of the nuclear structure are discussed.     

Comparison of one and two-neutron transfer near the coulomb barrier for the27Al(18O,16O)29Al,27Al(180,17O)28Al and27Al(13C,12C)28Al reactions

Total reaction cross sections for the transfer reactions²⁷Al(¹⁸O,¹⁶O)²⁹Al,²⁷Al(¹⁸O,¹⁷O)²⁸Al and²⁷Al(¹³C,¹²C)²⁸Al are reported for center-of-mass energies between 13 and 20 MeV for¹⁸O projectiles and between 11 and 17.5 MeV for¹³C projectiles. The reaction products,²⁹Al and²⁸Al, beta decay to²⁹Si and²⁸Si, respectively, and the subsequentγ decays of²⁹Si and²⁸Si were measured. Due to the relatively long beta decay half lives, data were taken in a beam-off mode, resulting in very clean spectra. Total cross sections were calculated and compared with a theoretical model for barrier penetration proposed by C.Y. Wong. Differences between¹⁸O induced one and two-neutron total transfer reaction cross sections are discussed.     

Ranges and standard deviations of implanted ions

This paper presents a theoretical analysis and simple expressions for the calculation of ranges and standard deviations of implanted ions in amorphous targets. Nuclear energy loss models are discussed to introduce an approximation formula for the nuclear stopping cross section appropriate for Thomas-Fermi, Lenz-Jensen and intermediate type potentials. The Firsov electronic stopping model has been used to show its successful application. Algebraical expressions for the total range of ions in monoatomic and biatomic targets as a function of ion energy result from the considerations presented. A quasi-elastic multiscattering model is suggested, which permits an easy estimate of projected ion ranges. The standard range deviation is obtained by determining the total average-square energy loss fluctuations. Finally a comparison of calculated and experimental results is made to show that calculations based on the Firsov electronic stopping model and the nuclear stopping cross section proposed here provide a better agreement with the experimental results than the wellknown Johnson-Gibbons LSS-calculations.     

Reactions of 14N and 16O ions with p and s-d shell nuclei at Elab = 16 to 75 MeV

Yield curves were measured for formation of ⁷Be and of residual nuclei formed by α-particle and nucleon emission following the reactions of 16 to 75 MeV ¹⁴N and ¹⁶O ions with thick, natural C, Mg, Al and Si targets. The results are discussed in terms of statistical model calculations. Yield curves calculated with computer codes based on the statistical model are compared with the experimental results.     

Velocity dependence in low-velocity electronic stopping power of heavy ions

The velocity dependence in the low-velocity electronic stopping power of heavy ions has been studied for Al and Si ions in Ta in the velocity region 0.4v₀−4v₀ (v₀ is the Bohr velocity). The first experimental information is obtained from the range distribution and Doppler-shift-attenuation data.     

Radiative pion capture in 12C and 16O

Radiative pion capture in ¹²C and ¹⁶O is investigated. An effective interaction Hamiltonian based upon the CGLN theory is employed. Capture rates in ¹²C and ¹⁶O from Is and 2p pionic orbits are calculated by using the nuclear model of Kamimura, Ikeda and Arima for the odd parity states of ¹²C, and that of Walker with strong ground state correlations, for the odd parity states of ¹⁶O. The results are compared with those of the 1p-1h nuclear model under the Tamm-Dancoff and random phase approximations of Gillet and Vinh Mau. Detailed examinations are made for the transitions to low-lying states with 1⁺ and 2⁺ for ¹²C and with 1^?, 2^? and 3^? for ¹⁶O by using the Cohen-Kurath and the Walker models, respectively. The results are in good agreement with the recent experimental data from Berkeley.     

A study of the 26Mg(12C, 12B)26Al charge-exchange reaction

The reaction ²⁶Mg(¹²C, ¹²B)²⁶A1(5⁺, 3⁺) has been studied using a beam of 102 MeV of ¹²C. Shell-model, microscopic direct model and finite-range coupled reaction channel (CRC) calculations including recoil effects, have been performed, for comparison with the experimental data. DWBA calculations were performed for the intermediate states of interest in the ¹¹B + ²⁷Al and in the ¹³C + ²⁵Mg channels and these results were also compared with the experimental ones. The dominant reaction mechanism for ²⁶Mg(¹²C, ¹²B)²⁶Al(5⁺, 3⁺) appears to be the sequential mode.     

Competition between exit channels leading to the same residual nucleus in heavy-ion reactions

Competition between pn and d as well as between p2n, dn and t emission in the production of individual residual states has been observed in nuclear reactions induced by ¹⁶O on ¹²C and ¹³C targets. The experimental relative yields for the production of the 417 keV state in ²⁶Al by pn and d emission, measured as a function of bombarding energy in the reaction ¹²C(¹⁶O,pn/d)²⁶Al, are successfully described by Hauser-Feshbach calculations.     

Dsa measurement of short lifetimes in 27Al

Lifetimes or upper limits of 17 bound states in ²⁷Al have been measured using the Doppler shift attenuation method applied to the ²⁶Mg(p, γ)²⁷ Al reaction in the proton energy range 1.4–2.2 MeV. For the effective stopping of recoils, the targets were prepared by implanting ²⁶Mg into tantalum backings. The Monte Carlo method and the experimental stopping values were used in the DSA analysis. In the Monte Carlo simulations the scattering angles of recoiling ions were calculated directly from the Thomas-Fermi interaction potential, rather than from the LSS theory.     

Non statistical reaction contributions in (α, n) excitation functions

The excitation function²⁴Mg(α, n)²⁷Si has been measured from threshold to 27 MeV excitation energy. A survey is given of the experimental excitation functions¹²C(α, n)¹⁵O,¹⁶O(α, n)¹⁹Ne,²⁰Ne(α, n)²³Mg and²⁴Mg(α, n)²⁷Si and HF calculations have been made for them. The agreement is good within a factor of 2. The deviations of the experimental data from the pure statistical cross sections show common structures which can be interpreted as direct contributions.     

Formation and deexcitation of the 32S compound nucleus via the 20Ne+12C and 16O+16O entrance channels

Reaction-product cross sections following ²⁰Ne+¹²C and ¹⁶O + ¹⁶O collisions at several incident energies have been measured with a E-ΔE counter telescope. They are compared to statistical model predictions. Fair agreement is obtained for the high-Z evaporation residue cross sections, but a strong discrepancy is observed for the lower-Z reaction products. Possible explanations are discussed. It is shown that the compound nucleus formation does not depend on the structure of the colliding ions in the entrance channel and also that it is not limited by the ³²S yrast line.     

Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory

The role of tensor force on the collision dynamics of ¹⁶O+¹⁶O is investigated in the framework of a fully three-dimensional time-dependent Hartree-Fock theory. The calculations are performed with modern Skyrme energy functional plus tensor terms. Particular attention is given on the analysis of dissipation dynamics in heavy-ion collisions. The energy dissipation is found to decrease as an initial bombarding energy increases in deep-inelastic collisions for all the Skyrme parameter sets studied here because of the competition between the collective motion and the single-particle degrees of freedom. We reveal that the tensor forces may either enhance or reduce the energy dissipation depending on the different parameter sets. The fusion cross section without tensor force overestimates the experimental value by about 25%, while the calculation with tensor force T11 has good agreement with experimental cross section.     

Fragmentation cross sections of16O at 60 and 200 GeV/nucleon

We used CR39 plastic nuclear track detectors (C₁₂H₁₈O₇) in combination with automatic track measurement to determine total charge changing and partial cross sections for the production of fragments of chargeZ=6 andZ=7 in collisions of¹⁶O beam nuclei at energies of 60 GeV/nucleon and 200 GeV/nucleon in targets H, C, CR39, CH₂, Al, Cu, Ag and Pb. Total charge changing cross sections due to the process of electromagnetic dissociation are calculated based on a theoretical model and found to be consistent with total and partial electromagnetic dissociation cross sections derived from this experiment. The energy dependence of pure nuclear fragmentation is investigated.     

S-matrix approach for description of refraction and absorption effects in9Be elastic scattering

A newS-matrix model was employed for analysing cross sections of⁹Be elastic scattering by¹²C,¹⁶O,²⁶Mg,²⁷Al,⁴⁰Ca,⁶⁰Ni and¹⁹⁷Au nuclei at 158 MeV. The results obtained are compared with those of optical model.     

Light ion fusion in deformation model

Experiments with heavy ions at moderate energies show the importance of deformation in heavy ion collisions. A deformation model which takes deformation dynamically into account is developed. Having described fusion and deep inelastic collision for a very heavy system (Xe + Bi) and a medium heavy system (Ar + Th) at various energies successfully, we turn to some comparatively lighter heavy ions where fusion is the most dominant feature. Fusion cross-sections for six pairs of lighter systems (³⁵Cl +¹¹⁶Sn,⁵⁸Ni+⁶²Ni,³⁵Cl+⁶²Ni,³²S+²⁴Mg,²⁴Mg+²⁴Mg and¹²C+²⁷Al) have been obtained using our deformation model which agree well with experiment. The two-slope-behaviour of fusion excitation function which is an important feature of light ion fusion systematics is also obtained, in our model calculations for all the systems studied.     

Peculiarities of Λ hyperon and π−-meson production in nucleus-nucleus collisions at high energy

The analysis of the data on the production of Λ hyperons and π^- in⁴He?Li,¹²C?C,¹²C?Ne and¹⁶O?Ne at 4.5 A GeV/c and¹²C?C collisions at 4.2 A GeV/c are presented. Kinematical features of Λ's are shown to depend on the collision centrality in contrast to the stable behaviour of the pion characteristics. The correlation between the characteristics of Λ's and accompanying pions is observed. The effects seem to be incompatible with the intranuclear cascade approach. The data suggest the formation of a fully stopped and thermalized hot source in central nucleus-nucleus collisions, in which Λ hyperons are produced.