On the energy losses of fast charged particles

The energy losses of fast charged particles colliding with atoms have been considered in the eikonal approximation. It has been shown that the nonperturbative contribution to the effective stopping from the region of the intermediate impact parameters (comparable with the characteristic sizes of the electron shells of the target) not only can be significant as compared to shell corrections to the Bethe-Bloch formula (usually considered in the first order of perturbation theory), but also can provide significant (up to 50%) corrections to this formula.     

Eikonal approximation in the theory of energy loss by fast charged particles

Energy losses in fast charged particles as a result of collisions with atoms are considered in the eikonal approximation. It is shown that the nonperturbative contribution to effective stopping in the range of intermediate impact parameters (comparable with the characteristic sizes of the electron shells of the target atoms) may turn out to be significant as compared to shell corrections to the Bethe-Bloch formula calculated in perturbation theory. The simplifying assumptions are formulated under which the Bethe-Bloch formula can be derived in the eikonal approximation. It is shown that the allowance for nonperturbative effects may lead to considerable (up to 50%) corrections to the Bethe-Bloch formula. The applicability range for the Bethe-Bloch formula is analyzed. It is concluded that calculation of the energy loss in the eikonal approximation (in the range of impact parameters for which the Bethe-Bloch formula is normally used) is much more advantageous than analysis based on the Bethe-Bloch formula and its modifications because not only the Bloch correction is included in the former calculations, the range of intermediate impact parameters is also taken into account nonperturbatively; in addition, direct generalization to the cases of collisions of complex projectiles and targets is possible in this case.     

Energy losses of fast heavy multiply charged structural ions in collisions with complex atoms

A nonperturbatve theory of energy losses of fast heavy multiply charged structural ions in collisions with neutral complex atoms is elaborated with allowance for simultaneous excitations of ionic and atomic electron shells. Formulas for the effective deceleration that are similar to the well-known Bethe-Bloch formulas are derived. By way of example, the energy lost by partially stripped U ^q+ ions (10 ≤ q ≤ 70) colliding with argon atoms and also the energy lost by Au, Pb, and Bi ions colliding with various targets are calculated. The results of calculation are compared with experimental data.     

Effective stopping of fast heavy highly charged structure ions in collisions with complex atoms

The nonperturbative theory of the energy losses of fast heavy highly charged structure ions colliding with neutral complex atoms is developed with allowance for simultaneous excitations of the electron shells of an ion and an atom. Formulas for effective stopping that are similar to the Bethe-Bloch formulas have been derived. As an example, the energy losses of partially stripped uranium ions colliding with argon atoms are calculated.     

Energy loss straggling in collisions of fast finite-size ions with atoms

The influence of ion size on straggling of energy losses by fast partially stripped ions is studied using the nonperturbative approach based on the eikonal approximation. It is shown that such a consideration of collisions of ions with complex atoms can lead to considerable corrections in calculating root-mean-square straggling of energy losses by fast ions compared to the results obtained for point ions. The root-mean-square straggling of energy losses are calculated for bromide and iodine ions in collisions with copper, silver, and aluminum atoms. It is shown that allowance for the size of the electron “coat” of an ion noticeably improves the agreement with experimental data.     

Theory of the stopping of fast heavy highly charged structured ions in their collisions with complex atoms

We have developed a nonperturbative theory of the energy losses by fast heavy structured ions in their collisions with neutral complex atoms by taking into account all of the possible, including multiple, excitations and ionizations of both projectile and target. We have been able to achieve a significant simplification of the problem by considering multielectron targets and by restricting our analysis to highly charged structured ions with charges much larger than unity, when the characteristic size of the electron coat of the projectile ion is much smaller than that of the neutral target atom. The errors in the approximations used and in the calculations of inelastic cross sections are estimated. We have derived formulas for the effective stopping similar to the well-known Bethe-Bloch formulas. To illustrate the contribution from multielectron excitations of the ion coat to the effective stopping, we make a comparison with the calculations based on the perturbation theory. The energy losses of U ^q+ (10 ≤ q ≤ 70) ions in their collisions with argon atoms and the energy losses of Pb and Bi ions on several targets have been calculated. A comparison with experiment is made.     

Revelations from stopping power analyses

Abstract

Recent measurements of the stopping powers of various composite-material targets have been analyzed in the presence of Barkas-effect and Bloch corrections in order to extract appropriate values of Bethe-Bloch parameters. Mylar, Kapton, and Havar targets have been studied in particular, primarily using measurements with light projectiles. The present investigation focuses on results for Havar analyses, where dispersion among sets of measurements appears to separate extracted parameter-values into at least two groups. An hypothesis pertaining to target properties is advanced in explanation. In another study, analyses of experimental results for alpha particle projectiles traversing Ti and V targets have yielded parameter-values reasonably consistent with expectation. Finally, the importance of including all pertinent correction terms when analyzing data with Bethe-Bloch stopping power theory is emphasized.     

The bremsstrahlung of electrons on atoms calculated in a broad range of photon energies

The total bremsstrahlung spectra for electrons colliding with atoms have been calculated for krypton atoms in a photon energy range from 10 eV to 25 keV and for lanthanum atoms in the vicinity of the 4d shell ionization energy. The generalized atomic polarizabilities were calculated using a simple semiclassical local energy density approximation and experimental data on the photon absorption. The results are compared to those obtained using the distorted partial wave approximation for Kr and to the experimental data available for La.     

On the cohesive energy and charge density of uranium dioxide

Self-consistent band structure calculations have been used to calculate the cohesive energy of UO₂. The computed cohesive energy was 1.641 Ry/formula unit compared with an experimental value of 1.614 Ry/formula unit. The self consistent charge density has been compared with free atom charge densities to illustrate the formation of bonding charge between the atoms.     

Comparison study of the charge density distribution induced by heavy ions and pulsed lasers in silicon

Heavy ions and pulsed lasers are important means to simulate the ionization damage effects on semiconductor materials. The analytic solution of high-energy heavy ion energy loss in silicon has been obtained using the Bethe-Bloch formula and the Kobetich-Katz theory, and some ionization damage parameters of Fe ions in silicon, such as the track structure and ionized charge density distribution, have been calculated and analyzed according to the theoretical calculation results. Using the Gaussian function and Beer's law, the parameters of the track structure and charge density distribution induced by a pulsed laser in silicon have also been calculated and compared with those of Fe ions in silicon, which provides a theoretical basis for ionization damage effect modeling.     

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two-component Fermi gas as a function of the number of particles, angular momentum, and excitation energy. The result includes smooth low-energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy-Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low-lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.     

Expression for the Mott corrections to the Bethe-Bloch formula in terms of the Mott partial amplitudes

It is shown that the calculation of the Mott corrections to the Bethe-Bloch formula can be reduced to summation of a series whose terms are bilinear in the Mott partial amplitudes. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 9, 604–607 (10 November 1996)     

Comparison study of the charge density distribution induced by heavy ions and pulsed lasers in silicon

Heavy ions and pulsed lasers are important means to simulate the ionization damage effects on semiconductor materials. The analytic solution of high-energy heavy ion energy loss in silicon has been obtained using the Bethe-Bloch formula and the Kobetich-Katz theory, and some ionization damage parameters of Fe ions in silicon, such as the track structure and ionized charge density distribution, have been calculated and analyzed according to the theoretical calculation results. Using the Gaussian function and Beer＇s law, the parameters of the track structure and charge density distribution induced by a pulsed laser in silicon have also been calculated and compared with those of Fe ions in silicon, which provides a theoretical basis for ionization damage effect modeling.     

Influence of the shell effects on fission fragment angular anisotropies

The influence of the damping shell corrections with increasing excitation energy on the fission fragment angular anisotropies is considered. In the framework of the statistical approach to nuclear fission, experimental data on fission fragment angular anisotropies obtained in the ⁴He + ²³⁸U reaction is analyzed. Information about the energy dependence of the shell corrections is obtained from this analysis.     

Quasiclassical approach to the interpretation of the Barkas effect

A correction to the Bohr formula making it possible to explain the difference between the stopping powers of positively and negatively charged particles (the Barkas effect) is obtained in the quasiclassical approximation taking into account the difference between electron motion in a hydrogen atom as a function of the charge sign of the moving particle. The influence on the atomic electron of the moving particle leads to a change in the contribution of the adiabatic interaction, in the case of which the energy is not transferred in the majority of collisions, which is the reason for a decrease in the energy losses of slow particles compared with Bohr theory. The results of calculations show that the energy losses per path length unit can be represented in the form of the product of two functions, namely, the energy loss function (in accordance with Bohr theory) and the dynamic function taking into account corrections related to correction of the electron position in the target atom during the collision. Calculations carried out within the framework of classical dynamics make it possible to qualitatively estimate differences between the interaction of protons and antiprotons with target material atoms.     

Macroscopic-microscopic theory of semi-spheroidal atomic cluster

The macroscopic-microscopic method is adapted to atomic clusters deposited on a surface. Analytical relationships for the deformation-dependent liquid drop model (LDM) energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. A superdeformed prolate semi-spheroid is the most stable semi-spheroidal shape within LDM. It is also the shape with maximum degeneracy of quantum states of the semi-spheroidal harmonic oscillator used to compute the shell and pairing corrections. The microscopic corrections as well as total deformation energy show parabolic valley and ridges of the potential energy surfaces in the plane (deformation, number of atoms). The ground state and isomeric state deformation of clusters of various sizes depends on the interplay between the minima of LDM and shell correction energies.     

碱土金属ns(n-1)d1D-ns21S电四极跃迁的能级和振子强度

利用全相对论性多组态Dirac-Fock方法系统地计算了碱土金属激发态1D-1S电四极光谱跃迁的能级间隔,跃迁几率和振子强度,计算中考虑了重要的核的有限体积效应,Breit修正和QED修正,所得结果和最近的实验数据及理论计算值进行了比较,并探讨了采用电四极矩作为中间共振,获得碱土金属元素的高里德伯态,特别是自电离态的可能性.     

Angular momentum and energy dependence of fission andn,p,4He emission from194Hg compound nucleus

Spin and temperature dependence of the fission and particle emission is studied for¹⁹⁴Hg. The compound nucleus is described using the Strutinsky shell correction approach extended for finite angular momenta and temperature. The shell corrections to the potential energy, free energy and the angular momentum are calculated using the Woods-Saxon average field. Results are compared with the experimental data and show a good qualitative agreement. It is found that the inclusion of the shell effects is necessary to understand the decay properties of¹⁹⁴Hg even for temperatures as high as 1.5–2.0 MeV.     

r-过程路径核β——衰变半衰期的估算

分析了20 < A < 190范围内丰中子核β衰变的实验数据,根据半衰期随质子数、中子数以及衰变能变化所呈现的壳效应和对效应等特点,提出了一种有效估算丰中子核β衰变寿命的公式。新的计算公式形式简单包含了较少的参数、计算量小。用该公式能较为准确地再现丰中子核的β衰变半衰期。用RIKEN最新测量丰中子核半衰期检验了该公式的外推能力,本工作可以为r-过程研究提供可靠的输入数据。Experimental data of the β--decay half-lives for the nuclei with atomic number between 20 and 190 are investigated. We have systematically studied the shell effects and pairing effects on β--decay half-lives versus the decay energy Q and nucleon numbers (Z, N). An empirical formula has been proposed to calculate the β--decay half-lives of neutron-rich nuclei. The empirical formula is simple and has relatively few parameters. Experimental β--decay half-lives of the neutron-rich nuclei are well reproduced by the new formula. In addition, the extrapolating capacity of this formula has been checked with the very recent experimental data from RIKEN. The predicted half-lives for r-process relevant nuclei with the current formula can be served as the reliable input of r-process model calculations.     

Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment(NQM) is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin,charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizs¨acker-Skyrme(WS) nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.