Energy loss of charged particles in matter

A new method of determining the differential energy loss of charged excited nuclei in matter is described. The method is based on the velocity dependence of the Doppler shift of the gamma quanta emitted by moving nuclei. No theoretical assumptions concerning the velocity dependence of atomic or nuclear collisions are necessary. The method and mathematical analysis, described in detail, are applied to the energy loss of Li ions emitting gamma quanta of 477 keV in the kinetic energy range between 100 and 800 keV. It is found that the energy loss of Li ions is linearly proportional to the velocity within 2% for several substances ofZ=1 to 74. The small limits of error, which can be obtained, allow an application of this method to questions as e.g. theZ-dependence of the stopping power on the nuclear charge of the stopping material, chemical binding effects, the time dependence of the adjustment of the equilibrium charge of the projectile after nuclear reactions, or the determination of nuclear angular correlations.     

Effect of density on the equilibrium charge distribution of carbon and oxygen ions

Theoretical estimation of the equilibrium charge distribution of carbon and oxygen ions passed through a matter is obtained. The coefficient considering the effect of density on the charge distribution of these ions is calculated for an amorphous medium consisting of atoms with the nuclear charge Z _t (Z _t ≤ 54). An oscillating dependence of the average ion charge on the nuclear charge of the target atom is obtained which cannot be described by empirical relations.     

Asymptotics of the cross section of the electron loss by fast ions in light media

The dependence of the single electron loss cross section on the nuclear charge Z of a projectile and on the nuclear charge Zt of a target atom for fast collisions is studied theoretically using the plane-wave Born approximation and the sum rule. The results of calculations for fast singly and triply charged ions show that the single electron loss cross section increases monotonically as Z and Zt increase. This can be used to interpolate cross sections of processes if there are no experimental data. The results of calculations compare with the experimental and theoretical data of other authors.     

Asymptotics of the cross section for the electron loss by atoms and ions in light media

The dependence of the cross section of electron loss on the nuclear charge Z of a bombarding ion and on the nuclear charge Z _t of a target atom for fast collisions is studied theoretically using the plane-wave Born approximation and the sum rule. The results of calculations show that the cross section of electron loss for fast collisions increases monotonically as Z and Z _t increase, which can be used to interpolate cross sections for the processes for which there are no experimental data.     

High Z effects in accounting for radiative component of the electron magnetic moment in hydrogen-like atoms

The behavior of electron energy levels in hydrogen-like atoms is studied while taking into account the nonperturbative interaction between the radiative component of the magnetic moment of a free electron Δg _free and the Coulomb field of an atomic nucleus with charge Z, including those with Z > 137. It is shown that for Zα ? 1 the energy-level shift is rather effectively determined through the matrix elements of the corresponding Dirac-Pauli operator with relativistic Coulomb wave functions. At the same time, for superheavy nuclei with Z ～ 170, this shift, generated by Δg _free, is genuinely nonperturbative, behaves like ～Z ⁵ near the threshold of negative continuum, exceeds all the estimates of radiative corrections coming from vacuum polarization and electron self-energy known so far, and turns out to be at least of the same order as the effects of nuclear charge screening by filled electron shells.     

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.     

Effect of the nuclear charge of a fast structural ion on its internal effective stopping in collisions with atoms

The energy losses of fast structural ions in collisions with atoms have been considered in the eikonal approximation. The structural ions are ions consisting of a nucleus and a certain number of electrons bound to it. The effect of nuclear charge Z of the ion on its effective deceleration κ^(p) (energy losses associated with excitation of only intrinsic ion shells) has been analyzed. It is shown that the allowance for the interaction of an atom with the ion nucleus for Z _a Z/v > 1, where Z _a is the charge of the atomic nucleus and v is the velocity of collisions in atomic units, considerably affects the value of κ^(p), which generally necessitates taking into account nonperturbatively the effect of both charges Z _a and Z on κ^(p).     

Description of single-electron capture by fast multielectron ions

An analytical approximation of wave functions has been derived for the excited states of atoms and ions. The nuclear charge and the number of electrons are Z ≤ 10 and N _e ≤ 10, respectively. It is shown that the cross section of electron capture by fast ions must be estimated with allowance for their Coulomb interactions. The theoretical dependence between the single-electron capture cross section and the collision energy is close to the experimental, when ion interactions in the final state are taken into account. This proximity enables us to analyze the correlation between theoretical and experimental results.     

Energy loss of light ions with allowance for the presence of metastable particles in the ion beam

The change in the average ion charge due to the presence of particles in metastable states in beams of helium-like ions has been studied. The charge distributions and average charges have been calculated for ions with nuclear charges Z = 3?7 and a velocity of 3.65 au in nitrogen. The previously obtained data on the cross sections of loss and capture of electrons by metastable ions and ions in the ground state were used in the calculations. It is shown that the presence of metastable particles in ion beams leads to an increase in the average charge and energy loss for all considered ions.     

Screened self-energy correction to the 2<Emphasis Type="Italic">p</Emphasis><Subscript>3/2</Subscript>-2<Emphasis Type="Italic">s</Emphasis> transition energy in Li-like ions

We present an ab initio calculation of the screened self-energy correction for 1s² 2p_3/2 and 1s² 2s states of Li-like ions with nuclear charge numbers in the range Z = 12?100. The evaluation is carried out to all orders in the nuclear strength parameter Zα. This investigation concludes our calculations of all two-electron QED corrections for the 2p_3/2-2s transition energy in Li-like ions and thus considerably improves theoretical predictions for this transition for high-Z ions.     

A fast calculation of excitation autoionization cross-sections of Na-like ions

In this work, based on the calculation in detail, two new fitting formulae of total excitation and excitation autoionization cross-sections for Na-like ions (18?Z?39) are given. For discussing the variation of the total excitation autoionization cross-section, a systematic study of the dependence of the overall branching ratio on incident electron energy and nuclear charge is also carried out.     

Fragmentation cross sections of32S at 0.7, 1.2 and 200 GeV/nucleon

We used CR39 plastic nuclear track detectors (C₁₂H₁₈O₇) in combination with automatic track measurement techniques to determine total charge changing and partial cross sections for the production of fragments of chargeZ _F =6 toZ _F =15 in collisions of³²S beam nuclei at energies of 0.7, 1.2 and 200 GeV/nucleon in targets H, C, CR39, CH₂, Al, Cu, Ag and Pb. By application of factorization rules measured partial cross sections are separated into pure nuclear and electromagnetic components. Total and partial cross sections for electromagnetic dissociation are compared with theoretical models. The energy dependence of pure nuclear cross sections is investigated.     

Nuclear charge distribution of mass-separated isobars from thermal-neutron-induced fission of 235U

The nuclear charge distribution of fission products with mass numbers A = 90, 91, 94, 99, 100, 101 and 104 provided by the mass separator “Lohengrin” was measured. Adjacent elements in the group of the light fission products could be separated by their different energy loss in a carbon absorber. The Z-yields were found to be strongly dependent on the kinetic energy of the fission products. The widths of the nuclear charge distributions are very small, in general, and strongly dependent on A as well as on the kinetic energy. The influence of the neutron evaporation and odd-even effects are clearly detected. An asymmetric nuclear charge distribution was found for A = 104 indicating the suppression of fission fragments with Z = 43. The average nuclear charges of the fission products at their average kinetic energy are in good agreement with the results from measurements of the number of β-decays and K X-ray measurements. The average nuclear charge of the isobar A = 132 was measured at its average kinetic energy with a calibrated secondary electron detector to be Z = 51.14 ± 0.15 which is in very good agreement with the radiochemical results. Thus previous physical measurements indicating a large independent yield for the doubly magic nucleus ¹³²Sn could not be confirmed.     

Fission yields at different fission-product kinetic energies for thermal-neutron-induced fission of 239Pu

At the recoil spectrometer “Lohengrin” of the Institut Laue-Langevin in Grenoble, the yields of the light fission products from the thermal-neutron-induced fission of ²³⁹Pu were measured as a function of A, Z, the kinetic energy E and the ionic charge states q. The nuclear charge and mass distributions summed over all ionic charge states were determined for different light fissionproduct kinetic energies between 93 and 112 MeV. The proton odd-even effect which was measured to be (11.6 ± 0.6)% causes considerable fine structure in the yields. The average kinetic energy of even-Z elements in the light fission-product group is 0.3 ± 0.1 MeV larger than for odd-Z elements. The neutron odd-even effect is (6.5 ± 0.7)%. The comparison with previously published data ¹) for thermal-neutron-induced fission of ²³⁵U reveals a correlation between the proton odd-even effect in the yield and in the kinetic energy of the elements. The dependence of the proton odd-even effect on the fragmentation is very similar for ²³⁵U and ²³⁹Pu when it is considered as a function of the nuclear charge of the heavy fission products. The isobaric variances σ_z². for thermal-neutron fission of ²³⁵U and ²³⁹Pu coincide at all kinetic energies if the influence of the proton odd-even effect is averaged out. This supports the hypothesis that the magnitude of σ_z² is determined only by quantum-mechanical zero-point fluctuations. The influence of the spherical shells Z = 50 and N = 82 on the fragmentation is discussed.     

Registration of accelerated multiply charged ions from the cathode jet of a vacuum discharge

The parameters of Cuⁿ⁺ and Taⁿ⁺ ions from the plasma of a vacuum spark with a voltage up to 2.5 kV and a current rise rate up to 2 × 10¹⁰ A/s are studied using the time-of-flight method. At the initial stage of the discharge, bursts of beams of accelerated multiply charged ions from the cathode flame have been detected. It is established that the charge state distribution and energy of a beam are controlled by the initial voltage U ₀ of the capacitor. Upon an increase in this voltage, the average charge of copper ions attains the value +9, and the average charge of tantalum ions can be as high as +20, while the energy attains values of 150 and 350 keV, respectively. It is found that the average energy of ions with charge Z increases in proportion to the charge and is close to the energy eZU ₀ which would have been acquired by ions accelerated in the electric field of the discharge gap.     

Some regularities within the Stark widths and shifts of resonance ion lines from Li to Ca

A periodic dependence of the Stark widths and shifts of resonance lines, for singly- and doubly-ionized elements, has been found on nuclear charge number Z. These periodicities were found for Griem's theoretical values of the Stark parameters of resonance lines of some singly charged ions from Li to Ca; for other singly- and doubly- charged ions, this parameter was calculated from Griem's semiempirical formula. The dependence of the Stark parameters of the resonance lines on atomic polarizability X has been determined and used to estimate Stark widths and shifts for other singly-charged ions. These values are compared with estimates derived form Griem's semiempirical formula for the Gaunt factor g = 0.2.     

Features of energy loss for ions with K vacancy

The change in the average charge of helium-like ions when metastable particles are present in the beam is studied. The charge fractions and average charges are calculated as functions of the target thickness for ions with Z = 3–8 at a velocity of 3.65 au. Previous data on the cross sections for electron capture and loss by metastable ions are used in the calculations. It is shown that, for all ions under consideration, the presence of metastable particles in the beam leads to an increase in the average equilibrium charge and, possibly, to a corresponding increase in energy loss and ion ranges.     

Electron shells in over-critical external fields

When the charge of a nucleus exceedsZ=Z _cr≈ 164–172 the energy of the 1s-electron level is lowered beyond the critical value of ?m _e c ². Then this bound level is degenerated with negative energy continuum solutions of the Dirac equation and becomes a resonance, whose shape varies and is approximately of Breit-Wigner type forZ?Z _cr?5. The physical meaning of this resonance can be understood most easily if the 1s-level is unoccupied (K-hole). In this case a positron may escape ifZ>Z _cr, a process, that can be interpreted as auto-ionization of the positron. This fundamentally new process of quantum electrodynamics of strong fields can be tested experimentally by scattering very heavy ions (Z≧80) on each other since in such collisions superheavy electronic molecules occur (superheavy quasimolecules).     

Study of emission characteristics of the projectile fragments produced in the interaction of 84Kr36 with nuclear emulsion detector at 1 GeV

This article is focused on the characteristics of the projectile fragments of charge 1 ≤ Z ≤ 10 produced in the interaction of the ⁸⁴Kr₃₆ with nuclear emulsion detector at 1 GeV per nucleon. We have studied the average charge distribution and multiplicity distribution of the projectile fragments having charge 1 ≤ Z ≤ 10. We have also studied the emission behavior of various projectile fragments produced from the interaction with different target groups of nuclear emulsion detector. From this study we have observed that the emission of projectile fragments is strongly dependent on the interaction with different type of the target groups of nuclear emulsion detector as well as on the mass of the projectile beam. The results are compared with other experimental observations carried out at relativistic energy and found to be consistent.     

Investigation of cross sections for the formation and destruction of negative boron ions

The electron loss and electron capture cross sections σ _i,i+m and σ _i,i−m for boron ions and atoms traveling at the velocities V=1.19 and 1.83 a.u. in H₂, He, N₂, Ne, Ar, and Xe are measured. The known experimental data on these cross sections at velocities near the cross-section maximum are analyzed. It is found that the electron loss cross sections can be described by a formula which was previously derived in the free-collision approximation and takes into account features of both the ions and the ambient atoms. As the nuclear charge Z _t of the ambient atoms increases, the cross sections vary nonmonotonically, increasing on average as Zt _t ^1/2 . A formula based on the model of independent electrons is proposed for electron capture by ions with small values of the charge i. It describes the dependence of the electron capture cross section σ _i,i−1 on the mean binding energy of an electron in an ion with the charge i−1. The total electron capture cross section σ _i,i−1 is proportional to the number of vacancies in the unfilled electron shell nearest the nucleus. The cross sections 0σ _i,i−1 exhibit substantially nonmonotonic variation with Z _t, increasing on average as Z _t ^1/3 . Zh. éksp. Teor. Fiz. 116, 1539–1550 (November 1999)