N.V.Novikov, Ya. A. Teplova

Scobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia

Cross Sections Equilibrium Fractions FBA References Analysis Notation Help CCCS code


Charge - changing phenomena have increasing interest in connection with the design of radiation detectors, with radiation damage, with studies of astrophysics, with controlled thermonuclear fusion, with the acceleration of multiply charge heavy ions, and with slowing down or energy loss of heavy ions in matter. The capture and loss of one or more electron cross sections are summarized in tables and figures as a function of the energy of the incident projectile. The experimental, theoretical and recommended data are compiled. Cross sections on gas and vapor targets are presented. We save the units of original papers and transform them to Mev/amu and 10-16 cm2/atom. There are the First Born Approximation (FBA) cross section tables for proton-impact ionization of atoms (Zt =1-92) and for proton-impact excitation of atoms (Zt =2-10).


Charge Changing Cross Sections, Electron Capture Cross Section, Electron Loss Cross Sections, Equilibrium-charge-state fractions, Average equilibrium charge, First Born Approximation.


The charge - changing process can be represented as
Xi+(Z) + A(Zt) → Xk+(Z) + Am+(Zt) + (k+m-i) e- (1)
where an incident projectile X with initial charge i collides with a target atom or molecule A, initially neutral and undergoes the loss (k > i) or capture (i < k) of electrons into charge state k, while the target acquires charge m. Thus (k+m-i) electrons are released in this process. The cross section for this process is denoted by σi,k 0m, where the superscripts pertain to the initial and final charge states of the target, and the subscripts pertain to those of the projectile. The cross section
σi,k = ∑m σi,k 0m (2)
is the sum over all cross sections of processes in which the ion with charge i transformed into ion with the charge k. The cross section (2) also containes the sum on all quantum states of scattered projectile Xk+ and residual target Am+(Zt). The indices i,k in (2) can range from -1 (if the negative ion exists) to nuclear charge of the projectile Z.


Z is the nuclear charge of the projectile;
Zt is the nuclear charge of the target atom;
i is the charge of the projectile before collision;
k is the charge of the projectile after collision;
V is the velocity of the projectile;
E is the energy of the projectile;
E [MeV/amu] = 0.025 * (V/Vo)2; Vo=2.188 × 10 8 cm/s
σi,k is the charge - changing cross section ;
Fq is the equilibrium-charge-state fraction ( ∑q Fq = 1);
qav is the average equilibrium charge (qav = ∑q q* Fq) ;
d is the width ( d2 = ∑q (q -qav)2 * Fq) ;
s is the skewness ( s = ∑q (q -qav)3 * Fq/d3 ) .
In case of a precisely Gaussian distributions, s is zero and d is related to the full width at half maximum h and to the full e -1 width Γ by h=d (ln 2) ½ ; Γ=2d √2.

Average equilibrium charge models

qTF = Z { 1 - exp[ - V/(V0 Z2/3)] } is Thomas-Fermi model estimation
qSRIM = { S(Z, Zt, V) / S(Z=1, Zt, V) }1/2 is SRIM estimation, where S(Z, Zt,V) is the stopping cross section
qgas is calculated by the approximation of experimental data in gases [SC01]

qsolid is calculated by the approximation of experimental data in solid [SC01]

Fisrt Born Approximation

n,l are the subshell parameters ;
Inl [a.u.] is electron binding energy of subshell;
σnl is the ionization cross section;

σion = ∑nl σnl is the total ionization cross section;
σnl-n'l' is the excitation cross section.
RHF - Roothaan-Hartree-Fock wave function


[1] N V Novikov and Ya A Teplova. Database on charge changing cross sections in ion atom collisions J. Phys.: Conf. Ser. 194 Volume 194 (2009) 082032