### Abstract

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} cm^{2}/atom.
There are the First Born Approximation (FBA) cross section tables
for proton-impact ionization of atoms (Z_{t} =1-92)
and for proton-impact excitation of atoms (Z_{t} =2-10).

### Keywords

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

### Introduction

The charge - changing process can be represented as

X^{i+}(Z) + A(Z_{t}) → X^{k+}(Z) + A^{m+}(Z_{t}) + (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
σ_{i,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

σ_{i,k} = ∑_{m} σ_{i,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 X^{k+} and residual target A^{m+}(Z_{t}).
The indices i,k in (2) can range from -1
(if the negative ion exists) to nuclear charge of the projectile Z.

### Notation

Z is the nuclear charge of the projectile;

Z_{t} 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/V_{o})^{2}; V_{o}=2.188 × 10 ^{8} cm/s

σ_{i,k} is the charge - changing cross section ;

F_{q} is the equilibrium-charge-state fraction ( ∑_{q} F_{q} = 1);

q_{av} is the average equilibrium charge (q_{av} = ∑_{q} q* F_{q}) ;

d is the width ( d^{2} = ∑_{q} (q -q_{av})^{2} * F_{q}) ;

s is the skewness ( s = ∑_{q} (q -q_{av})^{3} * F_{q}/d^{3} ) .

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

q_{TF} = Z { 1 - exp[ - V/(V_{0} Z^{2/3})] } is Thomas-Fermi model estimation

q_{SRIM} = { S(Z, Z_{t}, V) / S(Z=1, Z_{t}, V) }^{1/2} is SRIM estimation,
where S(Z, Z_{t},V) is the stopping cross section

q_{gas} is calculated by the approximation of experimental data in gases
[SC01]

q_{solid} is calculated by the approximation of experimental data in solid
[SC01]

### Fisrt Born Approximation

n,l are the subshell parameters ;

I_{nl} [a.u.] is electron binding energy of subshell;

σ_{nl} is the ionization cross section;

σ_{ion} = ∑_{nl} σ_{nl} is the total ionization cross section;

σ_{nl-n'l'} is the excitation cross section.

RHF - Roothaan-Hartree-Fock wave function

### References

[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