INTRODUCTION
Chargestate evolution is one of the most important aspects in ionsolid interactions. Various processes, such as electron capture, ionization, excitation, vacancy production (Imai et al., 2005; Abufager et al., 2005) and the consequent phenomena like energy loss and stopping (Bentini et al., 2002) are closely related to the projectile chargestate evolution in the target. When energetic ions collide with a solid target, the ions undergo repeated electroncapture and electronloss with target atoms and consequently, equilibrium of the chargestate distribution is attained for the moving ions (Arafah, 1998). The knowledge of such equilibrium chargestate distributions is of interest for a number of applications including nuclear physics, gas filled recoil separators and accelerator design (Itoh et al., 1999).
Chargestate fractions of backscattered ions from solid surfaces have been studied experimentally by a number of investigators. Recently, Bianconi et al. (2002) have obtained the equilibrium chargestate fractions of He ions transmitted from silicon in a random direction in the energy range 0.16  3.3 MeV. Nakajima et al. (2004) have carried out experimental studies of the chargestate distribution of He ions backscattered from three different surfaces; Si, SiO_{2} and Ag. In their work, they obtained the dependence of the chargestate on the exit angle of the scattered ions by measuring the energy spectra for both He^{+ }and He^{2+} ions at various exit angles for each surface.
In this research, we report measurements of chargestate distributions of 0.125  0.50 MeV/amu He ions backscattered from Ag surfaces of different thicknesses (i.e., 5.4  24.8 μg cm^{–2}). We also perform a technique in which all chargestates fractions of backscattered ^{ 4}He ions are measured simultaneously in one experimental run using single surface barrier detector (SBD).
APPARATUS AND DATA ACQUISITION
Layout of the apparatus: The present measurements have been obtained
on a postaccelerator (Fig. 1). ^{4}He^{+} ions within energy range between 0.125 and 0.50 MeV/u were produced by the 4.75
MeV Jordan University Van de Graff Accelerator (JUVAC). Then the ions were bended
through a 90° angle by the analyzing magnet and guided toward the switching
magnet. The selected beam was directed into a 9.5 m beam line and passed through
a pair of collimators toward the scattering chamber where the interactions take
place. A thin solid silver film, prepared by vacuum evaporation on siliconwafer
substrates under an applied pressure of order 10^{4} Pa and evaporation
rate of 0. 27 μg cm^{–2} s^{1}, was mounted on a target
holder inside the scattering chamber at an angle of 45° with respect to
the beam direction where the scattering geometry was chosen in such away that
the beam feels the symmetrical environment along the inward and outward paths.

Fig. 1: 
Block diagram showing the experimental setup and the 60 keV
postaccelerator built as a chargestate separator of backscattered ions 
After the collisions, the scattered ions were detected by a surface barrier
detector (SBD), placed at right angle with respect to the direction of the incident
beam and furnished with the necessary voltage of 60 V supplied by a bias power
supply, after passing a small aperture of 1 cm in diameter located in front
of the detector. The conventional electronics needed for backscattering measurements
with SBD and a multichannel analyzer (MCA) were all set at negative potential
relative to ground. The observations in this experimental study showed that
with an additional electrostatic energy, e.g.,  60 keV (=  0.015 MeV/amu)
between the target and the SBD, the backscattered ions will gain multiples of
this acceleration energy depending on their ionic chargestate n (i.e., n*60
keV). This, however, allows all chargestate fractions to be collected and measured
simultaneously in one experimental run. The kinematics behavior of the backscattered
ions is given by the wellknown Rutherford Backscattering Spectrometry (RBS)
Technique (Ziegler et al., 1985; Chu et al., 1978).
Data acquisition: Two procedures of accumulating the RBS energy spectrum were conducted. In the first procedure, energy spectrum was accumulated without postacceleration. The spectrum is then fitted by analytical function f (E), Exponentially Modified Gaussian (EMG), which is given by Gouri and Johnson (1977):
where a_{0} is the area under the peak, a_{1} is the peak center, a_{2} is the width (standard deviation), a_{3} is the distortion and erf is the error function. The second procedure was performed by accumulating the RBS energy spectrum with a fixed postacceleration voltage, 60 kV in this case. As in the first procedure, the resulting spectrum is fitted by analytical function, which is the sum of weighted function f (E + nqV), according to the following relation (Arafah et al., 1989):
where f (E) is the fitted analytical function without postacceleration voltage,
E is the energy spanned over the RBS energy spectrum as obtained without postacceleration,
n is the charge state, q is the electronic charge, C_{n} is fitting
coefficient for the nfold chargestate fractional contribution accelerated
by an energy of nqV and Y(E) is the yield corresponding to a RBS spectrum with
a fixed postacceleration voltage V. Therefore, the chargestate fractions were
determined from the total curve fitting to the postaccelerated spectra. In more
details, the peak intensity, the area under the observed peak due to a certain
chargestate, which is obtained from the fitted model, is a measure of its mean
chargestate fraction. It is important to mention that in both procedures the
obtained spectra were normalized to the same accumulated charge, i.e., the backscattering
yield from a certain depth within the silicon substrate is the same, within
experimental uncertainties, as that of single isolated peak without postacceleration.
Also, present study neglect the chargestate fraction of ^{4}He ions
backscattered from the silicon substrate, therefore, the signals due to the
silicon substrate in the obtained RBS energy spectra (with and without postacceleration)
were subtracted.
The energy dependence of the peak due to the scattering from the surface is, however, governed by the corresponding wellknown kinematics equation (Arafah, 1998):
where K is the RBS kinematic factor, E_{0} is the incidention energy,
n is the charge state, q is the electronic charge and V is the acceleration
potential. The approach followed in separating all charge state components ensures
that neither the intensity nor the peak position is disturbed by the analysis.
RESULTS AND DISCUSSION
RBS spectra of ^{4}He ions backscattered from Ag films at impact
energy of 0.188 MeV/amu: Figure 2 shows the observed RBS
energy spectra for backscattered ions from the interaction of 0.188 MeV/amu
^{4}He with different silver thin film thicknesses, with and without
applying postacceleration. Also shown are the results of the fitting procedures
generated by EMG model. The full width at halfmaximum (FWHM) of the energy
spread of the single isolated peak is about 27.6 keV (= 0.007 MeV/amu), for
the thickness of 14.8 μg cm^{–2}, which is the same as those for
He^{0}, He^{+} and He^{2+}. The shape and the peak position
are almost the same for all thicknesses. In addition, considerable overlapping
between the charge state fractions is observed which is increased as the thickness
increases. It should be mentioned that the significant overlap between the higher
chargestate fractions resulting from the silicon substrate and the lower one
resulting from Ag film, makes the experimental measurements of the fractions
rather impossible.

Fig. 2: 
The
observed RBS energy spectra for ^{4}He ions backscattered from
the interaction of 0.188 MeV/amu ^{4}He^{+} with different
silver thin film thicknesses, with (○) and without (●) applying
postacceleration. The solid and dashed curves are generated data from
EMG model 
Repeated measurements were done in order to check whether the calculated fractions,
backscattered from the same thickness at certain energy, changed or not. Insignificant
changes were detected for some repeated measurements. However, the sharp increase
of the measured neutral fractions from 7.56 to 14.64% (Table 1)
could be considered due to the surface effects and nonuniformities in the deposited
films. This is expected at this energy for the neutral fraction since its probability
is small.
RBS spectra of^{ 4}He ions backscattered from Agfilm at different
impact energies: The variation of the RBS energy spectra of^{ 4}He
ions backscattered from 24.8 μg cm^{–2} silver films as a function
of impact energy, with and without postacceleration voltage, is shown in Fig.
3. The results also shown the fitting procedures with and without postacceleration.
At impact energy of 0.125 MeV/amu, the single isolated peak due to ^{4}He
backscattering from Ag film before applying postacceleration splits into three
distinct peak features after postacceleration.
Table 1: 
Equilibrium
charge fractions, mean charges and distribution width, d, for ^{4}He
ions backscattered from different silver film thicknesses at various impact
energies 

^{(1)}Calculated from Eq. 5, ^{(2)}Calculated
from Eq. 6 and ^{(3)}Obtained from the Gaussian
fit Eq. 4 
The wellresolved peaks are
corresponding to the chargestates of helium (He^{0}, He^{+} and He^{2+}). On the other hand, at incident energies ≥0.313 MeV/amu, the peak splits
into two wellresolved peaks corresponding to He^{+} and He^{++}.
It can be seen that the energy difference between the peaks for all charge states
(i.e., peak in the spectrum without postacceleration) and the peaks corresponding
to He^{+} and He^{++} is always 60 keV (= 0.015 MeV/amu). As
the incident energy is increased, the doubly charged peak (fraction) increases
and become dominate at incident energy ≥0.25 MeV/amu but the relative importance
of the neutral and singly charged peaks (fractions) is strongly decreased. This
is attributed to the fact that at low energies, the projectile ions spend enough
time near the target atom and as a result their probabilities to capture an
electron from the target are large (Sols and Flores, 1984). However, at higher
energies, the projectile ion spends little time near the target, therefore,
the interaction is swiftly completed and the projectile's electron is stripped
off by the silver atom since the electrons in the conduction band do not have
enough time to screen the incoming energetic ion (Goluvev et al., 2001;
Tordoir et al., 2001).
Equilibrium chargestate fractions: In the Gaussian model (Stuchbery, 2006; Baudniet et al., 1978) the chargestate fractions is given by
Where q is the charge state, is the mean charge state and d is the width of
the chargestate distribution. Specifically, the mean chargestate is defined
as:
However, the distribution width is denoted by:

Fig. 3: 
The
variation of the RBS energy spectra of ^{4}He ions backscattered
from 24.8 μg cm^{–2} silver films at different impact energies
with (o) and without (●) postacceleration voltage. The solid and
dashed curves are generated data from EMG model 
The extracted chargestate fractions for ^{4}He ions at various energies from different silver film thicknesses, along with the relative uncertainties are listed in Table 1. In addition, and d calculated from experimental data are also tabulated, together with those from the Gaussian fits, in Table 1. Chargestate equilibrium is, however, reached when the variation of the fraction during the passage of depth λ ceases, d F(q)/dλ→0, as λ increased. In order to determine the equilibrium chargestate fractions of backscattered ions, the thickness dependence of the chargestate fractions has to be measured (Baudinet, 1982; Lennard et al., 1981).
The dependence of the singly ionized helium fractions at different incident
energies on the silver film thickness is displayed in Fig. 4.
These fractions are reasonably constant at target thicknesses ≥ 14.8 μg
cm^{–2} and fluctuate for thin thicknesses. This indicates that the
measured chargestate fractions for ^{4}He ions backscattered from 14.8
μg cm^{–2} Ag films, in the energy range studied, represent the
equilibrium fractions.

Fig. 4: 
The
measured backscattered fractions of the chargestates He^{+} and
He^{++} at different impact energies plotted as a function of
silver thin film thickness. Smooth solid and dashed lines are drawn to
guide the eye 
On the contrary, the fractions obtained from thin targets, i.e., 5.5 and 10.3
μg cm^{–2}; represent the nonequilibrium fractions since there
are differences in their distributions.
Focusing Effects on the backscattered ions: The negative voltage applied to the postaccelerator is inverted to positive value. The same chargestate fractions are obtained for the same energy of the incident ions as in the case of negative value (Fig. 5). It must be emphasized that for the same accumulated charge, the integrated yield with and without post acceleration is the same. These facts exclude any significant influence on focusing the beam when the accelerated voltage is applied. Therefore, insignificant effects on the measured charge state fractions are observed. If, however, such focusing effects are present, then serious consequences could affect the accuracy of the experiment since the accelerating column would act as a series of lenses between the scattering centers and the detector system when using the accelerated configuration (Arafah et al., 1989).
Energy dependence of the backscattered fractions: The equilibrium charge
fractions of ^{4}He ions emerging from Ag film of thickness 14.8 μg
cm^{–2} are depicted as a function of projectile energy in Fig.
6. It can be seen that the measured neutral and singly charged fractions
decreases with increasing impact energy.

Fig. 5: 
RBS
energy spectra of ^{4}He ions backscattered from 10.3 μg
cm^{–2} silver thin film at impact energy of 0.438 MeV/amu. The
experimental data without postacceleration, with postacceleration voltage
of +60 kV and with postacceleration voltage of 60 kV are represented
by (●), (o) and (Δ), respectively. Solid, dashed and doted
curves are generated data from EMG model 

Fig. 6: 
The
equilibrium charge fractions of ^{4}He ions emerging from Ag film
of thickness 14.8 μg cm^{–2} are plotted as a function of
projectile energy. The measured neutral, singly and doubly charged fractions
are respectively represented by (■), (●) and (▲). Smooth solid
lines are drawn to guide the eye 

Fig. 7: 
Mean
charge versus energy after the backscattering. Solid circles (●)
represent the experimental data from this study. The open circles (o)
represent the mean charge from Gaussian fit ( Eq. 4).
The solid line is the exponential fit ( Eq. 7). Error
Bars represent the variance of the standard deviation of our measurements 
On the other hand, the measured doubly
charged fractions slowly increases with increasing impact energy and becomes
dominant at energy above 0.188 MeV/amu.
Semiempirical formula for the mean charge : Various semiempirical
or empirical formula for of rapid
ions interacting with matter have been proposed in the past (Tordoir et al.,
2001; Itoh et al., 1999). Each of them is only valid within the limited
domain of derivation. In our case, all available experimental data of
in the energy range 0.125 0.50 MeV/amu are fitted by the exponential function
given by:
A good fit has been obtained (Fig. 7), where the offset, Y_{0} = 194±0.0345, the center, x_{0} = 0.12493±0.0034 the amplitude A = 0.763±0.0408 and the decay constant t = 0.11553±0.01668. These parameters could be physically interpreted as follows: x is the impact energy, Y(x) is the mean charge as a function of impact energy, Y_{0} is the mean charge at impact energies ≥0.50 MeV/amu, x_{0} is the lowest impact energy of the studied energy range. The values; x, x_{0} and t are measured in MeV/amu. Figure 7 also shows the values of obtained from the Gaussian fit (Table 1).
The inherent uncertainties arising from this work were kept at minimum level. The uncertainties are estimated within 6% in the lower probabilities, e.g., the neutral fractions at 0.188 and 0.25 MeV/amu and the singly charged fractions at 0.438 and 0.50 MeV/amu. On the other hand, the uncertainties are markedly reduced (better than 4%) with higher fractions, e.g., doubly charged fractions at 0.375, 0.438 and 0.5 MeV/amu (Table 1).
CONCLUSIONS
We have carried out a comprehensive study of chargestate fractions of ^{4}He ions backscattered from Agfilms of different thicknesses (5.424.8 μg cm^{–2}) at impact energies within the range between 0.125 and 0.50 MeV/amu. The energy spectra that represent these fractions are nicely fitted by the exponentially modified Gaussian function. It turned out that the measured chargestate fractions for ^{4}He ions backscattered from 14.8 μg cm^{–2}Ag films represent equilibrium fractions. The mean chargestate and the width of the charge state distributions, d, at different impact energies are also measured. Empirical formula for calculating the mean charge state has been proposed. The success in separating and collecting all chargestates ^{4}He ions in one measurement and their measurements using total curve deconvolution to the experimental data, both add new measurement and reliability to our determinations with the minimum inherent uncertainties due to the variations in the experimental conditions. Experiments on the angle dependence of the chargestate fractions are proposed. Furthermore, measurement of charge state fractions of ^{4}He ions at different energy ranges is, however, in progress.