International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 9, September 2015
ISSN 2319 - 4847
Thecalculations oftheeffective number of
electrons in DNA and liquid water by using
(MELF-GOS) method
Ahmed M. Abid1, Khalid A. Ahmad2
1
Al-Mustansiriyah University, College of Science, Department of Physics Baghdad-Iraq
2
Al-Mustansiriyah University, College of Science, Department of Physics Baghdad-Iraq
Abstract
The effective number of electrons for DNA and liquid water which is a function to the energy that contributes in the excitations
of the target using the dielectric formalism which has been calculated in present work. The electronic response of DNA and
liquid water is described by the MELF-GOS model, in which the outer electron excitations of the target are accounted by
Mermin-type energy loss functions, whereas the inner-shell electron excitations are modeled by the generalized oscillator
strengths of the constituent atoms. The mathematical equations have been program by writing a Fortran-90 program for
numerical calculations.
Keywords:MELF-GOS, Effective number of electrons, DNA target, Liquid water, dielectric function, valance shell,
inner shell.
1.INTRODUCTION
The study of interaction aion beams with biological materials is very important for predicting the effects of radiation in
living tissues [1-3].Since the amount of energy deposited by the ionizing radiation to tumour cells will determine the
outcome of the treatment [1, 4].Using energetic ion beams for radiation therapy has become a promising technique
because high doses can be deposited locally at tumor sites, reducing the damage to the surrounding critical organsand
the selection of ion beam energies and the determination of ion ranges are crucial for the calculation of the delivered
dose [5].Research on the effects of radiation on DNA, the most important biological material, is very active, because
determining the relationship between the energy deposited by fast particles in the target and the damage they cause is
important to radiation biophysics [6, 7]. DNA damage can be produced by direct ionization and excitation of DNA
electrons [8] or by indirect chemical reactions of water radiolysis products with DNA [9]. Even electrons with
subionizing energies can cause lethal lesions in DNA [10, 11]. An effort to study the interaction of energetic ion beams
with liquid water at intermediate energies has been carried out recently, since water represents over 80% of the content
of the cellsof soft tissues [12, 13]Therefore, a detailed study of the energy loss of ions in biological targets (such as
DNA or liquid water) is desirable to improve our understanding and modeling capabilities of the action of radiation in
ion-beam cancer therapy [7, 14, 15].
2.THEORETICAL BACKGROUND
Energy loss function for valance electron and inner shell
The dielectric formulation is one of the most used methods to describe the interaction of swift ions and other charged
particles with matter [16],
dielectric function is the basic of many applications and because it is applicable to
only a limited number of so-called nearly-free-electron materials like aluminum [17].
derived an expression to
the dielectric function, in terms of the
dielectric function by replacing the frequency (ω) into a complex
frequency(   i ) by using Random Phase Approximation dielectric function (RPA) dielectric function and the result


is
dielectric function M (k ,  ) which can be written in terms of  ( k ,  ) , as follows [18,19]:
M

( k , )  1 

1
Volume 4, Issue 9, September 2015
L
1  i γ /   L k ,   i γ   1
i γ/   L k ,   i γ   1   L k , 0   1 
,(1)
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 9, September 2015
ISSN 2319 - 4847
The excitations of the outer electrons of the solid, including both collective and single-particle excitations, are
described by
-type ELF,
Where
is the Mermin dielectric function [18]. The suitable parameter
and are represented position and width,
respectively, of the
Mermin-type ELF, while the coefficients
are the corresponding weights. While
is the
threshold energy [25]. The parameters for DNA and liquid water are shown in table (1).
Table (1) Parameters used to fit the outer electron excitations contribution to the ELF (See Eq. 3) of DNA and liquid
water
Target
1
2
3
19
25.2
43
9
15
35
0.159
0.397
0.0707
1
2
3
22
0.34
0.47
140
19
31.97
0.23
0.131
1.15
On the other hand, inner-shell electrons keep their atomic character since they have large binding energies; thus, they
are designed in terms of the generalized oscillator strengths (GOS). The connection between the ELF and the GOS
model is given by
Where
(
) is the GOS of the ( ) sub-shell and
is the molecular density of the target. In the present work the
hydrogenic approach is used to get the GOS because it is analytical and describes the contribution of the K-shell
ionization corresponding to C, N, O and P atoms well [20]. A one electron atommodelled by a harmonically bound
electron. A formula for generalized oscillator strengths (GOS) derived from harmonic oscillator as follows [26]:
For n = 1, 2 ….. This represents a Poisson distribution.
We use the MELF-GOS method to getting the f-sum rule at any transferredmomentum [27] because one of the
advantages of the MELF-GOS method is that the fit of the ELF in the optical limit is analytically and automatically
extended to (
) through the properties of the Mermin dielectric function and the GOS model [20, 28]; therefore, it
is not necessary to assume a particular ELF dependence on the momentum transfer. For the materials where
experimental data are available for the ELF at (
), the MELF-GOS reproduces the experimental ELF well [28,29,
30, 31]. Therefore, we use the procedure described previously to extend the optical ELF to the whole Bethe surface. The
resulting ELF should satisfy the f-sum rulefor any wave number k[27].
The effective number of electrons is defined as the number of electrons per atom or per molecule share in optical
transfers [32]. Where the effective number of electrons in the optical processes is a function of transferred energy
(ω),
could be defined in three clear ways, a situation which had led to massive confusion. This is a result of the
fact that oscillator-strength sums may be structure from the imaginary part of the dielectric function
and the
Volume 4, Issue 9, September 2015
Page 47
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 9, September 2015
ISSN 2319 - 4847
refractive index
or the energy-loss function
,these quantities are studied for an electronic system
embedded in a polarizable medium of dielectric constant , optical constants of materials presenting different rules ,
the f-sum rule may be written in three forms for the analysis of optical spectra and this includes the imaginary part of
dielectric function
and the imaginary part of the refractive index
and the energy-loss function
.
The three forms are [27]:
So, the previous rules indicate to define the effective number of electrons which contributing to the optical properties up
to energy   and writes in terms of
Where:
Is a constant and equal to (
m
A ). In the present work Eq. (11) used to calculate the effective number of
2
2

Na
2 e
electron that may be excited up to a maximum transferred energy (  ) from an incident projectile.
3.RESULTS AND DISCUSSION
The calculation of the previous magnitudes requires the descriptionof its energy-loss function (ELF),
. Sothe
calculation of the energy loss function (ELF) as a function of the transferred energy ( ) based on Eq. (3, 4) is shown in
figures (1, 2) in 2 and 3-dimensions plot and by using (MELF-GOS) method for DNA and liquid water.The calculation
of the effective number of electrons of DNA and liquid water as a function of the transferred energy based on the energy
loss function (ELF) of theouter and inner shell is shown in Figures (3).
Volume 4, Issue 9, September 2015
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 9, September 2015
Figure (1) Mermin’s energy loss function (ELF) of (a) DNA and (b) liquid water at
number (k) and the transferred energy ( ) in 2-dimension.
ISSN 2319 - 4847
as a function of wave
Figure (2) Mermin’s energy loss function (ELF) of (a) DNA and (b) liquid water as a function of wave number (k) and
the transferred energy ( ) in 3-dimension.
Volume 4, Issue 9, September 2015
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International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org
Volume 4, Issue 9, September 2015
ISSN 2319 - 4847
Figure (3) the effective number of electrons of (a) DNA and (b) liquid water as a function of the transferred energy
.
4.CONCLUSIONS
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Volume 4, Issue 9, September 2015
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