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International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962
Volume-12, Issue-3 (June 2022)
www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29
195 This work is licensed under Creative Commons Attribution 4.0 International License.
Total Ionization Cross Sections due to Electron Impact of Ammonia
from Threshold to 10 MeV
Pramod Kumar1
, Amrita2
, Yogesh Kumar3
, Lalit Kumar4
and Kiran Pal5
1
Department of Physics, Vardhman College, Bijnor, INDIA
2
Department of Physics, D.A.V. College, Muzaffarnagar, INDIA
3
Department of Physics, D.A.V. College, Muzaffarnagar, INDIA
4
Department of Physics, D.A.V. College, Muzaffarnagar, INDIA
5
Department of Physics, D.A.V. College, Muzaffarnagar, INDIA
2
Corresponding Author: amritaiitd@yahoo.com
ABSTRACT
In the present paper, we have employed modified
Khare-BEB method [Atoms, (2019)] to evaluate total
ionization cross sections by the electron impact for
ammonia in energy range from the ionization threshold to
10 MeV. The theoretical ionization cross sections have
been compared to the available previous theoretical and
experimental results. The collision parameters dipole
matrix squared and CRP also have been calculated. The
present calculations were found in remarkable agreement
with the available experimental results.
PACS: 34.50
Keywords-- Collision, Cross Section, Electron-Impact
Ionization
I. INTRODUCTION
The total ionization cross sections of molecules
due to electron impact are not only important to
understand the basic collision mechanism but also in
wide range of practical applications, for example the
modelling of semi conduction manufacturing by plasma
processing needs ionization cross sections of molecules
used as the ideal gas. Furthermore, the ionization cross
sections are needed in various research areas such as
atmospheric physics, astrophysics, radiation physics etc.
As we know conventional technologies are powered by
fossil fuel exploitation that creates expensive
environmental concerns, hydrogen may be replacement
of fossil fuels which is also a carbon free energy carrier
but its storage for long distance transportation remains a
challenge. Ammonia may be used as indirect hydrogen
storage and transportation links to make it an accessible
fuel source. Furthermore, ammonia is identified as a
promising sustainable fuel for solid oxide fuel cells.
These fuels release less toxic gas on burning in the
internal combustion engine, during combustion of fuel in
car engine, plasma is produced. The ionization cross
section is needed for modelling of car engine. In
industries, ammonia is required as source of nitrogen to
fabricate nitride films and also used to create the N2 – H2
plasma. This molecule is detected in the interstellar
space medium and also in the atmosphere of planets in
the solar system, where it plays important role in the
chemistry of environments. Thus electron impact
ionization cross sections of ammonia have an importance
and needed in various fields [1-6].
Bederski et al. [7] have reported experimentally
the partial ionization cross sections for production of
ions NH3
+
, NH2
+
, NH+
, H+
and N+
from NH3 and get the
total cross sections by summing all partial ionization
cross sections. Rao & Srivastava [8] have measured the
cross sections by using crossed electron beam-molecular
beam collision geometry with 15% uncertainty in their
experiment. Mark et al. [9] measured the ionization cross
sections by using double focussing spectrometer.
Rejoub et al. [10] have measured the partial
ionization cross sections in group of ions. They have
used a time-of-flight mass spectrometer and detected
with a position-sensitive detector whose output shows
that all product ion species are collected with equal
efficiency irrespective of their initial kinetic energies. At
relativistic energies, we have only one experimental data
set, which was measured by Reike and Prepejchal [11] in
terms of two collision parameters, dipole matrix squared
and CRP, in energy range .1-27 MeV. Recently
Kumar and Kumar [12] calculated the ionization cross
sections for considered molecule.
II. THEORY
In the modified Khare-BEB model [12], the
electron impact ionization cross section of a molecule
for jth molecular orbital is given by
where, Mott term (the ionization cross section due to the
hard collision) is given by
[ ]
[ ]
International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962
Volume-12, Issue-3 (June 2022)
www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29
196 This work is licensed under Creative Commons Attribution 4.0 International License.
where , * + ,
The notations U, , I, N, T, m, c and R
represent the average kinetic energy of bound electron,
the first Bohr radius, the ionization energy, the
occupation number of molecular orbital, the kinetic
energy of the incident electron, rest mass of electron,
velocity of light and Rydberg energy, respectively. The
Bethe cross-section is
[ ]
[ ( ) ]
where the term X is given by
(√ √ )
{
(
√
)
(
√
) (
√
)
(
√
√
)
}
and the cross section due to the transverse interaction is
[ ]
where β is the ratio of the incident velocity v and the
velocity of light c, represents the total dipole matrix
squared measured in units of and given by
∫
where the continuum optical oscillator strength (COOS)
per unit energy range is
The expression of collision parameter for jth
molecular orbit is given by [9]
∑
To evaluate total ionization cross section and
collision parameters of molecule, the contributions come
from all molecular orbital are added.
III. RESULTS AND DISCUSSION
The theoretical methods described in above
section are employed to calculate the total ionization
cross sections of ammonia. The required molecular
parameters binding energies I, kinetic energies of bound
electrons U and occupation numbers N are taken from
reference [14].
The figure (1) depicts total ionization cross
action due to electron impact of ammonia from
ionization threshold to 10 keV along with available
previous experimental data. A good agreement is found
among the present calculation and experimental data
those measured by Rejoub et al. [10] and Roa &
Srivastava[8] over whole range of incident energy
studied by them. The experimental results of Mark et al.
[9] and Bedeski et al. [7] are lower than present values
as well as other previous experimental and theoretical
results and do not agree them. Our cross section and
Kim-BEB calculations [14] are slightly greater then
calculated values of Kumar-Kumar [12].
In the figure (2), depicts the present cross section
along with the experimental data measured by of Reike
and Prapejchal [11] have been shown. In energy range .1
MeV to 10 MeV. The present calculations are found in
good agreement with the experimental data. The values
of our calculated collision parameters CRP and dipole
matrix squared are 39.9 and 3.31 (in unit of ),
respectively. On increasing the kinetic energy of incident
electron this value remains nearly constant, which is
according to expectation?
International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962
Volume-12, Issue-3 (June 2022)
www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29
197 This work is licensed under Creative Commons Attribution 4.0 International License.
Figure 1: Total ionization cross sections (TICS) for ammonia in 10-16
cm2
. Solid line, dashed line, and dotted line are
present results, theoretical results of Kumar & Kumar [12], and Kim-BEB calculations [14], respectively. Filled circles,
filled rhombus, filled triangles and open circles are the experimental results of Rejoub et al. [10]. Rao and Srivastava [8],
Mark et al. [9] and Bederski et al. [7] respectively
Figure 2: In this figure we compare the present total ionization cross sections in 10-16
cm2
to experimental results of Rieke
and Prepejchal (filled rectangles) [11] for ammonia at high energy range .1 MeV to 10 MeV
The calculated value of CRP is greater that the
experimental value (34.86) by 14.4 %, however present
value of dipole matrix squared is lower than the
experimental value (3.58) of Reike and Prapejchal [11]
by 7.5%.
IV. CONCLUSION
Khare-BEB model is used to calculate the
ionization cross action of ammonia from ionization
threshold to 10 MeV. The present cross sections are
found in the good agreement with available experimental
data over most of incident energy range. The calculated
0
0.5
1
1.5
2
2.5
3
3.5
1 10 100 1000 10000
TICS
(10
-16
cm
2
)
E(eV)
Ammonia
Present
Kim-
BEB
Kumar
Rejoub
Rao
Mark
0
0.005
0.01
0.015
0.02
0.025
0.1 1 10
TICS
(10
-16
cm
2
)
E(MeV)
Present
Rieke
International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962
Volume-12, Issue-3 (June 2022)
www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29
198 This work is licensed under Creative Commons Attribution 4.0 International License.
values of parameters are also found in good agreement
with the experimental values.
ACKNOWLEDGMENT
We are grateful to Dr Manoj Kumar, Meerut
college, Meerut (India) for fruitful discussion and also
thankful to principal, D.A.V. College, Muzaffarnagar,
(India) for providing the facilities for research work.
REFERENCES
[1] W. Lindinger & F. Howorka. (1985). Electron
impact ionization. eds. T. D. Mark, and Dunn, G. H.
Berlin: Springer.
[2] G. Jeerh, M. Zhang & S. Tao. (2021). Recent
progress in ammonia fuel cells and their potential
applications. J. Mater. Chem. A, 9, 727-752.
[3] A. C. Cheung, D. M. Rank, C. H. Townes, D. D.
Thornton, & W. J.Welch. (1968). Phys. Rev. Lett. 21,
1701.
[4] C. F. Mueller-Wodarg, D. F. Strobel, J. J. Moses, J.
H.Waite, J. Crovisier, R. V. Yelle, S. W. Bougher & R.
G. Roble. (2008). Space Sci. Rev. 139, 191.
[5] S. R. Federman & D. L. Lambert. (2002). J. Electron
Spectrosc. Relat. Phenom. 123, 161.
[6] M. Sode, W. Jacob, T. Schwarz-Selinger & H.
Kersten. (2015). J. Appl. Phys. 4117, 83303.
[7] K. Bederski, L. Wdjcik & B. Adamczyk. (1980).
International Journal of Mass Spcctrometry and Ion
Physics, 35, 171.
[8] M. V. V. S. Rao & S. K. Srivastava. (1991). Journal
of Geophysical Research, 96(17), 563.
[9] T. D. Märk, F. Egger & M. Cheret. (1977). The
Journal of Chemical Physics, 67, 3795.
[10] R. Rejoub, B. G. Lindsay & R. F. Stebbings.
(2001). J. Chem. Phys. 115, 5053.
[11] F. R. Rieke & W, Prepejchal. (1972). Phy. Rev. A 6,
1507.
[12] Y. Kumar & M. Kumar. (2020). Chem. Phys.
Letter, 740, 137071.
[13] Y. Kumar, M. Kumar, S. Kumar & R. Kumar.
(2019). Atoms, 7, 60.
[14] https/www.nist.gov.

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Total Ionization Cross Sections due to Electron Impact of Ammonia from Threshold to 10 MeV

  • 1. International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962 Volume-12, Issue-3 (June 2022) www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29 195 This work is licensed under Creative Commons Attribution 4.0 International License. Total Ionization Cross Sections due to Electron Impact of Ammonia from Threshold to 10 MeV Pramod Kumar1 , Amrita2 , Yogesh Kumar3 , Lalit Kumar4 and Kiran Pal5 1 Department of Physics, Vardhman College, Bijnor, INDIA 2 Department of Physics, D.A.V. College, Muzaffarnagar, INDIA 3 Department of Physics, D.A.V. College, Muzaffarnagar, INDIA 4 Department of Physics, D.A.V. College, Muzaffarnagar, INDIA 5 Department of Physics, D.A.V. College, Muzaffarnagar, INDIA 2 Corresponding Author: amritaiitd@yahoo.com ABSTRACT In the present paper, we have employed modified Khare-BEB method [Atoms, (2019)] to evaluate total ionization cross sections by the electron impact for ammonia in energy range from the ionization threshold to 10 MeV. The theoretical ionization cross sections have been compared to the available previous theoretical and experimental results. The collision parameters dipole matrix squared and CRP also have been calculated. The present calculations were found in remarkable agreement with the available experimental results. PACS: 34.50 Keywords-- Collision, Cross Section, Electron-Impact Ionization I. INTRODUCTION The total ionization cross sections of molecules due to electron impact are not only important to understand the basic collision mechanism but also in wide range of practical applications, for example the modelling of semi conduction manufacturing by plasma processing needs ionization cross sections of molecules used as the ideal gas. Furthermore, the ionization cross sections are needed in various research areas such as atmospheric physics, astrophysics, radiation physics etc. As we know conventional technologies are powered by fossil fuel exploitation that creates expensive environmental concerns, hydrogen may be replacement of fossil fuels which is also a carbon free energy carrier but its storage for long distance transportation remains a challenge. Ammonia may be used as indirect hydrogen storage and transportation links to make it an accessible fuel source. Furthermore, ammonia is identified as a promising sustainable fuel for solid oxide fuel cells. These fuels release less toxic gas on burning in the internal combustion engine, during combustion of fuel in car engine, plasma is produced. The ionization cross section is needed for modelling of car engine. In industries, ammonia is required as source of nitrogen to fabricate nitride films and also used to create the N2 – H2 plasma. This molecule is detected in the interstellar space medium and also in the atmosphere of planets in the solar system, where it plays important role in the chemistry of environments. Thus electron impact ionization cross sections of ammonia have an importance and needed in various fields [1-6]. Bederski et al. [7] have reported experimentally the partial ionization cross sections for production of ions NH3 + , NH2 + , NH+ , H+ and N+ from NH3 and get the total cross sections by summing all partial ionization cross sections. Rao & Srivastava [8] have measured the cross sections by using crossed electron beam-molecular beam collision geometry with 15% uncertainty in their experiment. Mark et al. [9] measured the ionization cross sections by using double focussing spectrometer. Rejoub et al. [10] have measured the partial ionization cross sections in group of ions. They have used a time-of-flight mass spectrometer and detected with a position-sensitive detector whose output shows that all product ion species are collected with equal efficiency irrespective of their initial kinetic energies. At relativistic energies, we have only one experimental data set, which was measured by Reike and Prepejchal [11] in terms of two collision parameters, dipole matrix squared and CRP, in energy range .1-27 MeV. Recently Kumar and Kumar [12] calculated the ionization cross sections for considered molecule. II. THEORY In the modified Khare-BEB model [12], the electron impact ionization cross section of a molecule for jth molecular orbital is given by where, Mott term (the ionization cross section due to the hard collision) is given by [ ] [ ]
  • 2. International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962 Volume-12, Issue-3 (June 2022) www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29 196 This work is licensed under Creative Commons Attribution 4.0 International License. where , * + , The notations U, , I, N, T, m, c and R represent the average kinetic energy of bound electron, the first Bohr radius, the ionization energy, the occupation number of molecular orbital, the kinetic energy of the incident electron, rest mass of electron, velocity of light and Rydberg energy, respectively. The Bethe cross-section is [ ] [ ( ) ] where the term X is given by (√ √ ) { ( √ ) ( √ ) ( √ ) ( √ √ ) } and the cross section due to the transverse interaction is [ ] where β is the ratio of the incident velocity v and the velocity of light c, represents the total dipole matrix squared measured in units of and given by ∫ where the continuum optical oscillator strength (COOS) per unit energy range is The expression of collision parameter for jth molecular orbit is given by [9] ∑ To evaluate total ionization cross section and collision parameters of molecule, the contributions come from all molecular orbital are added. III. RESULTS AND DISCUSSION The theoretical methods described in above section are employed to calculate the total ionization cross sections of ammonia. The required molecular parameters binding energies I, kinetic energies of bound electrons U and occupation numbers N are taken from reference [14]. The figure (1) depicts total ionization cross action due to electron impact of ammonia from ionization threshold to 10 keV along with available previous experimental data. A good agreement is found among the present calculation and experimental data those measured by Rejoub et al. [10] and Roa & Srivastava[8] over whole range of incident energy studied by them. The experimental results of Mark et al. [9] and Bedeski et al. [7] are lower than present values as well as other previous experimental and theoretical results and do not agree them. Our cross section and Kim-BEB calculations [14] are slightly greater then calculated values of Kumar-Kumar [12]. In the figure (2), depicts the present cross section along with the experimental data measured by of Reike and Prapejchal [11] have been shown. In energy range .1 MeV to 10 MeV. The present calculations are found in good agreement with the experimental data. The values of our calculated collision parameters CRP and dipole matrix squared are 39.9 and 3.31 (in unit of ), respectively. On increasing the kinetic energy of incident electron this value remains nearly constant, which is according to expectation?
  • 3. International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962 Volume-12, Issue-3 (June 2022) www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29 197 This work is licensed under Creative Commons Attribution 4.0 International License. Figure 1: Total ionization cross sections (TICS) for ammonia in 10-16 cm2 . Solid line, dashed line, and dotted line are present results, theoretical results of Kumar & Kumar [12], and Kim-BEB calculations [14], respectively. Filled circles, filled rhombus, filled triangles and open circles are the experimental results of Rejoub et al. [10]. Rao and Srivastava [8], Mark et al. [9] and Bederski et al. [7] respectively Figure 2: In this figure we compare the present total ionization cross sections in 10-16 cm2 to experimental results of Rieke and Prepejchal (filled rectangles) [11] for ammonia at high energy range .1 MeV to 10 MeV The calculated value of CRP is greater that the experimental value (34.86) by 14.4 %, however present value of dipole matrix squared is lower than the experimental value (3.58) of Reike and Prapejchal [11] by 7.5%. IV. CONCLUSION Khare-BEB model is used to calculate the ionization cross action of ammonia from ionization threshold to 10 MeV. The present cross sections are found in the good agreement with available experimental data over most of incident energy range. The calculated 0 0.5 1 1.5 2 2.5 3 3.5 1 10 100 1000 10000 TICS (10 -16 cm 2 ) E(eV) Ammonia Present Kim- BEB Kumar Rejoub Rao Mark 0 0.005 0.01 0.015 0.02 0.025 0.1 1 10 TICS (10 -16 cm 2 ) E(MeV) Present Rieke
  • 4. International Journal of Engineering and Management Research e-ISSN: 2250-0758 | p-ISSN: 2394-6962 Volume-12, Issue-3 (June 2022) www.ijemr.net https://doi.org/10.31033/ijemr.12.3.29 198 This work is licensed under Creative Commons Attribution 4.0 International License. values of parameters are also found in good agreement with the experimental values. ACKNOWLEDGMENT We are grateful to Dr Manoj Kumar, Meerut college, Meerut (India) for fruitful discussion and also thankful to principal, D.A.V. College, Muzaffarnagar, (India) for providing the facilities for research work. REFERENCES [1] W. Lindinger & F. Howorka. (1985). Electron impact ionization. eds. T. D. Mark, and Dunn, G. H. Berlin: Springer. [2] G. Jeerh, M. Zhang & S. Tao. (2021). Recent progress in ammonia fuel cells and their potential applications. J. Mater. Chem. A, 9, 727-752. [3] A. C. Cheung, D. M. Rank, C. H. Townes, D. D. Thornton, & W. J.Welch. (1968). Phys. Rev. Lett. 21, 1701. [4] C. F. Mueller-Wodarg, D. F. Strobel, J. J. Moses, J. H.Waite, J. Crovisier, R. V. Yelle, S. W. Bougher & R. G. Roble. (2008). Space Sci. Rev. 139, 191. [5] S. R. Federman & D. L. Lambert. (2002). J. Electron Spectrosc. Relat. Phenom. 123, 161. [6] M. Sode, W. Jacob, T. Schwarz-Selinger & H. Kersten. (2015). J. Appl. Phys. 4117, 83303. [7] K. Bederski, L. Wdjcik & B. Adamczyk. (1980). International Journal of Mass Spcctrometry and Ion Physics, 35, 171. [8] M. V. V. S. Rao & S. K. Srivastava. (1991). Journal of Geophysical Research, 96(17), 563. [9] T. D. Märk, F. Egger & M. Cheret. (1977). The Journal of Chemical Physics, 67, 3795. [10] R. Rejoub, B. G. Lindsay & R. F. Stebbings. (2001). J. Chem. Phys. 115, 5053. [11] F. R. Rieke & W, Prepejchal. (1972). Phy. Rev. A 6, 1507. [12] Y. Kumar & M. Kumar. (2020). Chem. Phys. Letter, 740, 137071. [13] Y. Kumar, M. Kumar, S. Kumar & R. Kumar. (2019). Atoms, 7, 60. [14] https/www.nist.gov.