Ghanshyam Purohit
プロヒット

ガンシャム

Department of Physics, University College of Science,
Mohanlal Sukhadia Univesrity, Udaipur-313001, India (インド)

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Kailash Chandra Dhakar
Ph. D Student

Alpana Pandey
SERB JRF, Ph. D student

Suneel Kumar
Meena, Ph. D
Student

Email: ghanshyam.purohit@mlsu.ac.in
gvpurohit1974@gmail.com

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• INTRODUCTION• KINEMATICS and GEOMETRY – ionization process• THEORY• RESULTS
TDCS for Ar, Xe, W, W+
TICS for W, W+ and Be
TDCS for N2, H2O and CO2• Conclusions• Outlook
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Scattering – Important tool to know the structure of targets(Rutherford et al. (1909)).
Electron impact ionization – Important in many physical processes(The first theoretical paper on electron impact ionization of atoms - by
Sir J. J. Thompson “Ionization by moving electrified particles”.)

everyday processes both natural and man made are driven bycollision between charged particle and atoms /or moleculesAtomic and subatomic micro world information
Interaction of complex target with charged projectile
Development of Quantum Mechanics
Recent advancement in experimental technique.
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Few applications of a fundamental collision process;* plasma physics - Fusion Plasma, Industrial Plasmas* astrophysics* atmospheric modeling
Atmospheres- Stellar and Planetary* discharge physics and radiobiology.
However, there are many more
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What happens when target(atom, ion or molecule) is hit bya projectile?
Projectile

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Scattering processes

There are basically following electron-atom
scattering processes:
Elastic scattering : A+B→A+B
Inelastic scattering : A+B→A#+B
Excitation processes :A+B→A*+B
Ionization processes :A+B→A+B+
Electron-Electron exchange:
A++B→A+B+

Scattering cross sections

The collision which take place between a
projectile and a target isconveniently described in terms of a crosssection.
dσ
σ = ∫ dΩdΩsingly differential cross section (SDCS)d 2 σ(θ)
σ=∫
dEdΩ
d
Ω
dE
double differential cross section (DDCS)

triple differential cross section (TDCS)
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five- fold differential cross sectiond 3σ
dΩ1 dΩ 2 dE1d 5σ
11dΩ1dΩ 2 dΩ s dE1dE2

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Incident Beam
dΩ


i k⋅r

e
ψ sc ≈ f (θ) rNIFS, June 16 202312

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Scattered ea(e, 2e) Processes
Definition :- An electron impact single ionization, which is referred to as (e, 2e) processes
In order to gain information about the (e, 2e) ionization process, we measure
the triple differential (TDCS) or fully differential cross section (FDCS)

e- + A

A+ + e- + eEjected eb(e, 3e) Processes

scattered ea

Definition :- An electron impact double ionization, which is referred to as (e, 3e)
processes. In order to gain information about the (e, 3e) ionization process, we measure
the Five-fold differential cross section (FDCS) .

e- + AA++ + e- + e- + eejected eb

Motivation:- Theoretical modeling of few-body dynamics such as electron
impact ionization is very challenging since the few-body problem is one of themost fundamental unsolved
ejected eb
problems in physics.
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Kinematics
Coplanar symmetric kinematics :-Coplanar asymmetric kinematics:-

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Patel et al. Phys. Rev. A 105, 032818 (2022)

ψ = 00The incident electron momentum can be moved from being in thedetection plane to being perpendicular to this plane

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THEORETICAL FORMALISM OF CHARGED PARTICLE IMPACT IONIZATION OF ATOMS,IONS AND MOLECULES

e − ( E0, k0 ) + A → A+ + e − ( E1 , k1 ) + e − ( E2 , k 2 )(e, 2e) – Coincidence technique
Delivers most precise data for the study of ionization by electron
impact(e, 2e) measurements – Differential cross sections (DCS) which
depends on all three momenta
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In the electron impact single ionization process, anincident electron of linear momentum ki andenergy Ei ionizes the target (atom / ion) and thetwo emerging electrons are described by the linear
momentum and energy (kf, Ef) and (ke, Ee), where
the scattered (primary) electron is specified bysubscript ‘f’ and the ejected (secondary) electronis specified by subscript ‘e’.
The energy conservation principle states;
E i = Ef + Ee + Eb
(1)
where Eb is the energy of the bound electron.
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The momentum conservation equation iski = ke + kf + k r
Momentum transfer from incident electron totarget is given by

K = ki − kf

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The triple differential cross section (TDCS) for the electron
impact single ionization, which is the probability of single
ionization, is expressed in atomic units as

d3σ
2
4 kf ke
T
(
k
,
k
,
k
)
= (2π)∑f e i
dΩf dΩe dE f
k i av(2)

The expression in Eq. (2) includes a sum over final and averageover initial magnetic and spin state degeneracy. The T matrix
in Eq.(2), which is the subject of approximation, includes
interaction between the incident and target electrons and thenucleus.

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TDCS (eq. 2) for the ionization is written in termsof direct and exchange amplitude as

(

(

l
d 3σ
2
2
4 kf ke
*
f
g
Re
f
g
= (2π)+−∑dΩ f dΩ e dE i
k i m=−l))wheref = χ (f− ) (k f , rf ) χ (e− ) (k e , re ) v fe χ i(+ ) (k i , rf ) χ b (re )g = χ(f− ) (k f , re ) χ(e− ) (k e , rf ) vfe χi(+ ) (k i , rf ) χ b (re )NIFS, June 16 202320

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The second order Born term is given as
fB2 = χ 1(−)

( k a , ra ) χ 2(−)+( k b , rb ) V G 0 V ψ i χ 0(+)( k i , ra )Where G 0+ is Green’s function having the form;
+

G0

1

=
E

0

− H + iεhere H is the Hamiltonian of the target atom defined by1 ∇ 2  zH =−± −2  ra ra − rb 

where the symbol ± is for the projectile charge, E0
represents incident energy and ε → 0 + .
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* The initial-state distorted waves are generated in

the equivalent local ground state potential of theatom.
* The final-state distorted waves and are obtained in
the equivalent local ground state potential of theion.
* Hartree-Fock orbitals for the bound target state* E. Clementi and C. Roetti, At. Data Nucl. Data
Tab. 14, 177 (1974).
* A. D. McLEAN and R. S. McLEAN, At. Data Nucl.
Data Tab. 26, 287 (1981).

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6/16/2023χ (+ ) (k0 , r1 ) =

( )

2 1
i L e i σL u L (k0 , r1 )YL∗, M kˆ0 YL , M (rˆ1 )∑π k0 r1 L ,M()

2 1
− L' i σ L'i e u L' (k0 , r1 )YL∗' , M ' kˆ1 YL' , M ' (rˆ1 )χ1 (k 1 , r1 ) =∑π k1 r1 L' ,M '
(− )

()

2 1
− L" i σ L"
∗
ˆ
(
)
(rˆ )
i
e
u
k
,
r
Y
χ 2 (k 2 , r2 ) =""" k2 Y "
∑
2
2
L
L ,M
L ,M" 2""π k 2 r2 L ,M(− )

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Modified spin-averaged static-exchange potential of Riley and Truhlar (1975)

{

}

1

1
2
2 2
VE (r ) = E + VD (r ) − (E + VD (r ) ) − 2π ρ(r ) 2The distorting potentials[]

VD (r ) = ∑ N n l ∫ dr ' un l (r ' ) / r>nl2

where r> is the greater of r and r ' and N n l is the number of electrons in eachorbital nl . where ρ (r ) is the electron density.

Ref.:- Riley M. E. and Truhlar D. G., “Approximations for the exchange potential in electrons
scattering,” J. Chem. Phys. 63, 2182 (1975).
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The TDCS expression including Post Collision Interaction (PCI)

(

(

l
d 3σ
2
2
4 k1k 2*= M ee (2π )
f
+
g
−
Re
f
∑
nlm
nlm
nlm g nlmdΩ1 dΩ 2 dE1
k 0 m = −l))Correlation-polarization potential
N. T. Padial and D. W. Norcross, Phys. Rev. A 29, 1742 (1984).
J. P. Perdew and A. Zunger, Phy. Rev. B 23, 5048 (1981).
PCI
S. J. Ward and J. H. Macek, Phys. Rev. A49, 1049 (1994).
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• For the positron impact ionization there is no
exchange amplitude• The distorted waves for the incident and scatteredpositrons are generated in the static potential of theatom (target).
• The distorted waves for the ejected electron is
generated in the static exchange potential of theion.

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Using partial wave expansion and performing angular integrations
the total ionization cross section is given by
E

16
2
(
)
dE
2
L
1
F
σ(E i ) =+e ∑π E i ∫0li ,le ,lf
where li, lf are electron orbital angular momentum quantum
numbers in incident and final channels respectively, le is theejected electron quantum number and L is the total orbital
angular momentum. Energies obey the conservation defined
F is the ionization amplitude, can be written as

F = ∑ f λ (l b li le lf L ) χ b χi V χ e χ f λλ27

The total ionization cross sections have been calculated in two
variants of distorted wave approximation (DWA) namely Cowan
structure calculation and HULLAC code.
The Hartree-Fock target wave function and Hartree potential withsemi-classical exchange and correlation correction has been used
for the semi relativistic DWA calculations with Cowan
formalism.
Ionization cross sections using Cowan formalism have been
calculated in fine-structure and configuration mode.
We have also used Modified Khare and modified Kim BEB
Methods to calculate the TICS
Ref.:

R. D. Cowan, The Theory of Atomic Structure and Spectra (Univ. of Cali. Press, Berkeley, 1981).
A. Bar-Shalom, M. Klapisch, and J. Oreg, J. Quant. Spec. Radiat. Transf. 71, 169 (2001).
28
M. E. Riley and D. G. Truhlar, J. Chem. Phys. 63, 2182 (1975).

*W - the tungsten (W) and tungsten basedmaterials have been recommended as one of thematerials to be used as plasma facing
components for the International Thermonuclear
Experimental Reactor (ITER) [1] and theDemonstration Power Station (DEMO) as thesematerials have thermo-physical properties
suitable for fusion application [2-4].

[1] G. Federici, Phys. Scr. T124, 1 (2006).
[2] S. Wurster et al., J. Nucl. Mater. 442, S181 (2013).
[3] J. de Prado et al., Mater. Des. 112, 117 (2016).
[4] J. W. Coenen et al., Phys. Scr. T167, 014002 (2016).
29

*Tungsten is already in use as plasma facing
components in tokamaks such as JET [5] and
ASDEX-Upgrade [6].

*In the fusion devices the tungsten and relatedmaterials may exhibit high melting temperature,strong resistance against sputtering and shorter
penetration depth etc.

[5] M. Groth et al., Nucl. Fusion 53, 093016 (2013).
[6] M. Mayer et al., Phys. Scr. 128, 106 (2007).
30

* Be - recommended as surface materials in ITER project* Erosion of the Be walls will occur when it is in contact withthe hot plasma containing hydrogen and its isotopes [7, 8].
* This leads to the formation of gas-phase Be in various charge
states and of Be hydrides, i.e. BeH2. The presence of these
species in the fusion edge and diverter plasmas influencesthem due to electron collision processes* There is not much cross section information available
concerning Be and its hydrides up to now.
[7] R. Doerner, M.J. Baldwin, D. Buchenauer, G. De Temmerman, D. Nishijima, J. Nucl.
Mater. 390, 681 (2009)[8] C. Bjorkas, K. Vortler, K. Nordlund, D. Nishijima, R. Doerner, New J. Phys. 11,123017 (2009)31

*Electron induced processes such as excitationand ionization are prevalent in such magnetic
fusion devices in a wide range of energies withsignificant variation of temperature and density.

*A reliable data base is required for the electron

impact ionization and excitation cross sections
for W and Be atoms and their charged states tomodel the electron induce interactions andunderstand the spectroscopy involved.
32

Results – Coplanar ionization of Ar (3p) atoms

G. Purohit Nuclear Inst.and Methods in Physics Research, B 487 (2021) 52–60
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Results – Coplanar ionization of Ar (3p) atoms

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Results – Coplanar ionization of Ar (3p) atoms

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Results – Coplanar ionization of Ar (3p) atoms

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Results – Coplanar ionization of Ar (3p) atoms

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Results – Coplanar ionization of Ar (3p) atoms

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e+Ar(3p)8TDCS (normalized to unity at φ = 1800)

TDCS (normalized to unity at φ = 1800)

Results – Perpendicular Plane ionization of Ar (3p) atoms

E1 = E2 = 27.5 eV

6

4

2

e+Ar(3p)

E1 = E2 = 30.0 eV

8

6

4

2

0

0
0

60

120

180

240

Mutual angle φ (degree)

300

0

360

60

120

180

240

Mutual angle φ (degree)

300

Experimental Data: Patel and Murray Phy. Rev. A 105, 042815 (2022)
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360

Results – Perpendicular Plane ionization of Ar (3p) atoms

E1 = E2 = 35.0 eV

8TDCS (normalized to unity at φ = 1800)

TDCS (normalized to unity at φ = 1800)

6e+Ar(3p)642

e+Ar(3p)

E1 = E2 = 40.0 eV

4

2

0

0
0

60

120

180

240

300

0

360

Mutual angle φ (degree)

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60

120

180

240

Mutual angle φ (degree)300

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360

Results – Perpendicular Plane ionization of Ar (3p) atoms
6

e+Ar(3p)

E1 = E2 = 45.0 eV
5

4

3

2

1

0
0

60

120

180

240

300

360

TDCS (normalized to unity at φ = 1800)

TDCS (normalized to unity at φ = 1800)

6

5

4

3

2

1

0
0

Mutual angle φ (degree)

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e+Ar(3p)

E1 = E2 = 50.0 eV

42

60

120

180

240

Mutual angle φ (degree)300

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360

Results – Perpendicular Plane ionization of Ar (3p) atoms

4

e+Ar(3p)

E1 = E2 = 60.0 eV

TDCS (normalized to unity at φ = 1800)

TDCS (normalized to unity at φ = 1800)

4

3

2

1

E1 = E2 = 80.0 eV

e+Ar(3p)
3

2

1

0

0
0

60

120

180

240

300

360

Mutual angle φ (degree)

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0

60

120

180

240

Mutual angle φ (degree)300

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360

Results – Perpendicular Plane ionization of Ar (3p) atoms

TDCS (normalized to unity at φ = 1800)

4e+Ar(3p)

E1 = E2 = 100.0 eV

2

0
0

60

120

180

240

300

360

Mutual angle φ (degree)

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 60 eV above IP

Experimental Data: Patel and Murray Phy. Rev. A 105, 032818 (2022)
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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 60 eV above IP

Experimental Data: Patel and Murray Phy. Rev. A 105, 032818 (2022)
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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 60 eV above IP

Experimental Data: Patel and Murray Phy. Rev. A 105, 032818 (2022)
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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 80 eV above IP

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 80 eV above IP

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 80 eV above IP

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 100 eV above IP

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 100 eV above IP

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Results – Coplanar to Perpendicular Plane ionization of Xe (5p)at 100 eV above IP

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Results – Coplanar Asymmetric Ionization of W (6s) atoms

G Purohit
Journal of Physics B: Atomic, Molecular andOptical Physics 54 (6), 065203 (2021)
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Results – Coplanar Asymmetric Ionization of W (5d) atoms

G Purohit
Journal of Physics B: Atomic, Molecular and Optical
Physics 54 (6), 065203 (2021)
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Results – Coplanar Asymmetric Ionization of W (5p) atoms

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G Purohit
Journal of Physics B:
Atomic, Molecularand Optical Physics
54 (6), 065203 (2021) 6/16/2023

Results – Coplanar Asymmetric Ionization of W (4f) atoms

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G Purohit
Journal of Physics B:
Atomic, Molecularand Optical Physics
54 (6), 065203 (2021)

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Results – Coplanar Asymmetric Ionization of W+ ions

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Results – Coplanar Asymmetric Ionization of W+ ions

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Results – Coplanar Asymmetric Ionization of W+ ions

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Results – Coplanar Asymmetric Ionization of W+ ions

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Total Ionization cross section(10-18 cm2)

e- - W

103

102

results of [6]results of [7]DWA results in HULLAC [5]
DWA results in Cowan configuration mode [5]DWA results in Cowan fine-structure [5]results of [8]present modified Khare [10] resultspresent modified Kim [9] results

101

10

100

Electron energy (eV)1000

Purohit, Kato, Murakami et al Eur. Phys. J. D
75, 9 (2021).

[5] G. Purohit, D. Kato and I.
Murakami, Plasma andFusion Research 13, 3401026(2018). [6]M. S. Pindzola, S.
D. Loch and A. R. Foster, J.
Phys. B: At. Mol. Opt. Phys.
50, 095201 (2017).[7] F.
Blanco, F. Ferreira da Silva,
P. Limao-Vieira and G.
Garcia, Plasma Sources Sci.
Technol. 26, 085004(2017).[8] B. Goswami, R.
Naghma and B. Antony, Int.
J. Mass Spectrom. 8, 372(2014).[9]Y.K. Kim and M.E.
Rudd, Phys. Rev. A 50, 3954–
67 (1994).[10]S.P. Khare,
M.K. Sharma and S. Tomar, J.
Phys. B: At. Mol. Opt. Phys.
32, 3147 (1999).

Ionization cross section( cm2)

1.0x10-15

6s
present DWA Cowan fine-structure mode [5] resultspresent modified Kim [9] resultse -Wpresent modified Khare [10] results
DWA results in HULLAC [5]TDCC results of [6]rDWBAresults of [6]srDWBA results of [6]8.0x10-16

6.0x10-16

4.0x10-16

2.0x10-16
0

30

60

90

120

150

Electron energy (eV)Purohit, Kato, Murakami et al Eur. Phys. J. D
75, 9 (2021).

[5] G. Purohit, D. Kato and I.
Murakami, Plasma andFusion Research 13, 3401026(2018). [6]M. S. Pindzola, S.
D. Loch and A. R. Foster, J.
Phys. B: At. Mol. Opt. Phys.
50, 095201 (2017).[7] F.
Blanco, F. Ferreira da Silva,
P. Limao-Vieira and G.
Garcia, Plasma Sources Sci.
Technol. 26, 085004(2017).[8] B. Goswami, R.
Naghma and B. Antony, Int.
J. Mass Spectrom. 8, 372(2014).[9]Y.K. Kim and M.E.
Rudd, Phys. Rev. A 50, 3954–
67 (1994).[10]S.P. Khare,
M.K. Sharma and S. Tomar, J.
Phys. B: At. Mol. Opt. Phys.
32, 3147 (1999).

Purohit, Kato, Murakami et al Eur. Phys. J. D
75, 9 (2021).

Ionization cross sections of W
atom 4f subshell

Purohit, Kato, Murakami et al Eur. Phys. J. D
75, 9 (2021).

Red solid circles: DWA results in HULLAC[Plasm. Fus. Res. 13, 3401026 (2018)],
black solid up- and down- triangles: DWA
results in Cowan formalismwith fine-structure and configuration
mode [Plasm. Fus. Res. 13, 3401026(2018)]; blue solid squares: results of [J.
Phys. B At. Mol. Opt. Phys. 44, 125201(2011)] and red hollow squares: results of[Phys. Rev. A 46, 2486 (1992)], Red
hollow up triangles: present results inmodified Kim [Phys. Rev. A50, 3954–67(1994)] and purple hollow circles: present
modified Khare [J. Phys. B At. Mol.
Opt. Phys. 32, 3147 (1999)]
results;solid black circles: measurements [J. Phys. B At. Mol. Opt. Phys. 28, 4853 (1995)]; black
hollow circles: measurements [J. Phys. B At. Mol. Opt. Phys. 17, 2707 (1984)]; blue up
triangles: results of [Int. J. Mass Spectrom. 252, 213 (2006)], black hollow up triangles:
results of [Phys. Rev. A 20, 445 (1979)] and black hollow down triangles: results of [Z.
Phys. 216, 241 (1968)]
Purohit, Kato and Murakami, et al. Eur. Phys. J.

D 75, 219 (2021)

Dotted Curve: DWA results in
HULLAC [Plasm. Fus. Res. 13,
3401026 (2018)],
Solid and dashed curves: DWA
results in Cowan formalismwith fine-structure andconfiguration mode [Plasm. Fus.
Res. 13, 3401026 (2018)];
Dash dotted line: present resultsin modified Kim [Phys. Rev. A50,
3954–67 (1994)] and Dash dot
dotted line: present modified
Khare [J. Phys. B At. Mol.
Opt. Phys. 32, 3147 (1999)]
Purohit, Kato and Murakami, et al. Eur. Phys. J. results;

D 75, 219 (2021)

Dotted Curve: DWA results in
HULLAC [Plasm. Fus. Res. 13,
3401026 (2018)],
Solid and dashed curves: DWA
results in Cowan formalismwith fine-structure andconfiguration mode [Plasm. Fus.
Res. 13, 3401026 (2018)];
Dash dotted line: present resultsin modified Kim [Phys. Rev. A50,
3954–67 (1994)] and Dash dot
dotted line: present modified
Khare [J. Phys. B At. Mol.
Opt. Phys. 32, 3147 (1999)]
Purohit, Kato and Murakami, et al. Eur. Phys. J. results;

D 75, 219 (2021)

Dotted Curve: DWA results in
HULLAC [Plasm. Fus. Res. 13,
3401026 (2018)],
Solid curve: DWA results in
Cowan formalism
With configuration mode [Plasm.
Fus. Res. 13, 3401026 (2018)];
Dash dotted line: present resultsin modified Kim [Phys. Rev. A50,
3954–67 (1994)] and Dash dot
dotted line: present modified
Khare [J. Phys. B At. Mol.
Opt. Phys. 32, 3147 (1999)]
results;

Purohit, Kato and Murakami, et al. Eur. Phys. J.
D 75, 219 (2021)

Dotted Curve: DWA results in
HULLAC [Plasm. Fus. Res. 13,
3401026 (2018)],
Solid curve: DWA results in
Cowan formalism
With configuration mode [Plasm.
Fus. Res. 13, 3401026 (2018)];
Dash dotted line: present resultsin modified Kim [Phys. Rev. A50,
3954–67 (1994)] and Dash dot
dotted line: present modified
Khare [J. Phys. B At. Mol.
Opt. Phys. 32, 3147 (1999)]
results;

Purohit, Kato and Murakami, et al. Eur. Phys. J.
D 75, 219 (2021)

A significant challenge - distributed nuclei.
Contrasts to atoms which have a single nuclear
scattering centre - can be described using a sphericalbasis.
Molecular wave-functions - generally not spherical, thenuclei within the molecule providing multiple scattering
centres.
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So, there is a key challenge in developing an accurate
multi-centered wave-function.
A further challenge arises - difficult to align themolecules (experimentally) prior to the collision, so
the models must consider the random orientation of
the targets for accurate comparison.
This becomes a computationally intensive problem,and so approximations are usually made to allow
these calculations to become tractable.
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d 3σ
2
4 k k
= (2π) 1 2 ∑ T (k1 , k 2 , k 0 )dΩ1 dΩ 2 dE1
k 0 av
2

2

(

2

*
T = f dir + f ex − Re f dir
f ex)

f dir = X1(− ) (k1 , r1 ) X (2− ) (k 2 , r2 ) −Z OA
ψ (r2 ) X (0+ ) (k 0 , r1 )r12

f ex = X1(− ) (k1 , r2 ) X (2− ) (k 2 , r1 ) −Z OA
ψ (r2 ) X (0+ ) (k 0 , r1 )r12

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is the initial bound state wave function for the moleculartarget which is approximated as the orientation averaged molecularorbitalThe molecular wave functions for N2 molecule have been calculatedusing the density functional theory with B3LYP/TZ2P basis set[C. Lee, W. Yang and R. G. Parr, Phys. Rev. B 37, 785 (1988)]

The initial state distorting potential representing the interaction
between projectile and target molecular electrons constitutes thecontribution from molecular nuclei and a spherical symmetricpotential obtained by averaging over all orientations using B3LYP
basis sets.

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The post collision interaction (PCI) has been calculated using the WardMacek factor (Mee)2

M ee = N ee 1 F1 (−iλ 3 ,1,−2k 3r3ave ) ,
where
Nee =

γ
eγ − 1γ =−2π
k1 − k 2

λ3 = −

1
k1 − k 2

(

)

π2
0.627
(1 +
ε ln ε ) 2
r3ave =16επ

ε = k12 + k 22 / 2

The TDCS expression including PCI

(

(

l
d 3σ
2
2
4 k1k 2*= M ee (2π )
+
−
f
g
Re
f
∑
nlm
nlm
nlm g nlmdΩ1 dΩ 2 dE1
k 0 m = −l))

S. J. Ward and J. H. Macek, Phys. Rev. A49, 1049 (1994).
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Electron-impact TDCS for N2 molecule calculated for the weighted andaverage sum of the outer orbital
The ejected electron energy is
37 eV. Kinematics and legends used are displayed in the figure frame.
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Pandey and Purohit Atoms 10 (2), 50 (2022)

Electron-impact TDCS for N2 molecule calculated for the weighted andaverage sum of the outer orbital
The ejected electron energy is
74 eV. Kinematics and legends used are displayed in the figure frame.
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Electron-impact TDCS for N2 molecule calculated for the weighted andaverage sum of the outer orbital
The ejected electron energy is
205 eV. Kinematics and legends used are displayed in the figure frame.
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The third most abundant molecule on the earth - Of great
importance in numerous multi-disciplinary research fields;* Radiobiology where it is commonly used as surrogate of the living
matter, the latter being composed of water for about 60% in mass.

* Energetic and angular distributions resulting from electroninduced collisions with water molecules are commonly used incharged particle track structure codes for modeling the radioinduced damages in biological samples.

* Particularly, the knowledge of the collision dynamics of

low-energy electrons with biological systems remain
crucial so as to develop robust numerical models of
chargedmatter.
NIFS, June
16 2023 particle tracking in biological
6/16/2023
82

H2O

Projectile

Slow electron

Energy deposition and angular distributions resulting
from electron collisions with water are used incharged particle track structure analyses to model
radiation damage in biological samples. These models
are an active area of research since the observation thathigh energy radiation that is used to treat cancers
also liberates many low energy electrons, causing
additional damage to cell DNA.
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DNA

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The TDCS in terms of second Born approximation is given as

The second Born term in the DWBA is expressed by

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Exp. - X. Ren, S. Amami, K. Hossen, E. Ali, C. Ning, J. Colgan, D. Madison, and A. Dorn
Phys. Rev. A 95, 022701(2017)
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93Exp. – Hossen et al.J. Phys. B: At., Mol. and Opt. Phy. 51(21), 215201 (2018)
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Exp. – Hossen et al.J. Phys. B: At., Mol. and Opt. Phy. 51(21), 215201 (2018)
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Exp. – Hossen et al.J. Phys. B: At., Mol. and Opt. Phy. 51(21), 215201 (2018)
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6/16/2023Ar (3p) – electron and positron impact* Present attempt helps to probe the antiparticle – matter and particlematter interactions and it is observed that the DBWA is able to produce
the differences in the trends of TDCS which are projectile charge
dependent.
* The binary electron emission is increased for positron impact and therecoil emission is decreased, however in case of measurements both thebinary and recoil emission increases for positron impact which may beof interest for further investigation.
* Systematic shift of peaks, shifting away from the momentum transfer
direction for positron impact and shifting towards each other forelectron impact, is observed with increasing momentum transfer.
* The post collision interaction and target polarization has not beenfound significant, further theoretical efforts with accurate treatment
for electron exchange may be important to understand thedisagreement with the experiments.
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6/16/2023Ar (3p) – Coplanar Asymmetric Ionization at 1 keV

 Second Born approximation is significant at smaller scattering
angles – i.e. for the small momentum transfer conditions
 Significant shift observed in the binary peak positions.
 Post Collision Interaction (PCI) and Target Polarization Potential
not found to be significant in this energy regime

Ar (3p) – Perpendicular Plane Ionization
 Reasonable agreement with measurements in the 55 eV to 200
eV above IP projectile energy range.
 The DCS at the higher energies evolves into a broad flat
structure with the side lobes reducing in magnitude
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Xe (5p) – Coplanar to Perpendicular Plane Ionization

 Reasonableagreement with measurements withdisagreement in the lower scattering angle regime

certain The trends of TDCS seems to depend on kinematics rather thantarget

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W and W+* Present distorted wave TICS results show nearly same magnitude
as obtained by semi-relativistic distorted wave results obtained
earlier for the W atoms.
* The distorted wave TICS results for the W+ ions overestimate themeasurements and Coulomb-Born results however the distorted
wave TICS calculated with fine-structure mode for W+ ions show
smaller values.
* The TICS results for W and W+ have been in agreement with therelativistic DWA and TDCC results* The differential cross sections for the W atoms and W+ ions isfound to sensitive on the direction of momentum transfer i.e.
scattering angle.
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N2 molecule - 3σ g orbital The trends of TDCS are extracted as a function of momentum
transfer through various energy loss values.

 The effect of reversal of the direction of Coulomb field between

the projectile and molecular target is studied through therelative intensities of binary lobe for positron and electron
impact and the directions of the binary lobes.

 There are points of agreement and disagreement between thetheoretical and experimental results with large discrepancies.

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N2 molecule - 3σ g orbital Both the theory and measurements show enhanced binary
emission of electron for positron impact ionization.

 Nearly same recoil intensities for positron and electron impact
are observed for the higher momentum transfer both in thetheoretical and experimental results.

 There are significant discrepancies in the relative magnitude ofbinary lobes for electron impact case.

 The binary lobe positions obtained by the theoretical results are

shifted towards lower values of ejected electron angles incomparison to the experimental positions

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H2O molecule - 1b1+ 3a1 orbital* In conclusion present DWBA2 results obtained for water molecule are in
reasonable agreement with the measurements with certain
discrepancies in terms of binary to recoil peak ratios and positions ofpeaks.

CO2 moleculeTwo peak structure is observed in the present DWBA calculations asmeasurements
Better agreement with measurements observed for higher ejected
electron energies
Second order Born effects found to be significant
Further investigations underway
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* Electron impact cross sections of beryllium hydrides andBoron hydrides* Electron impact cross sections of W ions, q=2,3…. ….
* Study of electron /positron / ion impact processes on simple
to complex molecules of biological importance* Study of electron impact processes on high Z targets

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* Prof. Daiji Kato, NIFS, Toki, Japan* Prof. Fumihiro Koike, Sophia University, Tokyo, Japan* Prof. Yoshiro AZUMA, Sophia University, Tokyo, Japan* Prof. Alexander Dorn, Max Planck Institute for Nuclear

Physics, Heidelberg, Germany* Dr. Christophe Champion, University of Bordeaux, France* Prof. Masahiko Takahashi, Tohoku University, Japan* Dr. Didier Sebielleu, University of Rennes, France* Dr. Chuguang Ning, Tsinghua University, Beijing, China* Prof. L. C. Tribedi, TIFR, Mumbai, India* Dr. Jiro Itatani, ISSP, Tokyo University, Japan* Prof. Yasuyuki Nagashima, Tokyo University of Science,
Tokyo, Japan* Prof. Wolfgang Quint, GSI, Germany (new initiative)
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Acknowledgments
I acknowledge NIFS, Toki, Japan for inviting as Visiting
Associate Professor
I also acknowledge the Quantum Plasma Processes Unit,
NIFS for accommodating me, with special thanks to Prof.
Izumi Murakami and Prof. Daiji Kato
Thanks to Dr. Priti for help in calculations of Be and W
I acknowledge the grant received from Science andEngineering Research Board(SERB), New Delhi in the formof SERB CRG project (CRG/2019/001059).
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