DIFFERENTIAL AND TOTAL IONIZATION OF HELIUM BY ELECTRON IMPACT

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DIFFERENTIAL AND TOTAL IONIZATION OF HELIUM BY

ELECTRON-IMPACT

Maqsood Alam and Anil Kumar

Department of Physics,

Al-Falah University, Dhauj, Faridabad,121004 (Haryana)

ABSTRACT

Many methods have been investigated for calculation of cross section of charged ions. The

electron impact excitation of metal atoms is modified some extant and applied to Coulomb Born

cross section for excitation of Single charged ions. The Scaling method applied for Plane Wave

Born cross section for neutral atoms. It has been observed that charged ions is more convenient

than the scaling for neutral atoms .The comparison to available theoretical and experimental

result for He+ is presented. Helium He+ is ideally suited to serve as a cross section standard.

Atomic Hydrogen is simple target but it is difficult to use experimentally. All atoms have the

complication in calculation of inner shell ionization from double excitation state. The

experimental results are compared to calculations resulting from a number ofdifferent

approaches. For ionization leading to He+(1s2)1S, cross sections are calculated by the highly

accurate Convergent Close-Coupling(CCC) method.The differential ionization cross section

dσ/dE is obtained for electron energies E<37eV. This energy range includes a wide

non-resonant region as well as the resonance structures due to the autoionizing Helium states

(2s2)1S, (2s2p)1P and (2p2)1D.Earlier measurements of single-differential cross sections for

Helium were made by J.B Crooks et al19 (1972) Grissom et al17(1972) and C.D Opal et

al18(1972) with different approaches

KEY WORDS:

Excitation cross sections, ionization, multiphoton, single charged ions, Molecular and atomic

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INTRODUCTION:

There is acute requirement of experimental and theoretical methods to calculate a large number

of excitation cross section for neutral and highly charged ions. it has many use such as modeling

of fusion ,Plasma, processing of semiconductors and other field of planetary atmosphere .Y-K.

Kim et al4 (2001) has developed Scaling method but yet effective tools to evaluate such cross

section from Scaling BE Scaling and f Scaling method .For the first order Plane Wave Born

(PWB) cross section for electron impact excitation of neutral atom have been shown to produce

cross section for many neutral atom. The modification from the BE scaling can be applied to

Coulomb Born (CB)cross section for electron impact excitation of single charged ions of He+ in

combination with f Scaling. The modification scaling used only the excited energy E and

obtained similar remarkable feature with convergent close coupling CCC result for He+ ions. The

single differential cross section (SDCS) on the energy distribution of ejected electron is not clear.

The Binary Encounter Dipole (BED) model W.R. Johnson et al10 (1996) combines a modified

form of the cross section with the Asymptotic form the H.A Bathe et al2(1961) cross section to

calculate the SDCS. The experimental SDCS is commonly obtained by integrating angular

distribution of ejected electron . Single-electron ionization and excitation cross sections as well

as cross sections for excitation into the first excite dp state of the alkali-metal atoms Li(2s),

Na(3s), and K(4s) colliding with antiprotons and protons were calculated using a time-dependent

channel-coupling approach. For antiprotons an impact-energy range from 0.25 to 1000 keV and

for protons from 2 to 1000 keV was considered. The target atoms are treated as effective

one-electron systems using a model potential. The mass spectra of all materials show similar

characteristic features independent of the chosen ionization technique .The electron impact

ionization as well as nano-second and femto-second multi-photon excitation. The

Photoionization excitation of Helium has performed by Yuhai Jiang et al9(2000 ) with R-matrix

method with a 20-term target representation for incident photon energies between

the N=2 and N=5 thresholds (69–76.8 eV) of the He+ ion. Team researchers reported that

between the N=3 and N=5 thresholds of the He+ ion, results for He+ in the N=2,3,4 states are

agree with experiment available data. The high energy electron excitation cross section of

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matrix code within the first Borb Approximation and E. Schow K. Halet et al11 (2005 )has

presented normalized doubly differential cross sections for the electron-impact ionization of

Helium at low energies. the incident electron energies of 26.3, 28.3, 30.3, 32.5, 34.3, 36.5, and

40.7 eV and for scattering angles of 10°–130°.They obtained well established experimental

diffraction cross section for excitation of the N=2 on absolute scale. More recent theoretical

cross sections for Helium like ions were given by Kim and Rudd et al16(1994)in a semi-empirical

model, which combines the binary-encounter theory with the dipole interaction of the Bethe

theory for fast incident electrons.

In the lower-size range the abundance distributions can be explained by an electronic shell

structure which produce significant uncertainties in estimating the forward and backward angle

cross section outside the range of direct measurement .Many attemptshave been made for the

accurate description of the ionization process has eluded satisfactory solution. The successful

application for Convergent Close Coupling CCC methods to electron impact ionization of He+

by I. Bray et al3(1995)and his associates offer satisfactory results. However, the CCC method is

basically for a single electron target. Kazuhiro Sakimoto et al6(2009) presented reaction in

electron scattering from anti-protonic Helium ions (p̅ He2+) in highly excited states e+p̅ He2+→p̅

+He+ is theoretically investigated by using the R-matrix method. This type of reaction can be

identified as dissociative recombination (DR) which is well known in molecular physics. . The

calculations are performed for H-, the Helium atom and the Helium like ions in the ground and

some excited states using high-precision wave functions. The nuclear charge dependence of this

correction for Helium like ions in the ground and four lowest 1S excited states is calculated. The

possibility to detect this correction experimentally discussed by R. Krivecet al7 (2001).The

propertyofproportionalitybetweenthedouble-tosinglephotoionization cross section of electron

impact ionization of the ion is tested by A. S. Kheifets et al8 (2000) by to examine the relative

contributions of different mechanisms of the two-electron photoionization in the ground and

meta-stable states of the Helium atom . Total cross sections measured by Smith et al14 (1930) and

Single-differential and total cross sections for He were calculated by Biswas and Sinha et al15

(1996) in the correlated three-body Coulomb continuum method, including the

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DISCUSSION AND CONCLUSION

The figure 1 and 2 represent that Unscaled CB cross section agree with unscaled PWB cross

section at T=300ev and higher than it, while E scaling and CCC results are also agree with PWB

cross section at 2 kev even higher than this results. When we compare figure 1 & 2 for excitation

1s-2p and 3p excitation of he+,we observe that higher CB for 2p excitation A. Burgess et

al1(1961)the E scaling reduced the shortcoming of Born approximation. E scaling is expected to

be effective for both light and heavy single charged ions we can say that the application for more

single charged ions may eventually provide some source to E scaling as well as The BE scaling

for neutral atoms. Since E scaling and f scaling do not exhibits separate characteristic between

molecular and atomic ions. The E scaling for single charged ions and BE Scaling for neutral

atoms simply implies that shifting of T in equation (2)for multiple charged ions may be smaller.

The electron impact cross section of dipole and single neutral atoms, there has been shortcoming;

therefore E-scaling should be both light and single ions W.T Rogers et al5 (1982)has performed

to obtain reliable cross section. It allows us to predict the ionization state and the excitation

energy of the cluster after collision. Comparison is also made for electron-capture cross sections

into various nl levels of the target with atom the experimental and other theoretical results,

whenever possible. Single-differential and total cross sections of He were computed by Bransden

et al13 (1979)in the distorted wave polarized-orbital method, The low-energy behavior of the

excitation cross sections for both of the targets is also fairly satisfactory. Photoionization

excitation of Helium has been performed employing the R-matrix method with a 20-term target

representation for incident photon energies between the N=2 and N=5 thresholds (69–

76eV) of the He+ ion. Partial differential cross sections for photo-ionization leaving

the He+ ion in the N=2,3,4 levels at emission angles 0° and in the N=2 level 90° are provided.

Our results to He+ in the N=2 state give fairly good agreement with the available experimental

data and theoretical calculations below the N=3 threshold.

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The First Order Coulomb Born (CB) cross-section 𝛹for inelastic collision in generic form can be

written as

𝛹𝐶𝐵 = 4𝜋𝑟02𝑅

𝑇 𝐹𝐶𝐵 𝑇 --- (1)

Where r0 is the Bohr radius and R is the Rydberg energy.T is energy of incident electron and

𝐹_𝐶𝐵 𝑇 is the collision strength. The treatment of BC scaling for excitation of neutral atoms is

given by

𝛹_𝐵𝐸 = 𝛹_PWBT(T + B + C)--- (2)

Where BE presents binding energy of target atom for single charged ions. The E scaling below

was found to reproduce known as accurate results.

𝛹_𝐸 = 𝛹_𝐶𝐵𝑇 𝑇 + 𝐸 --- (3)

The F scaling is based on ratio of an accurate F value to a less reliable f value produced by wave

function may be expressed as

𝛹𝐶𝐵𝑚𝑐 = 𝑓_{𝑚 𝐶}

𝑓𝑠𝐶 𝛹𝐶𝐵𝑠𝑐--- (4)

In the above expression 𝛹_{𝐶𝐵𝑚𝑐}represent CB cross section corresponding f value denoted𝑓_𝑚_𝐶

While 𝛹_{𝐶𝐵𝑠𝑐} stands for the CB cross section with the corresponding to f value denoted by

𝑓_𝑠𝐶.the E scaling and the fscaling can be applied whichis as follow

𝛹_𝐸𝑓 = 𝛹_𝐸 𝑓𝑚𝑐

𝑓sc --- (5)

The E scaling reduce the cross section at low T while keeping the high T validity of the CB

approximation .Due to simple nature of the CB approximation resonance often observed near the

threshold cannot be reproduced .The escaped cross section go through the rapidly oscillating

resonance as a smooth curve.

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Atom Transition

State

E facc

He1 1s-2p 40.825 0.4153

He1 1s-3p 48.366 0.0783

Observation table-2

Observation T(ev) Energy He(1s-2p) He (1s-3p)

1 40 0.04660 0.005565

2 50 0.05112 0.007882

3 60 0.05463 0.008735

4 70 0.05672 0.009168

5 80 0.05768 0.009428

6 90 0.05756 0.009562

7 100 0.05782 0.009594

8 200 0.05063 0.008456

9 300 0.04345 0.007254

10 400 0.03765 0.006235

11 500 0.03365 0.005573

12 600 0.02943 0.005024

13 700 0.02725 0.004527

14 800 0.02519 0.004235

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Figure-1-This figure represent the comparison of the 1s-2p excitation cross section of

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Figur-2 represent the unsealedCB cross section which is agree which unscaled PWB cross

section at T=300 eV and more higher energy. The unscaled CB cross section are compared

with CB scaled cross section. After going through so called 1st order CB cross section

which is co-related in term of Bohr radius and Rydberg constant R the relation between

incident electron and collision strength found increasing. The validity of Coulomb Born

fuction ΨCB is found in good agreement at low T energy value which is shown in table-1 and

table-2 that is 1s-2p excitation cross section of He ions is self-explanatory in graph and is

cross section verses Energy, where as unscaled figure -2 is in full agreement. Our finding

therefore with coulomb Born analysis for scaled and unscaled are in good agreement, further

suggest paper be extended for other ions too.

Acknowledgement:

Authors are very grateful to Prof M .Mohshin Ex head Applied Science Delhi College of

Engineering( Delhi) and Prof Krishna Mohan Singh P.G Head ,Veer Kunwer Singh

University(Bihar) for their valuable suggestions and guidance in preparation of the paper.

.

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