ELECTRON IMPACT ATOMIC-MOLECULAR COLLISION PROCESSES RELEVANT IN PLANETARY AND ASTROPHYSICAL SYSTEMS - A THEORETICAL STUDY

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1 ELECTRON IMPACT ATOMIC-MOLECULAR COLLISION PROCESSES RELEVANT IN PLANETARY AND ASTROPHYSICAL SYSTEMS - A THEORETICAL STUDY By Sumona Gangopadhyay SPU-VVN Department of Physics Sardar Patel University Vallabh Vidyanagar, Gujarat, INDIA Research Field : THEORETICAL ATOMIC & MOLECULAR PHYSICS Research Topic : CROSS SECTIONS OF ATOMS, MOLECULES & CLUSTERS

2 Acknowledgement My Ph. D guide Prof. K. N. Joshipura (Head of the Department) ISRO Respond Project, Bangalore Organizers of present ICTP/IAEA Workshop

3 Outline of the Talk Why this work? Theoretical Methods Employed SCOP & CSP-ic Theory Results Summary &Conclusion Merits & Demerits

4 Applications Electron is an effective source for ionization Applications of e-atom / molecule CS to, Atmospheric Sciences (Ozone, Climate change etc.) Astrochemistry (Auroral phenom., Electro Glow, UV emissions, etc) Astrophysics (Comets, molecular processes in stellar formation, interpreting new spectral measurement, etc) Plasma Physics (Plasma etching, Semiconductor Physics) Understanding & modeling plasmas in fusion devices In Bio-physics (medical science) etc, Radiation therapy.

5 Experimental methods Different research groups work on different regions of E i Problems of reactive targets, e.g. radicals (CH, NH, OH, NO etc) Ionization measurements are generally uncertain by 10-15% Neutral dissociation e.g. CH 4 fragmentation (experimental uncertainty 30-35% (Nakano et al. 1991)) Bio-molecular targets and condensed matter experiments Accurate theoretical methods Slow calculations Limitation to energy range Limitation to targets Current scenario Need for simple, reliable and fast calculations

6 Present Theoretical Method Total elastic cross sections Q el Total (complete) cross sections Q T Total inelastic cross sections Q inel Grand total cross section Q TOT Total ionization cross sections Q ion Summed total excitation cross sections ΣQ exc Rate Coefficients, Macroscopic cross sections (Σ inel, Σ ion, Σ el ), Collision Frequency (ν), Mean Free Path (Λ el, Λ inel, Λ el ). Total non spherical cross sections Q rot Rotational cross sections Polar molecule e.g. H 2 O Present energy range From ionization threshold to 2 kev

7 Spherical Complex Optical Potential (SCOP) Spherical Complex Optical Potential, V opt = V R + i V I Complex Optical Potential Real Imaginary Short Range Long Range Absorption Static Exchange Polarization Modified Model RHF WF Hara Buckingham Energy Dependent Zhang Polarization model Final Form of the Complex Optical Potential V opt = V st + V ex + V pol + i V abs J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 199, K N Joshipura, Sumona Gangopadhyay & Bhushit Vaishnav

8 Variable Phase Method The PHASE EQUATION given by Calogero is of the form 2 δ ( kr) = V ( r)[cos δ ( r) ˆj ( kr) sin δ ( r) ηˆ ( kr)] k ' 2 l l l l l The function δ l (kr) is the phase function. It vanishes at the origin It yields asymptotically directly the value of scattering phase shift Using Spherical Complex Optical Potential and complex phase shift, δ l (kr) = δ R (kr) + i δ I (kr) and V(r)= V R (r) + i V I (r) F Calogero, Variable Phase Approach to Potential Scattering (Academic, New York,1974)

9 We get a set of first order coupled differential equations for real (δ R ) and imaginary (δ I ) parts of the complex phase shift function under the VPA. δ ' R ( kr) = 2 k [ V R ( r) ( X 2 Y 2 ) + 2V abs ( r) XY] δ ' I ( kr) = 2 k [ 2V R ( r) XY + V abs ( r) ( X 2 Y 2 )] where X = cosh δ ( kr)[cos δ ( kr) ˆj ( kr) sin δ ( kr) ηˆ ( kr)] I R l R l Y = sinh δ ( kr)[sin δ ( kr) ˆj ( kr) + cos δ ( kr) ηˆ ( kr)] I R l R l We solve these set of coupled equation by fourth order Runge Kutta - Method and obtain the complex phase shift

10 1.6 e _ -C O R eal Im agin ary e _ - H 2 R eal Im agin ary For l = 0, at 100 ev Phase Shift R adial D istance (a 0 )

11 Scattering Calculations Calculate the S - matrix S l ( k) = exp( 2δ I )exp( i2δ R ) Finally the cross sections Q inel = π k l max 2 (2l + 1)[1 S ( k) l= 0 l 2 ] Q el = π k l max 2 (2l + 1) 1 S ( k) l= 0 l 2 Q T = max 2π (2l + 1)[1 ReS ( k)] k 2 l l= 0 l

12 Scattering Calculations continued The total (complete) cross section is given by Q T( Ei) = Qel( Ei) + Qinel( Ei) + Q ( E) = Q ( A n ) + Q inel i ion exc n Where ΣQ ion (E i ) = The total of all total ionization cross-sections for all energetically allowed states with A +n as the charge state of the ion. ΣQ exc (E i ) = Summed total electronic excitation cross section The quantity Q inel is not measurable directly in experiments. Q el is obtained by integrating measured elastic DCS. Q T (or Q TOT for polar molecules) is separately determined in total transmission experiments.

13 The Complex Scattering Potential-ionization contribution, CSP-ic method for Q ion The CSP-ic originates from the inequality, Q inel ( E) Q ( E i ion i ) The Q inel contains Q ion, but how to extract it? It is reasonable to define a ratio First ever estimate of ionization in relation to excitation processes was made by Turner et al for e - H 2 O scattering near 100 ev. R ( E ) = ( σ i ion σ Q Q ion inel ion + σ exc ) ( E i ( E i ) ) 0.75 J. Phys. B : At. Mol. Opt. Phys. 40 (2007) 199, K.N.Joshipura, Sumona Gangopadhyay & Bhushit G Vaishnav

14 CSP-ic method continued.. The ratio R is proposed to be of the form, 1 f(u) U Ei = Target specific I C2 f ( U) = C1 U + a + lnu U ( ) 1 C lnu 2 R Ei = C1 + U + a U Above ratio has three conditions to satisfy: R( E ) i = 0, Rp, ~1, at Ei I at E = E fore i i p >> E p This is the method of CSP-ic. Int. J. Mass Spectrom. 261 (2007) , K N Joshipura, Bhushit Vaishnav & Sumona Gangopadhyay

15 CSP-ic method continued.. At E p, R p is found to be between %. 80% observed in the case of higher IP like Ne (21.56 ev). Most of the target studied here have their IP varying from 9-15 ev. Thus we have selected the lower R p limit. For polar targets we add rotational dipole cross sections (non-spherical contribution) to the Q T and calculate grand total cross section Q TOT J. Phys: Conference Series 80 (2007) , K. N. Joshipura, Sumona Gangopadhyay..

16 Targets studied in present work Atoms Atmospheric molecules Radicals and parent molecules Compounds of Silicon Oxides of Sulfur Exotic atomicmolecular systems C N O H 2 O 2 N 2 CH OH CS x (x =1, 2) O 3 CN CO NH x (x =1-3) NO NF x (x =1-3) N 2 O CF x (x =1-4) NO 2 SF x (x =1-6) NO 3 N CH 4 2 O 5 H 2 O (Free) Si SiO SiO 2 SiH 4 Si 2 H 6 Si(CH 3 ) 4 SiN SiS SO SO 2 SO 2 Cl 2 SO 2 F 2 SO 2 ClF C 2 C 3 C 2 O H 2 CO H 2 O (Ice) H 2 O(Liquid) CH 4 (Ice) Diamond

17 Results e - H 2 O e - H 2 O Q ion TOT Present Present = IE Present = IE+1 Itikawa Kim Starub Sueoka Prsent Salgam ΣQ exc Garcia Szmytkowski Zecca TCS (Å 2 ) Q el Present Danjo Katase E i (ev)

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19 e - SO Present Q inel Q ion Present Tarnovsky Tarnovsky TCS (Å 2 ) E i (ev)

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23 Summary & Conclusions The present calculations that the SCOP along with CSP-ic method is a useful theoretical tool for determining all the major cross sections within the framework of a common general formulation. The well known Complex Optical Method formalism is modified by us to include single & multi-centre molecules using the single centre and group additivity methods. Under the same umbrella of the present method, we are capable of producing reliable various total cross sections for targets from small atoms to complex polyatomic molecules. We have successfully done a first initiation to obtain Q ion from Q inel using our method called CSP-ic. Results on most of the targets studied shows satisfactory agreement with the previous investigations where ever available.

24 Merits & Demerits Merits of the theory: Quantum mechanical approach Calculating different CS under the same formalism Can investigate large/reactive molecules Simple and fast method First initiation to extract Q ion from Q inel Limitations of the theory: Spherical approximation Lower energy limit Semi-empirical method to find Q ion

25 Recent publications 1 SO, SO 2, SO 2 Cl 2, SO 2 CLF and SO 2 F 2 K N Joshipura and Sumona Gangopadhyay 2 SO, SO 2, CH 3 OH & CH 3 NH 2 MV, CGL, K N Joshipura, BGV and Sumona Gangopadhyay 3 NO, N 2 O, NO 2, NO 3 and N 2 O 5 K N Joshipura, Sumona Gangopadhyay and BGV 4 SiH 4, Si 2 H 6, Si(CH 3 ) 4, SiO, SiO 2, SiN and SiS K N Joshipura, BGV and Sumona Gangopadhyay 5 H 2 O (Ice) and H 2 O (Liquid) K N Joshipura, Sumona Gangopadhyay, CGL and MV 6 H 2 O Free Sumona Gangopadhyay and K N Joshipura 7 H 2 and CO K N Joshipura and Sumona Gangopadhyay J. Phys. B: At. Mol. Opt. Phys. 41 (2008) J. Phys: Conf. Series 115 (2008) J. Phys. B : At. Mol. Opt. Phys. 40 (2007) J. Phys. B: At. Mol. Opt. Phys. 40 (2007) Int. J. Mass Spectrom. 261 (2007) J. Phys: Conf. Series 80 (2007) Prajna J. Pure & Applied Sciences, 15 (2007) Prajna J. Pure & Applied Sciences, 14 (2006)

26 Thank you Prof. K N Joshipura Minaxi Mam, Bobby, Chetanbhai, Bhushitbhai Prof. P C Vinodkumar Foram Shelat, Harshit Kothari, Pooja Bhowmik, Manisha & My Friends Department of Physics, Sardar Patel University, Vallabh Vidyanagar , Gujarat, INDIA