Cross Sections: Key for Modeling Vasili Kharchenko Department of Physics, University of Connecticut Harvard-Smithsonian Center for Astrophysics, Cambridge, USA 1. Introduction: a) non-thermal atoms and molecules in planetary atmospheres b) escape processes and energy deposition into planetary atmospheres b) kinetics of momentum-energy relaxation, the Boltzmann equation c) differential and total cross sections for collisions of atmospheric atoms and molecules 2. Momentum-Energy Relaxation in Elastic and Inelastic Atmospheric Collisions: a) momentum-energy transfer in atomic and molecular collisions b) differential cross sections of elastic and inelastic collisions, quantum calculations and comparisons with laboratory measurements c) collisions of H, He, N, O, S, Ar, Xe, H 2, N 2, and O 2 atoms and molecules Collaborators: Alex Dalgarno, Peng Zhang, Balakrishnan Naduvalath, Yutaka Matsumi, Kenshi Takahashi, Michael Jamieson and Students and Postdocs: Stefano Bovino, Nick Lewkow, and Marko Gacesa
Collisions of Atmospheric Atoms and Molecules electrons H + He q+ O q+ S q+ ions H C He O N S energetic neutral atoms escape fluxes of atoms and molecules hot atoms and molecules Energy deposition by precipitating fluxes of electrons, ions and energetic neutrals Energy relaxation of fast particles; non-thermal upward and escape fluxes; ro-vibrational excitation of molecules; non-thermal reaction Modeling the energy deposition and evolution of planetary atmospheres requires detailed knowledge of (a) momentum and energy exchange (b) reactions and internal degree excitations in collisions of atmospheric species target X(ν,j) atom-projectile v i Laboratory Frame X(ν',j') v t θ v f
Focus of our investigations: Momentum-Energy Relaxation in Real Atomic and Molecular Gases Astrophysical Applications: Energy relaxation of energetic H, He, N, S, Ar, Xe and O atoms in astrophysical environments Energy relaxation in atomic-molecular collisions; hot molecules H 2, CO, N 2 and O 2 Kinetics of metastable atoms in the planetary and cometary atmospheres Escape processes in the planetary atmospheres Determination of non-maxwellian distributions of energetic atoms in atmospheres and the interstellar gas Energy deposition by ENAs precipitating into planetary atmospheres Computational Methods: Quantum-mechanical calculations of differential cross sections, describing the momentumenergy relaxation in elastic, inelastic and reactive collisions (energy range 0.001eV -10 kev) Solution of the time-dependent kinetic equation or/and Monte Carlo simulations Calculations of non-equilibrium rates of atmospheric reactions.
Simple Definitions from the Scattering Theory φ n- particle density scattering center θ solid angle dω incoming flux (particles of EM waves) J = n v v f dd(r, θ, dω) v i differential cross section dσ(e, θ) dω = dd(r, θ, dω) dω J total cross section σ(e) = dω 4π dσ dω angular Probability Density Function (PDF) ρ E, θ, φ = 1 σ E The angular PDF governs the distribution of transferred energy (momentum), diffusion and other transport processes: dσ(e, θ, φ) dω diffusion (momentum-transfer) cross section σ D E = dω 4π dσ dω (1 cos θ)
example 1: Elastic scattering of isotopes O + H and O+ D Differential cross sections are strongly peaked forward (this plot is in a logarithmic scale!) Zhang et al. (2009)
example 2: Elastic Collisions N( 4 S) + He, Ar Small angle scattering dominates Angular dependence are also important at thermal energies. Total cross section may be described by the semi-classical Landau-Schiff formula, which only takes into account C 6. Results are in good agreement with experimental data on N( 4 S) energy relaxation (log. scale!) Reason for the strong angular anisotropy in colisions of atoms, molecules, and ions: the long-range interatomic forces (polarization force, van der Waals, electric quadrupole etc.) Zhang et al. (2008,2011) F R F V R = C n R n n R a B interparticle distance a B
Kernel B T (E E ) of the Boltzmann Kinetic Equation E' Initial energy Laboratory Frame E B T (E E ) is the rate of the energy transfer Final energy Thermal gas /plasma E' E Final energy ε'/2 Center of Mass Frame ε/2 Initial energy Initial energy ε'/2 ε/2 Doubly differential cross sections of elastic and inelastic collisions Inelastic collisions: ε = ε' Inelastic collisions: ε = ε' Kharchenko et al. (1998)
Energy relaxation kinetics and comparison with experiments Experiment: T.Nakayama, K. Takahashi and Y. Matsumi, Geophys. Res. Lett., 109, D18311 (2005). Theoretical data: Zhang et al. (2007, 2008) Energetic N( 4 S) atoms were produced by the laser photolysis of NO 2
Experimental vs Theoretical Doppler Profiles N( 4 S)+He Zhang et al. (2008) In collaboration with Y. Matsumi & K. Takahashi
example 3: Angular anisotropy increases with collision energy O + H Zhang et al., JGR (2009)
Differential Cross Sections for O + H Collisions ( global view) Zhang et al., JGR (2009)
Differential Cross Sections for 4 He + 4 He Collisions 4 experiment: Nitz et al. 1987 theory: Lewkow et al. (2012) fffffxcf 0.5keV This data are important for modeling of the energy deposition of precipitating ions/neutral atoms Hddasccc 1.5keV 5keV
Differential Cross Sections for O( 3 P) + He Collisions experiment: Schfer et al. 1987 theory: Lewkow et al. 2012 1.5 kev 500eV 1eV This data are important for modeling of the energy deposition of precipitating ions/neutral atoms 5keV
Differential Cross Sections for He + H Collisions experiment: Schafer et al. 1987 Smith et al. 1996 theory: Lewkow et al. 2012
Probability Density for Distribution of Scattering Angles Lewkow et al. (2012)
Angular part of cross sections is important for a determination of the upward and escape fluxes of energetic atoms O( 3 P) Earth H max Kharchenko and Dalgarno ( 1999) H in
Energy loss in collisions of O( 3 P) and O( 1 D) atoms with He Bovino et al. (2011) The energy loss rate is normalized to a single particle in cm -3.
Energy Distributions of Secondary Hot Atoms in O + 4 He and 3 He Collisions 4 He escape energy for Mars Bovino et al. 2011 3 He escape energy for Mars
Example: Escape of different He isotopes from the Mars Atmosphere Bovino et al. 2011 Volume production rate of escaping He atoms [cm -3 s -1 ]
Effective Hard-Sphere Cross Sections σ(e,t) for O + H, D Collisions Zhang et al., JGR (2009)
Collision Ejection of H2 Molecules by Energetic O Atoms from Mars M. Gacesa, P. Zhang and V. Kharchenko (submitted to GRL) O + H 2 (v,j) OH(v,j) production Experiment (reaction channel): Garton et al. JCP 118, 1585 (2003) Theory: reaction cross section is close to Balakrishnan, JCP 121, 6346 (2004)
Escape of H 2 (v,j) molecules induced by hot O atoms in Martian Atmosphere Fraction of H2 received in collisions the energies above the escape threshold Gacesa et al. 2012 submitted to the GRL
Escape of H 2 (v,j) molecules from the Mars Atmosphere energetic O thermal H 2 O + H 2 (v,j) O + H 2 (v',j') Gacesa et al. 2012 submitted to the GRL
Rotational-Vibrational Distribution of H 2 Molecules Escaping from Mars: H 2 escape fluxes for different (v,j) O + H 2 (v,j) O + H 2 (v',j') Gacesa et al. (2012) submitted to the GRL
CONCLUSIONS Accurate evaluation of non-thermal escape fluxes and non-maxwellian distributions of energetic atoms, molecules and ions requires accurate differential cross sections of elastic, inelastic, and reactive collisions. Theoretical data on the energy/velocity relaxation of fast atoms are in very good agreement with results of the laboratory measurements Theoretical and experimental data on the differential cross sections and momentum-energy relaxation parameters are available for H, He, N, O, Ne, Ar, Xe, and S atoms. Atom-molecule collisions have been studied for O + N 2, N+ N 2, H + O 2, He + H 2 and some other collision partners. Collision ejection of light molecules from the Mars atmosphere has been analysed For exoplanets: modeling of the energy deposition by precipitation ENAs/ions, escape of atmospheres and their interaction with stellar winds require angular and energy dependent cross sections in a broad interval of energies from a few mev to several kev
Theoretical Cross Sections for S + He and S + Xe Bovino et al. J. Chem. Phys. (2011) S( 1 D) + Xe
S + Xe Bovino et al. J. Chem. Phys. (2011)
The kernel of the Boltzmann equation for the energy relaxation of fast N(4S) atom in the He gas. Zhang et al. (2007)
Time-dependent energy distributions of N( 4 S) atoms Double-Peak features arise in a early stage of the energy relaxation. Numerical and analytical investigations show the presence of two characteristic times: a) t G - the time of formation of a Maxwellian-like distribution with the quasi-temperature T eff (t) >> T gas b) t G the thermalization time, required for the relaxation of the quasi-temperature T eff to the bath gas tempature T gas. Maxwellian-like initial f(e,t=0)
Final Energy E' [ ev] Difference between the Hard Sphere Model and Realistic Kernel B(Ε Ε') Zhang et al.2008 Effective hard sphere model