Electron-impact rotational excitation of H3 : relevance for thermalization and dissociation

1
Electron-impact rotational excitation of H3
relevance for thermalization and dissociation

• Alexandre Faure
• Laurent Wiesenfeld Jonathan Tennyson
• Laboratoire dAstrophysique de Grenoble, France
• University College London

2
Electron-molecule collisions

• Rotational excitation of molecules by
  electron-impact is very efficient
• k(e) 10-6 cm3s-1
• By comparison
• k(H, H2) 10-10 cm3s-1
• Electrons are the dominant exciting partners as
  soon as
• n(e)/n(H) gt 10-4

3
H3 in the diffuse ISM

• Unexpected high abundance of H3 in diffuse
  clouds
• Three uncertain key parameters ke, n(e) and ?
• Observations suggest
• n(e)/n(H2) 4 10-4
• high CR ionization rate (? 10-15s-1)

Laboratory and space spectra of H3, from McCall
et al. Nat. 2003
4
H3 toward the galactic center

• Large column densities in the (3, 3) metastable
  state
• Very low column densities in the (2, 2) state
• Provide evidence of
• high T ( 250 K)
• low n ( 100 cm-3)
• high ? (gt 10-15s-1)

H3 and CO spectra toward GCS3-2, from Oka et al.
ApJ 2005
5
Rotation and DR measurements

• H3 internal excitation known to influence DR
  rate measurements
• Influence of electron-impact excitation?
• Rotational cooling and heating by electrons
  observed at TSR (talk by A. Wolf)

CRYRING (McCall et al. 2003)
TSR, short storage time
TSR, long storage time
DR rate coefficients, from Lammich et al. 2005
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Electron-impact (de-)excitation

• Experiments extremely difficult
• Vibrational excitation negligible at relevant
  temperatures (first threshold at 0.3 eV)
• Rotational excitation standard theory is the
  long-range Coulomb-Born approximation (Chu
  Dalgarno 1974, Chu 1975)
• However, short-range forces are crucial! (Rabadán
  et al. 1998, Faure Tennyson 2001)

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The R-matrix method
Internal region exchange, correlation (adapt
quantum chemistry codes)
external region
electron
internal region
External region Multipolar potential (adapt
electron-atom codes)
R-matrix sphere
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Electron-H3 calculations

• H3 wavefunction taken from R-matrix calculations
  of Faure Tennyson (2002)
• Ground-state quadrupole 0.914 ea02 (close to
  0.9188 ea02 calculated by Meyer et al. 1986)
• Scattering model includes four target states, via
  CI expansion.
• Continuum functions represented by Gaussian-type
  basis functions with l?4 (Faure et al. 2002).
• Resonances in good agreement with Orels results

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Rotational excitation calculations

• H3 is taken at its equilibrium geometry
• The adiabatic nuclei rotation (ANR) method
  (sudden approximation) is employed
• Cross sections are expressed as a partial wave
  expansion with high partial waves deduced from
  long range approximations
• Excitation cross sections are corrected (forced
  to zero) near threshold (Morrison Sun 1995)

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Rotational cross sections and selection
rules

• Cross sections computed from 10 meV to 10 eV
• Entirely dominated by short range interactions
• Selection rules
• ?J(0), 1, 2, (3, )
• Ortho ? para forbidden
• ?K0, (3)
• ?J1, 2 comparable in magnitude

Faure Tennyson JPB 2002
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Rate coefficients

• Rates obtained from 100 to 10,000K
• No dipole and large rotational thresholds
• Excitation rates generally peak above 1,000K, at
  about 10-7 cm3s-1
• Deexcitation rates increase slightly below 1,000K
  

Faure Tennyson MNRAS 2003
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Comparison with DR rate
coefficients

• Latest measurements with rotationally cold H3
• k(23K)2.6 10-7 cm3s-1
• k(300K)6.8 10-8 cm3s-1
• Two possible regimes
• Rotational cooling important below 100K
• Rotational heating important above 100K

McCall et al. PRA 2004
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Thermalization of H3 in space

• Centrifugal distorsion causes  forbidden 
  transitions ?J0, 1 ?K3
• Spontaneous emission times comparable to
  collision intervals
• Nonthermal rotational distribution expected (Oka
  Epp 2004)

Forbidden rotational transitions, from Pan Oka
ApJ 1986
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Reactive collisions with H2

• In contrast to standard neutral collisions,
  collisions between H3 and H2 are reactive
• H3 H2 ? (H5) ? H3 H2
• Random selection rules ortho/para conversion is
  allowed
• Langevin potential rates expected to lie between
  between 10-10 cm3s-1 and 10-9 cm3s-1
• Rigorous quantum (or even classical) calculations
  greatly needed!

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Thermalization by H2 (Oka Epp 2004)

• Collision rates based on Langevin rate and
  detailed balance
• Steady state approximation
• Lifetime 109 s
• Collision time 107 s
• Results consistent with observations for
• T 250K
• n(H2) 100cm-3

Population ratios and Tex as a function of n(H2)
and T, from Oka Epp 2004
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Thermalization by e-impact?

• The electron effect is estimated by Oka Epp to
  be 2 orders of magnitude less than that of H2
• k(e)/k(H2) 102
• n(e)/n(H2) 10-4
• However, it is not unreasonable to assume
• k(e)/k(H2) 103 , i.e. k(H2) 10-10 cm3s-1
• n(e)/n(H2) 10-3, i.e. high ionization rate
• In such conditions, might electrons compete with
  neutrals?

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Steady-state approximation

• Solve the rate equation
• Ortho/para conversion forbidden
• Initial n(1, 0)/n(1, 1) is crucial
• The steady state solution is NOT compatible with
  observations!

Obs 0.7!
n(e)
Obs 0.5!
Population ratios as a function of T and n(e)
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Time dependent approach?

• However, steady state approximation is NOT valid
• t(lifetime)3 108 s
• t(steady-state)gt109 s
• Proper modelling needs inclusion of rates for
• formation (H2H2)
• destruction (H3 e)

t(lifetime)
Level populations as a function of time for
T300K, n(e)5 10-2 cm-3
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Conclusions

• Electron-impact rotational (de)excitation rates
  of H3 are comparable in magnitude to the DR rate
  at 300K, i.e. about 10-7 cm3s-1
• Ortho-para conversion is collisionally forbidden
• We now provide rotational rates for all allowed
  transitions up to (5, 4) from 100 to 10,000K
• Future works
• Modelling of H3 thermalization by electrons in
  space
• Modelling of H3 cooling and heating by electrons
  in storage rings
• Isotopologs of H3