Primer on Collisions
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II) Electron-Impact Excitation out of the ground state of Atoms

D. Pressure Effects

Collision Transfer

Let us again consider excitation into level-i (for simplicity we will neglect cascades and radiation trapping). We now consider two possible paths for populating level-i.

(a)    Direct:    Atom(g) + e- --> Atom(i)

    n(i) proportional to n(g) proportional to P

(b)    Collision Transfer:

    Atom(g) + e- --> Atom(j)

    Atom(j) + Atom(g) --> Atom(i) + Atom(g)

    n(i) proportional to n(j) n(g) proportional to P2

Where the two levels i and j must have energies within kT of one another. Note in particular that the two step collision transfer mechanism is proportional to P2, so it is more important at high pressure.

In general, both processes will be at work. If we look at the total effect:

At low pressures the collision transfer term (b) approaches zero, and the measured cross section is independent of pressure- the direct Qi term (a). At higher pressures, the measured cross section has a component linear with pressure. If Qi and Qj have different energy dependence (different shapes of excitation functions), the shape of (Qi)High P would change with pressure.

  • Collision Transfer Mechanism for He 33D
Let us now see how collision transfer plays in a role in the case of helium. In particular, we wish to explain the pressure effects of the 33D level of helium. Besides the value of the apparent cross section increasing with pressure, the shape of the excitation function changes from a sharply peak to a broad maxima.
1.7 mTorr33 mTorr 130 mTorr
33D Cross section (in arbitrary units) versus Electron energy (in eV).
Click here to see a little animated movie of the 33D excitation function at different pressures.

Recall that in the absence of collision transfer (i.e. at low pressures) we saw that

Level Shape of Excitation Function
Q for n3L narrow peak near threshold
Q for n1P broad peak at 100 eV
Q for n1S, n1D intermediate (peak at 50 eV)

This suggests that there is some collision transfer between the n1P levels and the 33D level that would cause the 33D level to exhibit the n1P's broad peak. Consider the particular case of collision transfer from the 31P.

Note, however, that the total spin before the collision transfer process is not equal to the total spin after the collision. This violates Wigner's Spin Rule, and is thus very unlikely to happen.

Wigner's Spin Rule: Total spin must be conserved for collision between atoms that conform to the LS-coupling.
In fact, to the extent that helium is a LS-coupled atom, there is no way for collision transfer to explain the 33D pressure effects.

  • Mixed F collision transfer
To what extent is then helium (1s)(nl) an LS-coupled atom? The LS-coupling will break down if the spin-orbit interaction is larger than the exchange interaction.

Exchange interaction of (1s) with (nl ) » spin-orbit coupling of (nl)
Yes for S, P, D (l = 0,1,2)
No for F ( l >= 3)

So (1s)(nf ) n1F & n3F not valid descriptions. We should instead express the nF levels as a mixture:

The nF levels can act as a bridge for transfer from singlet to triplet levels, without violating the Wigner Spin Rule. Collision transfer can occur between the n1P levels and the mixed nF levels. The nF levels can then cascade down into the 33D level.

He(11S) + e- --> He(n1P)

He(n1P) + He(11S) --> He(nF) + He(11S)

He(nF) --> He(33D) + hv
--> He(31D) + hv
Thus, in addition to explaining the 33D pressure effects, this mechanism would also explain the 31D and 41D pressure effects. and would predict strong pressure effects in the nF levels.

Since the 5F-->33D transition lies in the infared, until recently it has not been measured directly. Using a near-infared weak emission Fourier Transform Spectrometer, we have recently measured it and it too shows the expected pressure effects.

3 mTorr10 mTorr 50 mTorr
5F Cross section (in arbitrary units) versus Electron energy (in eV).

Theory of Collision Transfer of Excitation in Helium Chun C. Lin, and Richard G. Fowler, Annal of Physics 15 (1961) 461-469.

Collisional Excitation Transfer to the 41D State in Helium by Multiple State Mechanism Chun C. Lin, and Robert M. St. John, Physical Review 128 (1962) 1749-1753.

Electron-impact excitation and collisional transfer into the nF levels of helium J. Ethan Chilton and Chun C. Lin, Phys Rev. A 58 (1998) 4572-4580.
last updated: Dec-4-1998