Primer on Collisions

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 Q_i term (a). At higher pressures, the measured cross section has a component linear with pressure. If Q_i and Q_j have different energy dependence (different shapes of excitation functions), the shape of (Q_i)^{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 mTorr	33 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 mTorr	10 mTorr	50 mTorr

5F Cross section (in arbitrary units) versus Electron energy (in eV).

references:
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