E S T I M A T I O N OF E F F E C T I V E C R O S S S E C T I O N S IN S E N S I T I Z E D F L U O R E S C E N C E

N. A. Pri lezhaeva

Izvestiya VUZ. Fizika, No. 1, pp. 113-115, 1965

There are at present scarcely any data on the absolute effective cross sections of collisions of the second kind (ones accompanied by transfer of electronic excitat ion energy). Such processes can be important in emission from e lec t r ica l

(a) 8!

Fig. I.

(b) ~Z

d ~

:&

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discharges, in gas lasers, etc. The effect ive cross sections are de termin- able via sensitized fluorescence. The present paper derives the re levant

relations and analyzes their appl icabi l i ty .

Consider the following sequence:

(a) Gas 1, with constant concentration N cm "a, is exci ted by mono-

chromatic radiation of intensity I;

(b) The exci ted molecules or atoms of gas 1 (M D co l l ide with m o l e -

cules M 2 of gas 2 and exci te them:

(c) The excited molecules M2* of gas 2 radiate with intensity L

The concentration of non-excited M 2 molecules is n cm -s. The

�9 problem is to determine the effect ive cross sect ion of the col l is ion

process of (1).

In gas 1 at equilibrium (Fig. la ) , the probabil i ty of transition to

the higher state is B1, that of the radiat ive reverse transition is At, and that for collisions of the second kind with gas 2 is Z n. Then Z~ = Cn, where

(2)

gives the number of such collisions per molecu le of gas 1 per cm 3 per sec.

For equil ibrium,

B I l N = A I N * -t- CftN*. (3)

In gas 2 at equil ibr ium (Fig. lb) :

CN*ft = A~n*.

Eliminating N* from (3) and (4) and solving for n*,

(4)

The radiat ion intensity wil l be:

o r

n'*~- BIN Cn

A.2(A1 -t- Cft)

J = A2n* �9 h~ = BIlNh~ Cft

Al q- Cft

e f t j = K N . ,

A~ + Cft

where K is a constant.

We can use (5) to sketch the J -n curve. For smal l n, when Cn << A t , J increases l inear ly with n, i . e . , most of the

M r radiate without col l id ing with M z . As n increases, I increases more slowly (Fig. 2), and tends to the l imi t KN for n

8 2

large, when Cn >> A 1, when all the M~ energies are expended on exciting M2.

We can use (5) to determine Q by measuring J for two or more n. To provide some preliminary data, lated the n for several A 1 and Q when J = J0/2, The results are shown in the following table.

we ealcu-

TABLE

Values of n (cm -3) for which J - J0/2

~ A 1 see-i ] 102 104 10 ~ I 0 ~

2.10 -17

2.10 -16 2.10 - i s

I 015

lOU 1013

I01~. lOaS

I01~

101~

1016

101~

I(J18

1017

10 ~

1019

I0~8

101

These calculations assume that T = 400 ~ and p = 5 X 10 "~3 g, when a partial pressure of 1 mm Hg corresponds to a particle concentration of 1 X 1026 em'S.

The applicability of the method is limited by several assumptions made in deriving (5).

1. We assumed that gas 1 is excited by monochromatic light. Any other type of excitation is possible, provided

that the concentration of M~ remains constant.

2. We assumed that the entire population of the excited level of gas 2 arises from collisions of the second kind with Mr. If they also arise by some other processes, or by transitions from upper levels, suit- able corrections must be introduced into (5).

3. Discussion of the equilibrium conditions for gas 2 assumed a single radiative transition to the lower state. If transitions are possible to intermediate levels, we rftust substitute ~A i for A 2 in (4) and insert an additional constant multiplier Ak/~A i in (5), where A k is the tran- sition probability of the line chosen for the measurement of J(n) and the determination of Q.

d g

/2 -- /< I

T1

Fig. 2. 4. We derived (3) and (4) without allowing for various possible

quenching processes for M~ ~ and M~. However, these processes will produce only an additional constant multiplier in (5) and will not affect the relative intensities if the concentrations of quenching particles remain constant (number of quench-

ing processes per molecule also constant).

Intensity measurements on resonance lines may involve reabsorption. To eliminate this, the measurements should be made at partial pressures of gas 2 for which, by (5), t depends linearly on n. Fortunately, sensitized fluorescence ex-

periments are usually performed at low pressures, where reabsorption is negligible.

The above method is simple and requires knowledge of only one atomic constant. Its applicability is l imited by only one condition: the corresponding level of gas 2 must be excited only by collisions of the second kind with excited

particles of gas 1.

15 Suly 1963 Siberian Institute of Technical Physics, Kuibyshev University, Tomsk

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