J. Phys. Chem. 1982, 86,676-677
678
Oscillator Strength and Rare-Gas- I nduced Broadening of the Electric-Quadrupole Transition 4s2 'S0-4s3d 'D, in Calcium K. Fukuda' and K. Ueda Department Of Engineering Physics. Facuky of Engineering, Kyoto University, Kyoto 606, Japan (Received July 27, 1981; In Final Form: September 22, 198 1)
The electric-quadrupole (E2) transition 4s2 'So-4s3d IDzin Ca I has been observed in the presence of rare-gas atoms by the total absorption method. The total absorption data are analyzed on the assumption that the line has a Voigt profile. The oscillator strength is determined to be 6.2 X The broadening rate coefficients are determined to be 1.3 X lo4, 1.3 X lo4. 1.2 X lo4, 1.1X lo4, and 1.4 X lo4 cm3s-' for the perturbing gases He, Ne, Ar, Kr, and Xe, respectively.
Introduction Recently, electronic properties of the low-lying levels of alkaline-earth atoms have received considerable attention. For example, Pasternack et al.' determined the lifetime of the metastable state 4s3d 'Dz of calcium to be 7 = 2.3 f 0.5 ms, and showed that the total decay rate 1 / =~430 s-' was far larger than the calculated electric-quadrupole (E2) transition rate of 90 s-l from the 'D2 to the ground 'So levels. Diffenderfer et a1.2 investigated theoretically spin-forbidden radiative transitions in calcium and confirmed that the above discrepancy was due to spin-forbidden dipole-allowed pathways (4s3d 'Dz -,4s4p 'Po,I,z). The interaction of alkaline-earth atoms with rare-gas atoms has been also investigated by several researchers. For example, Smith3 measured rare-gas-induced broadening of the intercombination line in calcium, and Hindmarsh and co-workers interpreted this measurement from the Lindholm theory with the Lennard-Jones (12-6) potentia14 and more recently with the 12-84 p ~ t e n t i a l . ~ Penkin and Shabanovas measured rare-gas-induced broadening of the resonance line of alkaline-earth atoms, and Shabanova7 tried to determine the force constants from this measurement. In the present paper we report measurements of the oscillator strength and rare-gas-induced broadening of the 4s2 'So-4s3d 'D, E2 transition in calcium. A part of the results has been published in a preliminary rePokg We adopt the total absorption method in the present experiment as in the broadening studies of the principal series lines.9 The measurements are carried out over a wide range of calcium and rare-gas densities in which the magnitude of the total absorption is comparable to the Doppler width. The data are therefore analyzed on the assumption that the line has a Voigt profile, and both the f value and the broadening rate coefficients are determined. The principle of the total absorption method for lines with Voigt counter, the experimental procedure, and the results are given. (1)L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, J . Phys. B , 13, 2231 (1980). (2) R. N. Diffenderfer, P. J. Dagdigian, and D. R. Yarkony, J. Phys. B , 14,21 (1981). (3)G.Smith, Proc. R. SOC.London, Ser. A, 297,288 (1967). (4)W. R. Hindmarsh, A. D. Petford, and G. Smith, Proc. R. SOC. London, Ser. A, 297,296 (1967). ( 5 ) W. R. Hindmarsh and J. M. Farr, 'Progress in Quantum Electronics", 2nd ed., Vol. 2,Part 3,J. H. Sanders and S. Stenholm, Ed., Pergamon, Oxford, 1972,p 141. (6)N.P.Penkin and L. N. Shabanova, Opt. Spectrosc., 25,795(1968). (7)L. N.Shabanova, Opt. Spectrosc., 36, 13 (1974). (8) K.Ueda and K. Fukuda, J.Phys. SOC.Jpn., 48,1047 (1980). (9)K. Ueda, Y.Hamaguchi, and K. Fukuda, to be published. ~~
Principle The total absorption A (the total absorption is independent of instrumental function) is defined as
A =
line
{l- exp[-k(v)l]) dv
where k ( v ) is the absorption coefficient at frequency v and E is the absorption length. If the line profile is a superposition of Lorentz broadening and Doppler broadening, it is given by the Voigt profilelo
where (3) (4)
(5)
and N is the number density of the radiator, f is the absorption oscillator strength, and 6vc and 8Vd are the fullwidth at half-height of the Lorentz and Doppler profiles, respectively. The total absorption is therefore a function of two parameters kl and a 2A/6vd = F(k'1,a) (6) and numerical tables of 2A/6vd are given as a function of k'l and a." If Lorentz broadening is due to collisions with rare-gas atoms admixed as the perturber, then 6vc is expressed as rSvc = KN,, (7) here K is the broadening rate coefficient and N p is the number density of the perturber. In the present experiment we determine the unknowns f (a k'l) and K (a a ) from the measured A. For this purpose we obtain a large number of data points of A for various values of Nl and Npand use a least-squares method. Experiment and Results A calcium vapor was contained in a heat-pipe cell heated over its central 60 cm length to 1095-1190 K. One of the (10)A. C. G.Mitchell and M. W. Zemansky, 'Resonance Radiation and Excited Atoms", Cambridge Unversity Press, London, 1934,p 319. (11)P. A. Jansson and C. L. Korb, J. Quant. Spectrosc. Radiat. Transfer, 8,1399 (1968).
0022-3654/82/2086-0676$01.25/00 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No.
Electric-Quadrupole Transition in Calcium
$
1
4 Np/ N I,crn-'
10
1o3
Figwe 1. Measured total absorption per unit Doppler haif-width 2A /6vd vs. N,/N/, where N , is the xenon density used as the perturber and Nl is the product of the calcium density and the absorption length.
TABLE I: Determined Oscillator Strength and Broadening Rate Coefficients of the 4s2 lSo-4s3d 'D, Transition in Calcium 109K,cm3 s" 107f He Ne Ar Kr Xe
lo" a/(v>,au
,
5, 1982 677
I
lo5
Flgure 2. Broadening cross sections as measured (0)and calculated (solM straight line) vs. CY/( v ), where CY and ( v ) are the polarizability of the rare-gas atom and the relative rms velocity between the calcium and raregas atoms, respectively, in atomic units.
TABLE 11: Calculated C, Values (aOse , ) for the Interaction of Calcium in the 4s3d ' D , State and in the 49, IS, State with Rare-Gas Atoms ' b
6.2(1.2) 1.3(0.5) 1.3(0.5) 1.2(0.4) l . l ( 0 . 4 ) 1.4(0.5)
rare gases (He, Ne, Ar, Kr, and Xe) at 60-960 mbar was admixed as the perturber. Photoelectric absorption measurements were carried out for the 49, 'So-4s3d 'D2 E2 transition at 4575.5 A, using the apparatus described elsewhere.12J3 The measurements were performed at more than 10 pressure and temperature conditions and repeated about 10 times for each condition. Immediately before and after the absorption measurement we applied the hook method to determine the Nl value, where the resonance line of calcium at 4226.7 was used with an oscillator strength 1.75.14 A typical value of N1 was 5.6 X 1017 cm-, at 1150 K. Figure 1 shows measured values of the total absorption per calculated Doppler width 2Albvd against NJN1, where xenon gas was used as the perturber. Under the present experimental conditions, 2A/6vd increases gradually with an increase in N when N1 is kept constant (the solid curved line), and Jecreases with a decrease in N1 when Np is kept constant (the dashed curved line). We obtained from 65 data points by the least-squares method six unknowns, i.e., one absorption oscillator strength and five rare-gas-induced broadening rate coefficients. The results are given in Table I. The estimated statistical uncertainties are 7% for the oscillator strength and 25% for the broadening rate coefficients. The total uncertainty given in the parentheses in Table I includes an estimate of the systematic uncertainty (10%). We also tried to evaluate the contribution from calcium-calcium collisions to the line broadening by the seven-parameter least-squares method and found that this contribution was negligible in the present experiment. The broadening rate coefficients are converted into a thermally averaged cross section u =K/(u) (8) where ( u ) is the relative root-mean-squares velocity between the interacting calcium and rare-gas atoms. These results are plotted in Figure 2.
a
Discussion Radiative Decay Rate. The radiative decay rate 'D, 'So is obtained from the measured absorption oscillator strength to be 40 f 8 s-'. We have a fador of 2 discrepancy
-+
(12)K.Ueda, T.Fujimoto, and K. Fukuda, J. Phys. SOC.Jpn., 49, 1147 (1980). (13)K. Ueda, Y. Ashizawa, and K. Fukuda, Mem. Fac. Eng. Uniu. Kyoto, 42,295 (1980). (14)W. L.Wiese, M. W. Smith, and B. M. Miles, "Atomic Transition Probabilities",Vol. 11, U.S.Goverment Printing Office, Washington, DC, 1969.
He Ne Ar Kr Xe
*
18 35 141 21 0 335
' b o
31 59 236 349 552
A C6
- 13
- 24 - 95
-139
- 217
between this experimental value and the theoretical one (80-90 8) that has been determined by a MCSCF/CI calculation.'I2 At present we have no explanation for this discrepancy. It is noted, however, that this discrepancy hardly affects the estimate of the lifetime of the 'D, level in ref 2. Interatomic Potential. If we assume that the interatomic potential between a calcium atom and a rare-gas atom is given by the van der Waals potential V ( R ) = -e&*, we can estimate the broadening cross section to be5
where Ac6= C6* is the difference between the van der Waals constants for the interaction of calcium in the excited state (4s3d 'D,) and in the ground state (49, 'So) with the rare-gas atom. As suggested by S h a b a n ~ v athe , ~ van der Waals constants for the calcium-rare-gas-atom pairs can be calculated from the London Formula
where CY and e are the polarizability and the ionization energy of the rare-gas atom, and f n k is the oscillator strength of the transition for calcium from a state with energy E , to a state with energy Ek. The oscillator strengths of the 'S0-'P1 transitions are taken from ref 14. For the oscillator strengths of the 'DZ-'P1, -'D2, and -'Fg transitions we use the theoretical values by Friedrich and Trefftz.15 Resulting c6 values are given in Table 11. We find that the van der Waals constant for the ground-state of calcium is larger than that for the 4s3d 'D, state of calcium. The calculated cross sections are compared with the experimental values u = K / ( u ) in Figure 2. This estimate gives larger values for the heavier rare-gas atoms (Ar, Kr, and Xe) and smaller values for He and Ne, but these discrepancies are within the estimated experimental errors. In the following paper we will discuss further the interaction of the calcium atom in the metastable state 4s3d 'D2 with the rare-gas atom. (15)H. Friedrich and E. Trefftz, J. Quant. Spectrosc. Radiat. Transfer,9,333 (1969).
