Approximate continuous opacity calculations for ionized titanium and chromium

I. Quant. Spectrosc.

Racht.

Transfer,

Vol. 2,

pp. 93-96.

NOTES

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APPROXIMATE CONTINUOUS OPACITY CALCULATIONS FOR IONIZED TITANIUM AND CHROMIUM* W. L. SHACKLEFORD Daniel and Florence Guggenheim Jet Propulsion Center, California Institute of Technology Pasadena, California (Received 16 November 1961) THE “modified

Raizer” technique of PAPPERT and PENNER(~) has been used to calculate Planck and Rosseland mean free paths for titanium and chromium. These calculations have been carried out for temperatures (0) of 5, 10. 15 and 20 eV and number densities 09 of 1015 to 10zl cm-3.

1020 Number

10’8

IO’9

density,

cm-3

IO" Number

10’5

10’6 density,

cm-3

FIG. 1. The Rosseland mean free path of titanium (in cm) as a function of number density (in cm-a) at temperatures of 5, 10, 15 and 20 eV. * Supported by the USAF Office of Scientific Research California Institute of Technology. 93

under Contract

AF 49(638)-984 with the

W. L. SHACKLEFORD

94

Number FIG. 2.

density,

Number

cmw3

The Planck mean free path of titanium (in cm) as a function (in cm-s),

density,

cme3

of number density

for temperatures of 5, 10, 15 and 20 eV.

The Saha equation was solved by using the approximate method of Raizer described by and PENNER.(~) Ionization potentials of ionized states as high as the neon configurations Cr XV and Ti XIII were taken from MOORE,(~) except for a few unknown values (Cr X, XI, XII; Ti VIII, X) which were obtained by interpolation between listed values. The calculated values of E (FE = number of free electrons per atom) are listed in Table 1. PAPPERT

TABLE 1. AVERAGE NUMBEROF FREEELECTRONSPER ATOM, I;, AS A FUNCTION OF N (Cm-“) AND 0 (eV) FOR TITANIUMAND CHROMIUM Titanium 0 (eV): N =

1015 cm-s 10’6 10” 10’8 10’9 1020 102’

5

10

15

4.09 3.88 3.75 3.56 3.33 2.85 2.04

7.70 6.84 5.85 4.80 4.10 3.76 3.40

IO.30 9.33 8.50 7.30 5.93 4.55 3.83

Chromium 20

5

10

15

20

11.80 11.57 10.40 9.13 7.87 6.28 4.38

4.99 4.41 3.93 3.46 2.97 2.33 1.67

6.95 6.31 6.00 5.69 4.99 4.00 3.10

10.05 9.08 7.85 6.51 6.04 5.57 4.20

12.57 11.35 10.15 8.84 7.19 6.14 5.51

Number

density,

cm3

Number

density,

cm

mean free path of chromium (in cm) as a function of number density (in cm-s), for temperatures of 5, 10, 15 and 20 eV.

FIG. 3. The Rosseland

,.”

-3

-

W. L. SHACKLEF~RD

96

Number Number

density,

density,

cmT3

cme3

FIG. 4. The Planck mean free path of chromium (in cm) as a function of number density (in cm-S), for temperatures of 5, 10, 15 and 20 eV.

The tendency of E to level off around high ionization potentials for the argon turn, causes some peculiar inflections in and Planck mean free paths are plotted in Figs. 14.

4 and 6 for Ti and Cr, respectively, is due to the configurations of these ions. The leveling of E, in the curves for the mean free paths. The Rosseland as functions of the density at various temperatures

REFERENCES 1. R. A. PAPPERT and S. S. PENNER,JQSRT 1,258(1961). 2. C. E. MOORE,Atomic Energy Levels, National Bureau of Standards, Washington 25, D.C., NBS Circular 467, Vols. I (1949) and II (1952).