The continuous absorption coefficient of the negative lithium ion

Volume 41A, number 1

PHYSICS LETTERS

28 August 1972

THE CONTINUOUS ABSORPTION COEFFICIENT OF THE NEGATIVE LITHIUM ION T. L. JOHN Department of ‘Ipplied Mathematics and Mathematical Physics. University College. C’ardif[ U. K. Received 31 \Iarch 1972 The continuous absorption coefficients of Li~are tabulated as functions of temperature and wave length.

The work of Ya’akobi and Avivi [1] has shown the importance of the negative lithium ion in identifying the primary source of radiative emission from cxploding lithium wires and plasmas, and in determining temperature and electron concentrations. The continuous emission and absorption spectra are the result of transitions between bound and continuous states of U: radiative attachment and photodetachment

0.0452 a.u. (0.615 e.v.) for the electron affinity, Saha’s relation N = 4.16 X 10 W @5/2 exp( I .4160). (I) Li

‘~C’

enables us to express the bound free absorption coetficient in these units, where PC is the electron pressure. TLi are the concentrations of the negative NLU and A ions and lithium atoms respectively and 0 is related to the absolute temperature by

+ Li liv + Li and between different continuous states: bremsstrahlung and inverse-bremsstrahlung

1(K) = 5040.2/0. (2) Values of the bound-free absorption coefficient, al-

e

lowingwere They for calculated stimulated from emission, the formula are given in table I

e

-

+ Li

he + e

+

~

In view of recent calculations of the absorption cross sections tor these processes 12. 31 more accurate estimates of the coefficients of continuous absorption and emission are now possible and they are presented here. The radiative attachment and photodetachment processes are confined to the transitions Is2 2skp~

kbf(O)

4.16 IO~~ @5/2 exp( 1 .4160)

=

X

X tI -—exp{ -285460/X (A)} K~ cm4/dyne, (3) .

.

.

was interpolated trom data given in table 2 ot ret, .

.

It can be shown that the tree-I ree absorption cue!ticient can be expanded in the torni

Is2 2s2 ‘S ~

and bremsstrahlung of free electrons in the field of lithium atoms (in their ground states), and the inverse process, to the transitions Is2 ~sk/~ Is2 ~skl~I —

—

.

Contributions from attachment and photodetachinent and free- free transitions into and from excited states of Li have been neglected. For convenience in applications we shall express the absorption coefficients per unit electron pressure per lithium atom. Adopting Weiss’s [4] values 34

0

=

I

the wave length being given by X(A) = 911 .2671 /~k2.

(5)

In our calculations we shall use o(0) tabulated in ret. 131 and a,,(0) = 0, thus the free-free calculations will be most accurate in the infrared spectrum (~k2—*0). In the ultra-violet the bound-free transitions dominate the total absorption coefficient and serious errors are not likely as a result of this approximation but further investigations are necessary. In table 1 we give separate

Volume 41A, number 1

PHYSICS LETTERS

28 August 1972

~0

V

H C

p

~ e~

C

C~ C N C~

C

C’l C”~ C — —

CC CN ‘0 — —

CC CN C N 00 ~

CC C~ C ~ C C’ —

CC CC~ C ~ C N

e-~

CC C’0 C ‘0 C

‘r~

CC CN C 00 C 00

N

N

CC CC C — C

m

CC CC C ~ C — N

m

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CC CC C N C N a’

CC CC C ~ C c~ N

-~j

~-

~

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~n

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C

~n 00

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C C C N — i

0 V

N

CC

C— C

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Cr~ CC’ ~

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~

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a’

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m

C 00

‘.0

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CC C~

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C ‘fl C —

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CC CC

CC

C r— C N

CC C ~C rn

~

-.

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00

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— —

—

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35

Volume 41A, number 1

PHYSICS LETTERS

(X> 20161 A)k~t(O)= 0 and j~,(O)is given by

entries for the absorption coefficients due to the bound-free and free-free transitions for a range of

wave lengths and temperatures. The coefficient of continuous emission /~(0)per electron pressure per lithium atom can be calculated from the Kirchhoff-Planck law [5] 6.6(~k2)3[exp(3l .326 Ok2)— 1] —l X k~(O)+k~’(O) =

,

using table I. Note that in the infrared

36

28 August 1972

(6)

=

u(O) {0.2l I O 1

3.30~k2)+ O((~k2)2). (7)

References

III B. Ya’akobi and P. Avivi, 3. Phys. B2 (1969)405,412. 121 T.L. John, submitted for publication. [31 TI.. John,J. Phys., to be published. [41 Weiss, Phys. Rev. 122 (1961)(McGraw-Hill, 1826. [51A.W. HR. Griem, Plasma spectroscopy 1964).