Abstract

Lifetime as well as transition probabilities of the first p-excited states of neon+, argon+, and krypton+ have been calculated.

© 1969 Optical Society of America

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References

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  1. R. H. Garstang, Monthly Not. Roy. Astron. Soc. 114, 118 (1954).
  2. D. W. Koopman, J. Opt. Soc. Am. 54, 1354 (1964).
    [Crossref]
  3. H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
    [Crossref]
  4. See T. Yamanouchi and A. Amemiya, Proc. Phys. Soc. Japan 1, 18 (1946), for the exchange and direct integral,and J. L. Tech, J. Res. Natl. Bur. Std. (U.S.) 67A, 555 (1963), for the spin–orbit terms (aij = bij = 1 for all i and j).
    [Crossref]
  5. It can be shown that the equations arising from the off-diagonal terms give no information.
  6. F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963).
  7. L. Minnhagen, Arkiv Fysik 25, 203 (1963).

1965 (1)

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

1964 (1)

1963 (1)

L. Minnhagen, Arkiv Fysik 25, 203 (1963).

1954 (1)

R. H. Garstang, Monthly Not. Roy. Astron. Soc. 114, 118 (1954).

1946 (1)

See T. Yamanouchi and A. Amemiya, Proc. Phys. Soc. Japan 1, 18 (1946), for the exchange and direct integral,and J. L. Tech, J. Res. Natl. Bur. Std. (U.S.) 67A, 555 (1963), for the spin–orbit terms (aij = bij = 1 for all i and j).
[Crossref]

Amemiya, A.

See T. Yamanouchi and A. Amemiya, Proc. Phys. Soc. Japan 1, 18 (1946), for the exchange and direct integral,and J. L. Tech, J. Res. Natl. Bur. Std. (U.S.) 67A, 555 (1963), for the spin–orbit terms (aij = bij = 1 for all i and j).
[Crossref]

Garstang, R. H.

R. H. Garstang, Monthly Not. Roy. Astron. Soc. 114, 118 (1954).

Herman, F.

F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963).

Horrigan, F. A.

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

Koopman, D. W.

Koozekanani, S. H.

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

Koster, G. F.

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

Minnhagen, L.

L. Minnhagen, Arkiv Fysik 25, 203 (1963).

Skillman, S.

F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963).

Statz, H.

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

Tang, C. L.

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

Yamanouchi, T.

See T. Yamanouchi and A. Amemiya, Proc. Phys. Soc. Japan 1, 18 (1946), for the exchange and direct integral,and J. L. Tech, J. Res. Natl. Bur. Std. (U.S.) 67A, 555 (1963), for the spin–orbit terms (aij = bij = 1 for all i and j).
[Crossref]

Arkiv Fysik (1)

L. Minnhagen, Arkiv Fysik 25, 203 (1963).

J. Appl. Phys. (1)

H. Statz, F. A. Horrigan, S. H. Koozekanani, C. L. Tang, and G. F. Koster, J. Appl. Phys. 36, 2278 (1965).
[Crossref]

J. Opt. Soc. Am. (1)

Monthly Not. Roy. Astron. Soc. (1)

R. H. Garstang, Monthly Not. Roy. Astron. Soc. 114, 118 (1954).

Proc. Phys. Soc. Japan (1)

See T. Yamanouchi and A. Amemiya, Proc. Phys. Soc. Japan 1, 18 (1946), for the exchange and direct integral,and J. L. Tech, J. Res. Natl. Bur. Std. (U.S.) 67A, 555 (1963), for the spin–orbit terms (aij = bij = 1 for all i and j).
[Crossref]

Other (2)

It can be shown that the equations arising from the off-diagonal terms give no information.

F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963).

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Tables (6)

Tables Icon

Table I Radial integrals for ionized Ne, Ar, and Kr as found by fitting and calculated by computer using Hartree–Fock wave-functions.6 The experimental value of F2(pcorepcore) was found from the relation 6F2(pcorepcore) = (1D) − (3P). For Ne, the iteratively found ζ′p−ex converges to a negative number, even when the starting conditions are changed. However, the effect of ζ′p−ex on the wavefunction is negligible even if the sign is reversed.

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Table II Experimental and theoretical energy levels of Ne ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).

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Table III Experimental and theoretical energy levels of Ar ii taken from Minnhagen7 and from this calculation. The mixing coefficients of aij are those given in Eq. (1).

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Table IV Experimental and theoretical energy levels of Kr ii taken from Moore,a tables of atomic energy levels and this calculation. The mixing coefficients aij are those given in Eq. (1).

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Table V Transition probabilities between 3p–3s levels of Ne ii, 4p–4s levels of Ar ii, and 5p–5s levels of Kr ii, each with ap4 [3P] core. A in sec−1. In this table for the purposes of comparison we have reproduced the results of Statz et al.3 and Garstang4 for the case of Ar ii and the experimental intensities I.

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Table VI Lifetimes of some of the 3p states of Ne ii, 4p states of Ar ii, and 5p states of Kr ii (in nsec).

Equations (16)

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A i j = ( 64 π 4 / 3 h λ i j μ i ) S i j ,
Ψ i ( E i ) = j p i j ϕ j = j p i j | p 4 L ¯ S ¯ ; l ex s ; L j S j J j M j .
A i j = ( 64 π 4 / 3 h λ i j 3 μ i ) | m , n p m i p n i { J i 1 J j L m S m L n } × { L m 1 L n l ex L m l ex } ( l ex 1 l ex 0 0 0 ) { ( 2 j j + 1 ) ( 2 J i + 1 ) × ( 2 L m + 1 ) ( 2 L n + 1 ) ( 2 l ex + 1 ) ( 2 l ex + 1 ) } 1 2 × δ ( L m , L n ) δ ( S m , S n ) | 2 R i j ,
H Ψ i ( E i ) = E i Ψ i ,
H = i 2 2 m i 2 i e 2 r i + i > j e 2 r i j + i ξ ( r ) l i · s i ,
F 2 = e 2 25 0 0 r < 2 r > 3 f 2 n p ( r 1 ) f 2 ( n + 1 ) p ( r 2 ) d r 1 d r 2 ,
G 0 = e 2 2 0 0 1 r > f n p ( r 1 ) f ( n + 1 ) p ( r 1 ) f n p ( r 2 ) × f ( n + 1 ) p ( r 2 ) d r 1 d r 2 ,
G 2 = e 2 50 0 0 r < 2 r > 3 f n p ( r 1 ) f ( n + 1 ) p ( r 1 ) f n p ( r 2 ) × f ( n + 1 ) p ( r 2 ) d r 1 d r 2 ,
ζ l = e 2 2 m 2 c 2 1 a 3 0 1 r d V e ( r ) d r [ f l 2 ( r ) ] d r ,
[ H 0 ] i j = ϕ i | H | ϕ j 0 = a i j [ ¹ D ] 0 + b i j [ ³ P ] 0 + c i j [ F 2 ] 0 + d i j [ G 0 ] 0 + .
[ M 0 ] 1 [ H 0 ] [ M 0 ] = [ E 0 ] ,
[ M 0 1 ] [ H ] [ M 0 ] = [ E ] ,
[ H ] i j = ϕ i | H | ϕ j = a i j [ ¹ D ] + b i j [ ³ P ] + c i j F 2 + d i j G 0 + ,
[ H 1 ] i j = a i j [ ¹ D ] 1 + b i j [ ³ P ] 1 + c i j ( F 2 ) 1 + d i j ( G 0 ) 1 + ,
[ M 1 ] 1 [ H 1 ] [ M 1 ] = [ E 1 ] .
[ M 1 ] 1 [ H ] [ M 1 ] = [ E ] ,