Abstract

The transition probabilities of the lines 1S03P0 and 1S03P2 of the s2sp arrays in Mg i, Zn i, Cd i, and Hg i, which arise by the interactions of the nuclear moments with the electrons, are computed for each odd isotope individually and for the naturally occurring isotopic mixture. The individual hyperfine structure component transition probabilities are given for the 1S03P2 lines. Part of the intensity of the lines arises from the interaction of 3P0 or 3P2 with 3P1 and part from the interaction of 3P0 or 3P2 with 1P1, the former being more important for 1S03P0 and the latter for 1S03P2. Spin-spin and spin-other-orbit interactions in Mg i are calculated for the 3s3p3P term and compared with observations.

© 1962 Optical Society of America

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References

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  1. I. S. Bowen, Astrophys. J. 132, 1 (1960).
    [Crossref]
  2. I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
    [Crossref]
  3. S. Mrozowski, Z. Physik. 108, 204 (1938).
    [Crossref]
  4. S. Mrozowski, Phys. Rev. 67, 161 (1945).
    [Crossref]
  5. K. G. Kessler, Phys. Rev. 77, 559 (1950).
    [Crossref]
  6. J. R. Holmes and F. E. Deloume, J. Opt. Soc. Am. 42, 77 (1952).
    [Crossref]
  7. E. Gaviola, Contrib. estud. cienc. fís. y mat., (La Plata), Ser. matem. fís. 5, 65 (1929).
  8. Rayleigh, Proc. Roy. Soc. (London) A117, 294 (1927).
    [Crossref]
  9. R. Einaudi, Atti accad. nazl. Lincei, Rend. Classe Sci. fis. mat. e nat. 17, 552 (1933).
  10. W. Opechowski, Z. Physik 109, 485 (1938).
    [Crossref]
  11. P. Kusch and V. W. Hughes, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1959), Vol. 37, p. 81ff.
  12. C. Schwartz, Phys. Rev. 97, 380 (1955).
    [Crossref]
  13. R. E. Trees, Phys. Rev. 92, 308 (1953).
    [Crossref]
  14. H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958), 2nd ed. Two important misprints in this English edition should be noted. In Eq. (29.9) a minus sign should be inserted in front of Km, thus changing the sign of a′′′. In Eq. (31.4) the radical in the numerator of the last term should read [l/(l+1)]12.
  15. eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
    [Crossref]
  16. G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
    [Crossref]
  17. C. Schwartz, Phys. Rev. 105, 173 (1957).
    [Crossref]
  18. M. N. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
    [Crossref]
  19. G. Racah, Phys. Rev. 62, 438 (1942).
    [Crossref]
  20. E. U. Condon and G. H. Shortley, Theory of Atomic Spectra, (Cambridge University Press, New York, 1951), Chap. XI.
  21. C. E. Moore, “Atomic Energy Levels,” Natl. Bur. Standards Circ. No. 467, Vols. I-III (1949–1958).
  22. G. W. King and J. H. Van Vleck, Phys. Rev. 56, 464 (1939).
    [Crossref]
  23. D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
    [Crossref]
  24. A. Lurio, Bull. Am. Phys. Soc. 4, 419 (1959).
  25. A. G. Blachman and A. Lurio, Bull. Am. Phys. Soc. 6, 74 (1961).
  26. Reference 24, p. 429.
  27. K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
    [Crossref]
  28. J. W. Schuttevaer and J. A. Smit, Physica 10, 502 (1943).
    [Crossref]
  29. W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
    [Crossref]
  30. H. Schüler and J. E. Keyston, Z. Physik 67, 433 (1931).
    [Crossref]
  31. H. W. Webb and H. A. Messenger, Phys. Rev,  66, 77 (1944).
    [Crossref]
  32. J. P. A. Van Hengstum and J. A. Smit, Physica 22, 86 (1946).
    [Crossref]
  33. A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge University Press, New York, 1934). p. 147.
  34. G. Boldt, Z. Physik 150, 205 (1958).
    [Crossref]
  35. W. Prokofjew, Z. Physik 50, 701 (1928).
    [Crossref]
  36. J. G. Frayne, Phys. Rev. 34, 590 (1929).
    [Crossref]
  37. P. J. Rubenstein, Phys. Rev.,  58, 1007 (1940).
    [Crossref]
  38. A. M. Naqvi and S. P. Talwar, Proc. Nat. Acad. Sci. India A21, 238 (1955).
  39. R. H. Garstang, Proc. Camb. Phil. Soc. 57, 115 (1961).
    [Crossref]
  40. H. H. Marvin, Phys. Rev. 71, 102 (1947), with phase correction in Garstang.39.
    [Crossref]
  41. L. Biermann and E. Trefftz, Z. Astrophys. 26, 213 (1949).

1961 (2)

A. G. Blachman and A. Lurio, Bull. Am. Phys. Soc. 6, 74 (1961).

R. H. Garstang, Proc. Camb. Phil. Soc. 57, 115 (1961).
[Crossref]

1960 (3)

I. S. Bowen, Astrophys. J. 132, 1 (1960).
[Crossref]

W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
[Crossref]

M. N. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
[Crossref]

1959 (1)

A. Lurio, Bull. Am. Phys. Soc. 4, 419 (1959).

1958 (2)

G. Boldt, Z. Physik 150, 205 (1958).
[Crossref]

D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
[Crossref]

1957 (2)

C. Schwartz, Phys. Rev. 105, 173 (1957).
[Crossref]

K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
[Crossref]

1955 (2)

C. Schwartz, Phys. Rev. 97, 380 (1955).
[Crossref]

A. M. Naqvi and S. P. Talwar, Proc. Nat. Acad. Sci. India A21, 238 (1955).

1954 (1)

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

1953 (1)

R. E. Trees, Phys. Rev. 92, 308 (1953).
[Crossref]

1952 (1)

1950 (1)

K. G. Kessler, Phys. Rev. 77, 559 (1950).
[Crossref]

1949 (1)

L. Biermann and E. Trefftz, Z. Astrophys. 26, 213 (1949).

1947 (1)

H. H. Marvin, Phys. Rev. 71, 102 (1947), with phase correction in Garstang.39.
[Crossref]

1946 (1)

J. P. A. Van Hengstum and J. A. Smit, Physica 22, 86 (1946).
[Crossref]

1945 (1)

S. Mrozowski, Phys. Rev. 67, 161 (1945).
[Crossref]

1944 (1)

H. W. Webb and H. A. Messenger, Phys. Rev,  66, 77 (1944).
[Crossref]

1943 (1)

J. W. Schuttevaer and J. A. Smit, Physica 10, 502 (1943).
[Crossref]

1942 (1)

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

1940 (1)

P. J. Rubenstein, Phys. Rev.,  58, 1007 (1940).
[Crossref]

1939 (1)

G. W. King and J. H. Van Vleck, Phys. Rev. 56, 464 (1939).
[Crossref]

1938 (2)

W. Opechowski, Z. Physik 109, 485 (1938).
[Crossref]

S. Mrozowski, Z. Physik. 108, 204 (1938).
[Crossref]

1933 (2)

R. Einaudi, Atti accad. nazl. Lincei, Rend. Classe Sci. fis. mat. e nat. 17, 552 (1933).

G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
[Crossref]

1931 (1)

H. Schüler and J. E. Keyston, Z. Physik 67, 433 (1931).
[Crossref]

1930 (1)

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

1929 (2)

J. G. Frayne, Phys. Rev. 34, 590 (1929).
[Crossref]

E. Gaviola, Contrib. estud. cienc. fís. y mat., (La Plata), Ser. matem. fís. 5, 65 (1929).

1928 (1)

W. Prokofjew, Z. Physik 50, 701 (1928).
[Crossref]

1927 (1)

Rayleigh, Proc. Roy. Soc. (London) A117, 294 (1927).
[Crossref]

Biermann, L.

L. Biermann and E. Trefftz, Z. Astrophys. 26, 213 (1949).

Blachman, A. G.

A. G. Blachman and A. Lurio, Bull. Am. Phys. Soc. 6, 74 (1961).

Böckmann, K.

K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
[Crossref]

Boldt, G.

G. Boldt, Z. Physik 150, 205 (1958).
[Crossref]

Bowen, I. S.

I. S. Bowen, Astrophys. J. 132, 1 (1960).
[Crossref]

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

Breit, G.

G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
[Crossref]

Condon, E. U.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra, (Cambridge University Press, New York, 1951), Chap. XI.

Deloume, F. E.

Einaudi, R.

R. Einaudi, Atti accad. nazl. Lincei, Rend. Classe Sci. fis. mat. e nat. 17, 552 (1933).

Faust, W.

W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
[Crossref]

Frayne, J. G.

J. G. Frayne, Phys. Rev. 34, 590 (1929).
[Crossref]

Garstang, R. H.

R. H. Garstang, Proc. Camb. Phil. Soc. 57, 115 (1961).
[Crossref]

Gaviola, E.

E. Gaviola, Contrib. estud. cienc. fís. y mat., (La Plata), Ser. matem. fís. 5, 65 (1929).

Hollander, J. M.

D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
[Crossref]

Holmes, J. R.

Houston, W. V.

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

Huff, L. D.

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

Hughes, V. W.

P. Kusch and V. W. Hughes, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1959), Vol. 37, p. 81ff.

Jaccarino, V.

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

Kessler, K. G.

K. G. Kessler, Phys. Rev. 77, 559 (1950).
[Crossref]

Keyston, J. E.

H. Schüler and J. E. Keyston, Z. Physik 67, 433 (1931).
[Crossref]

King, G. W.

G. W. King and J. H. Van Vleck, Phys. Rev. 56, 464 (1939).
[Crossref]

King, J. G.

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

Kopfermann, H.

H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958), 2nd ed. Two important misprints in this English edition should be noted. In Eq. (29.9) a minus sign should be inserted in front of Km, thus changing the sign of a′′′. In Eq. (31.4) the radical in the numerator of the last term should read [l/(l+1)]12.

Krüger, H.

K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
[Crossref]

Kusch, P.

P. Kusch and V. W. Hughes, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1959), Vol. 37, p. 81ff.

Lichten, W.

W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
[Crossref]

Lichten, W. L.

M. N. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
[Crossref]

Lurio, A.

A. G. Blachman and A. Lurio, Bull. Am. Phys. Soc. 6, 74 (1961).

A. Lurio, Bull. Am. Phys. Soc. 4, 419 (1959).

Marvin, H. H.

H. H. Marvin, Phys. Rev. 71, 102 (1947), with phase correction in Garstang.39.
[Crossref]

McDermott, M.

W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
[Crossref]

McDermott, M. N.

M. N. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
[Crossref]

Messenger, H. A.

H. W. Webb and H. A. Messenger, Phys. Rev,  66, 77 (1944).
[Crossref]

Mitchell, A. C. G.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge University Press, New York, 1934). p. 147.

Moore, C. E.

C. E. Moore, “Atomic Energy Levels,” Natl. Bur. Standards Circ. No. 467, Vols. I-III (1949–1958).

Mrozowski, S.

S. Mrozowski, Phys. Rev. 67, 161 (1945).
[Crossref]

S. Mrozowski, Z. Physik. 108, 204 (1938).
[Crossref]

Naqvi, A. M.

A. M. Naqvi and S. P. Talwar, Proc. Nat. Acad. Sci. India A21, 238 (1955).

Opechowski, W.

W. Opechowski, Z. Physik 109, 485 (1938).
[Crossref]

Prokofjew, W.

W. Prokofjew, Z. Physik 50, 701 (1928).
[Crossref]

Racah, G.

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

Rayleigh,

Rayleigh, Proc. Roy. Soc. (London) A117, 294 (1927).
[Crossref]

Recknagel, E.

K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
[Crossref]

Rubenstein, P. J.

P. J. Rubenstein, Phys. Rev.,  58, 1007 (1940).
[Crossref]

Satten, R. A.

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

Schüler, H.

H. Schüler and J. E. Keyston, Z. Physik 67, 433 (1931).
[Crossref]

Schuttevaer, J. W.

J. W. Schuttevaer and J. A. Smit, Physica 10, 502 (1943).
[Crossref]

Schwartz, C.

C. Schwartz, Phys. Rev. 105, 173 (1957).
[Crossref]

C. Schwartz, Phys. Rev. 97, 380 (1955).
[Crossref]

Seaborg, G. T.

D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
[Crossref]

Shortley, G. H.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra, (Cambridge University Press, New York, 1951), Chap. XI.

Smit, J. A.

J. P. A. Van Hengstum and J. A. Smit, Physica 22, 86 (1946).
[Crossref]

J. W. Schuttevaer and J. A. Smit, Physica 10, 502 (1943).
[Crossref]

Stroke, H. H.

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

Strominger, D.

D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
[Crossref]

Talwar, S. P.

A. M. Naqvi and S. P. Talwar, Proc. Nat. Acad. Sci. India A21, 238 (1955).

Trees, R. E.

R. E. Trees, Phys. Rev. 92, 308 (1953).
[Crossref]

Trefftz, E.

L. Biermann and E. Trefftz, Z. Astrophys. 26, 213 (1949).

Van Hengstum, J. P. A.

J. P. A. Van Hengstum and J. A. Smit, Physica 22, 86 (1946).
[Crossref]

Van Vleck, J. H.

G. W. King and J. H. Van Vleck, Phys. Rev. 56, 464 (1939).
[Crossref]

Webb, H. W.

H. W. Webb and H. A. Messenger, Phys. Rev,  66, 77 (1944).
[Crossref]

Wills, L. A.

G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
[Crossref]

Zemansky, M. W.

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge University Press, New York, 1934). p. 147.

Astrophys. J. (1)

I. S. Bowen, Astrophys. J. 132, 1 (1960).
[Crossref]

Atti accad. nazl. Lincei, Rend. Classe Sci. fis. mat. e nat. (1)

R. Einaudi, Atti accad. nazl. Lincei, Rend. Classe Sci. fis. mat. e nat. 17, 552 (1933).

Bull. Am. Phys. Soc. (2)

A. Lurio, Bull. Am. Phys. Soc. 4, 419 (1959).

A. G. Blachman and A. Lurio, Bull. Am. Phys. Soc. 6, 74 (1961).

Contrib. estud. cienc. fís. y mat., (La Plata), Ser. matem. fís. (1)

E. Gaviola, Contrib. estud. cienc. fís. y mat., (La Plata), Ser. matem. fís. 5, 65 (1929).

J. Opt. Soc. Am. (1)

Naturwissen-schaften (1)

K. Böckmann, H. Krüger, and E. Recknagel, Naturwissen-schaften 44, 7 (1957); Ann. Physik 20, 250 (1957).
[Crossref]

Phys. Rev (2)

W. Faust, M. McDermott, and W. Lichten, Phys. Rev,  120, 469 (1960).
[Crossref]

H. W. Webb and H. A. Messenger, Phys. Rev,  66, 77 (1944).
[Crossref]

Phys. Rev. (14)

H. H. Marvin, Phys. Rev. 71, 102 (1947), with phase correction in Garstang.39.
[Crossref]

J. G. Frayne, Phys. Rev. 34, 590 (1929).
[Crossref]

P. J. Rubenstein, Phys. Rev.,  58, 1007 (1940).
[Crossref]

I. S. Bowen, quoted in L. D. Huff and W. V. Houston, Phys. Rev. 36, 842 (1930).
[Crossref]

S. Mrozowski, Phys. Rev. 67, 161 (1945).
[Crossref]

K. G. Kessler, Phys. Rev. 77, 559 (1950).
[Crossref]

eg., V. Jaccarino, J. G. King, R. A. Satten, and H. H. Stroke, Phys. Rev. 94, 1798 (1954).
[Crossref]

G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
[Crossref]

C. Schwartz, Phys. Rev. 105, 173 (1957).
[Crossref]

M. N. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
[Crossref]

G. Racah, Phys. Rev. 62, 438 (1942).
[Crossref]

C. Schwartz, Phys. Rev. 97, 380 (1955).
[Crossref]

R. E. Trees, Phys. Rev. 92, 308 (1953).
[Crossref]

G. W. King and J. H. Van Vleck, Phys. Rev. 56, 464 (1939).
[Crossref]

Physica (2)

J. P. A. Van Hengstum and J. A. Smit, Physica 22, 86 (1946).
[Crossref]

J. W. Schuttevaer and J. A. Smit, Physica 10, 502 (1943).
[Crossref]

Proc. Camb. Phil. Soc. (1)

R. H. Garstang, Proc. Camb. Phil. Soc. 57, 115 (1961).
[Crossref]

Proc. Nat. Acad. Sci. India (1)

A. M. Naqvi and S. P. Talwar, Proc. Nat. Acad. Sci. India A21, 238 (1955).

Proc. Roy. Soc. (London) (1)

Rayleigh, Proc. Roy. Soc. (London) A117, 294 (1927).
[Crossref]

Revs. Modern Phys. (1)

D. Strominger, J. M. Hollander, and G. T. Seaborg, Revs. Modern Phys. 30, 585 (1958).
[Crossref]

Z. Astrophys. (1)

L. Biermann and E. Trefftz, Z. Astrophys. 26, 213 (1949).

Z. Physik (4)

G. Boldt, Z. Physik 150, 205 (1958).
[Crossref]

W. Prokofjew, Z. Physik 50, 701 (1928).
[Crossref]

H. Schüler and J. E. Keyston, Z. Physik 67, 433 (1931).
[Crossref]

W. Opechowski, Z. Physik 109, 485 (1938).
[Crossref]

Z. Physik. (1)

S. Mrozowski, Z. Physik. 108, 204 (1938).
[Crossref]

Other (6)

P. Kusch and V. W. Hughes, in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1959), Vol. 37, p. 81ff.

H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958), 2nd ed. Two important misprints in this English edition should be noted. In Eq. (29.9) a minus sign should be inserted in front of Km, thus changing the sign of a′′′. In Eq. (31.4) the radical in the numerator of the last term should read [l/(l+1)]12.

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra, (Cambridge University Press, New York, 1951), Chap. XI.

C. E. Moore, “Atomic Energy Levels,” Natl. Bur. Standards Circ. No. 467, Vols. I-III (1949–1958).

A. C. G. Mitchell and M. W. Zemansky, Resonance Radiation and Excited Atoms (Cambridge University Press, New York, 1934). p. 147.

Reference 24, p. 429.

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Tables (7)

Tables Icon

Table I Wavelengths of the ns2nsnp transitions.

Tables Icon

Table II Adopted values of parameters.

Tables Icon

Table III Coefficients in perturbed wave functions.a

Tables Icon

Table IV Transition probabilities for 1S03P1 and 1S01P1 lines in Mg i, Zn i, Cd i, and Hg i.

Tables Icon

Table V Absolute oscillator strengths for Mg i 3s2 1S0–3s3p1P1.

Tables Icon

Table VI Transition probabilities for intercombination lines in Mg i, Zn i, Cd i, and Hg i.

Tables Icon

Table VII Transition probabilities for hyperfine structure components of the 1S03P2 line.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

W = W J + 1 / 2 A K + B K ( K + 1 ) ,
a = A , b = 8 I ( 2 I 1 ) J ( 2 J 1 ) B / 3.
ϕ ( 3 P 1 ) = c 1 ( 1 2 , 3 2 , 1 ) + c 2 ( 1 2 , 1 2 , 1 ) , ϕ ( 1 P 1 ) = c 2 ( 1 2 , 3 2 , 1 ) c 1 ( 1 2 , 1 2 , 1 ) ,
A ( 3 P 2 ) = ( 1 / 4 ) a s + ( 3 / 4 ) a 3 2 ,
A ( 3 P 1 ) = ( 1 / 4 ) ( 2 c 2 2 c 1 2 ) a s + ( 5 / 4 ) c 1 2 a 3 2 + ( 1 / 2 ) c 2 2 a 1 2 + 2 c 1 c 2 a .
a 1 2 = 5 θ ( 1 δ ) 1 2 ( 1 ) 1 2 a 3 2 ,
a = 5 16 ξ a 3 2 ,
B ( 3 P 1 ) = 3 b 3 2 ( c 1 2 2 2 c 1 c 2 η ) 16 I ( 2 I 1 ) ,
B ( 3 P 2 ) = b 3 2 16 I ( 2 I 1 ) ,
( 3 P 2 I I | T e ( 2 ) · T n ( 2 ) | 3 P 0 I I ) = 1 4 [ ( 2 I + 2 ) ( 2 I + 3 ) I ( 2 I 1 ) ] 1 2 η b 3 2 .
( 3 P 1 I I | T e ( 1 ) · T n ( 1 ) | 3 P 0 I I ) = [ I ( I + 1 ) ] 1 2 × { 1 2 c 2 a s 5 16 2 c 1 ξ a 3 2 1 2 c 2 a 1 2 } .
ψ ( 3 P 0 ) = ϕ ( 3 P 0 ) + α ϕ ( 3 P 1 ) + β ϕ ( 1 P 1 ) + γ ϕ ( 3 P 2 ) , ψ ( 3 P 2 ) = ϕ ( 3 P 2 ) + α ϕ ( 3 P 1 ) + β ϕ ( 1 P 1 ) + γ ϕ ( 3 P 0 ) ,
S ( F , F ) = | ( J I F P ( 1 ) J I F ) | 2 ,
( 1 S 0 P ( 1 ) 3 P 1 ) = 2 ( c 2 2 c 1 ) σ , ( 1 S 0 P ( 1 ) 1 P 1 ) = 2 ( c 1 + 2 c 2 ) σ ,
S ( J , J ) = 1 2 I + 1 F , F S ( F , F ) .