Abstract

Recent absolute measurements of many helium excitation functions at low pressure and of the singlet and triplet D functions at several pressures have allowed an extension and upgrading of the multiple-state-transfer process.

Atoms excited to an n1P level are converted to a mixed singlet–triplet F state by an atomic collision. Low-lying singlet and triplet D levels are fed by the many F states thus populated.

Apparent excitation functions were computed by machine for the 33D, 43D, and 41D states and compared with the experimental excitation functions. The computed curves best match the experimental curves when it is assumed that: (a) the transfer cross section for the nth set of 1PF states is proportional to n1 or n2, and (b) the 1F3 and 3F3 components of the mixed state are active in the transfer–cascade processes, while the 3F2,4 states are inactive.

The energy is primarily transferred through n1PnF sets of states with n≤15.

© 1965 Optical Society of America

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References

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  1. E. Wigner, Nachr. Ges. Wiss. Göttingen, Jahresber, Geschäftsjahr, 375 (1927).
  2. R. M. St. John and R. G. Fowler, Phys. Rev. 122, 1813 (1961).
    [CrossRef]
  3. C. C. Lin and R. G. Fowler, Ann. Phys. (New York) 15, 461 (1961).
    [CrossRef]
  4. C. C. Lin and R. M. St. John, Phys. Rev. 128, 1749 (1962).
    [CrossRef]
  5. R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
    [CrossRef]
  6. A. V. Phelps, Phys. Rev. 110, 1362 (1958).
    [CrossRef]
  7. A. H. Gabriel and D. W. O. Heddle, Proc. Roy. Soc. (London) A258, 124 (1960).
  8. H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A140, 613 (1933).
  9. The calculated curves for x=3 and 4 lay between those of x=2 and x=5 for the 33D case, and for 43D, 41D, and 31D cases as well. Since the graphs of the functions for x=1, 2, and 5 show the trend of the variation of the calculated excitation functions, the graphs of the functions for x=3 and 4 are omitted for the sake of clarity of the figures.

1964 (1)

R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
[CrossRef]

1962 (1)

C. C. Lin and R. M. St. John, Phys. Rev. 128, 1749 (1962).
[CrossRef]

1961 (2)

R. M. St. John and R. G. Fowler, Phys. Rev. 122, 1813 (1961).
[CrossRef]

C. C. Lin and R. G. Fowler, Ann. Phys. (New York) 15, 461 (1961).
[CrossRef]

1960 (1)

A. H. Gabriel and D. W. O. Heddle, Proc. Roy. Soc. (London) A258, 124 (1960).

1958 (1)

A. V. Phelps, Phys. Rev. 110, 1362 (1958).
[CrossRef]

1933 (1)

H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A140, 613 (1933).

1927 (1)

E. Wigner, Nachr. Ges. Wiss. Göttingen, Jahresber, Geschäftsjahr, 375 (1927).

Fowler, R. G.

R. M. St. John and R. G. Fowler, Phys. Rev. 122, 1813 (1961).
[CrossRef]

C. C. Lin and R. G. Fowler, Ann. Phys. (New York) 15, 461 (1961).
[CrossRef]

Gabriel, A. H.

A. H. Gabriel and D. W. O. Heddle, Proc. Roy. Soc. (London) A258, 124 (1960).

Heddle, D. W. O.

A. H. Gabriel and D. W. O. Heddle, Proc. Roy. Soc. (London) A258, 124 (1960).

Lin, C. C.

R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
[CrossRef]

C. C. Lin and R. M. St. John, Phys. Rev. 128, 1749 (1962).
[CrossRef]

C. C. Lin and R. G. Fowler, Ann. Phys. (New York) 15, 461 (1961).
[CrossRef]

Massey, H. S. W.

H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A140, 613 (1933).

Miller, F. L.

R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
[CrossRef]

Mohr, C. B. O.

H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A140, 613 (1933).

Phelps, A. V.

A. V. Phelps, Phys. Rev. 110, 1362 (1958).
[CrossRef]

St. John, R. M.

R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
[CrossRef]

C. C. Lin and R. M. St. John, Phys. Rev. 128, 1749 (1962).
[CrossRef]

R. M. St. John and R. G. Fowler, Phys. Rev. 122, 1813 (1961).
[CrossRef]

Wigner, E.

E. Wigner, Nachr. Ges. Wiss. Göttingen, Jahresber, Geschäftsjahr, 375 (1927).

Ann. Phys. (New York) (1)

C. C. Lin and R. G. Fowler, Ann. Phys. (New York) 15, 461 (1961).
[CrossRef]

Nachr. Ges. Wiss. Göttingen, Jahresber, Geschäftsjahr (1)

E. Wigner, Nachr. Ges. Wiss. Göttingen, Jahresber, Geschäftsjahr, 375 (1927).

Phys. Rev. (4)

R. M. St. John and R. G. Fowler, Phys. Rev. 122, 1813 (1961).
[CrossRef]

C. C. Lin and R. M. St. John, Phys. Rev. 128, 1749 (1962).
[CrossRef]

R. M. St. John, F. L. Miller, and C. C. Lin, Phys. Rev. 134, A888 (1964).
[CrossRef]

A. V. Phelps, Phys. Rev. 110, 1362 (1958).
[CrossRef]

Proc. Roy. Soc. (London) (2)

A. H. Gabriel and D. W. O. Heddle, Proc. Roy. Soc. (London) A258, 124 (1960).

H. S. W. Massey and C. B. O. Mohr, Proc. Roy. Soc. (London) A140, 613 (1933).

Other (1)

The calculated curves for x=3 and 4 lay between those of x=2 and x=5 for the 33D case, and for 43D, 41D, and 31D cases as well. Since the graphs of the functions for x=1, 2, and 5 show the trend of the variation of the calculated excitation functions, the graphs of the functions for x=3 and 4 are omitted for the sake of clarity of the figures.

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Figures (7)

Fig. 1
Fig. 1

Energy level diagram of helium showing excitation by electron impact, transfer of excitation, and radiative transitions.

Fig. 2
Fig. 2

Apparent excitation functions for the 33D level: ——experimental; —○ —x=1; —△—x=2; —□—x=5; except where noted by the numerals beside the curves. In those cases —○— represents the curves whose x values are shown beside the curve. F-state model (a).

Fig. 3
Fig. 3

Apparent excitation functious for the 43D level: ——experimental;—○—x=1; —△—x=2; —□—x=5. F-state model (a).

Fig. 4
Fig. 4

Apparent excitation functions for the 41D level: ——experimental; —○ —x=1; —△—x=2; —□—x=5. F-state model (a).

Fig. 5
Fig. 5

Apparent excitation functions for the 41D level:——experimental; —○ —x=1; —△ —x=2; —□—x=5; except where noted by the numerals beside the curves. In those cases—○—represents the curves whose values are shown beside the curve. F-state model (b).

Fig. 6
Fig. 6

Apparent excitation functions for the 31D level computed for x=1 and F-state model (a). No experimental data are available.

Fig. 7
Fig. 7

Evaluations of R(gk), the cumulative percent of excitation transferred via states with ng to the 33D state at four pressures. Electron energy=100 eV; Qt(n)=7.3×10−16n1; F-state model (a).

Tables (1)

Tables Icon

Table I Transfer cross sections Qt(n) producing a fit for the 33D data at 63 μ pressure. (a) 3F2,4 states inactive, (b) 3F2,4 states active.

Equations (15)

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Q t ( n 1 P n F ) = [ G ( n F ) / G ( n 1 P ) ] Q t ( n F n 1 P ) = b Q t ( n ) ,
Q t ( n ) = Q t ( n F n 1 P ) and b = [ G ( n F ) / G ( n 1 P ) ] .
Q ( n 1 P ) I e N ( g ) / e S electron impact and cascade gain + N ( g ) N ( n F ) Q t ( n ) c ¯ transfer gain + f n N ( n 1 P ) A ( n 1 P 1 ) regained by imprisonment = N ( g ) N ( n 1 P ) b Q t ( n ) c ¯ transfer loss + N ( n 1 P ) A ( n 1 P ) radiative loss except to ground + N ( n 1 P ) A ( n 1 P 1 ) radiative loss to ground ,
Q ( n 1 P ) I e N ( g ) / e S + N ( g ) N ( n F ) Q t ( n ) c ¯ = N ( g ) N ( n 1 P ) b Q t ( n ) c ¯ + N ( n 1 P ) A ( n 1 P ) .
Q ( n F ) I e N ( g ) / e S electron impact and cascade gain + N ( g ) N ( n 1 P ) b Q t ( n ) c ¯ transfer gain = N ( g ) N ( n F ) Q t ( n ) c ¯ transfer loss + N ( n F ) A ( n F ) radiative loss .
Q h ( n 3 P ) I e N ( g ) / e S total net production = N ( n 3 P ) A ( n 3 P ) radiative loss .
Q ( k ) I e N ( g ) e S electron impact gain + n = 4 N ( n F ) A ( n F k ) gain by cascade from F + n = 4 N ( n 1 , 3 P ) A ( n 1 , 3 P k ) gain by cascade from P 1 or P 3 = N ( k ) A ( k ) radiative loss .
Q h ( k ) I e N ( g ) / e S = N ( k ) A ( k ) .
Q h ( k ) = Q ( k ) + e S I e N ( g ) n = 4 N ( n F ) A ( n F k ) + n = 4 N ( n 1 , 3 ) A ( n 1 , 3 P k ) .
N ( n 3 P ) = I c N ( g ) e S Q h ( n 3 P ) A ( n 3 P ) ,
N ( n F ) = I e N ( g ) e S { [ Q ( n 1 P ) + Q ( n F ) ] b A ( n 1 P ) + Q ( n F ) Q t ( n ) N ( g ) c ¯ } / [ 1 + b A ( n F ) A ( n 1 P ) + A ( n F ) Q t ( n ) N ( g ) c ¯ ] ,
N ( n 1 P ) = I c N ( g ) e S { [ Q ( n 1 P ) + Q ( n F ) ] A ( n F ) + Q ( n 1 P ) Q t ( n ) N ( g ) c ¯ } / [ b + A ( n 1 P ) A ( n F ) + A ( n 1 P ) Q t ( n ) N ( g ) c ¯ ] .
N ( n F ) total population = Q ( n F ) A ( n F ) I e N ( g ) e S direct excitation plus cascade + N t ( n F ) population from transfer .
P ( m k ) = N t ( m F ) A ( m F k ) / n = 4 N ( n F ) A ( n F k ) .
R ( g k ) = m = 4 g P ( m k ) .