Abstract

More than 250 spectrum shifts have been measured for lines of the neutral thorium atom (Th I) and of the singly-ionized thorium atom (Th II) in a sample of thorium containing 13 percent Th 230 (ionium). The observed isotope shifts between Th 230 and Th 232 spectrum lines range in magnitude up to 0.94 cm−1. The Th 232 line in every case is to longer wavelength, and hence the Th 230 energy levels are more tightly bound than the corresponding levels of Th 232. A summary is given of isotope shift data.

© 1953 Optical Society of America

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References

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  1. See, for example, P. Brix and H. Kopfermann, Anniversary Publication on the Occasion of the 200th Year of the Academy of Science, Göttingen, 1951.
  2. J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
    [Crossref]
  3. M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
    [Crossref]
  4. H. Schuler and J. E. Keyston, Z. Physik 70, 1 (1931).
    [Crossref]
  5. D. A. Jackson, Z. Physik 75, 223 (1932).
    [Crossref]
  6. H. Schuler and E. G. Jones, Z. Physik 74, 631 (1932).
    [Crossref]
  7. J. L. Rose and R. K. Stranathan, Phys. Rev. 49, 916 (1936).
    [Crossref]
  8. Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
    [Crossref]
  9. B. Jaeckel and H. Kopferman, Z. Physik 99, 492 (1936).
    [Crossref]
  10. S. Tolansky and E. Lee, Proc. Roy. Soc. (London) A158, 110 (1937).
    [Crossref]
  11. D. R. Long and D. D. Smith, unpublished material, Oak Ridge, Tennessee.
  12. Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
    [Crossref]
  13. See, for example, J. J. Katz and E. Rabinowitch, The Chemistry of Uranium (McGraw-Hill Book Company, Inc., New York, 1951).
  14. McNally, Harrison, and Park, J. Opt. Soc. Am. 32, 334 (1942);J. R. McNally, J. Opt. Soc. Am. 35, 390 (1945).
    [Crossref]
  15. deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
    [Crossref]
  16. P. F. A. Klinkenberg and R. J. Lang, Physica 15, 774 (1949).
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  17. MIT Wavelength Tables (John Wiley and Sons, New York, 1939).
  18. Y. Eisenberg, Physica 18, 177 (1952).
    [Crossref]

1952 (1)

Y. Eisenberg, Physica 18, 177 (1952).
[Crossref]

1950 (1)

Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
[Crossref]

1949 (3)

M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
[Crossref]

P. F. A. Klinkenberg and R. J. Lang, Physica 15, 774 (1949).
[Crossref]

Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
[Crossref]

1943 (1)

deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
[Crossref]

1942 (1)

1937 (1)

S. Tolansky and E. Lee, Proc. Roy. Soc. (London) A158, 110 (1937).
[Crossref]

1936 (2)

B. Jaeckel and H. Kopferman, Z. Physik 99, 492 (1936).
[Crossref]

J. L. Rose and R. K. Stranathan, Phys. Rev. 49, 916 (1936).
[Crossref]

1932 (3)

J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
[Crossref]

D. A. Jackson, Z. Physik 75, 223 (1932).
[Crossref]

H. Schuler and E. G. Jones, Z. Physik 74, 631 (1932).
[Crossref]

1931 (1)

H. Schuler and J. E. Keyston, Z. Physik 70, 1 (1931).
[Crossref]

Adams,

Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
[Crossref]

Anderson,

Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
[Crossref]

Breit, G.

J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
[Crossref]

Brix, P.

See, for example, P. Brix and H. Kopfermann, Anniversary Publication on the Occasion of the 200th Year of the Academy of Science, Göttingen, 1951.

Burkhart,

Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
[Crossref]

Crawford, M. F.

M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
[Crossref]

deBruin,

deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
[Crossref]

Eisenberg, Y.

Y. Eisenberg, Physica 18, 177 (1952).
[Crossref]

Harrison,

Jackson, D. A.

D. A. Jackson, Z. Physik 75, 223 (1932).
[Crossref]

Jaeckel, B.

B. Jaeckel and H. Kopferman, Z. Physik 99, 492 (1936).
[Crossref]

Jones, E. G.

H. Schuler and E. G. Jones, Z. Physik 74, 631 (1932).
[Crossref]

Katz, J. J.

See, for example, J. J. Katz and E. Rabinowitch, The Chemistry of Uranium (McGraw-Hill Book Company, Inc., New York, 1951).

Keyston, J. E.

H. Schuler and J. E. Keyston, Z. Physik 70, 1 (1931).
[Crossref]

Klinkenberg,

deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
[Crossref]

Klinkenberg, P. F. A.

P. F. A. Klinkenberg and R. J. Lang, Physica 15, 774 (1949).
[Crossref]

Kopferman, H.

B. Jaeckel and H. Kopferman, Z. Physik 99, 492 (1936).
[Crossref]

Kopfermann, H.

See, for example, P. Brix and H. Kopfermann, Anniversary Publication on the Occasion of the 200th Year of the Academy of Science, Göttingen, 1951.

Lang, R. J.

P. F. A. Klinkenberg and R. J. Lang, Physica 15, 774 (1949).
[Crossref]

Lee, E.

S. Tolansky and E. Lee, Proc. Roy. Soc. (London) A158, 110 (1937).
[Crossref]

Long, D. R.

D. R. Long and D. D. Smith, unpublished material, Oak Ridge, Tennessee.

Manning,

Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
[Crossref]

McNally,

Park,

Rabinowitch, E.

See, for example, J. J. Katz and E. Rabinowitch, The Chemistry of Uranium (McGraw-Hill Book Company, Inc., New York, 1951).

Rose, J. L.

J. L. Rose and R. K. Stranathan, Phys. Rev. 49, 916 (1936).
[Crossref]

Rosenthal, J. E.

J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
[Crossref]

Schawlow, A. L.

M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
[Crossref]

Schuler, H.

H. Schuler and E. G. Jones, Z. Physik 74, 631 (1932).
[Crossref]

H. Schuler and J. E. Keyston, Z. Physik 70, 1 (1931).
[Crossref]

Schuurmans,

deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
[Crossref]

Smith, D. D.

D. R. Long and D. D. Smith, unpublished material, Oak Ridge, Tennessee.

Stranathan, R. K.

J. L. Rose and R. K. Stranathan, Phys. Rev. 49, 916 (1936).
[Crossref]

Stukenbroeker,

Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
[Crossref]

Tolansky, S.

S. Tolansky and E. Lee, Proc. Roy. Soc. (London) A158, 110 (1937).
[Crossref]

Watson,

Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
[Crossref]

J. Opt. Soc. Am. (1)

Phys. Rev. (5)

Burkhart, Stukenbroeker, and Adams, Phys. Rev. 75, 83 (1949).
[Crossref]

J. E. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
[Crossref]

M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
[Crossref]

J. L. Rose and R. K. Stranathan, Phys. Rev. 49, 916 (1936).
[Crossref]

Manning, Anderson, and Watson, Phys. Rev. 78, 417 (1950).
[Crossref]

Physica (2)

P. F. A. Klinkenberg and R. J. Lang, Physica 15, 774 (1949).
[Crossref]

Y. Eisenberg, Physica 18, 177 (1952).
[Crossref]

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

S. Tolansky and E. Lee, Proc. Roy. Soc. (London) A158, 110 (1937).
[Crossref]

Z. Physik (5)

B. Jaeckel and H. Kopferman, Z. Physik 99, 492 (1936).
[Crossref]

H. Schuler and J. E. Keyston, Z. Physik 70, 1 (1931).
[Crossref]

D. A. Jackson, Z. Physik 75, 223 (1932).
[Crossref]

H. Schuler and E. G. Jones, Z. Physik 74, 631 (1932).
[Crossref]

deBruin, Schuurmans, and Klinkenberg, Z. Physik 121, 667 (1943).
[Crossref]

Other (4)

See, for example, J. J. Katz and E. Rabinowitch, The Chemistry of Uranium (McGraw-Hill Book Company, Inc., New York, 1951).

See, for example, P. Brix and H. Kopfermann, Anniversary Publication on the Occasion of the 200th Year of the Academy of Science, Göttingen, 1951.

MIT Wavelength Tables (John Wiley and Sons, New York, 1939).

D. R. Long and D. D. Smith, unpublished material, Oak Ridge, Tennessee.

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Figures (3)

F. 1
F. 1

Photograph of Th source showing inlet valve (A) and evacuation route of air from source (B) to canister.

F. 2
F. 2

Comparison spectrum of normal Th to spectrum of 13 percent Th and Th 232, showing isotope shift.

F. 3
F. 3

Approximate range of isotope shifts as a function of electronic configurations.

Tables (6)

Tables Icon

Table I Isotope shifts in Th I.

Tables Icon

Table IIA Isotope shifts in Th II (Group A).

Tables Icon

Table IIB Isotope shifts in Th II (Group B).

Tables Icon

Table III Relative level shifts in Th I.

Tables Icon

Table IVA Relative level shifts in Th II, Group A.

Tables Icon

Table IVB Relative level shifts in Th II, Group B.

Equations (409)

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

a 4 F 3 1 2 24757 °
a 2 D 1 1 2 20686 °
a 4 F 4 1 2 27249 °
a 4 F 2 1 2 22685 °
a 4 F 3 1 2 25440 °
a 4 F 2 1 2 23012 °
a 4 F 1 1 2 24132 °
a 4 F 3 1 2 26424 °
a 2 D 2 1 2 26424 °
a 4 P 2 1 2 31800 °
a 2 F 2 1 2 31353 °
a 2 D 2 1 2 26965 °
a 4 F 2 1 2 24463 °
a 2 D 1 1 2 23012 °
a 4 F 1 1 2 24873 °
a 4 F 2 1 2 24873 °
a 2 D 1 1 2 23372 °
a 4 F 2 1 2 25188 °
a 4 P 2 1 2 32957 °
a 4 F 2 1 2 25440 °
a 2 D 1 1 2 24132 °
a 2 D 1 1 2 24414 °
a 2 D 1 1 2 24463 °
b 4 F 1 1 2 31625 °
a 4 F 1 1 2 26626 °
a 2 D 1 1 2 24873 °
a 4 P 1 1 2 32933 °
a 2 D 1 1 2 25188 °
a 2 D 1 1 2 25440 °
a 2 D 2 1 2 29720 °
b 2 D 2 1 2 39396 °
a 4 F 1 1 2 28243 °
a 2 D 1 1 2 26424 °
a 2 D 1 1 2 26626 °
a 4 F 2 1 2 28243 °
a 2 D 1 1 2 26965 °
b 4 F 2 1 2 36687 °
a 2 P 1 2 35199 °
a 4 P 2 1 2 36444 °
a 4 P 2 1 2 36581 °
a 4 F 2 1 2 29095 °
a 4 F 3 1 2 31800 °
a 2 D 2 1 2 31810 °
a 4 F 2 1 2 29720 °
a 2 D 1 1 2 28243 °
a 4 P 2 1 2 37601 °
a 4 P 1 1 2 36581 °
a 4 F 3 1 2 32957 °
b 2 D 2 1 2 42112 °
a 2 D 2 1 2 32957 °
b 2 D 2 1 2 42219 °
a 2 D 1 1 2 29095 °
a 4 F 1 1 2 31353 °
a 4 F 2 1 2 31353
a 4 F 4 1 2 36193 °
a 4 F 1 1 2 31928 °
a 2 D 2 1 2 35156 °
a 4 F 2 1 2 32957
a 4 F 1 1 2 33355 °
a 4 F 2 1 2 33215
a 4 F 3 1 2 36193 °
a 2 D 2 1 2 36583 °
a 4 F 3 1 2 36687 °
a 4 F 4 1 2 39443 °
a 4 F 1 1 2 35156 °
a 4 P 2 1 2 43382 °
a 2 D 1 1 2 34330 °
a 4 F 1 1 2 36390 °
a 4 F 3 1 2 38764 °
a 2 D 2 1 2 38764 °
a 4 F 1 1 2 36687 °
a 4 F 2 1 2 36687 °
a 4 F 4 1 2 41448 °
a 2 D 2 1 2 40184
a 4 F 4 1 2 42318
a 2 D 2 1 2 40472
a 2 D 1 1 2 36390
a 4 F 3 1 2 40707
a 2 D 1 1 2 36581
a 2 D 1 1 2 37130
a 2 D 1 1 2 37716
a 2 D 2 1 2 42944
a 2 F 0 2 1 2 41676
a 2 F 0 2 1 2 40644
a 2 F 0 2 1 2 40411
a 2 F 0 3 1 2 43803
a 2 F 0 2 1 2 39150
a 4 H 0 3 1 2 40644
a 2 F 0 3 1 2 38757
a 2 F 0 3 1 2 38728
a 2 F 0 3 1 2 42518
a 2 F 0 3 1 2 42351
a 2 F 0 3 1 2 38389
a 2 G 0 4 1 2 43127
a 2 F 0 3 1 2 38291
a 2 F 0 3 1 2 38165
a 4 H 0 5 1 2 43809
a 2 F 0 2 1 2 38104
a 2 F 0 5 1 2 37944
a 4 F 0 3 1 2 43096
a 2 F 0 3 1 2 41688
a 4 F 0 4 1 2 45734
a 2 F 0 3 1 2 41488
a 4 F 0 3 1 2 42751
a 2 F 0 3 1 2 41328
a 4 H 0 5 1 2 43127
a 4 H 0 6 1 2 46216
a 2 F 0 2 1 2 37277
a 2 F 0 3 1 2 41047
a 4 H 0 4 1 2 39352
a 4 F 0 4 1 2 45126
a 2 G 0 3 1 2 41688
a 4 H 0 5 1 2 42645
b 2 F 0 2 1 2 43096
a 4 F 0 2 1 2 39700
a 4 F 0 3 1 2 41909
a 4 F 0 1 1 2 38866
a 4 H 0 4 1 2 38862
a 4 F 0 1 1 2 38835
b 2 F 0 2 1 2 42751
a 4 F 0 1 1 2 38757
a 4 H 0 3 1 2 38180
a 2 G 0 4 1 2 41047
a 4 H 0 4 1 2 37944
a 4 H 0 4 1 2 38389
a 4 F 0 3 1 2 41398
a 4 H 0 3 1 2 37840
a 2 F 0 2 1 2 36065
a 4 H 0 4 1 2 38179
a 2 F 0 2 1 2 35878
a 2 F 0 3 1 2 35741
a 4 H 0 5 1 2 41223
a 4 F 0 2 1 2 38291
a 4 H 0 3 1 2 37063
b 4 H 0 3 1 2 43227
a 4 G 0 4 1 2 44177
a 2 G 0 4 1 2 39939
a 4 H 0 3 1 2 36809
a 4 H 0 4 1 2 37063
a 2 G 0 3 1 2 39552
a 2 G 0 3 1 2 39458
a 4 G 0 2 1 2 39458
a 4 F 0 3 1 2 39458
a 2 F 0 3 1 2 38104
a 4 F 0 4 1 2 42200
a 2 G 0 4 1 2 38862
a 2 F 0 2 1 2 34020
a 2 F 0 2 1 2 33636
a 2 F 0 3 1 2 37465
a 4 F 0 1 1 2 35741
a 2 D 0 2 1 2 41487
a 2 G 0 3 1 2 38165
a 2 G 0 4 1 2 38165
a 4 H 0 4 1 2 35545
a 4 G 0 5 1 2 44177
a 4 H 0 4 1 2 35525
a 4 H 0 6 1 2 42146
a 4 G 0 2 1 2 38291
a 2 F 0 3 1 2 37063
a 4 D 0 2 1 2 43227
b 2 F 0 2 1 2 39150
a 2 F 0 3 1 2 36809
a 4 H 0 5 1 2 38518
a 2 G 0 3 1 2 37465
a 2 F 0 2 1 2 32736
a 4 H 0 3 1 2 34270
a 4 H 0 4 1 2 34726
b 4 H 0 4 1 2 43246
a 4 H 0 5 1 2 38179
a 4 H 0 4 1 2 34661
a 4 G 0 2 1 2 37465
a 4 F 0 1 1 2 37465
a 2 D 0 2 1 2 40216
b 2 F 0 2 1 2 38372
a 2 H 0 5 1 2 42146
a 2 G 0 4 1 2 36809
a 4 H 0 3 1 2 33637
a 4 F 0 4 1 2 39895
a 4 F 0 2 1 2 34726
a 4 H 0 6 1 2 40724
a 4 H 0 6 1 2 40574
b 2 F 0 2 1 2 37787
a 4 F 0 4 1 2 39458
a 4 H 0 4 1 2 33637
a 2 G 0 4 1 2 36125
a 4 G 0 5 1 2 42200
a 4 G 0 5 1 2 42146
a 2 F 0 2 1 2 31259
a 4 G 0 3 1 2 37840
a 4 G 0 3 1 2 37787
a 4 G 0 4 1 2 39895
a 2 G 0 4 1 2 35525
b 2 F 0 2 1 2 36809
a 4 F 0 2 1 2 33636
a 4 F 0 3 1 2 35741
a 4 H 0 5 1 2 36125
a 4 G 0 4 1 2 39352
b 2 F 0 2 1 2 39553
a 2 D 0 2 1 2 38104
a 4 G 0 4 1 2 39068
a 4 H 0 6 1 2 38862
a 2 H 0 5 1 2 39939
a 2 G 0 4 1 2 34661
b 2 F 0 2 1 2 36066
a 4 H 0 5 1 2 35525
a 4 F 0 4 1 2 37787
a 4 G 0 5 1 2 40574
a 4 G 0 2 1 2 34726
a 4 H 0 6 1 2 38518
b 2 F 0 2 1 2 35741
b 2 F 0 3 1 2 38836
a 4 F 0 3 1 2 34726
a 2 H 0 4 1 2 35545
a 2 H 0 4 1 2 35525
a 4 G 0 3 1 2 36065
a 2 F 0 3 1 2 33209
a 4 F 0 1 1 2 31259
a 2 D 0 1 1 2 36065
a 4 H 0 5 1 2 34661
a 4 F 0 2 1 2 31753
a 2 F 0 3 1 2 32735
a 2 F 0 2 1 2 28823
a 4 H 0 3 1 2 30452
b 2 F 0 2 1 2 34661
b 2 F 0 2 1 2 34726
a 4 G 0 2 1 2 33637
a 2 H 0 5 1 2 38518
a 4 F 0 2 1 2 31259
a 4 F 0 3 1 2 33637
a 4 H 0 4 1 2 30452
a 2 H 0 4 1 2 34270
a 4 F 0 4 1 2 36125
a 2 F 0 2 1 2 28026
a 2 G 0 3 1 2 32736
a 2 F 0 2 1 2 28011
a 4 F 0 3 1 2 33209
a 2 F 0 3 1 2 31773
a 4 H 0 3 1 2 29514
a 2 F 0 2 1 2 27631
a 2 F 0 5 1 2 37562
b 2 F 0 2 1 2 33637
a 2 F 0 2 1 2 27256
a 4 G 0 4 1 2 36125
a 4 G 0 3 1 2 33637
b 2 F 0 2 1 2 32959
a 4 F 0 1 1 2 28963
a 2 H 0 4 1 2 32620
a 2 F 0 2 1 2 29515
a 4 I 0 4 1 2 36309
a 2 H 0 4 1 2 30452
a 2 D 1 1 2
a 2 D 2 1 2
a 4 F 1 1 2
a 4 F 2 1 2
a 4 F 3 1 2
a 4 F 4 1 2
a 4 P 2 1 2
b 4 F 2 1 2
a 2 F 2 1 2
42 0 2 1 2
45 0 2 1 2
G 0 3 1 2
48 0 1 1 2
49 0 1 1 2
53 0 1 1 2
54 0 1 1 2
55 0 2 1 2
G 0 4 1 2
57 0 2 1 2
59 0 1 1 2
61 0 2 1 2
D 0 2 1 2
D 0 1 2
64 0 1 1 2
D 0 3 1 2
67 0 2 1 2
69 0 2 1 2
70 0 1 1 2
F 0 1 1 2
76 0 3 1 2
77 0 2 1 2
² D 0 1 1 2
80 0 2 1 2
81 0 3 1 2
82 0 1 1 2
² F 0 2 1 2
P 0 1 2
F 0 2 1 2
F 0 1 2
F 0 1 1 2
² P 0 1 1 2
1 1 2
F 0 3 1 2
G 0 2 1 2
D 0 1 2
D 0 1 1 2
² P 0 1 2
G 0 3 1 2
G 0 4 1 2
109 0 3 1 2
D 0 1 1 2
F 0 3 1 2
F 0 4 1 2
D 0 3 1 2
D 0 2 1 2
a 2 F 0 2 1 2
a 2 F 0 3 1 2
a 4 H 0 3 1 2
a 4 H 0 4 1 2
a 4 H 0 5 1 2
a 4 H 0 6 1 2
a 4 F 0 1 1 2
a 4 F 0 2 1 2
a 4 F 0 3 1 2
a 4 F 0 4 1 2
a 2 G 0 3 1 2
a 2 G 0 4 1 2
a 4 G 0 2 1 2
a 4 G 0 3 1 2
a 4 G 0 4 1 2
a 4 G 0 5 1 2
a 2 H 0 4 1 2
a 2 H 0 5 1 2
a 2 D 0 1 1 2
a 2 D 0 2 1 2
b 2 F 0 2 1 2
b 2 F 0 3 1 2
G 3 1 2
F 1 1 2
F 1 1 2
a 107 2 1 2
F 2 1 2
109 2 1 2
111 4 1 2
112 4 1 2
114 2 1 2
115 2 1 2
116 4 1 2
118 5 1 2
119 3 1 2
120 1 1 2
121 3 1 2
122 3 1 2
124 1 1 2
126 4 1 2
130 5 1 2
131 3 1 2
134 5 1 2
135 4 1 2
136 2 1 2
² G 3 1 2
139 2 1 2
140 4 1 2
143 3 1 2
145 4 1 2
146 3 1 2
147 2 1 2
149 5 1 2
152 3 1 2
b 152 4 1 2
153 2 1 2
154 2 1 2
155 3 1 2
156 4 1 2
157 3 1 2
158 1 1 2
159 3 1 2
16 0 6 1 2
161 2 1 2
163 1 1 2
164 3 1 2
G 5 1 2
167 1 2
168 3 1 2
169 1 1 2
a 169 5 1 2
171 3 1 2
² G 4 1 2
173 2 1 2
174 4 1 2
175 5 1 2
a 176 2 1 2
179 3 1 2
18 0 5 1 2
181 2 1 2
182 6 1 2
183 2 1 2
184 4 1 2
b 184 5 1 2
185 2 1 2
a 185 4 1 2
186 3 1 2
187 1 1 2
188 3 1 2
a 188 4 1 2
189 5 1 2
a 189 4 1 2
19 0 2 1 2
191 3 1 2
a 191 6 1 2
c 191 3 1 2
193 2 1 2
194 5 1 2
197 3 1 2
199 4 1 2
a 199 5 1 2
a 20 5 4 1 2
20 8 5 1 2
b 20 8 5 1 2