Abstract

A new optical method for the precise determination of hyperfine structure and isotope shifts has been developed. A selective method of excitation, accomplished by means of a source of a single isotope operated in a magnetic field, allows the various hyperfine components to be recorded one or a few at a time. These features permit the use of long interferometers (ours were about 218 mm) of high resolving power where the whole order difference between two of the components may be very large. The isotope shifts in the 2537-Å line of mercury have been measured with a precision unequalled previously. The hyperfine structure of the odd isotopes has been measured with equal precision, though in this case the precision is less than that which has been achieved by radio frequency, double-resonance experiments. Our results are in good agreement with the double-resonance results, a fact which gives added confidence in our isotope shift results. The structure of the line relative to the isotope 198 is: 199A(−513.99±0.43); 204(−510.77±0.43); 201a(−488.96±0.33); 202(−336.96±0.15); 200(−160.29±0.15); 201b(−22.56±0.09); 198(0.00); 199B(224.40±0.23); 201c(229.23±0.51); where the units are millikaysers. The stated limits indicate the spread of the individual determinations about the mean value of the quantity as measured by their standard deviations. The magnetic dipole interaction constants for the 63P1° state are: A(199)=492.24±0.20 mK and A(201)=−181.88±0.13 mK. The nuclear magnetic moments calculated from these constants by means of the theory of Breit and Wills for intermediate coupling are: μI(199)=0.450 nm and μI(210)=−0.499 nm. The agreement between these values and the nuclear magnetic resonance values of Cagnac and Brossel (about 10%) is presumably an indication of the reliability of the theory for this case. The electric quadrupole interaction constant for the 63P1° state of Hg201 is B=−9.35±0.18 mK. This leads to the value for the quadrupole moment: Q=0.49 barn.

© 1963 Optical Society of America

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References

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  1. W. G. Schweitzer, J. Opt. Soc. Am. 51, 692 (1961).
    [Crossref]
  2. P. Jacquinot and C. Dufour, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 2, 91 (1948).
  3. In Eq. (1) we have neglected the index of refraction of air in the interferometer since in all of the situations we are contemplating there will be so little air inside the interferometer that the index will be negligibly different from unity.
  4. R. L. Barger and K. W. Meissner, J. Opt. Soc. Am. 48, 22 (1958).
    [Crossref]
  5. J. Blaise, J. Opt. Soc. Am. 49, 1130 (1959).
  6. P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
    [Crossref]
  7. K. W. Meissner, Rev. Mod. Phys. 14, 68 (1942).
    [Crossref]
  8. R. L. Barger and K. G. Kessler, J. Opt. Soc. Am. 50, 651 (1960).
    [Crossref]
  9. K. G. Kessler, R. L. Barger, and W. G. Schweitzer, IRE Trans. Instr. 7, 181 (1958).
    [Crossref]
  10. R. Minkowski and H. Bruk, Z. Physik 95, 274 (1935).
    [Crossref]
  11. K. G. Kessler and W. G. Schweitzer, J. Opt. Soc. Am. 49, 199 (1959).
    [Crossref]
  12. For more detail refer to the author’s Ph.D. thesis, University of Maryland, 1962 (unpublished).
  13. H. B. G. Casimir, On the Interaction between Atomic Nuclei and Electrons (Teylers Tweede Genootshap, Haarlem, 1936).
  14. C. Stager and R. Kohler, Bull. Am. Phys. Soc. 5, 274 (1960).
  15. A comprehensive review of this material may be found in H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958).
  16. J. Blaise, Ann. Phys. 3, 1019 (1958).
  17. A. C. Melissinos, Phys. Rev. 115, 126 (1959).
    [Crossref]
  18. K. Murakawa, J. Phys. Soc. Japan 14, 1624 (1959).
    [Crossref]
  19. S. Goudsmit, Phys. Rev. 43, 636 (1933).
    [Crossref]
  20. E. Fermi and E. Segré, Z. Physik 82, 729 (1933).
    [Crossref]
  21. J. Rosenthal and G. Breit, Phys. Rev. 41, 459 (1932).
    [Crossref]
  22. M. F. Crawford and A. L. Schawlow, Phys. Rev. 76, 1310 (1949).
    [Crossref]
  23. A. Bohr and V. Weisskopf, Phys. Rev. 77, 94 (1950).
    [Crossref]
  24. G. Breit and L. A. Wills, Phys. Rev. 44, 470 (1933).
    [Crossref]
  25. J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952).
    [Crossref]
  26. W. G. Proctor and F. C. Yu, Phys. Rev. 81, 20 (1951).
    [Crossref]
  27. B. Cagnac and J. Brossel, Compt. Rend. 249, 77 (1959).
  28. J. Blaise and H. Chantrel, J. Phys. Radium 18, 193 (1957).
    [Crossref]
  29. H. C. Wolfe, Phys. Rev. 41, 443 (1932).
    [Crossref]
  30. M. McDermott and W. L. Lichten, Phys. Rev. 119, 134 (1960).
    [Crossref]
  31. R. M. Sternheimer, Phys. Rev. 95, 736 (1954).
    [Crossref]
  32. R. M. Sternheimer, Phys. Rev. 105, 158 (1957).
    [Crossref]
  33. H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
    [Crossref]
  34. R. V. Pound and G. K. Wertheim, Phys. Rev. 102, 396 (1956).
    [Crossref]

1961 (1)

1960 (3)

R. L. Barger and K. G. Kessler, J. Opt. Soc. Am. 50, 651 (1960).
[Crossref]

C. Stager and R. Kohler, Bull. Am. Phys. Soc. 5, 274 (1960).

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

1959 (5)

B. Cagnac and J. Brossel, Compt. Rend. 249, 77 (1959).

A. C. Melissinos, Phys. Rev. 115, 126 (1959).
[Crossref]

K. Murakawa, J. Phys. Soc. Japan 14, 1624 (1959).
[Crossref]

K. G. Kessler and W. G. Schweitzer, J. Opt. Soc. Am. 49, 199 (1959).
[Crossref]

J. Blaise, J. Opt. Soc. Am. 49, 1130 (1959).

1958 (4)

P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
[Crossref]

R. L. Barger and K. W. Meissner, J. Opt. Soc. Am. 48, 22 (1958).
[Crossref]

K. G. Kessler, R. L. Barger, and W. G. Schweitzer, IRE Trans. Instr. 7, 181 (1958).
[Crossref]

J. Blaise, Ann. Phys. 3, 1019 (1958).

1957 (2)

J. Blaise and H. Chantrel, J. Phys. Radium 18, 193 (1957).
[Crossref]

R. M. Sternheimer, Phys. Rev. 105, 158 (1957).
[Crossref]

1956 (1)

R. V. Pound and G. K. Wertheim, Phys. Rev. 102, 396 (1956).
[Crossref]

1954 (2)

H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
[Crossref]

R. M. Sternheimer, Phys. Rev. 95, 736 (1954).
[Crossref]

1952 (1)

J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952).
[Crossref]

1951 (1)

W. G. Proctor and F. C. Yu, Phys. Rev. 81, 20 (1951).
[Crossref]

1950 (1)

A. Bohr and V. Weisskopf, Phys. Rev. 77, 94 (1950).
[Crossref]

1949 (1)

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

1948 (1)

P. Jacquinot and C. Dufour, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 2, 91 (1948).

1942 (1)

K. W. Meissner, Rev. Mod. Phys. 14, 68 (1942).
[Crossref]

1935 (1)

R. Minkowski and H. Bruk, Z. Physik 95, 274 (1935).
[Crossref]

1933 (3)

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

S. Goudsmit, Phys. Rev. 43, 636 (1933).
[Crossref]

E. Fermi and E. Segré, Z. Physik 82, 729 (1933).
[Crossref]

1932 (2)

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

H. C. Wolfe, Phys. Rev. 41, 443 (1932).
[Crossref]

Barger, R. L.

Bitter, F.

P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
[Crossref]

J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952).
[Crossref]

Blaise, J.

J. Blaise, J. Opt. Soc. Am. 49, 1130 (1959).

J. Blaise, Ann. Phys. 3, 1019 (1958).

J. Blaise and H. Chantrel, J. Phys. Radium 18, 193 (1957).
[Crossref]

Bohr, A.

A. Bohr and V. Weisskopf, Phys. Rev. 77, 94 (1950).
[Crossref]

Breit, G.

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

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

Brossel, J.

B. Cagnac and J. Brossel, Compt. Rend. 249, 77 (1959).

J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952).
[Crossref]

Bruk, H.

R. Minkowski and H. Bruk, Z. Physik 95, 274 (1935).
[Crossref]

Cagnac, B.

B. Cagnac and J. Brossel, Compt. Rend. 249, 77 (1959).

Casimir, H. B. G.

H. B. G. Casimir, On the Interaction between Atomic Nuclei and Electrons (Teylers Tweede Genootshap, Haarlem, 1936).

Chantrel, H.

J. Blaise and H. Chantrel, J. Phys. Radium 18, 193 (1957).
[Crossref]

Crawford, M. F.

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

Dehmelt, H. G.

H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
[Crossref]

Dufour, C.

P. Jacquinot and C. Dufour, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 2, 91 (1948).

Fermi, E.

E. Fermi and E. Segré, Z. Physik 82, 729 (1933).
[Crossref]

Gordy, W.

H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
[Crossref]

Goudsmit, S.

S. Goudsmit, Phys. Rev. 43, 636 (1933).
[Crossref]

Jacquinot, P.

P. Jacquinot and C. Dufour, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 2, 91 (1948).

Kessler, K. G.

Kohler, R.

C. Stager and R. Kohler, Bull. Am. Phys. Soc. 5, 274 (1960).

Kopfermann, H.

A comprehensive review of this material may be found in H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958).

Lichten, W. L.

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

McDermott, M.

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

Meissner, K. W.

Melissinos, A. C.

A. C. Melissinos, Phys. Rev. 115, 126 (1959).
[Crossref]

P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
[Crossref]

Minkowski, R.

R. Minkowski and H. Bruk, Z. Physik 95, 274 (1935).
[Crossref]

Murakawa, K.

K. Murakawa, J. Phys. Soc. Japan 14, 1624 (1959).
[Crossref]

Pound, R. V.

R. V. Pound and G. K. Wertheim, Phys. Rev. 102, 396 (1956).
[Crossref]

Proctor, W. G.

W. G. Proctor and F. C. Yu, Phys. Rev. 81, 20 (1951).
[Crossref]

Robinson, H.

H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
[Crossref]

Rosenthal, J.

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

Sagalyn, P. L.

P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
[Crossref]

Schawlow, A. L.

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

Schweitzer, W. G.

Segré, E.

E. Fermi and E. Segré, Z. Physik 82, 729 (1933).
[Crossref]

Stager, C.

C. Stager and R. Kohler, Bull. Am. Phys. Soc. 5, 274 (1960).

Sternheimer, R. M.

R. M. Sternheimer, Phys. Rev. 105, 158 (1957).
[Crossref]

R. M. Sternheimer, Phys. Rev. 95, 736 (1954).
[Crossref]

Weisskopf, V.

A. Bohr and V. Weisskopf, Phys. Rev. 77, 94 (1950).
[Crossref]

Wertheim, G. K.

R. V. Pound and G. K. Wertheim, Phys. Rev. 102, 396 (1956).
[Crossref]

Wills, L. A.

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

Wolfe, H. C.

H. C. Wolfe, Phys. Rev. 41, 443 (1932).
[Crossref]

Yu, F. C.

W. G. Proctor and F. C. Yu, Phys. Rev. 81, 20 (1951).
[Crossref]

Ann. Phys. (1)

J. Blaise, Ann. Phys. 3, 1019 (1958).

Bull. Am. Phys. Soc. (1)

C. Stager and R. Kohler, Bull. Am. Phys. Soc. 5, 274 (1960).

Compt. Rend. (1)

B. Cagnac and J. Brossel, Compt. Rend. 249, 77 (1959).

IRE Trans. Instr. (1)

K. G. Kessler, R. L. Barger, and W. G. Schweitzer, IRE Trans. Instr. 7, 181 (1958).
[Crossref]

J. Opt. Soc. Am. (5)

J. Phys. Radium (1)

J. Blaise and H. Chantrel, J. Phys. Radium 18, 193 (1957).
[Crossref]

J. Phys. Soc. Japan (1)

K. Murakawa, J. Phys. Soc. Japan 14, 1624 (1959).
[Crossref]

J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) (1)

P. Jacquinot and C. Dufour, J. Rech. Centre Natl. Rech. Sci. Lab. Bellevue (Paris) 2, 91 (1948).

Phys. Rev. (15)

P. L. Sagalyn, A. C. Melissinos, and F. Bitter, Phys. Rev. 109, 375 (1958).
[Crossref]

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

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

A. Bohr and V. Weisskopf, Phys. Rev. 77, 94 (1950).
[Crossref]

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

J. Brossel and F. Bitter, Phys. Rev. 86, 308 (1952).
[Crossref]

W. G. Proctor and F. C. Yu, Phys. Rev. 81, 20 (1951).
[Crossref]

S. Goudsmit, Phys. Rev. 43, 636 (1933).
[Crossref]

A. C. Melissinos, Phys. Rev. 115, 126 (1959).
[Crossref]

H. C. Wolfe, Phys. Rev. 41, 443 (1932).
[Crossref]

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

R. M. Sternheimer, Phys. Rev. 95, 736 (1954).
[Crossref]

R. M. Sternheimer, Phys. Rev. 105, 158 (1957).
[Crossref]

H. G. Dehmelt, H. Robinson, and W. Gordy, Phys. Rev. 93, 480 (1954).
[Crossref]

R. V. Pound and G. K. Wertheim, Phys. Rev. 102, 396 (1956).
[Crossref]

Rev. Mod. Phys. (1)

K. W. Meissner, Rev. Mod. Phys. 14, 68 (1942).
[Crossref]

Z. Physik (2)

R. Minkowski and H. Bruk, Z. Physik 95, 274 (1935).
[Crossref]

E. Fermi and E. Segré, Z. Physik 82, 729 (1933).
[Crossref]

Other (4)

A comprehensive review of this material may be found in H. Kopfermann, Nuclear Moments (Academic Press Inc., New York, 1958).

For more detail refer to the author’s Ph.D. thesis, University of Maryland, 1962 (unpublished).

H. B. G. Casimir, On the Interaction between Atomic Nuclei and Electrons (Teylers Tweede Genootshap, Haarlem, 1936).

In Eq. (1) we have neglected the index of refraction of air in the interferometer since in all of the situations we are contemplating there will be so little air inside the interferometer that the index will be negligibly different from unity.

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Figures (15)

Fig. 1
Fig. 1

Alternate arrangement for photoelectric scanning of Fabry–Perot interference fringes.

Fig. 2
Fig. 2

Fabry–Perot scanning curve for two narrow lines separated by Δν wavenumber units.

Fig. 3
Fig. 3

Structure of the 2537-Å line of natural mercury.

Fig. 4
Fig. 4

Energy levels of mercury which give rise to the 2537-Å line.

Fig. 5
Fig. 5

Schematic diagram of the apparatus used for measuring the hyperfine structure and isotope shifts in the 2537-Å line of mercury.

Fig. 6
Fig. 6

Photocell outputs with a beam of a single isotope.

Fig. 7
Fig. 7

Absorption of radiation from a variable wavelength source by the atomic beam. (Example is for B≈2300 G.)

Fig. 8
Fig. 8

Scanning scheme made possible by the use of a Hg198 filter. If one of the desired components is 198, the filter is taken out for the 198 fringes and put in for the other fringes.

Fig. 9
Fig. 9

Atomic beam chamber. (Main walls are 1 2 in. thick but are shown thin for simplicity.)

Fig. 10
Fig. 10

Transmittance of a 2.5-cm layer of Hg198 vapor, at room temperature at 2537-Å. The dashed curve represents the approximate width and shape of the 2537-Å line from the cooled electrodeless discharge lamp.

Fig. 11
Fig. 11

Transmittance of a 2.5-cm layer of Hg198 vapor, at room temperature, for light at 2537-Å polarized parallel to a magnetic field acting on the vapor.

Fig. 12
Fig. 12

Transmittance of a 2.5-cm layer of Hg198 vapor, at room temperature, at 2537-Å, for light polarized perpendicular to the direction of a magnetic field of 740 G acting on the vapor. The field is also perpendicular to the direction of propagation of light through the vapor. The shaded region is the area under the product of the two components and represents the “band-pass” of the filter. The dashed curve represents the approximate width and shape of the 2537-Å line from the cooled electrodeless discharge lamp.

Fig. 13
Fig. 13

Electronic circuit arrangement.

Fig. 14
Fig. 14

Positions of the emission line σ component used to observe the 201a absorption fringes and the 199A–204 pair.

Fig. 15
Fig. 15

Synthesized curves corresponding to the observed patterns for the pair 199B–201c. The large dashed curve represents the 199B component alone and the small dashed curve represents the 201c component alone. The 199B–201c separation is 4.83 mK.

Tables (6)

Tables Icon

Table I Hyperfine structure and isotope shifts relative to 198.

Tables Icon

Table II Relative isotope shifts.

Tables Icon

Table III Hyperfine splittings.

Tables Icon

Table IV Magnetic dipole and electric quadrupole interaction constants for the 63P1° state of Hg199 and Hg201.

Tables Icon

Table V Relative isotope shift ratios compared with theory and with results of other authors. Relative isotope shifts (RIS) compared with the calculated values for a uniform volume distribution of charge in a spherical nucleus whose radius varies as R 0 A 1 3, where R0 is a constant. The numbers given are the ratios [RIS (Isotope Pair)/RIS(200–202)]. Also given, for comparison, are the results of Blaise, Melissinos, and Murakawa. My limits are standard deviations for a single determination of the ratio computed from the standard deviations of the original measurements. Those of Blaise are given just as he states them. Melissinos and Murakawa do not state limits of error.

Tables Icon

Table VI Nuclear electric quadrupole moment of Hg201.

Equations (26)

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Δ ν = ( 1 / 2 t ) Δ p = ( N + ) / 2 t ,
Δ ν β = 0.41 Δ ν v / C .
Δ ν = ± 0.0694 B mK .
W F = W J + A C 2 + B ( 3 / 4 ) C ( C + 1 ) - I ( I + 1 ) J ( J + 1 ) 2 I ( 2 I - 1 ) J ( 2 J - 1 ) .
A = μ I H ( 0 ) I J ;             B = e Q φ J J ( 0 ) .
a s = 8 3 R α 2 Z i Z a 2 n a 3 d n a d n F r ( j , Z i ) ( 1 - δ ) ( 1 - ) m m p 1 I μ I μ n ,
a l j = l ( l + 1 ) j ( j + 1 ) ζ l Z i F r ( j , Z i ) H r ( l , Z i ) m m p 1 I μ I μ n .
a = a l + 1 2 ;             a = a l - 1 2 .
δ = ( l + 1 2 ) ζ l .
ψ ( P 3 1 ) = c 1 ψ 1 ( 1 2 , 3 2 ) + c 2 ψ 2 ( 1 2 , 1 2 )
c 1 = sin ( θ 0 - θ ) ;             c 2 = cos ( θ 0 - θ ) .
cos 2 θ = l ( l + 1 ) ( g - 1 ) .
A ( P 3 1 ) = ( 1 / 4 ) ( 2 c 2 2 - c 1 2 ) a s + ( 5 / 4 ) c 1 2 a + ( 1 / 2 ) c 2 2 a + 2 c 1 c 2 a .
a = - 1 2 ( 2 l + 1 ) ζ l Z i G r ( l , Z i ) H r ( l , Z i ) m m p 1 I μ I μ n .
μ I μ n = A ( P 3 1 ) ( 1 / 4 ) ( 2 c 2 2 - c 1 2 ) a s μ + ( 5 / 4 ) c 1 2 a μ + ( 1 / 2 ) c 2 2 a μ + 2 c 1 c 2 a μ .
( μ I / μ n ) = A ( P 3 1 ) / ( 0.973 + 0.007 + 0.118 - 0.008 ) ,
μ I ( 199 ) = 0.450 nm .
μ I ( 201 ) = - 0.499 nm .
μ I ( 199 ) NMR = 0.4979 NM .
μ I ( 199 ) NMR = 0.5027 NM .
Q = B / e φ J J ( 0 ) ,
φ J J ( 0 ) = - e [ ( 3 cos 2 θ - 1 ) r 3 ] J J .
φ J J ( 0 ) = e ( c 1 2 R r - 2 2 c 1 c 2 S r ) ( ζ l / 10 μ 0 2 Z i H r ) .
Q = 10 μ 0 2 Z i H r e 2 ( c 1 2 R r - 2 2 c 1 c 2 S r ) B ζ l ,
Q = - 2.25 × 10 - 19 ( B / ζ l ) cm 2 .
Q = 0.49 barn .