Abstract

The frequencies of the different Zeeman components of the neutral calcium metastable (4s, 4p)3P1 and 3P2 levels were measured in a highly homogeneous magnetic field of the order of 0.4 T by a double-resonance technique in an atomic metastable beam. The Landé factor of the two levels was determined as gJ(3P1)=1.5010829(28) and gJ(3P2)=1.5011308(75).

© 1998 Optical Society of America

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References

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  1. G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
    [CrossRef]
  2. L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
    [CrossRef]
  3. F. Strumia, “A proposal for a new absolute frequency standard, using a Mg or Ca atomic beam,” Metrologia 8, 85–90 (1972).
    [CrossRef]
  4. J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
    [CrossRef]
  5. A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
    [CrossRef]
  6. E. R. Cohen and B. N. Taylor, “The 1986 adjustment of the fundamental physical constants,” Rev. Mod. Phys. 59, 1121–1148 (1987).
    [CrossRef]
  7. D. R. Hartree and W. Hartree, “Self-consistent field with exchange for calcium,” Proc. R. Soc. London, Ser. A 164, 167–191 (1938).
    [CrossRef]
  8. J. Sugar and C. Corliss, “Energy levels of calcium, Ca I through Ca XX,” J. Phys. Chem. Ref. Data 8, 865–916 (1979).
    [CrossRef]
  9. G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
    [CrossRef]
  10. D. A. Landman and A. Lurio, “gJ Values of the metastable 3P2 and 1D2 levels of Ca and the 1D2 level of Sr,” J. Opt. Soc. Am. 60, 986 (1970).
    [CrossRef]
  11. A. Abragam and J. H. Van Vleck, “Theory of the microwave Zeeman effect in atomic oxygen,” Phys. Rev. 92, 1448–1455 (1953).
    [CrossRef]
  12. E. W. Otten, “Bestimmung des gJ Faktors im 4s4p 3P1-Term des Ca I-Spektrums mit optischer Doppelresonanz,” Z. Phys. 170, 336–346 (1962).
    [CrossRef]

1993 (1)

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

1989 (1)

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

1988 (1)

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

1987 (1)

E. R. Cohen and B. N. Taylor, “The 1986 adjustment of the fundamental physical constants,” Rev. Mod. Phys. 59, 1121–1148 (1987).
[CrossRef]

1980 (1)

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

1979 (1)

J. Sugar and C. Corliss, “Energy levels of calcium, Ca I through Ca XX,” J. Phys. Chem. Ref. Data 8, 865–916 (1979).
[CrossRef]

1975 (1)

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

1972 (1)

F. Strumia, “A proposal for a new absolute frequency standard, using a Mg or Ca atomic beam,” Metrologia 8, 85–90 (1972).
[CrossRef]

1970 (1)

1962 (1)

E. W. Otten, “Bestimmung des gJ Faktors im 4s4p 3P1-Term des Ca I-Spektrums mit optischer Doppelresonanz,” Z. Phys. 170, 336–346 (1962).
[CrossRef]

1953 (1)

A. Abragam and J. H. Van Vleck, “Theory of the microwave Zeeman effect in atomic oxygen,” Phys. Rev. 92, 1448–1455 (1953).
[CrossRef]

1938 (1)

D. R. Hartree and W. Hartree, “Self-consistent field with exchange for calcium,” Proc. R. Soc. London, Ser. A 164, 167–191 (1938).
[CrossRef]

Abragam, A.

A. Abragam and J. H. Van Vleck, “Theory of the microwave Zeeman effect in atomic oxygen,” Phys. Rev. 92, 1448–1455 (1953).
[CrossRef]

Bava, E.

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

Cohen, E. R.

E. R. Cohen and B. N. Taylor, “The 1986 adjustment of the fundamental physical constants,” Rev. Mod. Phys. 59, 1121–1148 (1987).
[CrossRef]

Corliss, C.

J. Sugar and C. Corliss, “Energy levels of calcium, Ca I through Ca XX,” J. Phys. Chem. Ref. Data 8, 865–916 (1979).
[CrossRef]

Dagdigian, P. J.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Giusfredi, G.

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

Godone, A.

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

Hartree, D. R.

D. R. Hartree and W. Hartree, “Self-consistent field with exchange for calcium,” Proc. R. Soc. London, Ser. A 164, 167–191 (1938).
[CrossRef]

Hartree, W.

D. R. Hartree and W. Hartree, “Self-consistent field with exchange for calcium,” Proc. R. Soc. London, Ser. A 164, 167–191 (1938).
[CrossRef]

Helmcke, J.

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

Ishikawa, J.

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

Ito, N.

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

Kurosu, T.

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

Landman, D. A.

Lurio, A.

Minguzzi, P.

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

Morinaga, A.

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

Novero, C.

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

Otten, E. W.

E. W. Otten, “Bestimmung des gJ Faktors im 4s4p 3P1-Term des Ca I-Spektrums mit optischer Doppelresonanz,” Z. Phys. 170, 336–346 (1962).
[CrossRef]

Pasternack, L.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Riehle, F.

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

Silver, D. M.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

Strumia, F.

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

F. Strumia, “A proposal for a new absolute frequency standard, using a Mg or Ca atomic beam,” Metrologia 8, 85–90 (1972).
[CrossRef]

Sugar, J.

J. Sugar and C. Corliss, “Energy levels of calcium, Ca I through Ca XX,” J. Phys. Chem. Ref. Data 8, 865–916 (1979).
[CrossRef]

Sugiyama, K.

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

Taylor, B. N.

E. R. Cohen and B. N. Taylor, “The 1986 adjustment of the fundamental physical constants,” Rev. Mod. Phys. 59, 1121–1148 (1987).
[CrossRef]

Tonelli, M.

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

Van Vleck, J. H.

A. Abragam and J. H. Van Vleck, “Theory of the microwave Zeeman effect in atomic oxygen,” Phys. Rev. 92, 1448–1455 (1953).
[CrossRef]

Yarkony, D. R.

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

IEEE Trans Instrum. Meas. (2)

J. Helmcke, A. Morinaga, J. Ishikawa, and F. Riehle, “Optical frequency standards,” IEEE Trans Instrum. Meas. 38, 524–532 (1989).
[CrossRef]

A. Morinaga, N. Ito, J. Ishikawa, K. Sugiyama, and T. Kurosu, “Accuracy and stability of a Ca-stabilized dye laser by means of the optical Ramsey resonance,” IEEE Trans Instrum. Meas. 42, 338–341 (1993).
[CrossRef]

J. Appl. Phys. (1)

G. Giusfredi, A. Godone, E. Bava, and C. Novero, “Metastable atoms in a Mg beam: excitation dynamics and velocity distribution,” J. Appl. Phys. 63, 1279–1285 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. B (1)

L. Pasternack, D. M. Silver, D. R. Yarkony, and P. J. Dagdigian, “Experimental and theoretical study of the Ca I 4s3d 1D–4s2 1S and 4s4p 3P1–4s2 1S forbidden transitions,” J. Phys. B 13, 2231–2241 (1980).
[CrossRef]

J. Phys. Chem. Ref. Data (1)

J. Sugar and C. Corliss, “Energy levels of calcium, Ca I through Ca XX,” J. Phys. Chem. Ref. Data 8, 865–916 (1979).
[CrossRef]

Metrologia (1)

F. Strumia, “A proposal for a new absolute frequency standard, using a Mg or Ca atomic beam,” Metrologia 8, 85–90 (1972).
[CrossRef]

Phys. Rev. (1)

A. Abragam and J. H. Van Vleck, “Theory of the microwave Zeeman effect in atomic oxygen,” Phys. Rev. 92, 1448–1455 (1953).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

D. R. Hartree and W. Hartree, “Self-consistent field with exchange for calcium,” Proc. R. Soc. London, Ser. A 164, 167–191 (1938).
[CrossRef]

Rev. Mod. Phys. (1)

E. R. Cohen and B. N. Taylor, “The 1986 adjustment of the fundamental physical constants,” Rev. Mod. Phys. 59, 1121–1148 (1987).
[CrossRef]

Z. Phys. (1)

E. W. Otten, “Bestimmung des gJ Faktors im 4s4p 3P1-Term des Ca I-Spektrums mit optischer Doppelresonanz,” Z. Phys. 170, 336–346 (1962).
[CrossRef]

Z. Phys. A (1)

G. Giusfredi, P. Minguzzi, F. Strumia, and M. Tonelli, “Atomic beam measurement of the lifetime of the 3P1 metastable states of Mg and Ca,” Z. Phys. A 274, 279–287 (1975).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Experimental apparatus.

Fig. 2
Fig. 2

Energy-level diagram for Ca i (3P) in a magnetic field (not in scale). At a field near 0.4 T, the Zeeman frequencies are of the order of 8 GHz, and the quadratic correction are of the order of some megahertz.

Fig. 3
Fig. 3

Typical magnetic-field homogeneity available during a measurement run. The field at the central point of the magnet is 0.3750281 T. The coordinate system origin is at the midpoint of the magnet; the x axis is oriented along the atomic-beam direction; the z axis is along the magnetic-field direction. The interaction volume and the position of the NMR probe during the experimental runs are shown.

Equations (29)

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H=H0+ALS+μ0gJJB+e2/8ma(B×ra)2,
gJ=gL J(J+1)+L(L+1)-S(S+1)2J(J+1)
+gs J(J+1)-L(L+1)+S(S+1)2J(J+1).
δν=e2B2/8mJ, mJ|r2|J, mJ,
ν(2, +2)=2μ0g2B+4/5wB2,
ν(2, +1)=μ0g2B+1/4ε2B2+3/5wB2,
ν(2, 0)=+1/3ε2B2+8/15wB2,
ν(2, -1)=-μ0g2B+1/4ε2B2+3/5wB2,
ν(2, -2)=-2μ0g2B+4/5wB2,
v(1, +1)=μ0g1B-1/4ε2B2+3/5wB2,
v(1, 0)=+1/3(2ε1-ε2)B2+4/5wB2,
ν(1, -1)=-μ0g1B-1/4ε2B2+3/5wB2,
ν(0, 0)=-2/3ε1B2+2/3wB2,
ε1=μ02/(E1-E0)=125.1835(25) MHz/T2,
ε2=μ02/(E2-E1)=61.73025(61) MHz/T2,
fa=μ0g2B-1/4ε2B2,
fb=μ0g2B-1/12ε2B2,
fc=μ0g2B+1/12ε2B2,
fd=μ0g2B+1/4ε2B2,
fe=μ0g1B-(2/3ε1-1/12ε2)B2,
ff=μ0g1B+(2/3ε1-1/12ε2)B2.
(fa+fd)/2μ0B=g2,(fb+fc)/2μ0B=g2,
(fe+ff)/2μ0B=g1,
(ff-fe)/B2=(4/3ε1-1/6ε2),
(fb-fa)/B2=(fc-fb)/B2=(fd-fc)/B2=1/6ε2.
g1=1.5010829(28),g2=1.5011308(75),
ΔgJ=g1-g2=-4.79(80)×10-5,
ε1=125.905(30) MHz/T2,
ε2=61.61(24) MHz/T2.

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