Abstract

The Overhauser effect in an electron-nuclear coupled spin system (S = ½, I = 1) is studied in detail. From a population distribution analysis of the system, the nuclear orientation parameters are computed and their temperature dependence discussed. Conditions for achieving stimulated emission are examined in detail. Several significant features hitherto unknown are brought out.

© 1965 Optical Society of America

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References

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  1. W. A. Barker, E. A. Desloge, Bull. Am. Phys. Soc. 2, 226 (1957); L. Bennett, H. C. Torrey, Phys. Rev. 108, 499 (1957).
    [Crossref]
  2. E. Allias, Compt. Rend. 246, 2123 (1958); I. Solomon, J. Phys. Radium 19, 837 (1958); A. Ganssen, E. L. Sloan, Bull. Am. Phys. Soc. 7, 15 (1962).
    [Crossref]
  3. M. L. Narchal, W. A. Barker, Bull. Am. Phys. Soc. 6, 298 (1961).
  4. E. Allias, Compt. Rend. 246, 2123 (1958).
  5. W. A. Barker, Rev. Mod. Phys. 34, 173 (1962).
    [Crossref]
  6. D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
    [Crossref]
  7. J. M. Daniels, J. Goldenberg, Repts. Prog. Phys. 25, 1 (1962).
    [Crossref]
  8. L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.
  9. R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
    [Crossref]
  10. A. W. Overhauser, Phys. Rev. 89, 689 (1953).; Phys. Rev. 92, 411 (1953).
    [Crossref]
  11. C. D. Jeffries, Phys. Rev. 106, 164 (1957).
    [Crossref]
  12. A. Abragam, W. G. Proctor, Compt. Rend. 246, 2253 (1958).
  13. C. J. Gorter, Physica 14, 504 (1948); M. E. Rose, Phys. Rev. 75, 213 (1949); J. W. T. Dabbs, L. D. Roberts, S. Bernstein, Phys. Rev. 98, 1512 (1955).
    [Crossref]
  14. M. L. Narchal, W. A. Barker, Appl. Opt. 2, 787 (1963).
    [Crossref]
  15. Mary Duns Scotus Breitbart, W. A. Barker, Nucl. Phys. 52, 641 (1964).
    [Crossref]
  16. C. D. Jeffries, Progress in Cryogenics (Heywood & Co., London, 1961), Vol. 3, p. 131.
  17. R. H. Webb, Am. J. Phys. 29, 428 (1961); C. D. JeffriesDynamic Nuclear Orientation (Wiley, New York, 1963).
    [Crossref]
  18. J. D. Keating, W. A. Barker, J. Franklin Inst. 274, 253 (1962).
    [Crossref]
  19. E. W. Hobbs, J. Franklin Inst. 274, 270 (1962).
    [Crossref]
  20. A. M. Clogstan, J. Phys. Chem. Solids 4, 271 (1958).
    [Crossref]
  21. A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).
  22. C. H. Wang, T. M. Sanders, Proc. VIII Int. Conf. on Low Temperature Physics (University of Toronto Press, Canada, 1960), p. 148.
  23. T. G. Castner, W. Kanzig, J. Phys. Chem. Solids 3, 178 (1957).
    [Crossref]
  24. W. A. Barker, ANL Rept. 6069 (1959), unpublished.
  25. A. Abragam, Nuclear Magnetism (Oxford University Press, New York, 1962).
  26. T. O. Woodruff, W. Kanzig, J. Phys. Chem. Solids 5, 268 (1958).
    [Crossref]

1964 (1)

Mary Duns Scotus Breitbart, W. A. Barker, Nucl. Phys. 52, 641 (1964).
[Crossref]

1963 (2)

M. L. Narchal, W. A. Barker, Appl. Opt. 2, 787 (1963).
[Crossref]

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

1962 (4)

J. D. Keating, W. A. Barker, J. Franklin Inst. 274, 253 (1962).
[Crossref]

E. W. Hobbs, J. Franklin Inst. 274, 270 (1962).
[Crossref]

W. A. Barker, Rev. Mod. Phys. 34, 173 (1962).
[Crossref]

J. M. Daniels, J. Goldenberg, Repts. Prog. Phys. 25, 1 (1962).
[Crossref]

1961 (2)

M. L. Narchal, W. A. Barker, Bull. Am. Phys. Soc. 6, 298 (1961).

R. H. Webb, Am. J. Phys. 29, 428 (1961); C. D. JeffriesDynamic Nuclear Orientation (Wiley, New York, 1963).
[Crossref]

1960 (1)

D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
[Crossref]

1958 (5)

E. Allias, Compt. Rend. 246, 2123 (1958).

E. Allias, Compt. Rend. 246, 2123 (1958); I. Solomon, J. Phys. Radium 19, 837 (1958); A. Ganssen, E. L. Sloan, Bull. Am. Phys. Soc. 7, 15 (1962).
[Crossref]

A. M. Clogstan, J. Phys. Chem. Solids 4, 271 (1958).
[Crossref]

A. Abragam, W. G. Proctor, Compt. Rend. 246, 2253 (1958).

T. O. Woodruff, W. Kanzig, J. Phys. Chem. Solids 5, 268 (1958).
[Crossref]

1957 (3)

T. G. Castner, W. Kanzig, J. Phys. Chem. Solids 3, 178 (1957).
[Crossref]

C. D. Jeffries, Phys. Rev. 106, 164 (1957).
[Crossref]

W. A. Barker, E. A. Desloge, Bull. Am. Phys. Soc. 2, 226 (1957); L. Bennett, H. C. Torrey, Phys. Rev. 108, 499 (1957).
[Crossref]

1953 (2)

R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
[Crossref]

A. W. Overhauser, Phys. Rev. 89, 689 (1953).; Phys. Rev. 92, 411 (1953).
[Crossref]

1948 (1)

C. J. Gorter, Physica 14, 504 (1948); M. E. Rose, Phys. Rev. 75, 213 (1949); J. W. T. Dabbs, L. D. Roberts, S. Bernstein, Phys. Rev. 98, 1512 (1955).
[Crossref]

Abragam, A.

A. Abragam, W. G. Proctor, Compt. Rend. 246, 2253 (1958).

A. Abragam, Nuclear Magnetism (Oxford University Press, New York, 1962).

Allias, E.

E. Allias, Compt. Rend. 246, 2123 (1958); I. Solomon, J. Phys. Radium 19, 837 (1958); A. Ganssen, E. L. Sloan, Bull. Am. Phys. Soc. 7, 15 (1962).
[Crossref]

E. Allias, Compt. Rend. 246, 2123 (1958).

Barker, W. A.

Mary Duns Scotus Breitbart, W. A. Barker, Nucl. Phys. 52, 641 (1964).
[Crossref]

M. L. Narchal, W. A. Barker, Appl. Opt. 2, 787 (1963).
[Crossref]

W. A. Barker, Rev. Mod. Phys. 34, 173 (1962).
[Crossref]

J. D. Keating, W. A. Barker, J. Franklin Inst. 274, 253 (1962).
[Crossref]

M. L. Narchal, W. A. Barker, Bull. Am. Phys. Soc. 6, 298 (1961).

W. A. Barker, E. A. Desloge, Bull. Am. Phys. Soc. 2, 226 (1957); L. Bennett, H. C. Torrey, Phys. Rev. 108, 499 (1957).
[Crossref]

W. A. Barker, ANL Rept. 6069 (1959), unpublished.

Blinstoyle, R. J.

R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
[Crossref]

Breitbart, Mary Duns Scotus

Mary Duns Scotus Breitbart, W. A. Barker, Nucl. Phys. 52, 641 (1964).
[Crossref]

Castner, T. G.

T. G. Castner, W. Kanzig, J. Phys. Chem. Solids 3, 178 (1957).
[Crossref]

Clogstan, A. M.

A. M. Clogstan, J. Phys. Chem. Solids 4, 271 (1958).
[Crossref]

Conradi, J. J.

D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
[Crossref]

Dabbs, J. W. T.

L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.

Daniels, J. M.

J. M. Daniels, J. Goldenberg, Repts. Prog. Phys. 25, 1 (1962).
[Crossref]

Desloge, E. A.

W. A. Barker, E. A. Desloge, Bull. Am. Phys. Soc. 2, 226 (1957); L. Bennett, H. C. Torrey, Phys. Rev. 108, 499 (1957).
[Crossref]

Goldenberg, J.

J. M. Daniels, J. Goldenberg, Repts. Prog. Phys. 25, 1 (1962).
[Crossref]

Gorter, C. J.

C. J. Gorter, Physica 14, 504 (1948); M. E. Rose, Phys. Rev. 75, 213 (1949); J. W. T. Dabbs, L. D. Roberts, S. Bernstein, Phys. Rev. 98, 1512 (1955).
[Crossref]

Grace, M. A.

R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
[Crossref]

Halben, H.

R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
[Crossref]

Hobbs, E. W.

E. W. Hobbs, J. Franklin Inst. 274, 270 (1962).
[Crossref]

Jeffries, C. D.

C. D. Jeffries, Phys. Rev. 106, 164 (1957).
[Crossref]

C. D. Jeffries, Progress in Cryogenics (Heywood & Co., London, 1961), Vol. 3, p. 131.

Kanzig, W.

T. O. Woodruff, W. Kanzig, J. Phys. Chem. Solids 5, 268 (1958).
[Crossref]

T. G. Castner, W. Kanzig, J. Phys. Chem. Solids 3, 178 (1957).
[Crossref]

Keating, J. D.

J. D. Keating, W. A. Barker, J. Franklin Inst. 274, 253 (1962).
[Crossref]

Kessennikh, A. V.

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

Lushchikev, V. I.

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

Manenkov, A. A.

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

McClaren, G. A.

D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
[Crossref]

Narchal, M. L.

M. L. Narchal, W. A. Barker, Appl. Opt. 2, 787 (1963).
[Crossref]

M. L. Narchal, W. A. Barker, Bull. Am. Phys. Soc. 6, 298 (1961).

Overhauser, A. W.

A. W. Overhauser, Phys. Rev. 89, 689 (1953).; Phys. Rev. 92, 411 (1953).
[Crossref]

Parker, D. J.

D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
[Crossref]

Parker, G. W.

L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.

Proctor, W. G.

A. Abragam, W. G. Proctor, Compt. Rend. 246, 2253 (1958).

Roberts, L. D.

L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.

Sanders, T. M.

C. H. Wang, T. M. Sanders, Proc. VIII Int. Conf. on Low Temperature Physics (University of Toronto Press, Canada, 1960), p. 148.

Taran, Yu. V.

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

Walter, F. J.

L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.

Wang, C. H.

C. H. Wang, T. M. Sanders, Proc. VIII Int. Conf. on Low Temperature Physics (University of Toronto Press, Canada, 1960), p. 148.

Webb, R. H.

R. H. Webb, Am. J. Phys. 29, 428 (1961); C. D. JeffriesDynamic Nuclear Orientation (Wiley, New York, 1963).
[Crossref]

Woodruff, T. O.

T. O. Woodruff, W. Kanzig, J. Phys. Chem. Solids 5, 268 (1958).
[Crossref]

Am. J. Phys. (1)

R. H. Webb, Am. J. Phys. 29, 428 (1961); C. D. JeffriesDynamic Nuclear Orientation (Wiley, New York, 1963).
[Crossref]

Appl. Opt. (1)

Bull. Am. Phys. Soc. (2)

W. A. Barker, E. A. Desloge, Bull. Am. Phys. Soc. 2, 226 (1957); L. Bennett, H. C. Torrey, Phys. Rev. 108, 499 (1957).
[Crossref]

M. L. Narchal, W. A. Barker, Bull. Am. Phys. Soc. 6, 298 (1961).

Compt. Rend. (3)

E. Allias, Compt. Rend. 246, 2123 (1958).

E. Allias, Compt. Rend. 246, 2123 (1958); I. Solomon, J. Phys. Radium 19, 837 (1958); A. Ganssen, E. L. Sloan, Bull. Am. Phys. Soc. 7, 15 (1962).
[Crossref]

A. Abragam, W. G. Proctor, Compt. Rend. 246, 2253 (1958).

J. Chem. Phys. (1)

D. J. Parker, G. A. McClaren, J. J. Conradi, J. Chem. Phys. 33, 629 (1960).
[Crossref]

J. Franklin Inst. (2)

J. D. Keating, W. A. Barker, J. Franklin Inst. 274, 253 (1962).
[Crossref]

E. W. Hobbs, J. Franklin Inst. 274, 270 (1962).
[Crossref]

J. Phys. Chem. Solids (3)

A. M. Clogstan, J. Phys. Chem. Solids 4, 271 (1958).
[Crossref]

T. G. Castner, W. Kanzig, J. Phys. Chem. Solids 3, 178 (1957).
[Crossref]

T. O. Woodruff, W. Kanzig, J. Phys. Chem. Solids 5, 268 (1958).
[Crossref]

Nucl. Phys. (1)

Mary Duns Scotus Breitbart, W. A. Barker, Nucl. Phys. 52, 641 (1964).
[Crossref]

Phys. Rev. (2)

A. W. Overhauser, Phys. Rev. 89, 689 (1953).; Phys. Rev. 92, 411 (1953).
[Crossref]

C. D. Jeffries, Phys. Rev. 106, 164 (1957).
[Crossref]

Physica (1)

C. J. Gorter, Physica 14, 504 (1948); M. E. Rose, Phys. Rev. 75, 213 (1949); J. W. T. Dabbs, L. D. Roberts, S. Bernstein, Phys. Rev. 98, 1512 (1955).
[Crossref]

Progr. Nucl. Phys. (1)

R. J. Blinstoyle, M. A. Grace, H. Halben, Progr. Nucl. Phys. 3, 63 (1953); M. J. Steenland, H. A. Tolhock, Progress in Low Temperature Physics (North Holland, Amsterdam, 1957), Vol. 2, p. 297.
[Crossref]

Repts. Prog. Phys. (1)

J. M. Daniels, J. Goldenberg, Repts. Prog. Phys. 25, 1 (1962).
[Crossref]

Rev. Mod. Phys. (1)

W. A. Barker, Rev. Mod. Phys. 34, 173 (1962).
[Crossref]

Soviet Phys.—Solid State (1)

A. V. Kessennikh, V. I. Lushchikev, A. A. Manenkov, Yu. V. Taran, Soviet Phys.—Solid State 5, 321 (1963).

Other (5)

C. H. Wang, T. M. Sanders, Proc. VIII Int. Conf. on Low Temperature Physics (University of Toronto Press, Canada, 1960), p. 148.

C. D. Jeffries, Progress in Cryogenics (Heywood & Co., London, 1961), Vol. 3, p. 131.

L. D. Roberts, F. J. Walter, J. W. T. Dabbs, G. W. Parker, Proc. VII Int. Conf. on Low Temperature Physics (Univ. Toronto Press, Canada, 1960), p. 174.

W. A. Barker, ANL Rept. 6069 (1959), unpublished.

A. Abragam, Nuclear Magnetism (Oxford University Press, New York, 1962).

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Figures (5)

Fig. 1
Fig. 1

Energy level diagram of an electron-nuclear coupled spin system (S = ½, I = 1) when either the nuclear Zeeman or the hyperfine interaction dominates over the other.

Fig. 2
Fig. 2

Curves showing the relation between polarization and Δ for the four cases of interest,

Fig. 3
Fig. 3

Curves showing the relation between alignment and Δ. The primed curves are plotted on the scale marked on the right.

Fig. 4
Fig. 4

Curves showing the relation between enhancement and Δ. The primed curves are plotted on the scale marked on the right.

Fig. 5
Fig. 5

Curves showing the relation between normalized signal power output and Δ.

Tables (3)

Tables Icon

Table I Polarization. Static Value = [(1 − e−2δ) + e−Δ (e−2δ − 1)]/[(1 + e−Δ) (1 + eδ + e−2δ)].

Tables Icon

Table II (A + 2)/3 = ∑m2Nm/∑Nm. Static Value = (1 + e−2δ)/(1 + eδ + e−2δ).

Tables Icon

Table III Normalized Signal Power Output/nwn. Static Value = (e−2δ − 1)/(1 + eδ + e−2δ).

Equations (8)

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E ( M , m ) = - g β H 0 M - g n β n H 0 m + a M m ,
( - ½ , ± 1 ) , ( - ½ , 0 ) , ( - ½ , 1 ) , ( ½ , 1 ) , ( ½ , 0 ) , ( ½ , ± 1 ) , ( a = ± , γ n 0 ) ,
( - ½ , 1 ) , ( - ½ , 0 ) , ( - ½ , ± 1 ) , ( ½ , 1 ) , ( ½ , 0 ) , ( ½ , ± 1 ) , ( γ n = , a 0 ) .
P = 1 I N m = - L m = I m N m ,
A = 1 ( 2 I - 1 ) I [ 3 m m 2 N m m N m - I ( I + 1 ) ] ,
ɛ = m ( N m - N m - 1 ) m ( N m 0 - N m - 1 0 ) ,
S = 1 N [ i = 2 2 I + 1 ( N i - N i - 1 ) + i = 2 L + 3 4 I + 2 ( N i - N i - 1 ) ] h ν n W n .
P i k = ( N i - N k ) ( E i - E k ) ( g β 0 H 1 / h ) 2 2 T 2 M 2 .

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