Dirac–Fock Internal Conversion Coefficients

doi:10.1006/adnd.2002.0884

Atomic Data and Nuclear Data Tables

Volume 81, Issues 1–2, May 2002, Pages 1-334

https://doi.org/10.1006/adnd.2002.0884 Get rights and content

Abstract

Internal conversion coefficients (ICCs) obtained from relativistic self-consistent-field Dirac-Fock (DF) calculations are presented. The exchange terms of DF equations are included exactly, both for the interaction between bound electrons and for the interaction between bound and free electrons. Static and dynamic effects resulting from finite nuclear size are taken into account, the latter using the surface current model. Experimental electron-binding energies are used wherever possible. The hole in the atomic shell from which an electron was emitted is not taken into consideration because there is no compelling experimental evidence to warrant it. ICCs are given here for each Z between Z=10 and Z=126; for K, L₁, L₂, and L₃ atomic shells; for nuclear-transition multipolarities E1…E5, M1…M5; and for nuclear-transition energies from ∼1 keV above the L₁ threshold to 2000 keV. Also given are the total ICCs. Accurate (≤5%) experimental ICCs (K and total) are known for 77 transitions with multipolarities E2, M3, E3, M4, or E5. For these transitions, the theoretical DF values are, on average, about 3% lower than the theoretical relativistic Hartree–Fock–Slater (RHFS) values. The DF values are in better agreement with experimental results than the RHFS values.

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References (83)

H. R. Hulme, Proc. Roy. Soc. A, 138, 643,...
H. R. Hulme, Proc. Roy. Soc. A, 154, 487,...
H. M. Taylor, and, N. F. Mott, Proc. Roy. Soc. A, 138, 665,...
H. M. Taylor, and, N. F. Mott, Proc. Roy. Soc. A, 142, 215,...
V. B. Berestetzkii, A. Z. Dolginov, and, K. A. Ter-Martirosyan, Zh. Exp. Teor. Fiz, 20, 527,...
N. Tralli, and, G. Goertzel, Phys. Rev, 83, 399,...
M. A. Listengarten, in, Gamma Rays, edited by, L. A. Sliv, Acad. Sci. USSR, Moscow-Leningrad, 1961, p, 271, (in...
M. E. Rose, in, Internal Conversion Processes, edited by, J. H. Hamilton, Academic, New York, 1966, p,...
H. C. Pauli, K. Alder, and, R. Steffen, in, The Electromagnetic Interaction in Nuclear Spectroscopy, edited by, W. D....
M.E. Rose
Multipole Fields
(1955)

I.M. Band et al.

Anomalies in Gamma-Ray Internal Conversion Coefficients

(1976)

L. A. Sliv, Zh. Exp. Teor. Fiz, 21, 770,...

M. Mladjenović

The Defining Years in Nuclear Physics 1932–1960s

(1998)

M. E. Rose, in, Beta- and Gamma-Ray Spectroscopy, edited by, K. Siegbahn, North-Holland, Amsterdam, 1955, p,...

L. A. Sliv, and, I. M. Band, Tables of Gamma-Ray Internal Conversion Coefficients, Part I, K, Shell, Acad. Sci. USSR,...

M.E. Rose

Internal Conversion Coefficients

(1958)

R. S. Hager, and, E. C. Seltzer, N, UCL., D, ATA, A, 4, 1,...

F. Rösel, H. M. Fries, K. Alder, and, H. C. Pauli, ATOMIC DATAAND NUCLEAR DATA TABLES, 21, 91,...

I. M. Band, and, M. B. Trzhaskovskaya, Tables of Gamma Ray Internal Conversion Coefficients for K, L and M Shells,...

J. C. Slater, Phys. Rev, 81, 385,...

M. A. Listengarten, and, V. O. Sergeev, in, Proceedings of the IX Workshop on Nuclear Physics, Bukhara, Uzbekistan,...

W. B. Ewbank, Graphical Comparison of Calculated Conversion Coefficients, Oak Ridge National Laboratory Report...

I. M. Band, M. A. Listengarten, and, M. B. Trzhaskovskaya, A Comment on a Graphical Comparison of Calculated Internal...

M. A. Listengarten, and, V. O. Sergeev, Izv. Akad. Nauk SSSR, Ser. Fiz, 45, 814, 1981, [Bull. Acad. Sci. USSR, Phys....

W. Kohn, and, L. J. Sham, Phys. Rev. A, 140, 1133,...

I. M. Band, and, M. B. Trzhaskovskaya, ATOMIC DATAAND NUCLEAR DATA TABLES, 35, 1,...

I. M. Band, L. A. Sliv, and, M. B. Trzhaskovskaya, Nucl. Phys. A, 156, 170,...

I. M. Band, and, M. B. Trzhaskovskaya, Izv. Akad. Nauk SSSR, Ser. Fiz, 56, 1745, 1992, [Bull. Acad. Sci. USSR, Phys....

O. Dragoun, and, M. Rys̆avý, J. Phys. G, 18, 1991,...

S. Raman, T. A. Walkiewicz, R. Gunnink, and, B. Martin, Phys. Rev. C, 7, 2531,...

Zs. Németh, and, Á. Veres, Phys. Rev. C, 35, 2294,...

Zs. Németh, and, Á. Veres, Nucl. Instrum. Methods A, 286, 601,...

Zs. Németh, Á. Veres, T. Sekine, and, K. Yoshihara, in, Proceedings of the International Conference on Nuclear Data for...

I. M. Band, M. A. Listengarten, and, M. B. Trzhaskovskaya, Izv. Akad. Nauk SSSR, Ser. Fiz, 53, 910, 1989, [Bull. Acad....

I. M. Band, M. A. Listengarten, and, M. B. Trzhaskovskaya, Izv. Akad. Nauk SSSR, Ser. Fiz, 54, 15, 1990, [Bull. Acad....

I. M. Band, and, M. B. Trzhaskovskaya, Izv. Akad. Nauk SSSR, Ser. Fiz, 55, 2141, 1991, [Bull. Acad. Sci. USSR, Phys....

I. M. Band, and, M. B. Trzhaskovskaya, ATOMIC DATAAND NUCLEAR DATA TABLES, 55, 43,...

N. Coursol, V. M. Gorozhankin, E. A. Yakushev, C. Briançon, and, Vylov, Appl. Rad. Isotopes, 52, 557,...

K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, C. Johansson, T. Bergmark, S.-E. Karlsson, I....

W. Lotz, J. Opt. Soc. Am, 60, 206,...

M. S. Freedman, F. T. Porter, and, J. B. Mann, Phys. Rev. Lett, 28, 711,...

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¹: Permanent address: Accelerator Laboratory, P.O. Box 43, FIN-00014 University of Helsinki, Finland.

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