Inner radiation emitted during [Formula Presented] decay and related problems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 2, 1998, Pages 1212-1220

  Frolov, Alexei M ^a   Smith, Vedene H ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346178373     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.1212     Document Type: Article

References (34)

1. Probably, soon (Formula presented) will be used in all applications related to nuclear fission (and fusion as well 2) instead of (Formula presented) Indeed, the properties of (Formula presented) with respect to nuclear fission are significantly better than for (Formula presented) Furthermore, curium-247 is significantly (∼1000 times) more stable and less toxic than plutonium-239.
2. The fissionable elements are used for fusion purposes in the three following ways. First, to produce the extremely intense pulse of soft x rays (the so-called Teller’s light), which is used to compress the cold thermonuclear fuel (mainly (Formula presented) to the densities (Formula presented) Second, to heat such a highly compressed fuel to the temperatures ≈4–10 keV, and also to support and partially control the conducting thermonuclear reactions by outcoming high intense neutron fluxes. Third, to simplify and stabilize the thermonuclear burning and its propagation. Only for the last purposes are the fissionable elements used as the deuterides that are mixed (in small amounts) with the (Formula presented) deuteride. This way was found and successfully developed in the middle of the 1950s. Since that time all other approaches to produce self-supported nuclear fusion reactions have failed.
3. A. M. Weinberg and E. P. Wigner, The Physical Theory of Neutron Chain Reactors (University of Chicago Press, Chicago, 1958).
4. M. Haissinsky and J.-P. Adloff, Radiochemical Survey of the Elements (Elsevier Publishing Company, New York, 1965).
5. The usual bremsstrahlung radiation is emitted always when a fast charged particle moves in the nuclear fields of the surrounding atoms. This process was intensively studied previously (see, e.g., Ref. 6, and references therein). Likewise, this radiation can be also observed in other processes, i.e., it is not specific only for nuclear (Formula presented) decay. For these reasons we shall not discuss the usual bremsstrahlung in the present study.
6. J. D. Jackson, Classical Electrodynamics, 2nd ed. (J. Wiley and Sons, New York, 1975).
7. In the case (Formula presented) from the condition (Formula presented) follows the appropriate nonrelativistic threshold condition: (Formula presented), where (Formula presented) [compare with Eq. (9)]. As well as in the relativistic case, this inequality gives a relation between the two values (Formula presented) and (Formula presented).
8. A. B. Migdal, J. Phys. (Moscow) 4, 449 (1941).JOPYA6
9. A. B. Migdal and V. Krainov, Approximation Methods in Quantum Mechanics (W. A. Benjamin, Inc., New York, 1969), pp. 71–80.
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11. J. S. Levinger, Phys. Rev. 90, 11 (1953).PHRVAO
12. M. Wolfsberg, Phys. Rev. 96, 1712 (1954).PHRVAO
13. M. Weissbluth, Atoms and Molecules (Academic Press, San Diego, 1978).Note that in this section we assume that the scalar product between (Formula presented) and (Formula presented) functions is determined as follows: (Formula presented)
14. The binominal coefficients (Formula presented) used in the text designate the following expression: (Formula presented).
15. R. D. William and S. E. Koonin, Phys. Rev. C 27, 1815 (1983).PRVCAN
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18. E. G. Drukarev and M. I. Strikman, Phys. Lett. B 186, 1 (1986), and references therein.PYLBAJ
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21. V. A. Fock, Foundations of Quantum Mechanics (Nauka, Moscow, 1976) (in Russian).
22. For an arbitrary metric (or unitary) space X, the notation (Formula presented) means its completion, which is a complete metric (or Hilbert) space (for more detail see 23).
23. K. Maurin, Methods of Hilbert Spaces (PNW–Polish Scientific Publishers, Warsaw, 1967).
24. In general, (Formula presented) corresponds to the so-called tail representations 25 (for the hydrogenlike system with (Formula presented) which had never been used previously for the hydrogenlike atoms (ions). The reason why such representations appeared in the present study seems to be quite transparent: the appropriate Migdal amplitude (Formula presented) includes the wave functions for the two hydrogenlike systems with different charges. But both of these functions have the same argument, and hence, we may discuss the relation between the first (initial) and second (final) functions.
25. I. M. Gel’fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon Press, New York, 1963).
26. A. M. Frolov, J. Phys. B 23, 2401 (1990).JPAPEH
27. A. O. Barut and R. Raczka, Theory of Group Representations and Applications (PWN–Polish Scientific Publishers, Warsaw, 1977), and references therein.
28. A. R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, NJ, 1957).
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30. S. Larsson, Phys. Rev. 169, 49 (1968).PHRVAO
31. A. M. Frolov and V. H. Smith, Jr., Phys. Rev. A 53, 3853 (1996).PLRAAN
32. Z.-C. Yan and G. W. F. Drake, Phys. Rev. A 52, 3711 (1995).PLRAAN
33. M. Cantell, Phys. Rev. 101, 1747 (1956).PHRVAO
34. M. M. Hindi, L. Zhu, R. Avci, P. M. Miocinovic, R. L. Kozub, and G. L. Lapeyre, Phys. Rev. A 53, R3716 (1996). PLRAAN