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fact, one notices that all contributions resulting from the (Formula presented) term in (Formula presented) Eq. (2.44), cancel with corresponding tadpole diagrams obtained from the two-particle operator term in (Formula presented): For the (Formula presented)-(Formula presented) interaction part of any (Formula presented) (Formula presented)the two field operators in (Formula presented) can either be contracted with themselves or with any other field operator in a given expectation value (Formula presented) The former type of contractions, and only this type, leads to the so-called tadpole diagrams in which one or several simple fermion loops are connected to the remainder of the diagram by a single photon line. The same holds for (Formula presented) of course. The tadpole contractions can be taken care of by explicitly including them in (Formula presented) via addition of (Formula presented)(where symmetry under exchange of (Formula presented) and (Formula presented) has been used) and simultaneously excluding this type of contraction from the expectation value (Formula presented) However, using Eq. (2.17) the additional term exactly cancels with (Formula presented)This allows us to drop (Formula presented) in Eq. (2.44) if at the same time all tadpole contributions are omitted in the expectation value appearing in Eq. (2.45)
-
In fact, one notices that all contributions resulting from the (Formula presented) term in (Formula presented) Eq. (2.44), cancel with corresponding tadpole diagrams obtained from the two-particle operator term in (Formula presented): For the (Formula presented)-(Formula presented) interaction part of any (Formula presented) (Formula presented)the two field operators in (Formula presented) can either be contracted with themselves or with any other field operator in a given expectation value (Formula presented) The former type of contractions, and only this type, leads to the so-called tadpole diagrams in which one or several simple fermion loops are connected to the remainder of the diagram by a single photon line. The same holds for (Formula presented) of course. The tadpole contractions can be taken care of by explicitly including them in (Formula presented) via addition of (Formula presented)(where symmetry under exchange of (Formula presented) and (Formula presented) has been used) and simultaneously excluding this type of contraction from the expectation value (Formula presented) However, using Eq. (2.17) the additional term exactly cancels with (Formula presented)This allows us to drop (Formula presented) in Eq. (2.44) if at the same time all tadpole contributions are omitted in the expectation value appearing in Eq. (2.45).
-
-
-
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88
-
-
85037210142
-
-
Note that Eq. (2.47) includes all photon retardation and vacuum effects, so that renormalization is required to obtain finite results
-
Note that Eq. (2.47) includes all photon retardation and vacuum effects, so that renormalization is required to obtain finite results.
-
-
-
-
89
-
-
85037223743
-
-
Only the real part of the timelike component satisfies the transversality relation, (Formula presented)
-
Only the real part of the timelike component satisfies the transversality relation, (Formula presented)
-
-
-
-
90
-
-
85037187988
-
-
Note that in spite of the nontransversality of (Formula presented) the corresponding no-pair ground state current is conserved, (Formula presented)
-
Note that in spite of the nontransversality of (Formula presented) the corresponding no-pair ground state current is conserved, (Formula presented)
-
-
-
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95
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85037233179
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-
The small differences between the RHF transverse exchange energies for heavy atoms (Yb-No) given in
-
The small differences between the RHF transverse exchange energies for heavy atoms (Yb-No) given in 9 and those in Table IV originate from a minor coding error in the original GRASP program 74, which we have now corrected.
-
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85037184243
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M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957). The (Formula presented) are also often denoted as (Formula presented) and (Formula presented)
-
M. E. Rose, Elementary Theory of Angular Momentum (Wiley, New York, 1957). The (Formula presented) are also often denoted as (Formula presented) and (Formula presented)
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107
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Dover, New York
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85037199603
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J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 4: The Self-consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974), Appendix 3
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J. C. Slater, Quantum Theory of Molecules and Solids, Vol. 4: The Self-consistent Field for Molecules and Solids (McGraw-Hill, New York, 1974), Appendix 3.
-
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109
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11744341218
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PRVDAQ
-
In all our calculations the nuclei were represented by uniformly charged spheres with nuclear radii given by (Formula presented) fm, (Formula presented) being the atomic mass (weighted by isotopic abundances) taken from Table III.7 of K. Hisaka et al, Particle Data Group, Phys. Rev. D 45, 51 (1992), unless explicitly stated otherwise. The speed of light had been set to (Formula presented) a.u.PRVDAQ
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Hisaka, K.1
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