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Volumn 78, Issue 9, 2010, Pages 936-948

Magnetic multipolar contact fields: The anapole and related moments

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EID: 77957378095     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3427412     Document Type: Article
Times cited : (27)

References (58)
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    • Jr)=0 and then contract and To show that dr(LJ)=0, first write it as idr(rJ)=idr(rJ), then apply Gauss theorem with a distant surface, and use the fact that J(r) is localized near the origin of coordinates.
    • Jr)=0 and then contract and To show that dr(LJ)=0, first write it as idr(rJ)=idr(rJ), then apply Gauss theorem with a distant surface, and use the fact that J(r) is localized near the origin of coordinates.
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    • This expression for a can be shown to be equivalent to the one given in Sec. (see Ref. c30).
    • This expression for a can be shown to be equivalent to the one given in Sec. (see Ref. c30).
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    • 2(rJ+Jr)] given in Ref. c18 can be shown to be equivalent to Eq. using the methods in Refs. c29 c30.
    • 2(rJ+Jr)] given in Ref. c18 can be shown to be equivalent to Eq. using the methods in Refs. c29 c30.
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    • Jrrr]=0. The latter relation follows from dr(Jrrrr)=0 (use Gauss theorem with a distant surface and the fact that J(r) is localized near the origin) when we exp
    • Jrrr]=0. The latter relation follows from dr(Jrrrr)=0 (use Gauss theorem with a distant surface and the fact that J(r) is localized near the origin) when we expand out (Jrrrr) and use J=0.
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    • 2=2dr(rJ)r. A third possible definition of the anapole moment is a=(1/3c)drr(rJ). Note that our definition of a is a factor of (1/2c) times the definition in Ref. c12.
    • 2=2dr(rJ)r. A third possible definition of the anapole moment is a=(1/3c)drr(rJ). Note that our definition of a is a factor of (1/2c) times the definition in Ref. c12.
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    • 2b/c)=a fixed.
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    • 2. The point octopole limit is obtained for R0, d0, and I, with fixed.
    • 2. The point octopole limit is obtained for R0, d0, and I, with fixed.
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    • Tzz/2 because T is traceless. The continuum limit is obtained for N and I0, with NI fixed.
    • Tzz/2 because T is traceless. The continuum limit is obtained for N and I0, with NI fixed.
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    • 2r. This primitive electric moment is one of two terms constituting the Schiff moment (Refs. c12 c41), which arises in the discussion of Schiffs theorem (see Refs. c12 c41 c46). The latter theorem deals with the screening or antiscreening of electron and/or nuclear electric dipole moments in generating the net electric dipole moment of an isolated atom or molecule. Nonvanishing electron and nuclear electric dipole moments are possible if parity and time-reversal symmetries are violated (see Sec. ).
    • 2r. This primitive electric moment is one of two terms constituting the Schiff moment (Refs. c12 c41), which arises in the discussion of Schiffs theorem (see Refs. c12 c41 c46). The latter theorem deals with the screening or antiscreening of electron and/or nuclear electric dipole moments in generating the net electric dipole moment of an isolated atom or molecule. Nonvanishing electron and nuclear electric dipole moments are possible if parity and time-reversal symmetries are violated (see Sec. ).
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    • A derivation using spherical tensors is given in Ref. c22. A derivation using Cartesian tensors follows the same argument used to derive the corresponding relation for the electric quadrupole moment given in Ref. c3.
    • A derivation using spherical tensors is given in Ref. c22. A derivation using Cartesian tensors follows the same argument used to derive the corresponding relation for the electric quadrupole moment given in Ref. c3.
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    • Use dr(Jr)=0 from Gauss theorem with a distant surface and the fact that J(r) is localized near the origin and J=0.
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