Induced toroid structures and toroid polarizabilities

A. Costescu; E. E. Radescu

doi:10.1103/PhysRevD.35.3496

Access by Xinjiang University

Induced toroid structures and toroid polarizabilities

A. Costescu and E. E. Radescu

Joint Institute for Nuclear Research, Dubna, Moskow. U.S.S.R.

PDF

Phys. Rev. D 35, 3496 – Published 1 June, 1987

DOI: https://doi.org/10.1103/PhysRevD.35.3496

Abstract

The frequency-dependent toroid dipole polarizability γ(ω) of a (nonrelativistic, spinless) hydrogenlike atom in its ground state is calculated analytically in terms of two Gauss hypergeometric functions. The static result reads γ(ω=0)=(23/60) $α^{2}$ $Z^{- 4}$ $a_{0}$ $^{5}$ (α=fine-structure constant, Z=nucleus charge number, $a_{0}$ =Bohr radius). Comparing the present evaluations for atoms with previous ones for pions, one sees that the role of the induced toroid moments (as against that of the usual electric ones) increases considerably towards smaller distances (or higher characteristic excitation energies). It might become dramatic at the subhadronic level.

References (16)

Ya. B. Zel'dovich, Zh. Eksp. Teor. Fiz. 33, 1531 (1957) [Sov. Phys. JETP 6, 1184 (1958)].
V. M. Dubovik and A. A. Tscheshkov, Fiz. Elem. Chastits. At. Yadra 5, 791 (1974) [Sov. Part. Nucl. 5, 318 (1974)]; V. M. Dubovik and L. A. Tosunian, ibid. 14, 1193 (1983) ibid. [ 14, 504 (1983)].
V. L. Ginzburg and V. N. Tsytovich, Zh. Eksp. Teor. Fiz. 88, 84 (1985) [Sov. Phys. JETP 61, 48 (1985)].
E. E. Radescu, Phys. Rev. D 32, 1266 (1985).
E. E. Radescu, Joint Institute for Nuclear Research, Dubna Reports Nos. E4-85-165, P4-85-154, P4-85-155, and P4-85-156, 1985 (unpublished).
To understand intuitively what we mean by inducing a toroid dipole moment, we note that when a conduction or displacement current flows through the system, some of the constituent charges may well begin, for instance, to ``move'' (speaking in a classical language) on ``eightlike'' (closed) orbits. While inducing an usual magnetic dipole moment means, say, inducing a closed circular current, inducing a toroid dipole would mean inducing an ``eightlike'' current, or a (coplanar) pair of circular currents (equal, but opposite to each other), or a coaxial collection of such pairs of currents (a toroidal current). These latter current configurations, topologically nontrivial, have no resultant magnetic moment but still represent a certain kind of ``dipole'' characteristic, a ``toroid'' dipole.
For other details see Ref. 5.
C. K. Au, J. Phys. B 11, 2781 (1978).
I. Guiaşu and E. E. Radescu, Ann. Phys. (N.Y.) 120, 145 (1979); Phys. Rev. D 25, 1455 (1982) L. V. Filkov, I. Guiaşu and E. E. Radescu, ibid. 26, 3146 (1982).
A. Costescu and E. E. Radescu (unpublished).
L. Hostler and R. H. Pratt, Phys. Rev. Lett. 10, 469 (1963); L. Hostler, J. Math. Phys. 5, 591 (1964); J. Schwinger, ibid. 5, 1606 (1964); S. Okubo and D. Feldman, Phys. Rev. 117, 292 (1960); L. Hostler, J. Math. Phys. 5, 1235 (1964); V. G. Gorshkov, Zh. Eksp. Teor. Fiz. 47, 352 (1964) [Sov. Phys. JETP 20, 234 (1965)].
M. Gavrila, Phys. Rev. 163, 147 (1967); M. Gavrila and A. Costescu, Phys. Rev. A 2, 1752 (1970); A. Costescu and M. Gavrila, Rev. Roumaine Phys. 18, 493 (1973); A. Costescu, ibid. 21, 3 (1976).
E. Epstein, Phys. Rev. 28, 695 (1926); I. Waller, Z. Phys. 38, 635 (1926).
E. E. Radescu, Phys. Rev. D 27, 1409 (1983).
We must admit that things are going slowly with the measurements of polarizabilities for elementary particles. It is nonetheless encouraging that the pion's electric dipole polarizability has been extracted in two different experiments: Yu. M. Antipov et al., Phys. Lett. 121B, 445 (1983); T. A. Aibergenov et al., Kratk. Soobshch. Fiz. 6, 31 (1984).
E. E. Radescu (unpublished).

[c1] Ya. B. Zel'dovich, Zh. Eksp. Teor. Fiz. 33, 1531 (1957) [Sov. Phys. JETP 6, 1184 (1958)].

[c2] V. M. Dubovik and A. A. Tscheshkov, Fiz. Elem. Chastits. At. Yadra 5, 791 (1974) [Sov. Part. Nucl. 5, 318 (1974)]; V. M. Dubovik and L. A. Tosunian, ibid. 14, 1193 (1983) ibid. [ 14, 504 (1983)].

[c3] V. L. Ginzburg and V. N. Tsytovich, Zh. Eksp. Teor. Fiz. 88, 84 (1985) [Sov. Phys. JETP 61, 48 (1985)].

[c4] E. E. Radescu, Phys. Rev. D 32, 1266 (1985).

[c5] E. E. Radescu, Joint Institute for Nuclear Research, Dubna Reports Nos. E4-85-165, P4-85-154, P4-85-155, and P4-85-156, 1985 (unpublished).

[c6] To understand intuitively what we mean by inducing a toroid dipole moment, we note that when a conduction or displacement current flows through the system, some of the constituent charges may well begin, for instance, to ``move'' (speaking in a classical language) on ``eightlike'' (closed) orbits. While inducing an usual magnetic dipole moment means, say, inducing a closed circular current, inducing a toroid dipole would mean inducing an ``eightlike'' current, or a (coplanar) pair of circular currents (equal, but opposite to each other), or a coaxial collection of such pairs of currents (a toroidal current). These latter current configurations, topologically nontrivial, have no resultant magnetic moment but still represent a certain kind of ``dipole'' characteristic, a ``toroid'' dipole.

[c7] For other details see Ref. 5.

[c8] C. K. Au, J. Phys. B 11, 2781 (1978).

[c9] I. Guiaşu and E. E. Radescu, Ann. Phys. (N.Y.) 120, 145 (1979); Phys. Rev. D 25, 1455 (1982) L. V. Filkov, I. Guiaşu and E. E. Radescu, ibid. 26, 3146 (1982).

[c10] A. Costescu and E. E. Radescu (unpublished).

[c11] L. Hostler and R. H. Pratt, Phys. Rev. Lett. 10, 469 (1963); L. Hostler, J. Math. Phys. 5, 591 (1964); J. Schwinger, ibid. 5, 1606 (1964); S. Okubo and D. Feldman, Phys. Rev. 117, 292 (1960); L. Hostler, J. Math. Phys. 5, 1235 (1964); V. G. Gorshkov, Zh. Eksp. Teor. Fiz. 47, 352 (1964) [Sov. Phys. JETP 20, 234 (1965)].

[c12] M. Gavrila, Phys. Rev. 163, 147 (1967); M. Gavrila and A. Costescu, Phys. Rev. A 2, 1752 (1970); A. Costescu and M. Gavrila, Rev. Roumaine Phys. 18, 493 (1973); A. Costescu, ibid. 21, 3 (1976).

[c13] E. Epstein, Phys. Rev. 28, 695 (1926); I. Waller, Z. Phys. 38, 635 (1926).

[c14] E. E. Radescu, Phys. Rev. D 27, 1409 (1983).

[c15] We must admit that things are going slowly with the measurements of polarizabilities for elementary particles. It is nonetheless encouraging that the pion's electric dipole polarizability has been extracted in two different experiments: Yu. M. Antipov et al., Phys. Lett. 121B, 445 (1983); T. A. Aibergenov et al., Kratk. Soobshch. Fiz. 6, 31 (1984).

[c16] E. E. Radescu (unpublished).

Physical Review D

Export citation

Export citation

Induced toroid structures and toroid polarizabilities

Abstract

References (16)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation