Relativistic dynamics of half-spin particles in a homogeneous magnetic field: An atom with nucleus of spin 1/2
DSpace at IIT Bombay
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Title |
Relativistic dynamics of half-spin particles in a homogeneous magnetic field: An atom with nucleus of spin 1/2
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Creator |
MISRA, A
DATTA, SN |
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Subject |
dirac-equation
electron eigenvalues spectra |
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Description |
An investigation of the relativistic dynamics of N+1 spin-1.2 particles placed in an external, homogeneous magnetic field is carried out. The system can represent an atom with a fermion nucleus and N electrons. Quantum electrodynamical interactions, namely, projected Briet and magnetic interactions, are chosen to formulate the relativistic Hamiltonian. The quasi-free-particle picture is retained here. The total pseudomomentum is conserved, and its components are distinct when the total charge is zero. Therefore, the center-of-mass motion can be separated from the Hamiltonian for a neutral (N+1)-fermion system, leaving behind a unitarily transformed, effective Hamiltonian H(0) at zero total pseudomomentum. The latter operator represents the complete relativistic dynamics in relative coordinates while interaction is chosen through order alpha(4)mc(2). Each one-particle part in the effective Hamiltonian can be brought to a separable form for positive- and negative-energy states by replacing the odd operator in it through two successive unitary transformations, one due to Tsai [Phys. Rev. D 7, 1945 (1973)] and the other due to Weaver [J. Math. Phys. 18, 306 (1977)]. Consequently, the projector changes and the interaction that involves the concerned particle also becomes free from the corresponding odd operators. When this maneuver is applied only to the nucleus, and the non-Hermitian part of the transformed interaction is removed by another unitary transformation, a familiar form of the atomic relativistic Hamiltonian H-atom emerges. This operator is equivalent to H(0). A good Hamiltonian for relativistic quantum chemical calculations, H-Qchem, is obtained by expanding the nuclear part of the atomic Hamiltonian through order alpha(4)mc(2) for positive-energy states. The operator H-Qchem is obviously an approximation to H-atom. When the same technique is used for all particles, and subsequently the non-Hermitian terms are removed by suitable unitary transformations, one obtains a Hamiltonian H-T that is equivalent to H-atom but is in a completely separable form. As the semidiscrete eigenvalues and eigenfunctions of the one-particle parts are known, the completely separable Hamiltonian can be used in computation. A little more effort leads to the derivation of the correct atomic Hamiltonian in the nonrelativistic limit, H-nonrel. The operator H-nonrel is an approximation to H-T. It not only retains the relativistic and radiative effects, but also directly exhibits the phenomena of electron paramagnetic resonance and nuclear magnetic resonance. (C) 2005
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Publisher |
AMER INST PHYSICS
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Date |
2011-07-16T13:28:37Z
2011-12-26T12:49:47Z 2011-12-27T05:35:29Z 2011-07-16T13:28:37Z 2011-12-26T12:49:47Z 2011-12-27T05:35:29Z 2005 |
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Type |
Article
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Identifier |
JOURNAL OF CHEMICAL PHYSICS, 123(6), -
0021-9606 http://dx.doi.org/10.1063/1.1996574 http://dspace.library.iitb.ac.in/xmlui/handle/10054/4438 http://hdl.handle.net/10054/4438 |
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Language |
en
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