Exact solution of the eigenvalue problem for a spin system in the presence of a magnetic field

Muha, G. M.

doi:10.1016/0022-2364(83)90073-2

Cited by 20 publications

(14 citation statements)

References 31 publications

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“…with u n = 2p=3 + R cos[( + 2 n)=3]; n = 0; 1; 2; Table 4 Contributions arising from the Zeeman terms and cross-terms to the Stokes I; Q; U; V proÿles for a transition Ju= Cross-terms (mu = m u ) Although Muha [10] has given algebraic expressions for the eigen states | i corresponding to the above energy values, we found that it is much easier to generate the states numerically using Mathematica to determine the coe cients c i mu = 3 2 ; m u | i ; m u = 3 2 ; : : : ; − 3 2 . The numerical values of c i mu are shown in Table 3 for a particular choice of electric and magnetic ÿeld parameters.…”

Section: Arbitrary Orientation Of the Magnetic ÿEldmentioning

confidence: 99%

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

Oo¹,

Nagendra²,

Ananthamurthy³

et al. 2005

Journal of Quantitative Spectroscopy and Radiative Transfer

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In continuation of our earlier investigation (referred to hereafter as part I) where we considered the mathematically simple case of magnetic ÿeld orientation along the Z-axis of the principal axes frame (PAF) of the electric quadrupole ÿeld, we take up here the general problem of arbitrary orientation of the magnetic ÿeld with respect to the PAF, and investigate the nature of polarized line spectra of an atom making a transition from an upper level with spin J u to a lower level with spin J l . Explicit formulae for the emitted Stokes parameters are obtained and we discuss their physical signiÿcance by computing numerically the cases of transitions J u = 1 → J l = 0 and J u = 3 2 → J l = 1 2 . Speciÿc features or signatures of the polarized line spectra are discussed as functions of the relevant physical parameters. The Stokes parameters are also analyzed in terms of the Zeeman term contributions and the cross-term contributions (which arise due to quantum interference). ?

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Section: Arbitrary Orientation Of the Magnetic ÿEldmentioning

confidence: 99%

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

Oo¹,

Nagendra²,

Ananthamurthy³

et al. 2005

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…Bersohn [24] analysed the case in which the quadrupole interaction is larger than the magnetic field. Dean [25] developed a more general treatment and Muha [21] analysed the particular case of a system of spin I = 3/2. The total Hamiltonian H of a quadrupole nucleus interacting with an external homogeneous magnetic field B = B 0 e z and with an electric field gradient is…”

Section: Theorymentioning

confidence: 99%

“…In a subsequent paper the critical dynamics will be analysed. Hence, in this paper we start with a brief description of the exact calculation of the NMR spectra shifts for nuclei with quantum numbers of I = 3/2 for a strong quadrupole coupling tensor which is based on the well-known paper of Muha [21] (Section 2). In Section 3 we outline the conditions for the NMR experiments.…”

Section: Introductionmentioning

confidence: 99%

35Cl Nuclear Magnetic Resonance Study in Bis(4-Chlorophenyl)Sulphone [(ClC6H4)2SO2]

Taye

Michel

2002

phys. stat. sol. (b)

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Cl NMR measurements of the central transitions (--1/2 $ +1/2) on a multidomain crystal of bis(4-chlorophenyl)sulphone (BCPS) were performed at room temperature. The quadrupole tensors and the temperature dependence of the 35 Cl NMR resonance frequencies have been analysed. Since the Larmor frequency n L is of comparable size with the quadrupole frequency n Q an exact solution of the problem of the eigenvalues for a system of spins with I = 3/2 in presence of an external magnetic field was necessary in order to evaluate the principal values, the directions of the principal axes, and the asymmetry parameter h of the quadrupole coupling tensor from the angular dependent NMR spectra. The conclusions from the NMR measurements are in very good agreement with the results of the 35 Cl nuclear quadrupole resonance (NQR) and the X-ray diffraction (XRD) studies on BCPS.

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“…Using the following matrix elements of the spin operators Explicit solutions for the eigenvalues of the quadrupolar Hamiltonian for a spin-k nucleus require diagonalizing a (2k + 1) x (2k + I) matrix. This has been _ [27].…”

Section: Matrix Elements Of the Quadrupolar Hamiltonianmentioning

confidence: 99%

Dynamic-angle spinning and double rotation of quadrupolar nuclei

Mueller

1991

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Exact solution of the eigenvalue problem for a spin system in the presence of a magnetic field

Cited by 20 publications

References 31 publications

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

Polarization of line radiation in the presence of external electric quadrupole and uniform magnetic fields: II. Arbitrary orientation of magnetic field

35Cl Nuclear Magnetic Resonance Study in Bis(4-Chlorophenyl)Sulphone [(ClC6H4)2SO2]

Dynamic-angle spinning and double rotation of quadrupolar nuclei

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