Sum rules for multi-photon spectroscopy of ions in finite symmetry

Kibler, M.; Daoud, Mohammed

doi:10.1007/bf00761495

Cited by 7 publications

(14 citation statements)

References 23 publications

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“…(26)-(28), and bearing in mind the relatioñ l = 2l + 1/2 from (21), one finds Note that to ensure the natural relation between l andl, positive roots are chosen forã 0 andb 0 values. This choice leads to involve only the odd solutions, 5,18 which means that the states corresponding to the potential in (7) Thus, we have in this section shown that under the canonical transformations, energies and coupling constants of the non-central potentials of interest trade places and orbital angular momenta are re-scaled, which clarifies that there is really only one quantum mechanical problem, not two. We finally remark that although here we have only focused on eigenvalues and spherical polar coordinates, generalization of the technique used to describe eigenfunctions of the present systems in analytical form (using the discussion in Sec.…”

Section: Mappings Between the Two Distinct Systemsmentioning

confidence: 92%

Mapping of Non-Central Potentials Under Point Canonical Transformations

2002

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Section: Mappings Between the Two Distinct Systemsmentioning

confidence: 92%

Mapping of Non-Central Potentials Under Point Canonical Transformations

2002

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“…[25,27] and for the oscillator with AB field is shown in ref. [28]. The effect of the Dirac monopole g and AB flux F on the energy spectrum is shown in Figures 4 and 5, respectively.…”

Section: Casementioning

confidence: 97%

“…[20][21][22][23][24][25][26][27] Also, the oscillator potential in the presence of AB field has been studied. [28] The present article will study the exact analytical solutions and spectrum analysis of the pseudoharmonic oscillator potential in the presence of θ-dependent scalar potential and the sum of two vector potentials. The vector potentials are Dirac magnetic monopole and Aharonov-Bohm field.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions and spectrum analysis of a noncentral potential in the presence of vector potential

Ghosh¹,

Nath

2020

Int J of Quantum Chemistry

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We studied exact solutions and spectrum analysis of the pseudoharmonic oscillator in the presence of θ‐dependent scalar potential and the sum of two vector potentials Dirac magnetic monopole and Aharonov‐Bohm field. The effect of the Dirac magnetic monopole (g), Aharonov‐Bohm field (ℱ), the dissociation energy of diatomic molecules (D e), equilibrium intermolecular separation (r e), and the reduced mass (μ) on the energy spectrum for some diatomic molecules (CO, NO, N2, CH, H2, and ScH) are analyzed. We compared our results with theoretical experiments of pseudoharmonic oscillator potential in a molecular system.

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“…Further investigations of parity-allowed ED-TPA were conducted in Refs. [6][7][8][9][10][11] on the basis of microscopic models and symmetry adaptation methods [12] for the chain of groups SU(2) ⊃ G * (where G * is the double group of the group G).…”

Section: Preliminariesmentioning

confidence: 99%

Two-photon spectroscopy between states of opposite parities

Daoud

Kibler

1995

Phys. Rev. B

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Magnetic and electric dipole two-photon absorption (MED-TPA), recently introduced as a spectroscopic technique for studying transitions between states of opposite parities, is investigated from a theoretical point of view. An approximation referred to as weak quasiclosure approximation is used together with symmetry adaptation techniques to calculate the transition amplitude between states having well-defined symmetry properties. Selection rules for MED-TPA are derived and compared to selection rules for parity-forbidden electric dipole two-photon absorption. PRELIMINARIES Two-photon spectroscopy is now an experimental technique widely used in various domains, as for instance transition ions in crystals and excitons in semiconductors and insulators. Two-photon spectroscopy experiments on excitons were first achieved by Hopfield and Worlock. ' Recently, Frohlich et al. reported two-photon absorption measurements for the three alkali halides RbI, NaI, and NaBr. These authors considered nonlinear processes where two photons are simultaneously absorbed, one photon by magnetic dipole transition and the other by electric dipole transition. The resulting magnetic and electric dipole two-photon absorption (MED-TPA) has to be distinguished from the following.(i) The classical electric dipole two-photon absorption (ED-TPA) where the two photons are simultaneously absorbed by electric-dipole transition between states of the same parity. The standard theory for parity-allowed ED-TPA was given by Axe and the corresponding selection rules arising from the point symmetry group G of the absorbing site were derived by Inoue and Toyazawa and by Bader and Gold. Further investigations of parity-allowed ED-TPA were conducted in Refs. 6 -11 on the basis of microscopic models and symmetry adaptation methods' for the chain of groups SU(2)ZG* (where G* is the double group of the group G). (ii) The forced ED-TPA where the two photons are simultaneously absorbed by electric dipole transition between states of opposite parities. Several parity-violation mechanisms were introduced' ' for explaining parity-forbidden ED-TPA, especially for partly-filled shell ions in crystals. Selection rules based on the SU(2) D G* symmetry were obtained in Refs. 10, 11, and 17 for parity-forbidden ED-TPA. Of course, MED-TPA and (parity-allowed and parityforbidden) ED-TPA differ as far as simple considerations on spin are concerned. We may also a priori expect some differences regarding the selection rules coming from the point symmetry of the site. In this connection, the selection rules for MED-TPA used in Ref. 2 were obtained in the spirit of the pioneer work by Inoue and Toyazawa. However, it is to be realized that the selection rules introduced in Ref. 4 and extended by Bader and Gold were developed, on the basis of symmetry considerations only, for (parity-allowed) ED-TPA.It is the aim of this paper to show that the SU(2) DG* selection rules for parity-forbidden ED-TPA hold for MED-TPA when the two absorbed photons in both processes are different. We sh...

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Sum rules for multi-photon spectroscopy of ions in finite symmetry

Cited by 7 publications

References 23 publications

Mapping of Non-Central Potentials Under Point Canonical Transformations

Mapping of Non-Central Potentials Under Point Canonical Transformations

Exact solutions and spectrum analysis of a noncentral potential in the presence of vector potential

Two-photon spectroscopy between states of opposite parities

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