Symmetry adaptation techniques in n-photon absorption spectroscopy

Daoud, Mohammed; Kibler, M.

doi:10.1016/0925-8388(93)90354-p

Cited by 2 publications

(15 citation statements)

References 16 publications

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“…The number of independent intensity parameters I in (23) The computation, via Equations (18) or (19), (24) and (25), of the I parameters is a difficult task in general. Therefore, they may be considered, at least in a first step, as phenomenological parameters.…”

Section: Discussion and Closing Remarksmentioning

confidence: 99%

“…Therefore, they may be considered, at least in a first step, as phenomenological parameters. In this respect, Equations (18) or (19), (24) and (25) should serve as a guide for reducing the number of I parameters. Once the number of independent parameters I in the intensity formula (23) has been determined, we can obtain the polarization dependence of the intensity strength S i(Γ)→f (Γ ′ ) by calculating the tensor products P (K) a ′′ Γ ′′ γ ′′ (with K = k p−1 , ℓ p−1 and a ′′ = r, s) occurring in Equation (23).…”

Section: Discussion and Closing Remarksmentioning

confidence: 99%

“…which does not depend on γ ′′ . The I parameters in (24) can be calculated in an ab initio way or can be considered as phenomenological parameters. In both approaches, the following properties and rules are of central importance.…”

Section: Intensity Formulamentioning

confidence: 99%

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

Kibler

Daoud

1993

Lett Math Phys

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Section: Discussion and Closing Remarksmentioning

confidence: 99%

Section: Discussion and Closing Remarksmentioning

confidence: 99%

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

Kibler

Daoud

1993

Lett Math Phys

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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%

“…Selection rules based on the SU(2) ⊃ G * symmetry were obtained in Refs. [10,11,17] for parity-forbidden ED-TPA.…”

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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Symmetry adaptation techniques in n-photon absorption spectroscopy

Cited by 2 publications

References 16 publications

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

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

Two-photon spectroscopy between states of opposite parities

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