On the excitonic molecule

Wehner, R.K.

doi:10.1016/0038-1098(69)90206-3

Cited by 60 publications

(18 citation statements)

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“…We multiply the left hand side of Eq. (32) by Φ++ and by Φ ---a n d The values of parameters used in the calculation of the ground state energy E(biex) are listed in Table I Some of previous calculations of the biexciton binding (dissociation) energy EB in CuCl, based on the Hamiltonian without electron-hole exchange terms, are in excellent agreement with experimental data, for example that 44 meV deduced from Wehner's theorem [14]. However, the electron-hole exchange interaction taken into consideration in calculations reduces EB significantly, as it was shown by Forney et al [9] and also in our present calculations (see Table II).…”

Section: Numerical Results and Discussionsupporting

confidence: 63%

Excitonic Molecule in CuCl Crystal

Ungier

1993

Acta Phys. Pol. A

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The electronic structure of a biexciton is discussed while taking into account the detailed band structure of CuCl. The fine structure of the excitonic molecule is clarified with the effective electron-hole exchange effect taken into account beyond the effective mass approximation. The electron-hole exchange interaction mixes the states of opposite parities with respect to the permutation of electrons and holes. Two trial envelope functions, symmetric and antisymmetric under the permutation of two electrons or two holes, were used in the numerical minimization of the ground state energy of the biexciton. The obtained binding energy of the biexciton, as well as, the ratio of the mixing of the trial envelope functions of opposite parities are presented.

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Section: Numerical Results and Discussionsupporting

confidence: 63%

Excitonic Molecule in CuCl Crystal

Ungier

1993

Acta Phys. Pol. A

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“…In addition to these many-photon processes, the one-photon annihilation [12] is possible in the Ps − ion. The formula for the one-photon annihilation rate 1γ in the Ps − ion takes the form [12,13] 1γ = 64π 2 27…”

Section: Positron Annihilation In the Positronium Ion Bi-positroniummentioning

confidence: 99%

“…Note that each of these two formulae explicitly contain the expectation value of the electron-positron delta-function δ +− . The expression for the two-photon annihilation rate 2γ , equation (2), also includes the lowest order radiative correction to the two-photon annihilation rate [17].…”

Section: Positron Annihilation In the Positronium Ion Bi-positroniummentioning

confidence: 99%

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Influence of the pumping regime on lasing of an He–Xe optical-breakdown plasma

Аполлонов¹,

Bunkin²,

Derzhavin³

et al. 1984

Sov. J. Quantum Electron.

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Annihilation of the electron-positron pairs (or (e − , e + )-pairs, for short) in various polyelectrons e + n e − m = e − m e + n (where n 1 and m 1) is considered. In particular, we discuss the three-and four-photon annihilation of the (e − , e + )pairs in the three-body Ps − ion and four-body bi-positronium system Ps 2 . It is shown that the five-body e + 2 e − 3 ion is an unbound system. The closedform expression is derived for the amplitude-square |M| 2 of the three-photon annihilation of (e − , e + )-pair at arbitrary energies of the colliding particles. Analogous amplitude-square |M| 2 for the four-photon annihilation is reduced to the form which is convenient for future analytical calculations. A method which can be used to produce macroscopic polyelectrons is briefly discussed.

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“…The generalized Morse potential should be invariant under the replacement of s with 1=s, which reflects the symmtery of the Hamiltonian under the replacement of electrons with holes and of m * e with m * h . KM further required that this potential should satisfy the Feynman theorem for the ground-state energy [3,4], give the correct values of the binding energy between hydrogen molecules [5], and yield the binding energy of a biexciton which agrees with the results of Akimoto and Hanamura [6] for arbitrary s. With these stipulations, they constructed the following expression for the generalized Morse potential:where r 0 ¼ 1:4a s =S; a ¼ d ffiffiffi S p ; and S ¼ ð1 þ s 2 Þ=ð1 þ sÞ 2 . a s is the exciton radius and I is the ionization energy of an exciton with a given value of s. j and d are parameters which have the same value as for a hydrogen molecule.…”

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confidence: 99%

Excited States of Biexcitons

Varshni

2001

phys. stat. sol. (b)

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The calculation of the ground state energy of a biexciton is quite involved, and that of the excited states even more so. Karp and Moskalenko [1] (KM) proposed a model, which is intuitively very appealing, to get around this difficulty. They proposed to represent the interaction between two excitons by a Morse potential [2], in analogy with a diatomic molecule, but recognized that the Morse potential must be generalized to the case of an arbitrary ratio s (s ¼ m * e =m * h ) of the electron and hole masses. This ratio appears in the expression for the interaction potential because of the averaging of the energy of the Coulomb interaction of electrons and holes in two excitons over the functions of relative motion in excitons. This approach is justified if the binding energy of an exciton is greater than the binding energy of a biexciton. The generalized Morse potential should be invariant under the replacement of s with 1=s, which reflects the symmtery of the Hamiltonian under the replacement of electrons with holes and of m * e with m * h . KM further required that this potential should satisfy the Feynman theorem for the ground-state energy [3,4], give the correct values of the binding energy between hydrogen molecules [5], and yield the binding energy of a biexciton which agrees with the results of Akimoto and Hanamura [6] for arbitrary s. With these stipulations, they constructed the following expression for the generalized Morse potential:where r 0 ¼ 1:4a s =S; a ¼ d ffiffiffi S p ; and S ¼ ð1 þ s 2 Þ=ð1 þ sÞ 2 . a s is the exciton radius and I is the ionization energy of an exciton with a given value of s. j and d are parameters which have the same value as for a hydrogen molecule. KM found their values to be j = 0.351, and d = 1.44. At least when s ( 1, this model ought to work.Separating the three coordinates of the centre of gravity of a biexciton, KM obtained the Schrö -dinger equation for the relative motion of excitons in a biexciton, which takes place in the central force field given by the Eq. (1). The usual separation of the variable in problems with central forces can also be applied to the present case, and this led to the following Schrö dinger equation:where uðrÞ ¼ ryðrÞ, m s is the exciton mass, n is the total quantum number and ' is the angular momemtum quantum number. For ' ¼ 0, the Schrö dinger equation for the Morse potential can be solved analytically [2, 7] to a high degree of approximation [8]. In an analogous fashion, KM obtained the following expression for the energy of ' ¼ 0 states:However, for ' > 0, KM had to use an approximate method to calculate the energies. They obtained results for a number of levels for biexcitons in CuCl, CuBr and CuI.We shall represent the ratio of the binding energies of the biexciton and the exciton by R. Thus R ¼ Eð0; 0Þ=ðÀIÞ.Recently, Usukura, Suzuki and Varga [9] have calculated the binding energies and other properties of excitonic complexes by a precise variational method. A comparison of their ðR; sÞ curve with the one obtained from Eq. (2) with th...

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On the excitonic molecule

Cited by 60 publications

References 5 publications

Excitonic Molecule in CuCl Crystal

Excitonic Molecule in CuCl Crystal

Influence of the pumping regime on lasing of an He–Xe optical-breakdown plasma

Excited States of Biexcitons

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