Signatures of quantum chaos in rare-earth elements: II. Characterization of the energy eigenvalues and dipole moments of Ce<scp>I</scp>and Pr<scp>I</scp>

Using the configuration interaction Hartree-Fock method, the even and odd Hamiltonian matrices of Sm IX are studied in the ls and j j coupling schemes. Sm IX is isoelectronic with Xe but because of 4f orbital contraction, and the near degeneracy of 4f and 5p binding energies, the lowest configuration is a mixture of states with differing numbers of 4f and 5p electrons. Diagonalization of the Hamiltonian results in a set of eigenvalues and eignvectors which are characterized using various statistical tests of random matrix theory.

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“…level repulsion but with no correlation between E i and E i+2 . Similar behaviour was reported in [18] for odd Ce.…”

Section: Covariance Of Adjacent Spacingssupporting

confidence: 88%

“…± by Cummings et al [17,18], where the Hamiltonian and coupling matrices, energy eigenvalues and dipole moments of Pr I were also investigated, with possible multifractal behaviour found in several rare-earth elements including Ce [19].…”

mentioning

confidence: 99%

Characterization of the structure and eigenvalue spectra of the compound states of Sm IX

et al. 2006

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“…For cases intermediate between fully chaotic and regular systems, the correlation hole is less deep and/or abrupt. In particular a Poisson spectrum should show no correlation hole [38,40,26]. The jFourier transformj 2 , jC(t)j 2 and hjC(t)j 2 i of the rescaled quasienergies is shown in Fig.…”

Section: Correlation-hole Methodsmentioning

confidence: 99%

“…In reality a system has usually a mixture of both regular and chaotic characteristics and the Brody distribution [23][24][25][26] is used to investigate this:…”

Section: Nearest Neighbour Spacing Distributionmentioning

confidence: 99%

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Quantum statistics of a kicked particle in an infinite potential well

Kilbane

Cummings

O'Sullivan

et al. 2006

Chaos, Solitons & Fractals

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It is known that no one statistical test by itself can give conclusive evidence for the presence or absence of quantum chaos within a given system. For this reason a range of detailed tests, namely the nearest neighbour spacing distribution, covariance of adjacent spacings, spectral rigidity, correlation-hole method and inverse participation ratio have been applied to the quasienergies and quasieigenstates of a periodically kicked particle in a 1-D infinite potential well. The results are compared with the predictions of random matrix theory for various kick strengths in order to search for signatures of quantum chaos within this system.

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4f collapse, level density inflation and the emergence of `compound-like' atomic states in rare earth ions

Kilbane

Cummings

McGuinness

et al. 2002

J. Phys. B: At. Mol. Opt. Phys.

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4f collapse in rare earth ions produces an enormous level density due to the occurrence of near-degeneracies of 4f/5p and 4f/5s binding energies. As a result, there is a complete breakdown of the single-particle approximation and the level and line spectra satisfy many of the distributions associated with random matrix theory. Similar behaviour has been previously reported in spectra associated with wavefunction contraction effects or atoms containing open 4f subshells; here the effects of combining both phenomena are explored. In particular it is shown that the adjacent level separations satisfy a Wigner distribution, while transitions between them obey the Porter-Thomas distribution. Detailed Hartree-Fock calculations show that there is a strong correlation between line strength and transition energy. This correlation is pursued and parametrized for the particular case of 4f→5d, 5p→5d and 5s→5p transitions in Sm IX within the unresolved transition array model.

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Signatures of quantum chaos in rare-earth elements: II. Characterization of the energy eigenvalues and dipole moments of CeIand PrI

Cited by 5 publications

References 35 publications

Characterization of the structure and eigenvalue spectra of the compound states of Sm IX

Characterization of the structure and eigenvalue spectra of the compound states of Sm IX

Quantum statistics of a kicked particle in an infinite potential well

4f collapse, level density inflation and the emergence of `compound-like' atomic states in rare earth ions

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