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N. Billy, F. Bielsa, A. Douillet,
L. Hilico, J.P. Karr, S. Killiç
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Presentation
In the frame of the quantum three-body coulombian problem,
we are working on the precise calculation of the energy levels and wave
functions in systems such as He, H2+
or HD+ (among them, some of them are symmetric by exchange
of two particles, others are not).
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- Our method consists in writing the Schrödinger
equation in perimetric
coordinates, expanded in a variational basis of sturmian functions. The obtained
linear system is diagonalized
numerically using the Lanczos algorithm.
- The interest of this method is that the hamiltonian takes
the form of a sparse band matrix, allowing to converge the
eignenenergies with a very good accuracy of 10-14 atomic
unit and to obtain excellent wave functions.
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Résultats
- Energies and wave functions of all bound vibrational states
of the molecular ions H2+, D2+
and HD+ of total angular momentum J=0 and J=1
(S and P states).
- Static polarizabilities of the vibrational levels of J=0.
- Two-photon transition probabilities and light shifts
betweent bound states of J=0.
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Results
for exotic molecular ions
- Energies of the bound states (J=0 and J=1) of exotic
(muonic or pionic) molecular ions.
- Energies and widths (or coulombian lifetime) of the excited
states of these ions, as well as their radiative widths.
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Perspectives
- D states (J=2).
- Calculation of radiative and relativistic corrections.
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References
(publications)
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- L. Hilico, N. Billy, B. Grémaud, and D.
Delande, Ab initio calculation of the J=0 and J=1
states
of the
H2+
D2+ and HD+ molecular ions.Eur.
Phys. J. D 12, 449 (2000).
- L. Hilico, N. Billy, B. Grémaud, and D.
Delande, Polarisabilities,
light shifts and two-photon
transition
probabilities between J=0 states of the H2+
and D2+ molecular ions.
J.
Phys. B 34,
1-17
(2001).
- J. Carbonnel,R. Lazauskas,D.
Delande, L. Hilico, S. Kilic, A
new vibrationnel level of the H2+
molecular ion. Europhysics
lett. 64, 316-322, (2003).
- S. Kiliç, J-P. Karr, L. Hilico, Coulombic and radiative decay rates of the
resonances of the exotic molecular ions ppμ, ppπ, ddμ, ddπ and dtμ, Phys.
Rev. A.(2004)
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Collaborations
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Vladimir Korobov
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