Excited states and the transition moments of the hydrogen molecule

Wolniewicz, L.; Staszewska, G.

doi:10.1016/s0022-2852(03)00121-8

Cited by 118 publications

(120 citation statements)

References 15 publications

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“…49 Based on this clamped-nuclei curve, the level 2ppC À (v ¼ 0, N ¼ 1) has been predicted to lie 0.45 cm À1 above the experimental value in a fully ab initio coupled-equations approach, 50 whereas MQDT, with an eigenquantum-defect function extracted from the same clamped-nuclei curve and using the frame-transformation method, predicts the same level to lie 0.14 cm À1 below the experimental value. 51 Unfortunately, accurate quantum-chemical calculations of the type of Ref.…”

Section: A Clamped-nuclei Eigenquantum Defectsmentioning

confidence: 90%

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Towards measuring the ionisation and dissociation energies of molecular hydrogen with sub-MHz accuracy

et al. 2011

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The most precise determination of the ionisation and dissociation energies of molecular hydrogen H 2 was carried out recently by measuring three intervals independently: the X / EF interval, the EF / n ¼ 54p interval, and the electron binding energy of the n ¼ 54p Rydberg state. The values of the ionisation and dissociation energies obtained for H 2 , and for HD and D 2 in similar measurements, are in agreement with the results of the latest ab initio calculations [Piszczatowski et al., J. Chem. Theory Comput., 2009, 5, 3039; Pachucki and Komasa, Phys. Chem. Chem. Phys., 2010, 12, 9188] within the combined uncertainty limit of 30 MHz (0.001 cm À1 ). We report on a new determination of the electron binding energies of H 2 Rydberg states with principal quantum numbers in the range n ¼ 51-64 with a precision of better than 100 kHz using a combination of millimetre-wave spectroscopy and multichannel quantumdefect theory (MQDT). The positions of 33 np (S ¼ 0) Rydberg states of ortho-H 2 relative to the position of the reference 51d (Rydberg state have been determined with a precision and accuracy of 50 kHz. By analysing these positions using MQDT, the electron binding energy of the reference state could be determined to be 42.3009108(14) cm À1 , which represents an improvement by a factor of $7 over the previous value obtained by Osterwalder et al. [J. Chem. Phys., 2004, 121, 11810]. Because the electron binding energy of the high-n Rydberg states will ultimately be the limiting factor in our method of determining the ionisation and dissociation energies of molecular hydrogen, this result opens up the possibility of carrying out a new determination of these quantities. By evaluating several schemes for the new measurement, the precision limit is estimated to be 50-100 kHz, approaching the fundamental limit for theoretical values of $10 kHz imposed by the current uncertainty of the proton-to-electron mass ratio.

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Section: A Clamped-nuclei Eigenquantum Defectsmentioning

confidence: 90%

“…51 Unfortunately, accurate quantum-chemical calculations of the type of Ref. 49 are not possible presently for states beyond n z 5, because of inherent convergence problems arising in the computations. No significant improvement of this situation is in sight as far as we are aware.…”

Section: A Clamped-nuclei Eigenquantum Defectsmentioning

confidence: 99%

Towards measuring the ionisation and dissociation energies of molecular hydrogen with sub-MHz accuracy

et al. 2011

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“…As shown in section 2.2, these FCD are a prerequisite for the calculation of cross sections for the corresponding transitions. The potential curves of the six molecular states have been taken from [27], [28,29], [30], [31], [32,33] and [32,34], respectively. The potential curves of the ionic curves are from [15] and [35].…”

Section: Franck-condon Densitiesmentioning

confidence: 99%

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule

Wünderlich

2011

Chemical Physics

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Ionization cross sections for the hydrogen molecule have been calculated by applying the classical Gryzinski theory combined with the Franck-Condon theory. It is shown that -if the reaction channels, Franck-Condon factors and Franck-Condon densities are taken into account properly -the calculated cross sections for ionization of the molecular ground state X 1 Σ + g (v ′ = 0) are in almost perfect agreement with the latest and most reliable experimental results. A comprehensive database is established which includes vibrationally resolved cross sections for non-dissociative and dissociative ionization of the molecular ground state as well as for the first five non-repulsive electronically excited states in the molecule.

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“…We presented the first full calculation of photon-energy dependent Raman association cross sections including all rovibrational resonances associated with the intermediate states, based on the accurate electronic potential energy surfaces and properties computed by Wolniewicz and Staszewska. [18][19][20][21] We compared the exact results with those of the Placzek-Teller approximation and we showed that …”

Section: Discussionmentioning

confidence: 99%

“…The ab initio potential energy curves and electronic dipole transition moments are taken from calculations by Wolniewicz and Staszewska. [18][19][20][21] We use the vibrationally resolved lifetimes from the work by Fantz and Wu¨nderlich 22 where the sum of the initial state energy and the energy of the incoming photon exceeds the dissociation limit of an intermediate electronic state, we use the Green function absorbing boundary condition (ABC) method [23][24][25] to prevent the matrix in eqn (10) from becoming singular. The ABC method consists of replacing the constant ½G m by an r-dependent function g(r), thus effectively augmenting the potential V nO (r) with a negative imaginary potential which absorbs the wave function in the physically non-relevant outer region.…”

Section: Methodsmentioning

confidence: 99%

Raman association of H2 in the early universe

et al. 2006

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We investigate the contribution made by Raman scattering to the formation of molecular hydrogen in astrophysical environments characteristic of the early stages of the evolution of the universe. In the Raman process that we study, a photon is scattered by a pair of colliding hydrogen atoms leaving a hydrogen molecule that is stabilized by the transfer of kinetic and binding energy to the photon. We use a formulation for calculating the photon scattering cross section in which an infinite sum of matrix elements over rovibrational levels of dipole accessible electronic states is replaced by a single matrix element of a Green's function. We evaluate this matrix element by using a discrete variable representation.

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Excited states and the transition moments of the hydrogen molecule

Cited by 118 publications

References 15 publications

Towards measuring the ionisation and dissociation energies of molecular hydrogen with sub-MHz accuracy

Towards measuring the ionisation and dissociation energies of molecular hydrogen with sub-MHz accuracy

Vibrationally resolved ionization cross sections for the ground state and electronically excited states of the hydrogen molecule

Raman association of H2 in the early universe

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