Properties of the Hydrogen Molecular Ion II: Photo-Ionization from the 1s g, 2s gand 3s gStates

Bates, D. R.; Öpik, U.; Poots, G.

doi:10.1088/0370-1298/66/12/306

Cited by 62 publications

(34 citation statements)

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“…The angledifferential cross section is extracted by solving the timedependent Schrödinger equation (TDSE) on the preset mesh points and projecting the solution to uncoupled molecular Coulomb functions. The appealing features of the prolate coordinate system were already revealed in the pioneering work of Bates,Öpik, and Poots [12] on the H + 2 ion. Without attempting a comprehensive overview of its numerous implementations in treating diatomic molecules, we note that this coordinate system has been widely employed to capture the two-center characteristics.…”

Section: W/cmmentioning

confidence: 86%

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

2011

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Triple-differential cross sections for two-photon double ionization of the aligned hydrogen molecule at the equilibrium distance are presented for a central photon energy of 30 eV. The temporal response of the laser-driven molecule is investigated by solving the time-dependent Schrödinger equation in full dimensionality using two-center elliptical coordinates and a finite-element discrete-variablerepresentation approach. The molecular orientation is found to have a strong effect on the emission modes of the two correlated photoelectrons. This molecular effect is most noticeable when the molecular axis and the laser polarization vector are oriented parallel to each other. For intermediate cases between the parallel and perpendicular geometries, the dominant emission modes for twoelectron ejection oscillate between those for the two extreme cases. The contributions from different ionization channels are also analyzed in detail. Depending on the emission direction of the reference electron, the interference contributions from the various channels can be constructive or destructive at small alignment angles, while they always contribute constructively to the triple-differential cross sections near the perpendicular geometry.

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Section: W/cmmentioning

confidence: 86%

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

2011

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“…through numerical integration of the corresponding differential equation. 14 The diagrams involved in the calculation of A£ HD are similar in form to those one encounters in the perturbation of atomic systems in an external field. 11 The external fields in the present molecule are the hyperfine fields of nuclei at the sites of the electrons.…”

Section: ° and A O I -Lmentioning

confidence: 86%

Many-Body Perturbation Calculation of the Indirect Spin-Spin Coupling Constant in HD Molecule

Dutta

Das

1970

Phys. Rev. Lett.

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Nature 221, 947 (1969);Although the indirect spin-spin interaction between nuclei in molecules has been utilized extensively for qualitative understanding of electronic structures in molecules, its quantitative calculation even for the simple molecule HD has proved to be a formidable task, with the current situation far from conclusive. 1 " 8 The various theoretical approaches utilized so far can be divided broadly into two categories. In the first category is the conventional second-order perturbation as first proposed by Ramsey and Purcell. 1 ' 2 The difficulty with such an approach is that one requires a knowledge of the complete set of ground and excited states of the molecule, which is not usually available. 3 To obviate the knowledge of excited states, variation-perturbation procedures have been used by a number of authors. 4 " 8 In one class of such calculations, a diagonal-type perturbation procedure 4 * 5 was used, the second-order energy due to the hyperfine field of one nucleus being minimized to obtain the first-order perturbed wave function of the molecule. This function was then utilized to calculate the cross term in the second-order energy involving the other nucleus to obtain J HD . The difficulty with this procedure was that the second-order nuclear self-coupling W. M. Neupert and M" Swartz, Astrophys. energy is infinite in nonrelativistic theory, no real minimum thus being attainable in a variational approach. A second class of variation perturbation calculation has attempted to extremize the cross terms in the second-order energy proportional to J HD using variational functions which describe the first-order perturbation due to both nuclei. 6 " 9 The difficulty with this procedure is that the cross term due to two perturbations has by itself no minimum and one does in fact get oscillatory behavior as the number of parameters increased. 9 In this paper, we have revived the perturbation approach in a form that meets the major difficulty, namely, a knowledge of a complete set of states for the molecule. This is accomplished by using the linked-cluster many-body perturbation theory (LCMBPT), 10 where a neighboring Hamiltonian 3C 0 , for which the complete set of states can be obtained exactly, is used as the starting point for a perturbation treatment of A3C = 3C-3CQ. In our work here, a multiple perturbation approach is used in conjunction with the LCMBPT, using the sum of AJC and the two hyperfine interaction Hamiltonians 3C H ' and 3C D ' associated with the two nuclei. For the speed of convergence of the perturbation approach, it is nec-The linked-cluster many-body perturbation approach has been applied to the study of indirect nuclear spin-spin coupling constant J HD in HD molecule. The complete set of states used were the bound and continuum states of H 2 + molecular ion with the internuelear separation appropriate to H 2 molecule. Our calculated value of J HD through the Fermi contact interaction mechanism is +42.57 Hz in good agreement with the most recent experimental value of 442.7±0.7 ...

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“…Approximate wavelengths are given in Table V. Intensity calculations for quadrupole transitions have been performed by James and Coolidge (1938) and by Bates and Poots (1953). It was shown that the line strength is given by (34) where W aJ , ¥V/ are the normalized wave functions of the initial and final states, Ν is the quadrupole moment operator, A r s is its scalar, J is the idemfactor, and the square of the modulus denotes the double dot product of the tensor and its conjugate, i.e., the sum of the squares of its nine components.…”

Section: --mentioning

confidence: 99%

“…The intensity decrease for the overtone bands is slower than for most molecular spectra, partly because of a (frequency) 3 factor, instead of a first power as for dipole radiation, and partly because of the large anharmonicity of H 2 . Bates and Poots (1953) used exact wave functions for H 2 to study its quadrupole rotation-vibration spectrum. The Einstein spontaneous emission transition probabilities for the S(0) lines in the (1-0), (2-0), and (3-0) bands are 1.6 X 10~7, 3.1 Χ ΙΟ -8 , and 5 X 10~9 sec -1 , respectively.…”

Section: Tv = J φν-Ar) N(r) ψ ν~ γ-(κ) R 2 Drmentioning

confidence: 99%

“…The overtone band intensities fall off very slowly; this is quali tatively because the dipole moment is produced by the vibration and increases with it. Wu's formulae were applied to HD + by Bates and Poots (1953), who found a transition probability 18 sec -1 for the (1-0) band. They found a value of 0.02 sec' 1 for the (1-0) band in 14 N 15 N+.…”

Section: Transitions Violating Approximate Selection Rulesmentioning

confidence: 99%

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Forbidden Transitions

Garstang¹

1962

Atomic and Molecular Processes

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Properties of the Hydrogen Molecular Ion II: Photo-Ionization from the 1s _g, 2s _gand 3s _gStates

Cited by 62 publications

References 9 publications

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

Alignment effects in two-photon double ionization of H2in femtosecond xuv laser pulses

Many-Body Perturbation Calculation of the Indirect Spin-Spin Coupling Constant in HD Molecule

Forbidden Transitions

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