Molecular Siegert states in an electric field. II. Transverse momentum distribution of the ionized electrons

Pham, Vinh N. T.; Tolstikhin, Oleg I.; Morishita, Tōru

doi:10.1103/physreva.89.033426

Cited by 25 publications

(33 citation statements)

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“…(6) yields the same value as the definition used previously for atoms [40,47]. In general, the distribution is not always similar to a Gaussian [48,49]. Therefore, the definition according to Eq.…”

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confidence: 92%

Signatures of Molecular Orbital Structure in Lateral Electron Momentum Distributions from Strong-Field Ionization

2015

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Strong-field ionization of aligned diatomic and polyatomic molecules such as O 2 , N 2 , C 2 H 4 , and others in circularly polarized laser fields is investigated theoretically. By calculating the emission-angle-resolved lateral width of the momentum distribution perpendicular to the polarization plane, we show that nodal planes in molecular orbitals are directly imprinted on the angular dependence of the width. We demonstrate that orbital symmetries can be distinguished with the information obtained by observing the lateral width in addition to the angular distributions. DOI: 10.1103/PhysRevLett.114.103004 PACS numbers: 33.80.Rv, 33.20.Xx Progress in strong-field science has led to the possibility to image dynamics in atoms and molecules on the attosecond time scale and angstrom spatial scale [1][2][3]. Laser-based methods to image molecular structure include diffraction of recolliding electrons [4][5][6], Coulomb explosion imaging [7,8], and orbital tomography [9][10][11][12][13][14]. Information about the orbital structure of aligned molecules is also contained in the dependence of the ionization rate on the angle between the laser polarization direction and the molecular axis [15,16] with particular care needed for polar molecules [17]. Rich information is obtained by measuring three-dimensional photoelectron momentum distributions (PMDs) of aligned molecules. This is possible by combining laser-induced alignment of molecules [18,19] and velocity-map imaging [20,21]. Alternatively, PMDs can be measured in a reaction microscope [22], where information on the molecular orientation is obtained by electron-ion coincidence. For molecular imaging, circularly polarized light effectively delivers a 360°scan of the aligned molecule [23][24][25], which is an advantage over linear polarization. In the classical trajectory model without Coulomb effects, electrons measured at an emission angle ϕ originate from ionization at the angle ϕ AE 90°with the sign depending on the rotation direction of the field. Another advantage of circular polarization is the absence of electron recollisions that could obscure the measured distribution. Nodal structures have been measured successfully for various molecules using many-cycle circularly polarized pulses [26][27][28][29]. Theoretical prediction of the PMDs is complicated by the nonperturbative nature of the ionization process in the commonly used near-infrared fields. Only for very small molecules such as H 2 þ [30] or in proof-of-principle calculations with model orbitals [31], the solution of the timedependent Schrödinger equation (TDSE) is an option. In contrast, the strong-field approximation (SFA) can be used to calculate PMDs of arbitrary molecules and often yields accurate results [32][33][34]. In polar molecules, an extended SFA including the Stark shift is beneficial [35][36][37].To the authors' knowledge, none of the published experimental work on molecular imaging has made use of the lateral photoelectron momentum distribution (LPMD), i.e., the distribution of the m...

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confidence: 92%

Signatures of Molecular Orbital Structure in Lateral Electron Momentum Distributions from Strong-Field Ionization

2015

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“…(6) for a given m. In the numerical solution of Eq. (1) [12][13][14] it is more efficient to use an adiabatic (dependent on η) basis in the expansion (4), but in constructing the asymptotic solution for F → 0 [19,25] it is more convenient to use the diabatic (independent of η) basis (5). The functions (5) are orthonormal with respect to the inner product…”

Section: Siegert States In An Electric Fieldmentioning

confidence: 99%

“…[12] for axially symmetric potentials and in Refs. [13,14] for arbitrary potentials without any symmetry.…”

Section: Siegert States In An Electric Fieldmentioning

confidence: 99%

“…We have developed a powerful method to calculate oneelectron SSs in the combination of an atomic [12] or molecular [13,14] potential and an electric field. This method is capable of treating both the tunneling and the over-the-barrier ionization regimes.…”

Section: Introductionmentioning

confidence: 99%

“…At higher intensities, accurate but rather laborious calculations of the type reported in Refs. [12][13][14] are indispensable for obtaining theoretical predictions applicable at the quantitative level. Meanwhile, at lower intensities, an approximate analytical solution of the SS eigenvalue problem is possible.…”

Section: Introductionmentioning

confidence: 99%

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Weak-field asymptotic theory of tunneling ionization including the first-order correction terms: Application to molecules

et al. 2015

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The weak-field asymptotic theory (WFAT) of tunneling ionization including the first-order correction terms is validated for molecules by comparison with accurate calculations of molecular Siegert states in a static electric field. Both fundamental observables related to tunneling ionization, namely, the ionization rate and transverse momentum distribution of the ionized electrons, are considered. This complements our previous study of atoms [V. H. Trinh et al., Phys. Rev. A 87, 043426 (2013)]. Similarly to the atomic case, the first-order terms essentially improve the agreement between the WFAT and accurate results in a wide interval of fields up to the onset of over-the-barrier ionization. This establishes the WFAT including the first-order correction terms as an appealing alternative to accurate calculations in the tunneling regime. In addition to demonstrating the quantitative performance of the WFAT, the theory is shown to be helpful for understanding the field and orientation dependencies of the observables. In particular, we show that the first-order terms account for a deviation of the shape of the orientation dependence of the ionization rate of a molecule from that of the ionizing orbital as the field grows, which has important implications for strong-field molecular imaging techniques. This prediction of the WFAT is confirmed by comparison with time-dependent calculations.

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Structure factors for tunneling ionization rates of diatomic molecules

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Tolstikhin

Madsen

et al. 2015

Atomic Data and Nuclear Data Tables

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Molecular Siegert states in an electric field. II. Transverse momentum distribution of the ionized electrons

Cited by 25 publications

References 18 publications

Signatures of Molecular Orbital Structure in Lateral Electron Momentum Distributions from Strong-Field Ionization

Signatures of Molecular Orbital Structure in Lateral Electron Momentum Distributions from Strong-Field Ionization

Weak-field asymptotic theory of tunneling ionization including the first-order correction terms: Application to molecules

Structure factors for tunneling ionization rates of diatomic molecules

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