Simultaneously, the vibrational nuclear dynamics and full dimensional electronic dynamics of the deuterium molecular ion exposed to the linear polarized intense laser field are studied. The time dependent Schr\"odinger equation of the aligned D2+ with the electric laser field is solved for the simulation of the complicated dissociative ionization processes and compared with the recent related experimental results. In this work, the R-dependent ionization rate and the enhanced ionization phenomenon beyond the Born-Oppenheimer approximation (BOA) are introduced and calculated. The substructure of the nuclear kinetic energy release spectra are revealed as the Coulomb explosion energy spectra and dissociation energy spectra in the dissociation-ionization channel. The significant and trace of these distinct sub-spectra in the total spectra comparatively are displayed and discussed.
H 2 and H 2 + , two basic molecules, are extensively studied experimentally and theoretically. These studies cause to appear comprehensive new phenomena [1]. Studies of the dynamic of H 2 (D 2 ) and H 2 + (D 2 + ) exposed to intense laser field are very complicated because involved two processes, ionization and dissociation simultaneously. In intense laser field, electron dynamics occur in attosecond time scales and nuclear dynamics, vibration and rotation, takes place in femtosecond and picosecond time scales. It is possible based on Born
Oppenheimer approximation (BOA) to investigate these two dynamics, nuclear and electronic, separately. This approach is extensively used to investigate electronic dynamics of molecules in intense laser fields. When molecule is exposed to intense laser field, accurately probe of molecular dynamics that is involved simultaneously electronic and nuclear dynamics is very complicated. In these conditions, the perfect complicated simulation based on the solving of the time dependent Schrödinger equation (TDSE) beyond BOA, the most rigorous and adequate, abinitio theoretical approach, would require to the complete description molecular dynamics. For a molecule with two or farther electrons, this task is very far from present available computer ability, even through without consideration the nuclear dynamics [2]. For the linear molecule with only one electron, this rigorous approach is feasible only for aligned molecule with the electric laser field together with the reduction of the dimensions of the electronic motion.
Therefore, the most theoretical investigations were carried out for the dissociative ionization of the aligned H 2 + (D 2 + ) parallel to the electric field axis of the linear polarized laser pulse and three spatial coordinates of the electron in the TDSE are reduced to 1D based on an approximation known as quasi-Coulombic or soft-core (SC) Coulomb potential [3] to be able to carry out simulation, so that many research were done based on SC approximation [4][5][6] even for two electronic systems [7]. Nevertheless, the extent of ability and validity of SC approximation in the research of electron dynamics in multi-electron systems especially involved one and two electrons has been the subject controversy. The results of this work will explore this question. In this research, the previous studies are extended. We have done perfect complicated simulation of D 2 + beyond BOA and also without SC approximation, i.e., by the rigorous solution of the TDSE for the full dimensional electron dynamics and also with consideration the nuclear dynamics of D 2 + that is aligned with the electric laser field. ) located in the laser field as ( ) ( )
parallel to the inter-nuclear axis in
) reads as (throughout of this article we use the atomic unit unless stated)
where the total 3D electronic Hamiltonian is given by [8-10]
with 0 E being the laser peak amplitude, πυ ω 2
the angular frequency, and finally f(t) the laser pulse envelope which is set as
where p τ is the full width at half maximum (FWHM) duration of the Gaussian shape of the pulse of laser. σ state (Fig. 1).
In intense laser field, some parts of D 2 + wavepackage become unbound and outgoing through different channels. A part of this unbound wavepacket becomes outgoing as D+D + through dissociation channel (DC) that is not concerned in this article and an other part becomes outgoing through dissociation-ionization channel (DIC) as D + +D + (Fig. 1) that we study in this article. The nuclear components in this channel (DIC) possess both dissociation energy (DE) and
The accurate kinetic spectra of different decay channel, i.e. ionization and dissociation or both simultaneously, can be determined by the virtual detector method [10][11]. The virtual detector method makes it possible to precisely define and distinguish outgoing norms and energy from different DC and DIC channels. This method allows us to accurately determine CEE and DE of nuclear fragments through DIC. More details about the virtual detectors method and its abilities were represented in our previous reports [10,18].
One of the main purposes of this work is comparison between the present simulation results and the recent experimental results [5,6]. The experimental researches that up until now to be directly started with H 2 + and D 2 + molecular ion are extremely few [12]. Most experiments have been performed using H 2 and D 2 molecules and during the rise of the femtosecond laser pulse, H 2 + (D 2
) molecular ion are created. These pulses are usually focused to the peak intensities of ~10 13 -10 15 W/cm 2 into the gas jet of unaligned H 2 or D 2 neutral molecules. When H 2 (D 2 ) molecule is exposed to a linearly polarized intense femtosecond laser pulse, the first electron is ejected during rising laser pulse. We assume that the ejection of this first electron is occurred at the time on t instantaneously via tunneling (Fig. 1). Also, we suppose t
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