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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.

The thermodynamic functions of ideal Bose gases are important in fundamental physics and have been widely studied via both analytical and numerical methods. Studying these functions is important for undergraduates as it is the first step for exploring ultracold physics and quantum phenomena. However, the accuracy of the calculations is usually limited owing to the discontinuity of the functions at critical points. In this study, we present an analytical procedure for deriving the chemical potential, the total energy, and the heat capacity as functions of the absolute temperature. The approximated analytical results are compared with values obtained using the numerical method to evaluate their accuracy and to determine the applicable range of the procedure. Moreover, a correction for the chemical potential calculated around the critical temperature was proposed to reduce the deviation between the approximated and numerical approaches.

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This paper investigates the recollision dynamics of the nonsequential double ionization process induced by linearly polarized laser pulses with the three-dimensional classical ensemble model. The results show that the correlated two-electron momentum distribution is contaminated by the double recollision events for sufficiently short laser wavelength. When the laser wavelength increases from near-infrared to mid-infrared, the single-recollision events are more prominent than the double-recollision one. Moreover, the mechanisms governing the nonsequential double ionization process are also thoroughly studied in the case of double-recollision.

In this study the classical three-dimensional ensemble model is utilized for investigating the role of final state electron-electron repulsion in forming the ultimate correlated two-electron momentum distribution. For the first time, a comprehensive analysis has been made to thoroughly understand such repulsive force associating with each microscopic mechanism of nonsequential double ionization. The helium exposed to 800-nm laser with two representative intensities of 3.5×1014 W/cm2 and 4.5×1014 W/cm2 is used for illustration. The results indicate the dominance of electron-electron repulsion in direct and recollision-induced excitation with subsequential ionizations. While its contribution in case of exchanging-state mechanism gradually emerges as the laser intensity increases.

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