Photorecombination Cross Sections Research Articles

Retrieval of Angle-Dependent Strong-Field Ionization by Using High Harmonics Generated from Aligned N2 MoleculesSupported by the National Natural Science Foundation of China (Grant Nos. 11774175, 91950102, 11834004, and 91850209), the National Key Research and Development Program of China (Grant No. 2018YFB0504400), the Science and Technology Commission of Shanghai Municipality (Grant No. 18DZ1112700), the Strategic Priority Research Program of Chinese Academy

We propose a method to retrieve the angle-dependent strong-field ionization of highest occupied molecular orbital (HOMO) from high-order harmonic generation (HHG) of aligned molecules. This method is based on the single-molecule quantitative rescattering model with known alignment distribution and photo-recombination cross sections of fixed-in-space molecules. With the macroscopic HHG of aligned N2 molecules, we show that angle-dependent ionization of HOMO can be successfully retrieved at both low and high degrees of alignment. We then show that the error in the retrieved angular dependence of ionization becomes larger if the uncertainty in the alignment distribution is introduced in the retrieval procedure. We also examine that the retrieved ionization of HOMO is much deviated from the accurate one if the intensity of probe laser becomes higher such that inner HOMO-1 can contribute to HHG.

State-selective quantum interference studied in the photo-recombination of Ar17+ ion

We investigate the total and partial cross sections of the state-selective photo-recombination (PR) from the ground state 1sS01 of H-like Ar17+ ion to the 1s2S01, 1s2sS01,S13 and 1s2pP0,1,23,P11 states of He-like Ar16+ ion. The analysis is performed based on the close-coupling approximation and the fully relativistic Dirac R-matrix method, in which the unified treatments of the combined electron-ion PR process, including radiative and dielectronic recombination (DR) as coherent, interfering components are considered. The KLL PR resonance group are determined and identified according to the calculated energies and transition rates using the multiconfiguration Dirac–Fock (MCDF) method. The DR cross sections are also presented for comparison purposes. Our results show that the quantum interference between direct recombination and resonant recombination processes will strongly influence the intensity and shape of the PR cross sections, especially for the 2s2pP11 and 2p2D21 resonant regions. Comparison of our computed results with previously published experimental and theoretical values, when available, is made.

XUV-assisted high-order-harmonic-generation spectroscopy

Using the analytic time-dependent effective range theory, we study two-color high-order harmonic generation (HHG) involving a weak extreme ultraviolet (XUV) pulse and an intense infrared laser field. Our analysis shows that XUV-assisted HHG spectra contain multiple additional plateau structures originating from absorption of one or more XUV photons at the photorecombination step of HHG. We show also that the HHG rate corresponding to the $n\mathrm{th}$ plateau can be presented in a factorized form involving the XUV-assisted (multiphoton) photorecombination cross section (PRCS) corresponding to absorption of $n$ XUV photons of energy $\mathrm{\ensuremath{\Omega}}$ and emission of a harmonic of energy ${\mathrm{\ensuremath{\Omega}}}_{h}$. This factorization allows one to extract the PRCS from the HHG spectrum and to retrieve the cross section of the inverse process: the photoionization cross section involving absorption of a single photon of energy ${\mathrm{\ensuremath{\Omega}}}_{h}$ and emission of $n$ XUV photons of frequency $\mathrm{\ensuremath{\Omega}}$. The analytic HHG results are in excellent agreement with numerical solutions of the three-dimensional time-dependent Schr\odinger equation.

KLL Dielectronic Satellite Spectra from the Photorecombination of He-like Fe and Ni Ions

Abstract The radiative decay of a doubly excited autoionizing state is characterized by the dielectronic recombination in the photorecombination (PR) process. We calculate PR cross sections for the ground states of the Fe xxv and Ni xxvii ions by employing the Dirac R-matrix technique. The autoionizing states are treated in the framework of Davies and Seaton’s theory to account for the radiative decay. The strengths of the KLL resonances that equate directly to the dielectronic satellite line strengths are evaluated. Besides, the Multiconfiguration Dirac Fock formalism is utilized to obtain the dielectronic satellite line strengths under the isolated resonance approximation. A very good agreement is found for the wavelengths and transition parameters belonging to the KLL autoionizing states with the previous theoretical and experimental results. The dominant KLL dielectronic satellite line strengths from both theoretical models are consistent with each other and are in good agreement with the established theoretical models and measurements at the electron beam ion trap.

Atomic structure effects of a target on the polarization properties of high harmonics in the region of the cooper minimum

A significant increase in the absolute value of the degree of circular polarization of high harmonics in the energy region of the Cooper minimum in the photorecombination cross section of noble gas atoms has been predicted. A model independent estimate has been obtained for the maximum degree of circular polarization of harmonics in the energy range under consideration.

High-order-harmonic generation in an elliptically polarized laser field: analytic form of the electron wave packet

An analytic expression for the electron wave packet (EWP) describing high-order harmonic generation (HHG) by atoms in an intense laser field with small ellipticity is derived quantum mechanically in the tunneling limit within the time-dependent effective range theory. This result is valid over a wide interval of returned electron energies in the HHG plateau region and generalizes the previous result for HHG rates obtained by Frolov M V et al (2012 Phys. Rev. A 86 063406) only for the HHG plateau cutoff region. It is shown that the most important difference from the case of a linearly polarized field originates from a nonzero electron energy at the moment of ionization in an elliptically polarized field that, in turn, results in the dependence of ionization factor in the EWP on the returning electron energy. Our analytic result for the EWP averaged over interference oscillations in the HHG spectrum is applied for analysis of the laser wavelength scaling of the HHG yield induced by an elliptically polarized midinfrared laser field as well as for the improvement of the recently suggested method of elliptic HHG spectroscopy for retrieving both the energy and angular dependence of the photorecombination cross section of the target atom (see Frolov M V et al 2016 Phys. Rev. A 93 031403).

Effects of radiation damping on photorecombination ofC4+ions for theKLLresonance

A numerical method based on Zabaydullin and Dubau's work [O. Zabaydullin and J. Dubau, J. Phys. B: At. Mol. Opt. Phys. 45, 115002 (2012)] has been developed to calculate the Cauchy principal value integral in scattering matrices and obtain photorecombination (PR) cross sections of low-lying resonances according to Davies and Seaton's theory [J. Phys. B 2, 757 (1969)], in which radiation damping is included. The Dirac $R$-matrix method is employed to secure the dipole matrix. Using this method, PR cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are acquired, and compared with available experimental measurements and other close-coupling theoretical results. It is shown that our damped cross sections reproduce the experimental data and are in agreement with other theoretical results. Meanwhile, radiation damping can reduce the PR cross section for the $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ resonance (corresponding to two levels ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ by three orders of magnitude. The unresolved and underestimated resonances $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{4}P, 1s2s2p\phantom{\rule{4pt}{0ex}}^{4}P$, and $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ in the undamped Breit-Pauli $R$-matrix calculations [H. L. Zhang et al., J. Phys. B: At. Mol. Opt. Phys. 32, 1459 (1999)] are corrected. Besides, dielectronic recombination cross sections of ${\mathrm{C}}^{4+}$ for the KLL resonance are also presented for comparison using the relativistic configuration-interaction (RCI) method implemented in flexible atomic code (fac), which show radiation damping has pronounced influences on $1s2{p}^{2}\phantom{\rule{4pt}{0ex}}^{2}P$ due to much larger radiative rates compared with autoionization rates. Furthermore, radiative and autoionization rates for the intermediate states ${[{(1s2{p}_{1/2})}_{1}2{p}_{3/2}]}_{1/2}$ and ${[1s{(2{p}_{3/2}^{2})}_{2}]}_{3/2}$ of the He-like ions with $6\ensuremath{\le}\phantom{\rule{4pt}{0ex}}Z\ensuremath{\le}83$ are calculated using fac, scaling laws of which are checked. Autoionization rates comply with the ${Z}_{\mathrm{eff}}^{0}$ scaling law for $Z\ensuremath{\ge}32$, which is caused by relativistic effects.

Theoretical study on photorecombination of C V ion**Project supported by the National Natural Science Foundation of China (Grant Nos. 11274254, U1332206, and U1331122) and the International Scientific and Technological Cooperative Project of Gansu Province, China (Grant No. 1104WCGA186).

The partial and total photorecombination cross sections of the ground-state C V ion in the KLL and KLM resonant energy regions were calculated in detail by using the Dirac atomic R-matrix code based on a fully relativistic R-matrix method. Meanwhile, the principal resonant lines in each photorecombination channel have been classified according to the calculated transition energies and probabilities from the KLL and KLM resonant states to the 1s2nl (n = 2, 3 and l = s,p,d) final states. The validity of these calculations is assessed by comparison with previously published experimental and theoretical data. The good agreement between the present calculated results and those obtained using different approaches confirms the accuracy of the present results. In addition, it is found that the damping effect can be neglected for the KLL resonant, but not for the KLM resonant.

Harmonic generation spectroscopy with a two-colour laser field having orthogonal linear polarizations

The interpretation of many high-order harmonic generation (HHG) experiments is based on the assumption that the HHG yield of an atom can be factorized into (i) a laser-dependent ‘electron wave packet’ with rather simple properties, including a nearly universal shape, and (ii) an atomic photorecombination cross section. We show that this factorization is restricted to linearly polarized laser fields and fails in two-colour laser fields with orthogonal polarizations. At the same time, we show how two-colour HHG spectroscopy using orthogonally polarized intense fundamental and relatively weak second harmonic fields makes a complete experiment possible that enables the retrieval of the angle-resolved photorecombination cross sections for atomic p states.

Recombination-amplitude calculations of noble gases, in both length and acceleration forms, beyond the strong-field approximation

Transition of an electron from a free to a bound state is critical in determining the qualitative shape of the spectrum in high-order harmonic generation (HHG), and in tomographic imaging of orbitals. We calculate and compare the recombination amplitude, from a continuum state described by a plane wave and an outgoing scattering eigenstate, to the bound state for the noble gases that are commonly used in HHG. These calculations are based on the single active electron model and the Hartree-Fock-Slater method, using both the length form and the acceleration form of the dipole matrix element. We confirm that the recombination amplitude versus emitted photon energy strongly depends upon the wavefunction used to describe the free electron. Depending on the choice of the wavefunction and the dipole form, the square of the absolute value of the recombination amplitude can differ by almost two orders of magnitude near the experimentally measured Cooper minima. Moreover, only the outgoing scattering eigenstates with the length form roughly predict the experimentally observed Cooper minimum for Ar (~50 eV) and Kr (~85 eV). We provide a detailed derivation of the photorecombination cross sections (PRCSs) from photo ionization cross sections (PICSs) calculated by the relativistic random phase approximation (RRPA)., For Ar, Kr and Xe, compare the total PICSs calculated using our recombination amplitudes with that obtained from RRPA. We find that PICS calculated using the outgoing scattering eigenstates with the length form is in better agreement with the RRPA calculations than the acceleration form.

State selective photo-recombination cross sections in Be-like C and Al ions

We report results from detailed state selective photo-recombination study along with the doubly excited autoionizing resonances in Be-like C2+ and Al9+ ions. In the present investigation, the primary focus is on detailed energy profiles of the individual photo-recombination cross sections. The calculation was carried out for the excited Rydberg states of type 1s22sns(1Se) which interact with the odd-parity continua up to the C3+ and Al10+ 2p threshold limit. The numerical evaluation has been performed at a fine energy mesh across all the autoionizing Rydberg series of resonances 1s22pns(1P0) converging to Li-like ion 2p threshold. The method of calculation keeps the essential ingredients of the Feshbach projection operator approximation. The photo-ionization cross sections have been evaluated with and without relativistic effects included into the R-matrix numerical procedures, while the allowance for both quantum interference between dielectronic and radiative recombination, and overlapping resonances has been done utilizing results from the earlier R-matrix Floquet calculation. We discuss all these results with respect to the effect of quantum interference term on the energy dependence profile of photo-recombination cross section for studied transitions.

High-order-harmonic generation from molecular isomers with midinfrared intense laser pulses

We present theoretical calculations of high-order-harmonic generation (HHG) from stereoisomers of 1,2-dichloroethylene (C${}_{2}$H${}_{2}$Cl${}_{2}$) and 2-butene (C${}_{4}$H${}_{8}$) based on the quantitative rescattering theory. Our results show that the HHG spectra from these cis and trans isomers with intense midinfrared laser pulses are clearly distinguishable, even when the molecules are randomly oriented, in good agreement with the recent experiments by Wong et al. [Phys. Rev. A 84, 051403(R) (2011)]. We found that the angle-averaged tunneling ionization yields and photoionization cross sections from the cis and trans isomers for both molecules are nearly identical. The origin of the differences in HHG spectra is traced as due to the interplay in the angular dependence of the photoionization (or photorecombination) cross section and ionization rate.

High-order-harmonic-generation spectroscopy with an elliptically polarized laser field

Analytic formulas describing high-order-harmonic generation (HHG) by atoms in an intense laser field with small ellipticity are obtained quantum mechanically in the tunneling limit. The results show that factorization of the HHG yield in terms of an electron wave packet and the photorecombination cross section (PRCS) is valid only for $s$ states of a bound atomic electron, whereas the HHG yield for $p$ states involves two different atomic parameters. For the latter case, elliptic HHG spectroscopy enables one to retrieve both the energy and angular dependence of the PRCS of the target atom, as we illustrate for the case of HHG by Xe in a midinfrared laser field.

The effects of quantum interference between direct and resonant photorecombination of H-like Ar17+ ions

The multiconfiguration Dirac–Fock method has been used to study interference effects between direct and resonant photorecombination (i.e. radiative and dielectronic recombination) from the ground state 1s2S1/2 of H-like Ar17+ ions via doubly excited 2s21S0, 2s2p 3P0, 1, 2, 1P1 and 2p23P0, 1, 2, 1D2, 1S0 resonances of He-like Ar16+ ions combined with the Fano parameterization technique. In order to produce total photorecombination spectra, it is necessary to calculate the energy levels of the 1s of H-like Ar17+ ions, 1s2, 1s2l and 2l2l′ (l,l′ =0, 1) of He-like Ar16+ ions, the radiative and nonradiative properties of the doubly excited states of He-like Ar16+ ions, and the direct and resonant photorecombination cross sections from the 1s state of H-like Ar17+ ions into the ground state 1s2 and the single excited states of 1s2l (l=0, 1) of He-like Ar16+ ions, in detail. Based on good agreement between the present calculations and other available experimental and theoretical results, the interference profile determined by the so-called Fano parameters q and ρ2 is also shown. The results indicate that interference effects are remarkable at some resonances, especially near the doubly excited 2s2p 1P1 state of He-like Ar16+ ions, and strongly influence the intensity of the wing of the nonresonant background in the photorecombination of H-like Ar17+ ions through comparison between the final Fano and total radiative recombination to dielectronic recombination spectra.

Analytic confirmation that the factorized formula for harmonic generation involves the exact photorecombination cross section

High-order-harmonic generation (HHG) by atoms in a strong laser field is analyzed theoretically, taking into account atomic potential effects beyond the strong field approximation (SFA). Our analytical derivation extends the time-dependent effective range (TDER) theory, developed previously for a short-range potential supporting only a single bound state, to the case of a potential supporting two bound states having different angular momenta and dynamically interacting with the continuum. In contrast to the SFA and the single-state TDER model, in both of which the HHG rates in the region of the high-energy plateau cutoff involve only the plane-wave (first Born) approximation for the photorecombination cross section, our analytic expression for the HHG rates in the two-state TDER model involves the exact photorecombination cross section for this model. These results justify the factorization of HHG rates in the high-energy plateau region in terms of the electron wave packet and the exact (non-Born) photorecombination cross section, which was suggested previously using only phenomenological arguments.

Quantifying the strength and asymmetry of giant resonances in the photorecombination ofSc3+and the photoionization ofSc2+

We report on strong interference effects for the dominant, highly correlated, broad, and asymmetric 3p53d2(2F5/2,7/2o) giant resonances in the photorecombination of Sc3+. Using a nonorthogonal perturbative multiconfiguration Breit-Pauli approach, we present theoretical photorecombination cross sections that are in line with the Test Storage Ring measurements of Schippers et al. In order to reproduce the observed asymmetric resonance profiles near threshold, it was necessary to include resonance-continuum interference. Also, we present Sc2+ photoionization cross sections that agree with the Advance Light Source measurements of Schippers et al. This perturbative method is based on analytical expressions for the cross sections in terms of computed energies and transition rates, thereby directly determining resonance strengths and Fano asymmetry parameters. Of particular note, our reported absolute cross sections are in excellent agreement with experimental results, in contrast to all previous theoretical calculations. Furthermore, the apparent violation of the sum rule prediction, determined both from our integrated photoionization cross sections and from experimental results, is found to be due to radiative damping of narrow resonances.

Accurate retrieval of atomic structures from high-order harmonic spectra

We extracted the photorecombination cross sections from the high-order harmonic spectra generated from rare gases by intense femtosecond pulses. By taking the ratio between the observed high-order harmonic spectra and recolliding electron wave packets, we successfully obtained the photorecombination cross sections.

Retrieval of target photorecombination cross sections from high-order harmonics generated in a macroscopic medium

We investigate high-order harmonic generation (HHG) in a thin macroscopic medium by solving Maxwell's equation using microscopic single-atom induced dipole moment calculated from the recently developed quantitative rescattering (QRS) theory. We show that macroscopic HHG yields calculated from QRS compared well with those obtained from solving the single-atom time-dependent Schr\"odinger equation but with great saving of computer time. We also show that macroscopic HHG can be expressed as a product of a ``macroscopic wave packet'' and the photorecombination cross section of the target gas. The latter enables us to extract target structure from the experimentally measured HHG spectra, thus paves the way to use few-cycle infrared lasers for time-resolved chemical imaging of transient molecules with few-femtosecond temporal resolution.

Retrieving photorecombination cross sections of atoms from high-order harmonic spectra

We observe high-order harmonic spectra generated from a thin atomic medium, Ar, Kr, and Xe, by intense $800\text{\ensuremath{-}}\mathrm{nm}$ and $1300\text{\ensuremath{-}}\mathrm{nm}$ femtosecond pulses. A clear signature of a single-atom response is observed in the harmonic spectra. Especially in the case of Ar, a Cooper minimum, reflecting the electronic structure of the atom, is observed in the harmonic spectra. We successfully extract the photorecombination cross sections of the atoms in the field-free condition with the help of an accurate recolliding electron wave packet. The present protocol paves the way for exploring ultrafast imaging of molecular dynamics with attosecond resolution.

Extraction of the species-dependent dipole amplitude and phase from high-order harmonic spectra in rare-gas atoms

Based on high-order harmonic generation (HHG) spectra obtained from solving the time-dependent Schr\odinger equation for atoms, we established quantitatively that the HHG yield can be expressed as the product of a returning electron wave packet and photorecombination cross sections, and the shape of the returning wave packet is shown to be largely independent of the species. By comparing the HHG spectra generated from different targets under identical laser pulses, accurate structural information, including the phase of the recombination amplitude, can be retrieved. This result opens up the possibility of studying the target structure of complex systems, including their time evolution, from the HHG spectra generated by short laser pulses.