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DOI: 10.6084/m9.figshare.1012540.v1
title: Mean values of the various operators for the ro-vibrational states in the HT<sup>+</sup> molecular ion

description: <b>Table 3.</b> Mean values of the various operators for the ro-vibrational states in the HT<sup>+</sup> molecular ion. <strong>Abstract</strong> We present systematic calculations of the leading order relativistic corrections for a wide range of rotational and vibrational states of the HT<sup>+</sup> molecular ion. Finite size effects are also taken into account. These are the first complete <em>ab initio</em> calculations, which may be used for precision spectroscopy of the ro-vibrational spectrum in HT<sup>+</sup>.
DOI: 10.6084/m9.figshare.1012538
title: Coefficients <em>E<sub>i</sub></em> of the effective spin Hamiltonian (4) (in MHz), <em>a</em>[<em>b</em>] = <em>a</em> <b>×</b>

description: <b>Table 1.</b> Coefficients <em>E<sub>i</sub></em> of the effective spin Hamiltonian (4) (in MHz), <em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>. <strong>Abstract</strong> We present systematic calculations of the leading order relativistic corrections for a wide range of rotational and vibrational states of the HT<sup>+</sup> molecular ion. Finite size effects are also taken into account. These are the first complete <em>ab initio</em> calculations, which may be used for precision spectroscopy of the ro-vibrational spectrum in HT<sup>+</sup>.
DOI: 10.6084/m9.figshare.1012539.v1
title: Hyperfine splitting (in MHz) of ro-vibrational levels of the HT<sup>+</sup> molecular ion

description: <b>Table 2.</b> Hyperfine splitting (in MHz) of ro-vibrational levels of the HT<sup>+</sup> molecular ion. <strong>Abstract</strong> We present systematic calculations of the leading order relativistic corrections for a wide range of rotational and vibrational states of the HT<sup>+</sup> molecular ion. Finite size effects are also taken into account. These are the first complete <em>ab initio</em> calculations, which may be used for precision spectroscopy of the ro-vibrational spectrum in HT<sup>+</sup>.
DOI: 10.6084/m9.figshare.1012541.v1
title: <em>P</em>-odd interaction constant <em>W<sub>A</sub></em> (in Hz) for the ground state <sup>2</sup>∑<sub>1/2</sub> of the YbF molecule

description: <b>Table 1.</b> <em>P</em>-odd interaction constant <em>W<sub>A</sub></em> (in Hz) for the ground state <sup>2</sup>∑<sub>1/2</sub> of the YbF molecule. <strong>Abstract</strong> We present the result for the <em>P</em>-odd electron–nucleus interaction constant <em>W<sub>A</sub></em> of the YbF molecule in the ground (<sup>2</sup>∑<sub>1/2</sub>) state, computed by using a fully relativistic restricted active space configuration-interaction method, which yields the result <em>W<sub>A</sub></em> = 543 Hz, in reasonable agreement with previous calculations. This result will be useful for experimentalists proposing new experiments in the search for nuclear-spin-dependent parity-nonconserving effects in the YbF molecule.
DOI: 10.6084/m9.figshare.1012535
title: Experimental and calculated binding energies (<em>E<sub>b</sub></em>) and relative intensities of 3p photoionization in atomic Ga

description: <b>Table 1.</b> Experimental and calculated binding energies (<em>E<sub>b</sub></em>) and relative intensities of 3p photoionization in atomic Ga. <strong>Abstract</strong> The 3p photoionization and subsequent Coster–Kronig type of Auger decay of initially neutral atomic gallium were studied both experimentally and theoretically. The binding energies and relative intensities of the 3p photoelectron spectrum together with a satellite structure are given. The <em>M</em><sub>2, 3</sub><em>MM</em> and <em>M</em><sub>2, 3</sub><em>MN</em> Auger electron spectrum leading to doubly ionized final states is presented. The synchrotron radiation excited photoelectron and Auger electron spectra were interpreted using multiconfiguration Dirac–Fock calculations providing spectral identification for the main observed features.
DOI: 10.6084/m9.figshare.1012536
title: Experimental and calculated mean kinetic energies of 3p Auger decay lines of atomic Ga

description: <b>Table 2.</b> Experimental and calculated mean kinetic energies of 3p Auger decay lines of atomic Ga. <strong>Abstract</strong> The 3p photoionization and subsequent Coster–Kronig type of Auger decay of initially neutral atomic gallium were studied both experimentally and theoretically. The binding energies and relative intensities of the 3p photoelectron spectrum together with a satellite structure are given. The <em>M</em><sub>2, 3</sub><em>MM</em> and <em>M</em><sub>2, 3</sub><em>MN</em> Auger electron spectrum leading to doubly ionized final states is presented. The synchrotron radiation excited photoelectron and Auger electron spectra were interpreted using multiconfiguration Dirac–Fock calculations providing spectral identification for the main observed features.
DOI: 10.6084/m9.figshare.1012536.v1
title: Experimental and calculated mean kinetic energies of 3p Auger decay lines of atomic Ga

description: <b>Table 2.</b> Experimental and calculated mean kinetic energies of 3p Auger decay lines of atomic Ga. <strong>Abstract</strong> The 3p photoionization and subsequent Coster–Kronig type of Auger decay of initially neutral atomic gallium were studied both experimentally and theoretically. The binding energies and relative intensities of the 3p photoelectron spectrum together with a satellite structure are given. The <em>M</em><sub>2, 3</sub><em>MM</em> and <em>M</em><sub>2, 3</sub><em>MN</em> Auger electron spectrum leading to doubly ionized final states is presented. The synchrotron radiation excited photoelectron and Auger electron spectra were interpreted using multiconfiguration Dirac–Fock calculations providing spectral identification for the main observed features.
DOI: 10.6084/m9.figshare.1012538.v1
title: Coefficients <em>E<sub>i</sub></em> of the effective spin Hamiltonian (4) (in MHz), <em>a</em>[<em>b</em>] = <em>a</em> <b>×</b>

description: <b>Table 1.</b> Coefficients <em>E<sub>i</sub></em> of the effective spin Hamiltonian (4) (in MHz), <em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>. <strong>Abstract</strong> We present systematic calculations of the leading order relativistic corrections for a wide range of rotational and vibrational states of the HT<sup>+</sup> molecular ion. Finite size effects are also taken into account. These are the first complete <em>ab initio</em> calculations, which may be used for precision spectroscopy of the ro-vibrational spectrum in HT<sup>+</sup>.
DOI: 10.6084/m9.figshare.1012535.v1
title: Experimental and calculated binding energies (<em>E<sub>b</sub></em>) and relative intensities of 3p photoionization in atomic Ga

description: <b>Table 1.</b> Experimental and calculated binding energies (<em>E<sub>b</sub></em>) and relative intensities of 3p photoionization in atomic Ga. <strong>Abstract</strong> The 3p photoionization and subsequent Coster–Kronig type of Auger decay of initially neutral atomic gallium were studied both experimentally and theoretically. The binding energies and relative intensities of the 3p photoelectron spectrum together with a satellite structure are given. The <em>M</em><sub>2, 3</sub><em>MM</em> and <em>M</em><sub>2, 3</sub><em>MN</em> Auger electron spectrum leading to doubly ionized final states is presented. The synchrotron radiation excited photoelectron and Auger electron spectra were interpreted using multiconfiguration Dirac–Fock calculations providing spectral identification for the main observed features.
DOI: 10.6084/m9.figshare.1012527
title: Experimental and calculated Auger electron kinetic energies (in eV) following the 3d ionization of atomic gallium

description: <b>Table 2.</b> Experimental and calculated Auger electron kinetic energies (in eV) following the 3d ionization of atomic gallium. The mean kinetic energy error was estimated to be ±10 meV. The present assignment and leading mixing coefficients for the 3d ionized states in <em>LSJ</em> coupling are present in the last column. <strong>Abstract</strong> We present an experimental and theoretical study of 3d photoionization and subsequent Auger decay of atomic gallium. The synchrotron radiation-induced electron spectra have been compared and analysed using multiconfiguration Dirac–Fock calculations. It has been shown that the theoretically predicted photoelectron spectrum is in rather good agreement with the experiment allowing us to identify the main spectral features. However, prediction of the Auger decay intensities fails due to calculational difficulties for the continuum wavefunctions of very low kinetic energy Auger electrons.
DOI: 10.6084/m9.figshare.1012526
title: Experimental and calculated binding energies, intensities and natural linewidths (Γ) of the 3d photoelectron spectrum of the atomic gallium

description: <b>Table 1.</b> Experimental and calculated binding energies, intensities and natural linewidths (Γ) of the 3d photoelectron spectrum of the atomic gallium. The binding energies are given with respect to the ionization threshold of 26.522(6) eV (experimental) and 24.232 eV (calculated) corresponding to the <sup>2</sup>P<sub>3/2</sub> − 3d<sup>−1</sup>(<sup>3</sup>P<sub>2</sub>) transition. The relative binding energy error was estimated to be ±5 meV. The leading mixing coefficients for the 3d ionized states in <em>LSJ</em> coupling are present in table 2. <strong>Abstract</strong> We present an experimental and theoretical study of 3d photoionization and subsequent Auger decay of atomic gallium. The synchrotron radiation-induced electron spectra have been compared and analysed using multiconfiguration Dirac–Fock calculations. It has been shown that the theoretically predicted photoelectron spectrum is in rather good agreement with the experiment allowing us to identify the main spectral features. However, prediction of the Auger decay intensities fails due to calculational difficulties for the continuum wavefunctions of very low kinetic energy Auger electrons.
DOI: 10.6084/m9.figshare.1012527.v1
title: Experimental and calculated Auger electron kinetic energies (in eV) following the 3d ionization of atomic gallium

description: <b>Table 2.</b> Experimental and calculated Auger electron kinetic energies (in eV) following the 3d ionization of atomic gallium. The mean kinetic energy error was estimated to be ±10 meV. The present assignment and leading mixing coefficients for the 3d ionized states in <em>LSJ</em> coupling are present in the last column. <strong>Abstract</strong> We present an experimental and theoretical study of 3d photoionization and subsequent Auger decay of atomic gallium. The synchrotron radiation-induced electron spectra have been compared and analysed using multiconfiguration Dirac–Fock calculations. It has been shown that the theoretically predicted photoelectron spectrum is in rather good agreement with the experiment allowing us to identify the main spectral features. However, prediction of the Auger decay intensities fails due to calculational difficulties for the continuum wavefunctions of very low kinetic energy Auger electrons.
DOI: 10.6084/m9.figshare.1012518
title: Location of the correlation islands deduced from figure 2

description: <b>Table 1.</b> Location of the correlation islands deduced from figure 2. Their assignments are confirmed by comparison with theoretical predictions. The <em>E</em><sub>kin</sub> values given correspond to specific sequences of the multi-ionization processes as labelled in bold in the third column. To denote the Ne 1s<sup><em>r</em></sup>2s<sup><em>t</em></sup>2p<sup><em>k</em></sup> electron configurations, the notation <em>rtk</em> is used. <strong>Abstract</strong> We report on a detailed investigation into the electron emission processes of Ne atoms exposed to intense femtosecond x-ray pulses, provided by the Linac Coherent Light Source Free Electron Laser (FEL) at Stanford. The covariance mapping technique is applied to analyse the data, and the capability of this approach to disentangle both linear and nonlinear correlation features which may be hidden on coincidence maps of the same data set is demonstrated. Different correction techniques which enable improvements on the quality of the spectral features extracted from the covariance maps are explored. Finally, a method for deriving characteristics of the x-ray FEL pulses based on covariance mapping in combination with model simulations is presented.
DOI: 10.6084/m9.figshare.1012519
title: Integrated intensities of our model calculations and our experimental results associated with different features of the covariance maps relative to the intensity of the feature associated with the PAP process

description: <b>Table 2.</b> Integrated intensities of our model calculations and our experimental results associated with different features of the covariance maps relative to the intensity of the feature associated with the PAP process. The experimental values were corrected for the collection–detection efficiency of the spectrometer used, taking into account a decrease of about 50% for energetic valence and Auger electrons. <strong>Abstract</strong> We report on a detailed investigation into the electron emission processes of Ne atoms exposed to intense femtosecond x-ray pulses, provided by the Linac Coherent Light Source Free Electron Laser (FEL) at Stanford. The covariance mapping technique is applied to analyse the data, and the capability of this approach to disentangle both linear and nonlinear correlation features which may be hidden on coincidence maps of the same data set is demonstrated. Different correction techniques which enable improvements on the quality of the spectral features extracted from the covariance maps are explored. Finally, a method for deriving characteristics of the x-ray FEL pulses based on covariance mapping in combination with model simulations is presented.
DOI: 10.6084/m9.figshare.1012518.v1
title: Location of the correlation islands deduced from figure 2

description: <b>Table 1.</b> Location of the correlation islands deduced from figure 2. Their assignments are confirmed by comparison with theoretical predictions. The <em>E</em><sub>kin</sub> values given correspond to specific sequences of the multi-ionization processes as labelled in bold in the third column. To denote the Ne 1s<sup><em>r</em></sup>2s<sup><em>t</em></sup>2p<sup><em>k</em></sup> electron configurations, the notation <em>rtk</em> is used. <strong>Abstract</strong> We report on a detailed investigation into the electron emission processes of Ne atoms exposed to intense femtosecond x-ray pulses, provided by the Linac Coherent Light Source Free Electron Laser (FEL) at Stanford. The covariance mapping technique is applied to analyse the data, and the capability of this approach to disentangle both linear and nonlinear correlation features which may be hidden on coincidence maps of the same data set is demonstrated. Different correction techniques which enable improvements on the quality of the spectral features extracted from the covariance maps are explored. Finally, a method for deriving characteristics of the x-ray FEL pulses based on covariance mapping in combination with model simulations is presented.
DOI: 10.6084/m9.figshare.1012519.v1
title: Integrated intensities of our model calculations and our experimental results associated with different features of the covariance maps relative to the intensity of the feature associated with the PAP process

description: <b>Table 2.</b> Integrated intensities of our model calculations and our experimental results associated with different features of the covariance maps relative to the intensity of the feature associated with the PAP process. The experimental values were corrected for the collection–detection efficiency of the spectrometer used, taking into account a decrease of about 50% for energetic valence and Auger electrons. <strong>Abstract</strong> We report on a detailed investigation into the electron emission processes of Ne atoms exposed to intense femtosecond x-ray pulses, provided by the Linac Coherent Light Source Free Electron Laser (FEL) at Stanford. The covariance mapping technique is applied to analyse the data, and the capability of this approach to disentangle both linear and nonlinear correlation features which may be hidden on coincidence maps of the same data set is demonstrated. Different correction techniques which enable improvements on the quality of the spectral features extracted from the covariance maps are explored. Finally, a method for deriving characteristics of the x-ray FEL pulses based on covariance mapping in combination with model simulations is presented.
DOI: 10.6084/m9.figshare.1012507
title: Measured average momentum (<em>P</em><sub>av</sub>), average kinetic energy (KE<sub>av</sub>), and the corresponding abundances (1000 eV photon energy)

description: <b>Table 1.</b> Measured average momentum (<em>P</em><sub>av</sub>), average kinetic energy (KE<sub>av</sub>), and the corresponding abundances (1000 eV photon energy). <strong>Abstract</strong> We investigate the multiphoton ionization and the subsequent fragmentation of SF<sub>6</sub> molecules with intense x-ray-free electron laser pulses at different photon energies. We observe highly charged molecular and atomic ions which were absent in previous experiments with conventional x-ray sources. The observation of fully stripped fluorine ions suggests sequential multiphoton ionization processes with intermediate 1s electron excitation. We measure the average momentum and kinetic energy of each fragment, the comparison of which implies many-body fragmentation pathways of the molecular ions. The observed non-monotonic dependence of the kinetic energy on the charge states of fluorine indicates the multiphoton ionization of 'isolated' atomic neutral fluorine or fluorine ions resultant from bond cleavages and also implies the fragmentation of highly charged molecular ions that are produced at a later time during a single pulse.
DOI: 10.6084/m9.figshare.1012507.v1
title: Measured average momentum (<em>P</em><sub>av</sub>), average kinetic energy (KE<sub>av</sub>), and the corresponding abundances (1000 eV photon energy)

description: <b>Table 1.</b> Measured average momentum (<em>P</em><sub>av</sub>), average kinetic energy (KE<sub>av</sub>), and the corresponding abundances (1000 eV photon energy). <strong>Abstract</strong> We investigate the multiphoton ionization and the subsequent fragmentation of SF<sub>6</sub> molecules with intense x-ray-free electron laser pulses at different photon energies. We observe highly charged molecular and atomic ions which were absent in previous experiments with conventional x-ray sources. The observation of fully stripped fluorine ions suggests sequential multiphoton ionization processes with intermediate 1s electron excitation. We measure the average momentum and kinetic energy of each fragment, the comparison of which implies many-body fragmentation pathways of the molecular ions. The observed non-monotonic dependence of the kinetic energy on the charge states of fluorine indicates the multiphoton ionization of 'isolated' atomic neutral fluorine or fluorine ions resultant from bond cleavages and also implies the fragmentation of highly charged molecular ions that are produced at a later time during a single pulse.
DOI: 10.6084/m9.figshare.1012486
title: Cross sections at 91 eV photon energy and ionization potentials of N atoms and ions used in the simulation [29]

description: <b>Table 3.</b> Cross sections at 91 eV photon energy and ionization potentials of N atoms and ions used in the simulation [29]. <strong>Abstract</strong> Single-shot time-of-flight spectra for Coulomb explosion of N<sub>2</sub> and I<sub>2</sub> molecules have been recorded at the Free Electron LASer in Hamburg (FLASH) and have been analysed using a partial covariance mapping technique. The partial covariance analysis unravels a detailed picture of all significant Coulomb explosion pathways, extending up to the N<sup>4+</sup>–N<sup>5+</sup> channel for nitrogen and up to the I<sup>8+</sup>–I<sup>9+</sup> channel for iodine. The observation of the latter channel is unexpected if only sequential ionization processes from the ground state ions are considered. The maximum kinetic energy release extracted from the covariance maps for each dissociation channel shows that Coulomb explosion of nitrogen molecules proceeds much faster than that of the iodine. The N<sub>2</sub> ionization dynamics is modelled using classical trajectory simulations in good agreement with the outcome of the experiments. The results suggest that covariance mapping of the Coulomb explosion can be used to measure the intensity and pulse duration of free-electron lasers.
DOI: 10.6084/m9.figshare.1012484
title: Maximum kinetic energy (KE) per fragment for N<sub>2</sub> extracted from figure 4(f) and from simulation; effective internuclear distances for all observed charge pairs

description: <b>Table 1.</b> Maximum kinetic energy (KE) per fragment for N<sub>2</sub> extracted from figure 4(f) and from simulation; effective internuclear distances for all observed charge pairs. Statistical uncertainties in the last digits are given in parentheses (two sigma); however, larger systematic errors may not be excluded. <strong>Abstract</strong> Single-shot time-of-flight spectra for Coulomb explosion of N<sub>2</sub> and I<sub>2</sub> molecules have been recorded at the Free Electron LASer in Hamburg (FLASH) and have been analysed using a partial covariance mapping technique. The partial covariance analysis unravels a detailed picture of all significant Coulomb explosion pathways, extending up to the N<sup>4+</sup>–N<sup>5+</sup> channel for nitrogen and up to the I<sup>8+</sup>–I<sup>9+</sup> channel for iodine. The observation of the latter channel is unexpected if only sequential ionization processes from the ground state ions are considered. The maximum kinetic energy release extracted from the covariance maps for each dissociation channel shows that Coulomb explosion of nitrogen molecules proceeds much faster than that of the iodine. The N<sub>2</sub> ionization dynamics is modelled using classical trajectory simulations in good agreement with the outcome of the experiments. The results suggest that covariance mapping of the Coulomb explosion can be used to measure the intensity and pulse duration of free-electron lasers.
DOI: 10.6084/m9.figshare.1012485
title: Maximum kinetic energy (KE) per fragment for I<sub>2</sub> extracted from figure 5 and effective internuclear distances for all observed charge pairs

description: <b>Table 2.</b> Maximum kinetic energy (KE) per fragment for I<sub>2</sub> extracted from figure 5 and effective internuclear distances for all observed charge pairs. Statistical uncertainties in the last digits are given in parentheses (two sigma); however, larger systematic errors may not be excluded. <strong>Abstract</strong> Single-shot time-of-flight spectra for Coulomb explosion of N<sub>2</sub> and I<sub>2</sub> molecules have been recorded at the Free Electron LASer in Hamburg (FLASH) and have been analysed using a partial covariance mapping technique. The partial covariance analysis unravels a detailed picture of all significant Coulomb explosion pathways, extending up to the N<sup>4+</sup>–N<sup>5+</sup> channel for nitrogen and up to the I<sup>8+</sup>–I<sup>9+</sup> channel for iodine. The observation of the latter channel is unexpected if only sequential ionization processes from the ground state ions are considered. The maximum kinetic energy release extracted from the covariance maps for each dissociation channel shows that Coulomb explosion of nitrogen molecules proceeds much faster than that of the iodine. The N<sub>2</sub> ionization dynamics is modelled using classical trajectory simulations in good agreement with the outcome of the experiments. The results suggest that covariance mapping of the Coulomb explosion can be used to measure the intensity and pulse duration of free-electron lasers.