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An analytical expression of the angular correlation function of a pair of Lyman-$\ensuremath{\alpha}$ photons in the photodissociation of a hydrogen molecule is derived theoretically in a manner based on both atomic and molecular physics and quantum optics. The angular correlation function turns out to be expressed in terms of cosine (sine) functions of four angular variables of detectors with five coefficients. The angular correlation function is expanded in terms of the spherical harmonics for investigating which terms are involved, and we discuss the reason why they are involved. Interesting features are revealed in the expansion. We then search for a special detector arrangement where the angular-dependent terms vanish in the angular correlation function expressed in terms of the spherical harmonics. It turns out that no such detector arrangement in fact exists, but there is a special pair of detector arrangements where the angular-dependent terms vanish in the summation of two values of the angular correlation function expressed in terms of the spherical harmonics. We refer to such a pair of detector arrangements as a magic pair.

Multi-electron coincidence measurements have been performed at the photon energies for the core-to-valence (1s → π

The angular correlation functions (ACFs) of a pair of Lyman-$\ensuremath{\alpha}$ photons in photodissociation of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ are measured with linearly polarized incident light at a 33.66-eV incident photon energy in a wider angular range at a narrower angular step with smaller distortion than before [Y. Nakanishi et al., Phys. Rev. A 90, 043405 (2014)] so that we identify the atom-pair state emitting the pair of Lyman-$\ensuremath{\alpha}$ photons and find out whether the atom pair is entangled or not. Searching for reasonable $2p$ atom-pair states that reproduce the experimental ACFs to solve the issue, we show that hydrogen molecules are photoexcited to the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state in the Franck-Condon region and then the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state comes to superpose with the ${Q}_{2}{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}(2)$ state as the internuclear distance increases to infinity. The superposition is brought about by the spin-orbit coupling, which is effective around infinite internuclear distance because the potential-energy curves of those states are close to each other, but is negligibly small around the Franck-Condon region because they are apart from each other. The $2p$ atom pairs turn out to be in the ${1}_{u}$ superposition state, which is entangled. We therefore conclude that an entangled pair of hydrogen atoms is spontaneously produced through the photodissociation of a hydrogen molecule, and the entanglement originates from the ${1}_{u}$ symmetry properties, which are invariant during the dissociation from the Franck-Condon region towards infinite internuclear distance.

A set of cross sections for the formation of a pair of $2p$ atoms on an absolute scale is determined against the incident photon energy in the double photoexcitation of the isotopomers ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$, incorporating the same cross sections of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ obtained in our recent experiments [K. Hosaka et al., Phys. Rev. A 93, 063423 (2016)], and the oscillator strengths for the formation of a pair of $2p$ atoms from the precursor ${Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state, ${f}_{2p2p}^{{\text{H}}_{2}/\text{HD}/{\text{D}}_{2}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, are determined from the cross sections. The oscillator strength of HD, ${f}_{2p2p}^{\text{HD}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, is found to be larger than the value expected from ${f}_{2p2p}^{{\text{H}}_{2}/{\text{D}}_{2}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$, considering the same decay mechanism for ${\mathrm{H}}_{2}$, HD, and ${\mathrm{D}}_{2}$ molecules photoexcited to the ${Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1)$ state, a mechanism which was revealed in our recent experiments for ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ mentioned above. The origin of the enhancement in the oscillator strength for HD is discussed and we show that the enhancement is attributed to nonadiabatic transitions between a gerade electronic state and an ungerade one through a term neglected in the Born-Oppenheimer approximation that vanishes in the homonuclear isotopomers (${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$) but does not vanish in the heteronuclear isotopomer (HD). It turns out that approximately 10--20 % of ${f}_{2p2p}^{\text{HD}}({Q}_{2}\phantom{\rule{0.16em}{0ex}}{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}(1))$ originates from such nonadiabatic transitions due to the breaking of the space-inversion symmetry for electrons.

This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.; International audience; Multi-electron coincidence measurements have been performed at the photon energies for the core-to-valence (1s → π *) and core-to-Rydberg (1s → 3sσ and 3pπ) resonant excitations in N 2 , in order to investigate the dynamics of multiple Auger-electron emissions from these core-excited states in detail. Peaks due to slow electrons from superexcited atomic fragments are observed in the decay processes by emission of 2 or 3 Auger electrons, indicating stepwise (cascade) multiple Auger decays that involve faster dissociations than electronic relaxations. Energy partitions between the emitted electrons enable us to reveal the detailed decay mechanisms for these processes. Branching ratios among the decays by emission of 1, 2 or 3 Auger electrons and those between the simultaneous (direct) and stepwise (cascade) processes have been determined for each of the core excited states. Branching ratios of decay channels resulting in molecular or fragment ions have also been substantiated.

Superexcited states of ${\mathrm{H}}_{2}\mathrm{S}$ have been investigated with determining the cross sections for emission of dispersed and nondispersed atomic fluorescence against the incident photon energy in the range 11--40 eV to address the ionization and excitation of the valence electrons. This method enables us to extract the discrete electronic state from the superposition with continuous electronic states. The cross sections for H($2p$) formation have been put on an absolute scale. Ten superexcited states have been found, two in the range 13--15 eV are singly excited $2{b}_{2}^{\ensuremath{-}1}$(mo) states with a single configuration and the other eight states in the range 16--25 eV are doubly excited states with multiple configurations. State-resolved dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{S}$ have been determined. Similar experiments have been performed for ${\mathrm{H}}_{2}\mathrm{O}$. The state-resolved dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{S}$ are $\ensuremath{\sim}{10}^{\ensuremath{-}3}$, whereas those in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{O}$ range from $\ensuremath{\sim}{10}^{\ensuremath{-}3}$ to $\ensuremath{\sim}{10}^{\ensuremath{-}2}$. It is found that major fragment atoms are H($2p$) atoms in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{O}$ and ${\mathrm{S}}^{*}$ in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{S}$. The superexcited states of ${\mathrm{H}}_{2}\mathrm{O}$ and ${\mathrm{H}}_{2}\mathrm{S}$ are compared based on the similarity and difference of the electronic structures. It turns out from the comparison that (i) the smaller values of the dipole oscillator strengths for H($2p$) formation in the photoexcitation of ${\mathrm{H}}_{2}\mathrm{S}$ are related to the change of the major fragment atoms and (ii) the energy splitting of the doubly excited ``$4{a}_{1}^{\ensuremath{-}1}({\text{mo}}^{\ensuremath{'}})$'' states of ${\mathrm{H}}_{2}\mathrm{S}$ is enhanced in comparison with that of the doubly excited ``$2{a}_{1}^{\ensuremath{-}1}({\text{mo}}^{\ensuremath{'}})$'' states of ${\mathrm{H}}_{2}\mathrm{O}$. This enhancement is caused by the stronger electron correlation in ${\mathrm{H}}_{2}\mathrm{S}$ than in ${\mathrm{H}}_{2}\mathrm{O}$. The similarity in shape is indicated between the inner valence band and inner shell band in the fluorescence cross sections against the incident photon energy for ${\mathrm{H}}_{2}\mathrm{S}$ and ${\mathrm{H}}_{2}\mathrm{O}$.

The single, double, and triple Auger decays from the 1s shake-up states of O2 have been studied using a multi-electron coincidence method. Efficient populations of two-hole final states are observed in single Auger decays of the π-π* shake-up states, which is understood as a characteristic property of the Auger transitions from shake-up states of an open-shell molecule. The O23+ populations formed by double Auger decays show similar profiles for both the O1s-1 and shake-up states, which is due to the contributions from cascade double Auger processes. While the cascade contributions to the double Auger decays increase with the initial shake-up energy, the probability of direct double Auger processes remains unchanged between the O1s-1 and shake-up states, which implies a weak influence of the excited electron on the double Auger emission that originates from the electron correlation effect.

Synopsis We report here a detailed experimental study on multiple Auger decay after core excitation into the π* valence and Rydberg orbitals in N2 by an electron-electron coincidence technique.

An absolute total cross-section for electron scattering from O2 is obtained in the energy range from 20 eV down to 16 meV with a very narrow electron energy width of 7 meV, using the threshold-photoelectron source employing synchrotron radiation. The total cross-section obtained in the present study generally agrees well with those obtained in previous experimental works in the energy region where the previous experimental total cross-sections agree with each other. At lower energies, several features are found, including the very large contribution of the resonance to the total cross-section. The resonance energies and the resonance widths of the individual vibrational states of the resonance are determined from the analysis of the measured absolute total cross-section. The resonance width of the resonance of O2 is found to be much narrower than the value estimated from previous high-resolution experiments and theoretical calculations.

The absolute values of the cross section for formation of a $2p$ atom pair in the photoexcitation of ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ are measured against the incident photon energy in the range of doubly excited states by means of the coincidence detection of two Lyman-$\ensuremath{\alpha}$ photons. The cross-section curves are explained only by the contribution of the doubly excited ${Q}_{2}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Pi}}_{u}(1)$ state. The isotope effect on the oscillator strengths of $2p+2p$ pair formation for ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ from the ${Q}_{2}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Pi}}_{u}(1)$ state is almost the same as that on the oscillator strengths of $2s+2p$ pair formation from the ${Q}_{2}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Pi}}_{u}(1)$ state obtained by our group [T. Odagiri et al., Phys. Rev. A 84, 053401 (2011)]. This channel independence indicates that both isotope effects are dominated by the early dynamics of the ${Q}_{2}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Pi}}_{u}(1)$ state, before reaching the branching point into $2p+2p$ pair formation and $2s+2p$ pair formation.

Multielectron coincidence spectroscopy has been performed for Ar at a photon energy of only 0.2 eV above the $2{p}_{1/2}$ threshold. It is revealed that a postcollision interaction induced by double Auger decay leads to photoelectron recapture, followed by reemission of the captured electron, where the recapture of the slow photoelectron forms the $\mathrm{A}{\mathrm{r}}^{2+}$ Rydberg-excited states which subsequently undergo autoionization. The energy correlation of the emitted electrons discloses that both direct and cascade paths in the double Auger decay contribute to the photoelectron recapture.

The cross sections for the formation of the H(2p) and H(2s) atoms, σ2p and σ2s , respectively, in photoexcitation of C2H2 were obtained in an absolute scale for studying formation and decay of superexcited states in the extreme ultraviolet range. Several superexcited states of C2H2 including multiply excited states were found in the curve of the σ2p cross sections as a function of the incident photon energy. The same states seem to contribute to the variation in the σ2s cross sections as well, which can be ascribed to the non-adiabatic transitions between the 2p and 2s channels. The Σ/Π symmetry-resolved cross sections for the H(2s) atom formation, σ2sΣ and σ2sΠ , were also obtained on an absolute scale. The coupling between the Σu+1 and 1Π u states was found to be small.

The doubly excited states of methane produced in electron interaction have been investigated by measuring the electron-energy-loss spectra tagged with Lyman-α photons at 80 eV incident electron energy and electron scattering angles of 12° and 24°. The triply differential cross sections at both angles have been put on the same relative scale for the first time as a function of energy loss. It turned out that electron interaction with methane at 80 eV incident electron energy increases double excitation against single excitation as compared with photon interaction up to 24° electron scattering angle.

The cross sections for the emission of two photons of N fluorescence in photoexcitation of N2, differential with respect to each solid angle for the two photons, have been measured as a function of incident photon energy in the range of 28–49 eV to investigate the multiply excited states of N2. The resonance peaks attributed to the neutral excited states of N2 have been found at 36, 39, 40–44 and 45 eV in the ionization-free fluorescence cross section curve. It has turned out that these neutral excited states are multiply excited states of N2. It is remarkable that the multiply excited state of N2 at 45 eV embedded in the double ionization continuum makes a contribution comparable to those below the double ionization potential in the ionization-free cross section curve.

The formation and decay of doubly excited methane in photon and electron interactions have been investigated through measuring (i) the cross sections for the emission of the Lyman-α fluorescence in the photoexcitation of CH4 as a function of incident photon energy in the range 18–51 eV and (ii) the electron-energy-loss spectrum of CH4 tagged with the Lyman-α photons at 80 eV incident electron energy and 10° electron scattering angle in the range of the energy loss 20–45 eV. Five superexcited states have been found, three of which are doubly excited states with the others being singly excited states. It has been found that the electron interaction with CH4 at 80 eV incident electron energy and 10° electron scattering angle accelerates the double excitation against the single excitation as compared with the photon interaction.

The doubly differential cross sections for the emission of two Lyman-α photons in photoexcitation of H2 have been measured as a function of incident photon energy in the range of 30–44 eV with a photon–photon coincidence technique. A cross section curve that is free from ionization and thus is attributed entirely to the doubly excited states of H2 has been obtained for the first time. A simple theoretical calculation based on the reflection approximation and semiclassical treatment of the decay dynamics in the Q21Πu(1) state of H2 has reproduced well the experimental cross section curve. It has been shown that this method, the (γ, 2γ) method, is an excellent tool for investigating spectroscopy and dynamics of doubly or multiply excited molecules.

The cross sections for the emission of dispersed fluorescences in the ultraviolet and visible ranges by excited hydrogen atoms, OH radicals and OH+ fragment ions produced in the photoexcitation of H2O have been obtained as a function of incident photon energy in the range 17–41 eV, in which four superexcited states have been found. Two of these states around 25 and 28 eV are doubly excited states, which have been investigated in detail for the first time, and the others are single-hole one-electron superexcited states around 19 and 31 eV. It is remarkable that the doubly excited states around 28 eV give the oscillator strengths for Balmer fluorescences comparable to those given by the nearby single-hole one-electron states around 31 eV that are built on the (2a1)−1 ion core, which seems not to be amenable to the independent electron model. The state-resolved isotope effect on the oscillator strengths for Balmer-α fluorescence in H2O and D2O has been revealed. An overview of the doubly excited states of CH4, NH3 and H2O has been given in terms of the oscillator strengths for Balmer fluorescences and their energies based on the present investigation and preceding ones by Kato et al (2002 J. Phys. B: At. Mol. Opt. Phys. 35 4383 and 2003 J. Phys. B: At. Mol. Opt. Phys. 36 3541).

The cross sections for the collisional deexcitation of neon atoms in the lowest excited 1P1 state by Ar, Kr, Xe, N2, O2, CO, NO, and CH4, and in the lowest excited 3P1 state by O2 and CH4 have been measured at a mean collisional energy corresponding to room temperature. Data are also included for collisions of argon atoms in the lowest excited 1P1 and 3P1 states by C2H4, cyclo-C3H6, and C3H8, and collisions of krypton atoms in the lowest excited 1P1 and 3P1 states by C2H4 and cyclo-C3H6. The measured cross sections, together with those obtained in our previous studies, are compared with the cross sections calculated using the Watanabe–Katsuura theory. An extension of the Watanabe–Katsuura theory to the deexcitation of excited rare gas atoms in collisions with molecular quenchers, not atoms, is examined.

The cross sections for the emission of dispersed fluorescences in the ultraviolet and visible ranges by excited hydrogen atoms and NH radicals in the photoexcitation of ammonia have been obtained as a function of incident photon energy in the range of 13–40 eV, in which five superexcited states have been found. Three of these states around 22, 30 and 33 eV are doubly excited states, which have been investigated in detail for the first time and the others are single-hole one-electron superexcited states around 15 and 26 eV. It is remarkable that the doubly excited states around 30 eV give as large oscillator strengths for Balmer fluorescences as the nearby single-hole one-electron superexcited states around 26 eV that are built on the (2a1)−1 ion core, which seems not to be amenable to the independent electron model.

We have developed a new setup to measure temperature dependence on vacuum ultraviolet absolute photoabsorption cross sections for linear triatomic molecules from room temperature (~300 K) up to 700 K. The setup consists of a stainless steel absorption-cell wrapped by sheath wires of 1.2 in diameter and 2 m length. For the first set of measurement on CO2 in the photon energy range 10.6 – 11.8 eV, we found that the cross section values at room temperature are in very good agreement with previous measurements as well as the temperature dependence on the cross sections are clearly observed in the measured temperature range.

The absolute values of the fluorescence cross sections for CH(A, B ? X) and H(n = 4? 7 ? n' = 2) in the photoexcitation of methane have been obtained as a function of incident photon energy in the range 12.65?41 eV, in which five superexcited states have been found and discussed quantitatively in detail. The lower two of them are single-hole one-electron superexcited states and the higher three around 25, 29 and 35 eV are doubly excited states, which have been investigated in detail for the first time in this experiment. It is remarkable that the oscillator strengths for the emission of the fluorescences originating from the doubly excited states are as large as or even larger than those from the single-hole one-electron superexcited (2a1)?1 (npt2) 1T2 states, which seems not to be amenable to the independent electron model.

Cross sections for the formation of H(2p) atom in photoexcitation were measured for H2 in the lowest rotational level in the energy range of the doubly excited states for examining contribution of the non-adiabatic transition between the 1Σ u − 1Π u doubly excited states.

We have measured the coincidence time spectra for the pair of the Lyman-α and Lyman-β photons produced in the photodissociation of H2 in the range of the incident photon energy 32.5 - 42 eV. The result shows that the pair of H(2p) and H(3p) fragments is produced in the photodossociation of H2 molecules.

Absolute total cross sections for electron scattering from He and Ne are obtained in the energy range from 20 eV down to below 10 meV with a very narrow electron energy width of 6--8 meV using the threshold-photoelectron source. Total cross sections obtained in the present study generally agree well with those obtained in the previous experiments for both He and Ne above 100 meV, where several experimental works have been reported. Comparison of the present cross sections with the theoretical cross sections which have been regarded as the ``standard'' cross sections shows very good agreement even at very low energies below 10 meV, which confirms the validity of theoretical cross sections. The scattering lengths for electron scattering from He and Ne are also determined from the present total cross sections using the modified effective range theory. The resonant structures in the total cross sections due to Feshbach resonances of He and Ne are also observed. Analysis of the resonant structure was carried out based on the spin-dependent resonant scattering theory in order to determine the values of natural width of Feshbach resonance of Ne.

The ordinary and coincident electron-energy-loss spectra of N2 have been measured in an expected energy range for the formation of doubly excited states to investigate their formation and decay processes in electron-N2 collisions. The present results are compared with those obtained by photoexcitation experiments. Existence of the optically forbidden doubly excited states and their dissociative character have been revealed clearly for the first time.

The electron mobilities, μe, and electron-ion recombination rate constants, kr, in dense gaseous Ar and Kr with a small amount of N2 or CH4 as a molecular impurity have been measured as a function of electric field strength using a pulse radiolysis dc-conductivity method combined with a new decay-curve analysis method in which a space-charge effect is taken into account to obtain more accurate values of kr. The energy of electrons in recombination is controlled experimentally in two ways; one is heating-up by the electric field and the other is cooling-down by inelastic collisions with additive molecules. A large deviation of kr from the Debye theory obtained in the present experiment has been discussed in terms of the electron mean free paths and electron energies based on recent theories.

The state-resolved isotope effect on the cross sections of 2p atom formation via precursor doubly excited states of and is obtained at 80 eV incident electron energy and scattering angle by means of coincident electron-energy-loss spectroscopy as well as theoretical fits based on the reflection approximation and the survival probability. It turns out that the degree of the isotope effect depends strongly on the precursor doubly excited states and hence is a significant character of them. The origin of this dependence is discussed.

The cross-sections for the emission of two photons of N fluorescence differential with respect to each solid angle for the two photons in the photoexcitation of N2 have been measured as a function of incident photon energy in the range 34–40 eV by means of a new method, the ( γ , 2 γ ) method. A resonance peak attributed to the neutral excited state(s) of N2 appears around 36 eV in the measured cross-section curve that is free from ionization. We conclude that they are singly, doubly, or triply excited states of N2.

The absolute cross sections for the formation of the H(2s) and H(2p) atoms, σ2s and σ2p, respectively, in photoexcitation of CH4 and NH3 were measured in the range of the incident photon energy 15–48 eV for studying superexcited states of the molecules. The same superexcited states were found to contribute to the σ2s and σ2p cross sections. It was concluded that the non-adiabatic transitions play a significant role during the dissociation of the superexcited states and ionic states.

The doubly excited states of molecular hydrogen have been studied by means of electron-energy-loss spectroscopy in coincidence with the detection of H(2p) formation at 80 eV incident energy and scattering angle. This is the first observation of doubly excited states of in electron energy-loss spectra. It is shown that a forbidden doubly excited state makes a large contribution as well as allowed states. The measured spectrum has been analysed by theoretical fits based on the reflection approximation.

Absolute total cross sections for electron scattering from He, Ne, Ar, Kr and Xe at very low electron energies obtained using the technique employing the threshold-photoelectron source are presented. Comparison of the measured cross section for noble gas atoms with those of theoretical results are made.

The electron energy-loss spectra of H2 have been measured in coincidence with the neutral dissociation leading to H(1s)+H(2p) near the first ionization potential at the electron impact energy of 150 eV and the scattering angles of 2 degrees and 10 degrees , and compared with ordinary electron energy-loss spectra. The two spectra, the coincident and the ordinary ones, are similar to each other in shape below the energy level of H2+(X2 Sigma g+, upsilon i=1), while they are different from each other above this energy level. Such a large change around upsilon i=1 is discussed in terms of the dynamics of superexcited hydrogen molecules, and the availability of this method for such studies is examined.

Double Auger decay of O1s(-1) and its satellite states in H(2)O has been studied with a multi-electron coincidence method, and a process leading to autoionizing O* fragments has been revealed. The breaking of the two O-H bonds producing the autoionizing O* fragments occurs for highly excited H(2)O(2+) populated by the initial Auger decay. The O* fragments are more favorably produced in the decay from the satellite states, resulting from the larger population of highly excited H(2)O(2+) states inheriting the valence excitation in the initial state.

The cross sections for emission of two fluorescence photons from a pair of excited fragments in photoexcitation of H2O have been measured as a function of the incident photon energy using the photon–photon coincidence technique. The cross section increased in the range 30–45 eV, i.e. in the vicinity of the double ionization potential of H2O. The increase of the cross section was attributed to three-body neutral dissociations of a water molecule via multiply excited states: H2O** → H(2p) + OH** → H(2p) + H(2p) + O(3P). Some multiply excited states of H2O were also found in the cross section curve around 65 eV.

A new experimental technique for the measurements of the total cross section for electron scattering from atoms and molecules at very low energy is described. Momentum transfer cross sections for scattering from Ar, Kr and Xe at very low energies were carefully derived using the modified effective range theory from the recently measured total cross sections, which were obtained with a new experimental technique utilizing the threshold photoelectron source. A significant discrepancy between the momentum cross sections derived from the present analysis and those determined in the previous electron swarm studies was found at energies below 100 meV. The findings emphasize the need of further high precision experiments in the very low energy region as well as re-analysis of the previous swarm data.

Total cross sections for electron scattering from Ar, Kr, Xe and N2 at electron energies ranging below thermal energy to 20 eV with high-energy resolution obtained are presented. A new experimental technique which employs a combination of the penetrating field technique and the threshold photoionization of rare gas atoms using the synchrotron radiation as an electron source in order to produce a high resolution electron beam at very low energy was developed for the measurements. The lowermost energy of the present measurement reaches to the cold electron collisions regime, where the de Broglie wavelength of an electron becomes much lager than the typical size of target.

Absolute total cross sections for electron scattering from Ar and Xe at electron energies ranging from 7 meV to 20 eV were obtained with the experimental technique employing the threshold-photoelectron source. The measured total cross sections are in good agreement with those obtained by other groups down to 100 meV, above which several experimental works have been reported. Scattering lengths for electron scattering from Ar, Kr, and Xe were determined from the present total cross sections and our recent results for Kr using the modified effective range theory. The values of the scattering length obtained in the present analysis differ from the values determined from the previous swarm experiments and beam experiments. The resonant structures in the total cross sections due to Feshbach resonances of Ar, Kr, and Xe with an improved energy resolution were also measured. Analyses of the resonant structure were carried out based on the spin-dependent resonant scattering theory in order to determine the values of the natural width of Feshbach resonances of Ar, Kr, and Xe precisely.

The electron energy loss spectrum of H2O in coincidence with detecting Lyman-? photons (CoEELS) has been measured at the incident electron energy of 100 eV and electron scattering angle of 8? in the inner valence range in order to investigate the formation and decay of the doubly excited states. The present CoEELS has been compared with that at the infinite incident electron energy and 0? electron scattering angle, which was derived from the density of the dipole oscillator strength of H2O for the emission of the Lyman-? photons against the incident photon energy (Nakano et al 2010 J. Phys. B: At. Mol. Opt. Phys. 43 215206). It is remarkable that there exists a large difference in shape between these CoEELSs. This difference has turned out to be attributed to the noticeable contribution of the forbidden doubly excited states at 100 eV incident electron energy and 8? scattering angle. They lie at 25.0 and 27.4 eV and have been found out in this study. The differential cross sections for the excitation to the superexcited states resulting in H(2p) formation have been obtained at 100 eV and 8? and compared with those at the infinite energy and 0?. The electron collisions at 100 eV and 8? enhance the dissociative double excitation against the dissociative single excitation as compared with the electron collision at the infinite energy and 0?.

In this Reply to the preceding Comment by Sancho and Plaja, we point out the difference between the coincidence time spectrum of two Lyman-$\ensuremath{\alpha}$ photons measured by us and their theoretical one.

An experimental technique for the measurement of the total cross section for electron scattering from atoms and molecules at high resolution is described. The total cross sections for electron scattering from Kr in the energy range from 14 meV to 20 eV obtained with the technique are also reported. The present technique employs a combination of the penetrating field technique and the threshold photoionization of rare-gas atoms using synchrotron radiation as an electron source in order to produce a high-resolution electron beam at very low energy. The characteristics of the electron sources were determined by measuring the ionizing photon energy dependence of photoelectron yield. Absolute total cross sections for electron scattering are obtained by the attenuation method. The measured absolute values of the total cross sections for electron scattering from Kr agree with those obtained by other groups down to 175 meV, above which several experimental works have been reported. Below 175 meV, the present results generally agree with theoretical cross sections down to 14 meV. The resonant structures in the total cross sections due to Kr${}^{\ensuremath{-}}$ ($4{p}^{5}5{s}^{2 2}{P}_{3/2}$) and the Kr${}^{\ensuremath{-}}$ ($4{p}^{5}5{s}^{2 2}{P}_{1/2}$) Feshbach resonances are also reported. The resolution of the present setup has been estimated from a fit of the measured profile of the Kr${}^{\ensuremath{-}}$ ($4{p}^{5}5{s}^{2 2}{P}_{3/2}$) resonance by the theoretical curve obtained from the resonant scattering theory.

We have measured the coincidence time spectra of two Lyman-α photons emitted by a pair of H(2p) atoms in the photodissociation of H2 at the incident photon energy of 33.66 eV and at the hydrogen gas pressures of 0.40 and 0.02 Pa. The decay time constant at 0.02 Pa is approximately half the lifetime of a single H(2p) atom, 1.60 ns, while the decay time constant at 0.40 Pa is in agreement with the lifetime of a single H(2p) atom. It turns out that the decay faster than the lifetime of a single H(2p) atom originates from the entanglement in the pair of H(2p) atoms. We have demonstrated an effect of entanglement on atomic decay, The experiment was carried out under the approval of Photon Factory Program Advisory Committee for Proposal No. 2008G107. This work was partially supported by Grants- in-Aid for Scientific Research (C) (No. 19550011 and No. 22550008) from the Japan Society for the Promotion of Science. T.T. wishes to acknowledge the financial support by a Sasakawa Scientific Research Grant from the Japan Science Society, T.O. that of the Matsuo Foundation and Reimei Research Promotion Project of the Japan Atomic Energy Agency, and N.K. that of Research Foundation for Opto-Science and Technology. The authors are grateful to Dr. Kouichi Hosaka of the Department of Chemistry, Tokyo Institute of Technology, Dr. Atsushi Ichimura of the Institute of Space and Astronautical Science, JAXA, and Dr. James Harries of JAEA/SPring-8 for their fruitful discussions.

The angular distribution of two Lyman-alpha photons, i.e., the probability density that two Lyman-alpha photons are emitted in given directions, in the photodissociation of a hydrogen molecule have been measured at the hydrogen gas pressures of 0.40 and 0.13 Pa. We have found that the experimental angular distributions seem to approach the theoretical one by our group [J. Phys. B 40, 617 (2007)] with decreasing pressure, which indicates the generation of the entangled pair of H(2p) atoms shown in the theory and the role of the reaction of the entangled pair of H(2p) atoms with an H2 molecule that efficiently changes the entanglement.