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It has recently been argued that atoms and molecules may become good targets of determining neutrino parameters still undetermined, if atomic/molecular process is enhanced by a new kind of coherence. We compute photon energy spectrum rate arising from coherent radiative neutrino pair emission processes of metastable excited states of I$_2$ and its iso-valent molecules, $|Av \rangle \rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ and $|A'v \rangle \rightarrow |Xv' \rangle + \gamma + \nu_i\nu_j$ with $\gamma$ an IR photon and $\nu_{i(j)}$ $i(j)-$th neutrino mass eigenstates, and show how fundamental neutrino parameters may be determined. Energies of electronically excited states of I$_2$, including the effect of spin-orbit couplings were calculated by the multiconfigurational second order perturbation (CASPT2) method. Summation over many vibrational levels of intermediate states is fully incorporated. Unlike atomic candidate of a much larger energy difference such as Xe, I$_2$ transitions from a vibrational level $A(v=0)$ to $X(v' = 24)$ give an opportunity of determination of the mass type (Majorana vs Dirac distinction) and determination of Majorana CPV (charge-conjugation parity violating) phases, although the rate is much smaller., Comment: 24 pages, 19 figures

We report on theoretical Auger electron kinetic energy distribution originated from sequential two-step Auger decays of molecular double core-hole (DCH) state, using CH4, NH3 and H2CO molecules as representative examples. For CH4 and NH3 molecules, the DCH state has an empty 1s inner-shell orbital and its Auger spectrum has two well separated components. One is originated from the 1st Auger transition from the DCH state to the triply ionized states with one core hole and two valence holes (CVV states) and the other is originated from the 2nd Auger transition from the CVV states to quadruply valence ionized (VVVV) states. Our result on the NH3 Auger spectrum is consistent with the experimental spectrum of the DCH Auger decay observed recently [Phys. Rev. Lett. 105, 213005 (2010)]. In contrast to CH4 and NH3 molecules, H2CO has four different DCH states with C1s^{-2}, O1s^{-2} and C1s^{-1}O1s^{-1} (singlet and triplet) configurations, and its Auger spectrum has more complicated structure compared to the Auger spectra of CH4 and NH3 molecules. In the H2CO Auger spectra, the C1s^{-1}O1s^{-1} DCH -> CVV Auger spectrum and the CVV -> VVVV Auger spectrum overlap each other, which suggests that isolation of these Auger components may be difficult in experiment. The C1s^{-2} and O1s^{-2} DCH -> CVV Auger components are separated from the other components in the H2CO Auger spectra, and can be observed in experiment. Two-dimensional Auger spectrum, representing a probability of finding two Auger electrons at specific pair of energies, may be obtained by four-electron coincidence detection technique in experiment. Our calculation shows that this two-dimensional spectrum is useful in understanding contributions of CVV and VVVV states to the Auger decay of molecular DCH states., Comment: 49 pages, 14 figures. J. Chem. Phys. in press

We have theoretically investigated the double core-hole (DCH) states of the open-shell molecules and examined the possibility of DCH spectroscopy by means of X-ray two-photon photoelectron spectroscopy (XTPPS). Energies of many DCH states were obtained by the CASSCF calculations and the generalized intra- and interatomic relaxation energies were evaluated. We show that XTPPS can extract these quantities by the measurement of single and double core-hole ionization potentials. We discuss the influence of chemical environment on the DCH states with two holes at the same atomic site and at two different atomic sites., Comment: 17 pages. To appear in Chem.Phys.Lett

We explore the potential of double core hole electron spectroscopy for chemical analysis in terms of x-ray two-photon photoelectron spectroscopy (XTPPS). The creation of deep single and double core vacancies induces significant reorganization of valence electrons. The corresponding relaxation energies and the interatomic relaxation energies are evaluated by CASSCF calculations. We propose a method how to experimentally extract these quantities by the measurement of single and double core-hole ionization potentials (IPs and DIPs). The influence of the chemical environment on these DIPs is also discussed for states with two holes at the same atomic site and states with two holes at two different atomic sites. Electron density difference between the ground and double core-hole states clearly shows the relaxations accompanying the double core-hole ionization. The effect is also compared with the sensitivity of single core hole ionization potentials (IPs) arising in single core hole electron spectroscopy. We have demonstrated the method for a representative set of small molecules LiF, BeO, BF, CO, N2, C2H2, C2H4, C2H6, CO2 and N2O. The scalar relativistic effect on IPs and on DIPs are briefly addressed., Comment: 35 pages, 6 figures. To appear in J. Chem. Phys.

The R-matrix method has been used for theoretical calculation of electron collision with atoms and molecules for long years. The method was also formulated to treat photoionization process, however, its application has been mostly limited to photoionization of atoms. In this work, we implement the R-matrix method to treat molecular photoionization problem based on the UK R-matrix codes. This method can be used for diatomic as well as polyatomic molecules, with multi-configurational description for electronic states of both target neutral molecule and product molecular ion. Test calculations were performed for valence electron photoionization of nitrogen (N2) as well as nitric oxide (NO) molecules. Calculated photoionization cross sections and asymmetry parameters agree reasonably well with the available experimental results, suggesting usefulness of the method for molecular photoionization., Comment: 31 pages, 8 figures. J.Chem.Phys. in press.

Low-energy electron impact excitations of S_2 molecules are studied using the fixed-bond R-matrix method based on state-averaged complete active space SCF orbitals. Integral cross sections are calculated for elastic electron collision as well as impact excitation of the 7 lowest excited electronic states. Also, differential cross sections are obtained for elastic collision and excitation of the a^1 Delta_g, b^1 Sigma_g^+ and B^3 Sigma_u^- states. The integrated cross section of optically allowed excitation of the B^3 Sigma_u^- state agrees reasonably well with the available theoretical result., Comment: 12 pages, 3 figures. Chemical Physics Letters, in press

The spin-exchange effect in spin-polarized electron collisions with unpolarized open-shell molecules, O$_2$, B$_2$, S$_2$ and Si$_2$, has been studied by the R-matrix method with the fixed-bond approximation. All of these molecules have ${}^3 \Sigma_{g}^{-}$ symmetry in their ground states. Usual integrated cross sections with unpolarized electrons has also been studied. We used the complete active space self consistent field orbitals and put more than 10 target electronic states in the R-matrix models. In electron O$_2$ elastic collisions, calculated polarization fractions agree well with the experimental results, especially around the ${}^4 \Sigma_u^-$ resonance. In e-B$_2$, S$_2$ and Si$_2$ elastic collisions, larger spin-exchange effect is observed compared to the e-O$_2$ elastic collisions. In all four cases, spin-exchange effect becomes prominent near resonances. This association of resonance and magnitude of the spin-exchange effect was studied by explicitly removing the resonance configurations from the R-matrix calculations. In general, spin-exchange effect is larger in e-B$_2$ collisions than in e-S$_2$ and Si$_2$ collisions, and is smallest in e-O$_2$ collisions., Comment: Phys. Rev. A, in press

Low-energy electron impact excitations of N$_2$ molecules are studied using the fixed-bond R-matrix method based on state-averaged complete active space SCF orbitals. Thirteen target electronic states of N$_2$ are included in the model within a valence configuration interaction representations of the target states. Integrated as well as differential cross sections of the $A^{3} \Sigma_{u}^{+}$, $B^{3} \Pi_{g}$, $W^{3} \Delta_{u}$, ${B'}^{3} \Sigma_{u}^{-}$, ${a'}^{1} \Sigma_{u}^{-}$, $a^{1} \Pi_{g}$, $w^{1} \Delta_{u}$ and $C^{3} \Pi_{u}$ states are calculated and compared with the previous experimental measurements. These excitations, especially of the higher four states, have not been studied enough theoretically in the previous literature. In general, good agreements are observed both in the integrated and differential cross sections. However, some discrepancies are seen in the integrated cross sections of the $A^{3} \Sigma_{u}^{+}$ and $C^{3} \Pi_{u}$ states, especially around a peak structure., Comment: 28 pages, 11 figures, accepted for publication in Phys. Rev. A

Differential cross sections for electron collisions with the O$_2$ molecule in its ground ${X}^{3}\Sigma_g^-$ state, as well as excited ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states are calculated. As previously, the fixed-bond R-matrix method based on state-averaged complete active space SCF orbitals is employed. In additions to elastic scattering of electron with the O$_2$ ${X}^{3}\Sigma_g^-$, ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states, electron impact excitation from the ${X}^{3}\Sigma_g^-$ state to the ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states as well as '6 eV states' of ${c}^{1}\Sigma_u^{-}$, ${A'}^{3}\Delta_u$ and ${A}^{3}\Sigma_u^{+}$ states is studied. Differential cross sections for excitation to the '6 eV states' have not been calculated previously. Electron impact excitation to the ${b}^{1}\Sigma_g^+$ state from the metastable ${a}^{1}\Delta_g$ state is also studied. For electron impact excitation from the O$_2$ ${X}^{3}\Sigma_g^-$ state to the ${b}^{1}\Sigma_g^+$ state, our results agree better with the experimental measurements than previous theoretical calculations. Our cross sections show angular behaviour similar to the experimental ones for transitions from the ${X}^{3}\Sigma_g^-$ state to the '6 eV states', although the calculated cross sections are up to a factor two larger at large scattering angles. For the excitation from the ${a}^{1}\Delta_g$ state to the ${b}^{1}\Sigma_g^+$ state, our results marginally agree with the experimental data except for the forward scattering direction.

Low-energy electron collisions with O$_2$ molecules are studied using the fixed-bond R-matrix method. In addition to the O$_2$ ${X}^3\Sigma_{g}^-$ ground state, integrated cross sections are calculated for elecron collisions with the ${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ excited states of O$_2$ molecules. 13 target electronic states of O$_2$ are included in the model within a valence configuration interaction representations of the target states. Elastic cross sections for the ${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ excited states are similar to the cross sections for the ${X}^3\Sigma_{g}^-$ ground state. As in case of excitation from the ${X}^3\Sigma_{g}^-$ state, the O$_2^-$ $\Pi_u$ resonance makes the dominant contribution to excitation cross sections from the ${a}^1\Delta_{g}$ and ${b}^1\Sigma_{g}^+$ states. The magnitude of excitation cross sections from the ${a}^1\Delta_{g}$ state to the ${b}^1\Sigma_{g}^+$ state is about 10 time larger than the corresponding cross sections from the ${X}^3\Sigma_{g}^-$ to the ${b}^1\Sigma_{g}^+$ state. For this ${a}^1\Delta_{g}$ $\to$ ${b}^1\Sigma_{g}^+$ transition, our cross section at 4.5 eV agrees well with the available experimental value. These results should be important for models of plasma discharge chemistry which often requires cross sections between the excited electronic states of O$_2$., Comment: 26 pages, 10 figures