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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

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

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 ${}^3 ��_{g}^{-}$ 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 ${}^4 ��_u^-$ 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., 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.