arXiv subjects

Horacio Olivares Pilón

Publications and source records attributed to Horacio Olivares Pilón.

5 recordsLinked to original sources

arXiv2014

Quadrupole transitions in the bound rotational-vibrational spectrum of the tritium molecular ion

The nonrelativistic energies of the homonuclear ion T$_2^+$ are calculated for the ground state using the Lagrange-mesh method as was done for the isotopomers H$_2^+$ and D$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101 and {\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 46} 245101). Energies and eigenfunctions are obtained up to four of the lowest bound vibrational states ($v=0,1,2,3$) which support 62, 61, 60 and 58 bound rotational states, respectively. Some quasibound sates are also presented until $L =$ 68. From the obtained wave functions, electric quadrupole transitions per time unit are calculated between those states over the whole rotational bands. Extensive results are presented with 6 significant digits. The ground state energy of the symmetric systems $^{\infty}$H$_2^+$, $^{\infty}$H$^-$, Ps$^{-}$, H$^-$, D$^-$, T$^-$, $μ^+μ^+e$ and $μ^+e\,e$ is presented with high accuracy as a function of $β=m_3/(2m+m_3)$.

physics.atm-clus↗

arXiv2013

Quadrupole transitions in the bound rotational-vibrational spectrum of the hydrogen molecular ion

The three-body Schrödinger equation of the H$_2^+$ hydrogen molecular ion with Coulomb potentials is solved in perimetric coordinates using the Lagrange-mesh method. The Lagrange-mesh method is an approximate variational calculation with variational accuracy and the simplicity of a calculation on a mesh. Energies and wave functions of up to four of the lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated. The obtained energies have an accuracy varying from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibrational excited state. With the corresponding wave functions, a simple calculation using the associated Gauss quadrature provides accurate quadrupole transition probabilities per time unit between those states over the whole rotational bands. Extensive results are presented with six significant figures.

quant-ph↗

arXiv2013

Dipole transitions in the bound rotational-vibrational spectrum of the heteronuclear molecular ion HD$^+$

The non-relativistic three-body Schrödinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0-3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least 9 digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those levels are given over the whole $v=0-3$ rotational bands. Results are presented with six significant figures.

physics.atm-clus↗

arXiv2013

Quadrupole transitions in the bound rotational-vibrational spectrum of the deuterium molecular ion

After the study of the three body molecular system H$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101), its isotopomer, the deuterium molecular ion D$_2^+$ is studied. The three-body Schrödinger equation is solved using the Lagrange-mesh method in perimetric coordinates. Energies and wave functions for four vibrational states $v=0-3$ and bound or quasibound states for total orbital momenta from 0 to 56 are calculated. The 1986 fundamental constant $m_d=3670.483014\,m_e$ is used. The obtained energies have an accuracy from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibrational excited state. Quadrupole transition probabilities per time unit between those states over the whole rotational bands were calculated. Extensive results are presented with six significant figures.

physics.atom-ph↗

arXiv2011

He$_2^{3+}$ and HeH$^{2+}$ molecular ions in a strong magnetic field: the Lagrange mesh approach

Accurate calculations for the ground state of the molecular ions He$_2^{3+}$ and HeH$^{2+}$ placed in a strong magnetic field $B\gtrsim 10^{2}$ a.u. ($\approx 2.35 \times 10^{11}$G) using the Lagrange-mesh method are presented. The Born-Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9-10 s.d. The obtained results show that the molecular ions He$_2^{3+}$ and HeH$^{2+}$ exist at $B > 100$\,a.u. and $B > 1000$\,a.u., respectively, as predicted in \cite{Tu:2007} while a saddle point in the potential curve appears for the first time at $B \sim 80$ a.u. and $B \sim 740$ a.u., respectively.

astro-ph.HE↗