arXiv subjects

N. L. Guevara

Publications and source records attributed to N. L. Guevara.

7 recordsLinked to original sources

arXiv2011

Helium- and Lithium-like ionic sequences: Critical charges

In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed.

math-ph↗

arXiv2009

Charged Hydrogenic, Helium and Helium-Hydrogenic Molecular Chains in a Strong Magnetic Field

A non-relativistic classification of charged molecular hydrogenic, helium and mixed helium-hydrogenic chains with one or two electrons which can exist in a strong magnetic field $B \lesssim 10^{16} $G is given. It is shown that for both $1e-2e$ cases at the strongest studied magnetic fields the longest hydrogenic chain contains at most five protons indicating to the existence of the $\rm{H}_5^{4+}$ and $\rm{H}_5^{3+}$ ions, respectively. In the case of the helium chains the longest chains can exist at the strongest studied magnetic fields with three and four $\al-$particles for $1e-2e$ cases, respectively. For mixed helium-hydrogenic chains the number of heavy centers can reach five for highest magnetic fields studied. In general, for a fixed magnetic field two-electron chains are more bound than one-electron ones.

astro-ph.HE↗

arXiv2007

The $HeH^+$ molecular ion in a magnetic field

A detailed study of the low-lying electronic states ${}^1\Si,{}^3\Si,{}^3Π,{}^3\De$ of the $\rm{HeH}^+$ molecular ion in parallel to a magnetic field configuration (when $\al$-particle and proton are situated on the same magnetic line) is carried out for $B=0-4.414\times 10^{13}$ G in the Born-Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that the parallel configuration is stable with respect to small deviations for $\Si$-states. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet ${}^1\Si$ state for small magnetic fields $B\lesssim 0.5 $ a.u. to the spin-triplet ${}^3\Si$ unbound state for intermediate fields and to the spin-triplet strongly bound $^3Π$ state for $B \gtrsim 15 $ a.u. When the $\rm{HeH}^+$ molecular ion exists, it is stable with respect to a dissociation.

physics.atom-ph↗

arXiv2007

A note about the ground state of the hydrogen molecule

A trial function is presented for the $H_2$ molecule which provides the most accurate (the lowest) Bohr-Oppenheimer ground state energy among few-parametric trial functions (with $\leq 14$ parameters). It includes the electronic correlation term in the form $\sim \exp{(γr_{12})}$ where $γ$ is a variational parameter.

physics.atom-ph↗

arXiv2007

The $H_3^+$ molecular ion in a magnetic field in linear parallel configuration

A first detailed study of the ground state of the H$_3^+$ molecular ion in linear configuration, parallel to a magnetic field direction, and its low-lying $\Si,Π,\De$ states is carried out for magnetic fields $B=0-4.414 \times 10^{13} $G in the Born-Oppenheimer approximation. The variational method is employed with a single trial function which includes electronic correlation in the form $\exp{(\ga r_{12})}$, where $\ga$ is a variational parameter. It is shown that the quantum numbers of the state of the lowest total energy (ground state) depend on the magnetic field strength. The ground state evolves from the spin-singlet ${}^1\Si_g$ state for weak magnetic fields $B \lesssim 5 \times 10^{8} $G to a weakly-bound spin-triplet ${}^3\Si_u$ state for intermediate fields and, eventually, to a spin-triplet $^3Π_u$ state for $5 \times 10^{10} \lesssim B \lesssim 4.414 \times 10^{13} $G. Local stability of the linear parallel configuration with respect to possible small deviations is checked.

physics.atom-ph↗

arXiv2006

The $He_2^{2+}$ molecular ion can exist in a magnetic field

A detailed study of the ground state of the Coulomb system $(\al \al e e)$ which corresponds to the $He_2^{2+}$ molecular ion in a magnetic field $B=0-4.414 \times 10^{13} $ G in parallel configuration (infinitely massive $\al-$particles are situated along a magnetic field line) is presented. The variational method is employed using a trial function which includes electronic correlation in the form $\exp{(γr_{12})}$ where $γ$ is a variational parameter. It is shown that the quantum numbers of the lowest total energy state depend on the magnetic field strength. It evolves from the spin-singlet ${}^1\Si_g$ metastable state at $0 \leq B \lesssim 0.85$ a.u. to a repulsive spin-triplet ${}^3\Si_u$ state for $0.85 {a.u.} \lesssim B \lesssim 1100$ a.u. and, finally, to a strongly bound spin-triplet ${}^3Π_u$ state at stronger fields $B \gtrsim 1100$ a.u. The lowest vibrational energy for the latter case is calculated.

astro-ph↗

arXiv2004

The exotic $H_3^{2+}$ ion in a strong magnetic field. Linear configuration

An accurate study of the lowest $1σ_g$ and the low-lying excited $1σ_u$, $1π_{u,g}$, $1δ_{g,u}$ electronic states of the exotic molecular ion $H_3^{2+}$ in linear configuration parallel to a magnetic field is carried out. The magnetic field ranges from $10^{10}$ G up to $4.414 \times 10^{13}$ G where non-relativistic considerations are justified. The variational method is exploited and the {\it same} trial function is used for different magnetic fields. It is shown that the states of positive $z$-parity $1σ_g, 1π_u, 1δ_{g}$ are bound states of the $H_3^{2+}$ exotic ion for all magnetic fields studied. We also demonstrate that for magnetic fields $B\gtrsim 2.35\times 10^{12}$ G the potential energy surface well corresponding to the $1σ_g$ state contains at least one longitudinal vibrational state. It is also shown that the negative $z$-parity states $1σ_u, 1π_g, 1δ_{u}$, are purely repulsive in the whole range of magnetic fields studied, $B=10^{10}- 4.414 \times 10^{13}$ G.

astro-ph↗