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\begin{document}

\title{Few electron systems confined in gaussian potential wells and connection
to Hooke atoms}



\author[1]{Xabier Telleria}%
\author[2]{Jose Mercero}%
\author[1]{Jesus Ugalde}%
\author[1]{Xabier Lopez}%
\author[1]{Jon Matxain}%
\affil[1]{Euskal Herriko Unibertsitatea (UPV/EHU)}%
\affil[2]{Euskal Herrico Unibertsitatea, EHU and Donostia International Physics Center, DIPC}%


\vspace{-1em}



  
  \date{May 22, 2024}


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\begin{abstract}
In thiswork,we have computed and implemented one-body integrals
concerning gaussian confinement potentials over gaussian basis
functions. Then, we have set an equivalence between gaussian and Hooke
atoms and we have observed that, according to singlet and triplet state
energies, both systems are equivalent for large confinement depth for a
series of even number of electrons n = 2, 4, 6, 8 and 10. Unlike with
harmonic potentials, gaussian confinement potentials are dissociative
for small enough depth parameter; this feature is crucial in order to
model phenomena such as ionization. In this case, in addition to
corresponding Taylor series expansions, the first diagonal and
sub-diagonal Pad\selectlanguage{ngerman}é approximant were also obtained, useful to compute the
upper and lower limits for the dissociation depth. Hence, this method
introduces new advantages compared to others.%
\end{abstract}\selectlanguage{ngerman}%



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