Excitation Spectra of Alkali Atoms under Spatially Confined Core Potentials

This study presents an analysis that explains the confinement of valence electrons in five Alkali atoms within the domains of a potential delineated by the function $\mathcal{V}\left(h,r,l,{\alpha }_c,a_l\right)$ . The potential is devised to replicate the correct asymptotic behavior at large distances from the atomic core and is calibrated to align with the experimentally observed binding energy for the ground state at each angular momentum quantum number $l$ . The method is well-suited for localized potentials and works well in finite domains having boundary conditions that are well known. The eigenvalue spectra provide a visualization of the energies of the Alkali species under the confining potential.