\begin{document}$ ^{37}_{\; {\Lambda}} $\end{document}Ar obtained using the Skyrme-Hartree-Fock (SHF) model and a beyond-mean-field approach, including angular momentum projection (AMP) and the generator coordinate method (GCM). A comprehensive energy spectrum is given, which includes normally deformed (ND) and super deformed (SD) hypernuclear states with positive or negative parities. Energy levels corresponding to the configurations in which a \begin{document}$ {\Lambda} $\end{document} hyperon occupies the s-, p-, or sd-shell orbitals are discussed. For the s-shell \begin{document}$ {\Lambda} $\end{document}, we pay special attention to the ND and SD states corresponding to the configurations \begin{document}$ ^{36} $\end{document}Ar\begin{document}$^{{\rm{N}}} \otimes$\end{document} s\begin{document}$ _{\Lambda} $\end{document} and \begin{document}$ ^{36} $\end{document}Ar\begin{document}$^{{\rm{S}}} \otimes$\end{document} s\begin{document}$ _{\Lambda} $\end{document}, where \begin{document}$ ^{36} $\end{document}Ar\begin{document}$ ^{{\rm{N}}} $\end{document} and \begin{document}$ ^{36} $\end{document}Ar\begin{document}$ ^{{\rm{S}}} $\end{document} denote the ND and SD nuclear cores, respectively. The disagreements between different models over the \begin{document}$ {\Lambda} $\end{document} separation energy of the SD state in previous studies are revisited. For the p-shell \begin{document}$ {\Lambda} $\end{document}, four rotational bands are predicted, and the impurity effects are shown. Furthermore, two energy levels corresponding to the configurations \begin{document}$ ^{36} $\end{document}Ar\begin{document}$^{{\rm{S}}} \otimes {\Lambda}$\end{document}[101]\begin{document}$\frac{3}{2}^{-}$\end{document} and \begin{document}$ ^{36} $\end{document}Ar\begin{document}$^{{\rm{S}}} \otimes {\Lambda}$\end{document}[101]\begin{document}$\frac{1}{2}^{-}$\end{document} are obtained below the separation threshold of \begin{document}$ ^{36} $\end{document}Ar+\begin{document}$ {\Lambda} $\end{document} within 0.5 MeV. For the sd-shell \begin{document}$ {\Lambda} $\end{document}, three bound states are found near the separation threshold, and the mechanism behind these states are discussed."> Beyond-mean-field study of <inline-formula><tex-math id="M1">\begin{document}${{} ^{\bf 37}_{\; {\bf\Lambda}}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/a77fc071-27aa-443c-a265-d482e92af4c9/CPC-2022-0020_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/a77fc071-27aa-443c-a265-d482e92af4c9/CPC-2022-0020_M1.png"/></alternatives></inline-formula>Ar based on the Skyrme-Hartree-Fock model -
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