Asymptotic profile of least energy solutions to the nonlinear Schrödinger-Bopp-Podolsky system

Consider the following nonlinear Schrödinger–Bopp–Podolsky system in ${\mathbb{R}}^3$: $$\{\begin{array}{l}-\mathrm{\Delta }v+v+\phi v=v\mathrm{\mid }v{\mathrm{\mid }}^{p-2};\\ {\beta }^2{\mathrm{\Delta }}^2\phi -\mathrm{\Delta }\phi =4\pi v^2,\end{array}$$ where $\beta >0$ and $3<p<6$, the unknowns being $v$, $\phi \text{\hspace{0.17em}⁣}:{\mathbb{R}}^3\to \mathbb{R}$. We prove that, as $\beta \to 0$ and up to translations and subsequences, least energy solutions to this system converge to a least energy solution to the following nonlinear Schrödinger–Poisson system in ${\mathbb{R}}^3$: $$\{\begin{array}{l}-\mathrm{\Delta }v+v+\phi v=v\mathrm{\mid }v{\mathrm{\mid }}^{p-2};\\ -\mathrm{\Delta }\phi =4\pi v^2\mathrm{.}\end{array}$$