Let $K$ be a $p$-adic field and $\Omega^{(n)}_K$ the $n$-dimensional Drinfeld upper half space over $K$ (which is a rigid analytic space over $K$).
Is the Picard group of $\Omega^{(n)}_K$ known? More generally, I would like to know the Picard group of $\Omega^{(n)}_K$ base changed to any finite extension $L$ of $K$ (which is not the same as $\Omega^{(n)}_L$).
I'd appreciate any references where this question, or similar questions, are considered.