Azimuthal-sensitive three-dimensional HBT radius in Au-Au collisions at E${}_{beam}$ = 1.23 A GeV by the IQMD model

We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to simulate Au + Au collisions at beam energy E${}_{beam}$ = 1.23 A GeV, which corresponds to center of mass energy $\sqrt{s_{NN}}$ = 2.4 GeV. Firstly, we obtained reasonable rapidity and transverse mass spectra of ${\pi }^{-}$ and ${\pi }^{+}$ as well as "apparent" temperature parameters in comparison with the HADES data. Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of same charged pion-pairs, we obtained the square difference of outward radius and sideward radius, i.e. R${}_{out}^2$-R${}_{side}^2$, as well as the freeze-out volume (V${}_{fo}$), which were basically consistent with the trend of HADES experimental results. The azimuthal dependence of the HBT radii was also calculated by a matrix method, and corrected by the rotation matrix. In addition, the eccentricities of the xy- and zy- planes of pion-pair emissions were also extracted for different pair transverse momentum and collision centrality, which show that the xy-eccentricity increases with pair transverse momentum as well as centrality but not for zy-eccentricity, indicating a more asymmetric transverse emission of particle-pairs with higher transverse momentum in off-central collisions.