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

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