Exported STL files from the segmentation has intersection/penetration

do mean to add some empty space between the segments by shrinking the margin of the segments?

would you please let me know in which step I should avoid smoothing?

I need to create a volumetric mesh for these geometries, therefore, I have to work with the meshes and I have no idea how can I use the labelmap to create the volumetric mesh.

I thought that setting the smoothing factor to the zero only effects the 3D visualization and does not affect the exported geometries from the Slicer. Please correct me if I am wrong.

thank you in advance,

It affects the surface model contained in the segmentation, which is both displayed, and saved to file.

You can use Segment Mesher extension to create volumetric mesh directly from segments. Cleaver method generates mesh from the labelmap representation (not from surface mesh) and creates a joint, multi-material tetrahedral mesh, with guaranteed no overlap or gap between materials (segments).