Use of symmetry in collisions

Hello,
This is probably an odd question but, I do not see easily the answer.
The question is if these two problems are equivalent or not.
First problem: two identical particles collide at a given velocity (i.e in the X axis).
Second problem: one particle with the same properties than the previous collide with a perfectly rigid wall (a symmetry condition)

I'm doing this question because the collision times I had obtained and the ones that I expected to have. The restoring force in ESYS (and as long as I see in other codes too) is proportional to the overlapping between particles. It's like to have a spring between the particles centers with an inicial length equal to the sum of radius (if identical then two radius). In a symmetry conditions, if a particle approach to the other lets say delta, then the other do the same, so the overlapping is equal to 2 x delta. If I consider the problem as the particle colliding with the wall, then the spring contraction is only delta.

Well I have answered myself while writing this post. I'll leave it and I'll send it because it's possible that I made some bad reasoning, or perhaps it help someone else.

The explanation is:

If I model the problem as one particle colliding with the wall, then the force was kn x delta, and the forces I get from ESYS were twice the ones I expected, so the collision time I ESYS gave was 1/sqrt(2) the 'theoretical' one. Ok, the point is the Kn. The kn should be calculated probably from the Young Modulus. We have from elasticity sigma=Y x eps -> sigma = Y x (deltaX)/X0 -> F = sigma x A = (Y x A / X0) x deltaX, so the kn = Y x A / X0. Here is the problem of having the kn constant, because the area of contact changes with the stress. But the important point is that if we use this simplified model, then the kn of the first problem is half the kn of the second one, so the results are the same.

If you think that this post is not relevant, please let me know. I'm thinking on aspects of the problem that I had not done before, but probably are well known in the DEM community.
Thanks a lot, best regards,