Undergrad How does the collision between two atoms work?

[Ali Lavasani]

Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a regular elastic or inelastic collision between two macroscopic objects. Is it mainly due to the coulombic repulsion between the electrons of the two atoms? And, how is the trajectory of the two atoms after collision determined, and what factors contribute to it? Are these trajectories and the angle by which the atoms get deviated deterministic, or fuzzy just as the atoms themselves?

 

[hilbert2]

Practically all of the force between the Ca2+ ions is coulombic, most of it is because of the total charge of +2 on each ion, especially when they are not yet really close to each other (when closer, the shape of the charge distribution begins to have more effect). The trajectory of the center of mass of that kind of ion doesn't have to be as "fuzzy" as that of a single electron, as the ion is tens of thousands times more massive than an electron, but I don't think it's possible to follow the trajectory in liquid solution. In the case of two Ca ions colliding in vacuum it could be possible.

 

[Ali Lavasani]

Thanks for your response. How about neutral atoms or molecules? I mean, suppose that two H2O molecules or Hydrogen or Helium atoms approach each other on the x-axis. If they were solid macroscopic balls, they would collide and then move on the x-axis but in the reverse direction. So how would it be for this quantum-mechanical particles? Will they also remain on the x-axis, or their trajectories would be angled due to the uncertain charge distribution of electrons?

 

[hilbert2]

Even in a collision of two quantum point particles, the velocities after the collision don't have to be on the same line as before it. But if you know what direction one of the particles went to, it will limit the possible directions of the other particle due to momentum conservation.

 

[Ali Lavasani]

So you mean that, contrary to classical physics of macroscopic balls, there is more than one possible outcome when the two atoms/molecules collide? What exactly determines the velocity vectors after the collision?

 

[hilbert2]

There is some kind of "scattering matrix" that determines the likelihood of different directions after collision. I haven't done much of those calculations myself, so I won't try describe it in more detail.

 

[Ali Lavasani]

Thanks. I don't need the calculations, I'm just asking about how the collision works. My question is, WHY can the two atoms get deviated by some random angle after collision? Is that due to the uncertain charge distribution of their electrons?

 

[hilbert2]

Even in classical mechanics, a system with colliding billiard balls on a frictionless surface can be chaotic, so that just a little bit different initial velocities of the billiards can make them end up at completely different positions after a while. In QM there's also the element that positions and velocities are usually not precisely determined, which adds up to the difficulty.

 

[Ali Lavasani]

I was kinda discussing how the collisions work "in principle". In classical Newtonian physics, IN PRINCIPLE (and not in practice), everything is %100 predictable. On the other hand, the randomness in QM is not due to chaos or experimental errors, it's inherent randomness, and events are not predictable even on the paper.

So here also I was asking how the atomic collisions work in principle. According to what you say, the trajectories after collision are not deterministic due to uncertain velocities and positions. What do you mean by "positions and velocities"? Do you mean positions and velocities of the electrons within that atoms?