I am asking this question for theoretical understanding of the topic: What will happen if we keep bringing two protons closer and closer to each other, starting from a large distance?

I understand there will be electrostatic repulsion between them initially, which will continue to increase with a decrease in separation.

When we bring two protons very close to each other, within 1 Fermi distance, then I understand that nuclear forces will come into play, but I don't know what will happen next.

Could someone explain to me what will happen if we continue bringing two protons even closer?

How will protons behave?

If we try to understand it from the point of view of classical mechanics, then how the external agent will have to apply forces during this process of bringing protons closer and closer?


4 Answers 4


This really depends on the energy scale at which you bring them together. At CERN they do proton-proton collisions, where the protons move at speeds close to the speed of light. At those energy scales, the partons (constituents) of a proton, i.e. quarks and gluons, will scatter with each other, inducing a parton shower. The types of quarks/gluons that participate in the interactions are described by parton distribution functions.

As you mentioned, at low energies there is the Coulomb repulsion. Then the partons do not have enough energy to probe the proton. I'm not sure if there is a scale in between these extremes where the weak interaction is notable, since the electromagnetic and strong interaction are much stronger. For neutrons the story is different, they have no Coulomb repulsion.


If you did it slowly enough, you could create a very short-lived particle called a diproton, the 2He nucleus (Helium without any neutrons).

Wikipedia says its half time is 10-9 seconds because the strong force is not sufficient to counteract the electrostatic repulsion, so it's more a resonance than a "proper" particle, but still.


Proton-proton collision induces parton (constituents of proton) scattering. From here1:

Protons consist of three valence quarks, two up-quarks and one down-quark, held together by gluons and a sea of quark-antiquark pairs. Collectively, quarks and gluons are referred to as partons. In a proton-proton collision, typically only one parton of each proton undergoes a hard scattering – referred to as single-parton scattering – leaving the remainder of each proton only slightly disturbed. Here, we report the study of double- and triple-parton scatterings through the simultaneous production of three J/ψ mesons, which consist of a charm quark-antiquark pair, in proton-proton collisions recorded with the CMS (Compact Muon Solenoid) experiment at the Large Hadron Collider.

A visual representation is given here: enter image description here

For a video explanation, see What Happens Inside a Proton Collision? - with James Beacham.

In March 2024, the CMS collaboration announced the observation of two photons creating two tau leptons in proton–proton collisions

Notes and References:

  1. The CMS Collaboration. Observation of triple J/ψ meson production in proton-proton collisions. Nat. Phys. 19, 338–350 (2023), DOI: 10.1038/s41567-022-01838-y

The protons distract each other by the coulomb force. As you coerce them more and more close, you invest energy into the system.

At a point, beta decay of one of the protons becomes energetically favorable. That is because there is no direct coulomb distraction between the proton and a neutron, instead they have a bound state: the deuteron nucleus.

From that point, you have a deuteron nucleus. Also an electron, an electron anti-neutrino and possibly some gamma photons will leave the system as beta decay by-products.

The energy you invest to this is in the order of a billion K. That is the first step of fusing hidrogen into helium in small stars, and they need typically many billion years to do that (because their temperature is only some tens millions K).

Beside these, also other processes can happen, invoking various mesons or larger leptons, but these would require far more energy, thus odds are that it will happen first.

There is no known technology to do this with two protons, as we imagine the experiment with two bearing balls.

What is possible: shot protons into each other in accelerators, with gradually increasing proton energy. Cheaper solution is to shot a mostly hydrogen target, like a piece of polyethylene, with a proton beam. That is probably not much above the budget of a University with a low-budget education focus.

Problem is that the protons are not enough close to each other enough long, for such a beta decay to happen and this will be a very rare event. Increasing the energy will help, but at a point, also more energetic reactions will be able to happen.

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    $\begingroup$ The $\beta^{+}$ decay of a diproton does not happen very often; usually, the two simply have an amicable divorce and follow separate trajectories. If you try every second, time may well run out before you obtain a deuteron. $\endgroup$ Commented Jun 24 at 13:41
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    $\begingroup$ @Peter-ReinstateMonica Ok that is right, but afaik OP estimates a hyphothetical situation as the time where the protons are close, is much longer as the experimentally achievable. Roughly that happens in stars fusing hydrogen with the p-p process: there is no energy for the more exotic events, but the beta decay can happen, although slowly. I am thinking on, how to reformulate the post on this way. $\endgroup$
    – peterh
    Commented Jun 25 at 11:44
  • $\begingroup$ True. You could perhaps try something along the lines "if you could keep them magically together for an extended period of time"... then there is a decent chance a deuteron may emerge. I didn't find good information; the chance may still be very small: The two normally stay together 1E-9 s; a day would be 1E14 times that much but if the chance is only 1E-20/1E-9s for a deuteron it's still unlikely during that day! $\endgroup$ Commented Jun 25 at 11:51
  • $\begingroup$ As I mention in physics.stackexchange.com/a/540199/123208 It's estimated that (in the solar core) the probability of a diproton converting to a deuteron is in the order of $10^{-26}$. To put that into perspective, you have to mash around 1 Earth mass of solar core protons to make 1 gram of deuterons. $\endgroup$
    – PM 2Ring
    Commented Jun 25 at 15:49

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