# Do electrons combine to form a single particle

I was reading about exchange interactions and stumbled across this website that was discussing symmetry and the exchange interaction. The website stated

The exchange interaction is originated from the feature of our Nature that the state of a higher symmetry has a lower energy. The Higgs field may be only one exception. The reason why the energy is lower is that the interaction between two particle disappears when two particle join each other to create a single particle of a higher symmetry.

Now, the website goes on to explain an example and uses two electrons to illustrate the aforementioned explanation of the exchange interaction.

An example is two electrons of opposite spins. For each electron, the time-inverse symmetry is broken and the wavefunction is a spinor. When these two electrons of opposite spins occupy one quantum state, they become one single new particle with charge of -2e and no spin. The time-inverse symmetry for this new particle is not broken and its wavefunction is a scalar. This new particle is not a simple sum of two electrons of opposite spins. For simple sum of two electrons of opposite spins, the time- inverse symmetry is not broken!. For example, two opposite spins can be directed along the x- axis or the y-axis or the z-axis. Therefore, two electrons of opposite spins occupying one state is really a new particle. It is absolutely not a the sum of two individual particles, which are sitting in one place.

Here are my questions/concerns

This website isn’t a primary source and is a personal/science website so I wanted to check the validity of it. Do electrons combine to form single particles?

Additionally, I’ve never heard two electrons to be referred to as a single particle. I liked to know if it is correct for me to refer to two electrons, of opposite spin in an atomic or molecular orbital, as combining to form a single particle.

– Joe
Aug 10, 2022 at 19:55

It’s kind of a philosophical question, which depends on quite what you mean by “particle.” This particular language isn't common, and lots of people might have strong opinions that it's incorrect. However, a multi-electron composite state is different from a product of single-electron states in a number of different ways, and referring to the multi-electron state as "a particle" is a useful way to keep yourself from falling into some common traps.

A common situation where this language is useful is when thinking about emission and absorption of radiation by atoms. It's quite common to see language like

[misleading] The electron absorbs a photon and jumps to a higher-energy orbital.

The trouble with this statement is that a single electron can't emit or absorb energy. In hydrogen spectroscopy, the photons are emitted and absorbed by the atom, and the approximation that the nucleus remains stationary is just that: an approximation. For multi-electron atoms, it is useful to pretend like each electron is added to a hydrogen-like orbital, and to use the multiplicities of these orbitals explain the shape of the periodic table. (Orbital angular momentum states have odd multiplicities $$1,3,5,\cdots$$, which are doubled for the spin degree of freedom, so the different blocks of the periodic table have two columns, six columns, ten columns, fourteen columns.)

But only some features of the hydrogen-like orbitals are preserved in multi-electron atoms. The nucleus-electron-electron wavefunction for neutral helium atoms is actually too complicated to solve exactly, in the way that we have exact solutions for the hydrogen atom. And a consequence of this extra complexity is that, when a multi-electron atom (or ion) emits or absorbs photons, the approximation that "a single electron" jumps to a different orbital is likewise just an approximation. When a complicated atom changes state, its entire electronic wavefunction changes, in a way that we mostly can only solve numerically.

Another case where it's useful to think of a multi-electron state as "a particle" is in a superconductor. In a normal conductor, a useful model of electric current describes single electrons which scatter off of the nuclei in the crystal lattice and lose energy. However, in a superconductor, the conduction electrons form "Cooper pairs," named for the "C" in the BCS theory of superconductivity. A very handwaving way to think of superconductivity is that the two electrons in the Cooper pair scatter from the lattice in opposite ways, so the scattered states interfere with each other destructively and the entire material becomes transparent. But it's just as valid to think of the Cooper pair as "a particle," whose spin, mass, and charge are different from the electrons into which it will split at higher temperature.

A much more common case of a composite state being treated as a single particle is the nucleon (that is, the proton or neutron). At very high energies, nucleons undergo internal excitations which suggest they are "made" of "quarks." But at low energies, the quark-gluon degrees of freedom stop being useful for predicting the excitation spectra of nuclei. If I wanted to have a debate at a pub, I might argue that the neutron has a better claim to being a "particle" than an up quark does, because it is possible to build machines that spray mostly neutrons, but it is impossible to build machines that spray mostly up quarks.

You might also consider Gamow's influential cluster-tunneling model for alpha decay, in which "an alpha particle forms" within the complicated morass that is a heavy nucleus in its ground state, and then that alpha particle has some finite probability of leaking out of the nucleus. That model really does consider "an alpha particle" as a single object, rather than as a bound state of four nucleons.

Your quoted text seems to suggest you could describe a helium atom as a nucleus bound to "an electron spin singlet." I don't think that's very good language to use. But I would absolutely 100% consider "a helium atom" as "a particle," just as I do the alpha particle, and just as I do the two-electron Cooper pair.

• I am reminded of this passage from Jain's book on composite fermions: "A short digression is worthwhile to discuss what we mean by a "particle". [...] A most profound fact of nature – indeed the very reason why physics can make progress at many different levels – is that strongly interacting particles reorganize themselves to become more weakly coupled particles of a new kind. These new particles are, in a deep sense, the “true” particles of the system in question, because it is reasonable to reserve the title “particle” for nearly independent objects." Aug 10, 2022 at 10:39
• In Robert Laughlin's "A Different Universe," he sets the stage to ask whether there is really a fundamental difference between a "particle" versus a "quasiparticle." The differences he comes up with all vanish in limit of a very pure material at zero temperature.
– rob
Aug 10, 2022 at 20:38
• thank you for your explanation and for breaking my naive view of what can be considered a particle. Aug 10, 2022 at 21:54