The universe is full of surprises, and sometimes those surprises come in the form of ghostly, almost-there particles clinging to the edges of existence. A team of physicists at the University of Birjand and RIKEN have proposed the potential existence of a peculiar nucleus: a form of beryllium-9 (9Be) bound to a charmonium particle (c¯c) – a heavy, unstable particle made of a charm quark and its antiquark.
Charmonium Encounters the Nucleus
To understand why this is interesting, let’s break down the key players. Charmonium, represented as c¯c, isn’t your everyday particle. These are a family of mesons composed of a charm quark and a charm antiquark. Think of them as fleeting, exotic cousins of the more familiar protons and neutrons found in atomic nuclei. These particles, like the J/ψ and ηc, are incredibly short-lived, decaying rapidly into other particles.
Now, consider the nucleus of an atom. Normally, it’s a tightly packed collection of protons and neutrons, bound together by the strong nuclear force. But what happens when you introduce a charmonium particle into the mix? This is where things get interesting, because charmonium particles don’t play by the usual rules of nuclear interaction. Because charmonium and nucleons do not share light quarks, they interact through the exchange of gluons — the fundamental particles that carry the strong force. The theory suggests this gluon exchange creates a QCD van der Waals force — an attraction that might be strong enough to bind the charmonium to the nucleus.
A Borromean Oddity?
The research, led by Faisal Etminan, explores the possibility of a 9Be nucleus binding with a charmonium particle, creating a novel nuclear system. Their models suggest that while neither a charmonium-helium-4 (5He) nor a beryllium-8 (8Be) pair is stable on its own, the combination of charmonium with two alpha particles (which make up beryllium-8) could form a bound state. This is an example of a Borromean system, named after the Borromean rings, where three rings are interlocked in such a way that if any one ring is removed, the entire structure falls apart. None of the pairs are linked, but the set is inseparable.
“It is determined that, despite neither the 5c¯cHe nor the 8Be binary subsystems being bound, a bound state of the c¯c-αα nuclear system could potentially exist,” the researchers write.
Think of it like this: imagine you have two magnets that are too weak to pick up a paperclip on their own. But if you hold them close together on either side of the paperclip, their combined force might be enough to hold it in place. In this analogy, the alpha particles are the magnets, the charmonium is the paperclip, and the strong force is what holds it all together. The presence of both alpha particles is crucial; remove one, and the charmonium particle drifts away.
Lattice QCD and the Promise of Precision
The researchers didn’t just pull this idea out of thin air. Their calculations are rooted in something called Lattice Quantum Chromodynamics (Lattice QCD), a sophisticated approach to modeling the strong force. Lattice QCD is like creating a virtual universe on a computer, where physicists can simulate the interactions of quarks and gluons. By using Lattice QCD, the researchers could estimate the strength of the interaction between charmonium and nucleons (protons and neutrons).
These simulations, performed using the HAL QCD methodology, provide the most realistic calculations of these interactions to date, using nearly physical pion masses. “In particular, Ref. [21] presents a realistic lattice QCD investigation into low-energy charmonium-nucleon interactions, including spin-3/2 J/ψN, spin-1/2 J/ψN, and spin-1/2 ηcN. These interactions characterized by attraction over all distances.”
From these simulations, they derived effective potentials describing the interaction between charmonium and alpha particles. An alpha particle, the nucleus of a helium atom, is a tightly bound and stable configuration of two protons and two neutrons. The model treats the 9c¯cBe nucleus as a system of three clusters: the charmonium particle and two alpha particles. This approach simplifies the complex interactions within the nucleus, allowing for manageable calculations.
The Hyperspherical Harmonics Method: A Mathematical Microscope
To solve the equations that govern this three-body system, the researchers employed the hyperspherical harmonics (HH) method. This mathematical technique is like a powerful microscope, allowing physicists to zoom in on the intricate details of the nucleus. The HH method expands the wave function of the system – a mathematical description of its state – in terms of hyperspherical harmonics, which are special functions that capture the angular and radial dependencies of the particles’ positions. This expansion allows the researchers to solve the Schrödinger equation, the fundamental equation of quantum mechanics, and determine the energy and structure of the 9c¯cBe nucleus.
Imagine you’re trying to understand the shape of a complex object. You could describe it by breaking it down into simpler shapes, like spheres and cylinders. The hyperspherical harmonics method does something similar, but instead of shapes, it uses mathematical functions to describe the distribution of particles within the nucleus.
A Delicate Dance: Binding Energies and Nuclear Radii
The calculations suggest that the 9c¯cBe system could indeed exist as a bound state, with a binding energy of up to 1.71 MeV (million electron volts). This is a relatively small amount of energy, indicating that the system would be only loosely bound. The binding energy represents the amount of energy required to break the nucleus apart into its constituent particles. A higher binding energy means a more stable nucleus.
The researchers also calculated the nuclear matter radius of the 9c¯cBe nucleus, which is a measure of its size. They found that the radius would be around 2.6 to 3.05 fm (femtometers), slightly larger than that of ordinary beryllium-9. This makes sense, as the presence of the charmonium particle would tend to push the alpha particles further apart. The calculations also considered the spin interactions between the charmonium and the nucleons, and incorporated the Coulomb interaction – the electrical repulsion between the protons in the nucleus.
“The maximum central binding energy was found to be approximately 1.71(1.60) MeV, corresponding to the J/ψN(2S1/2) interaction, while a minimum value of around 0.56(30) MeV was obtained using the spin-1/2 ηcN interaction,” the authors write.
Why Does This Matter?
So, why should we care about this ghostly form of beryllium? First, it would provide a unique window into the strong force, allowing physicists to study the interaction between ordinary nuclear matter and exotic particles like charmonium. Second, it could shed light on the structure of nuclei, helping us understand how these complex systems are held together. And third, it could have implications for our understanding of neutron stars, the ultra-dense remnants of supernova explosions. The conditions inside neutron stars are so extreme that exotic particles like charmonium might play a significant role in their structure and behavior.
While this research is theoretical, it’s not just speculation. It builds upon rigorous calculations based on Lattice QCD, and it makes testable predictions. The next step is for experimental physicists to try to create and detect these exotic nuclei in the laboratory. This won’t be easy, as charmonium particles are notoriously difficult to produce and observe. But if they succeed, it would open up a new chapter in nuclear physics, revealing the hidden connections between the familiar world of atoms and the exotic realm of quarks and gluons.
The researchers acknowledge that creating and detecting these systems will be an experimental challenge. They suggest that facilities such as Jefferson Lab, J-PARC, and FAIR might be able to create these exotic nuclei through hadron-beam experiments. Relativistic heavy-ion collisions at RHIC and LHC could also provide an avenue for observation.
