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Interactions and dynamics of metastable triplet-state helium dimer with Ne and Ar

This paper presents the first theoretical investigation of the intermolecular interactions and collision dynamics of metastable triplet-state helium dimers with neon and argon, utilizing high-level quantum chemical calculations to construct potential energy surfaces and analyze low-energy scattering resonances that provide benchmarks for future experimental studies.

Original authors: Dibyendu Sardar, François Lique

Published 2026-09-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Dibyendu Sardar, François Lique

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the coldest corners of the universe, where temperatures drop so low that atoms barely move, matter behaves in ways that defy our everyday experience. This realm of ultracold physics offers a unique window into the fundamental laws of nature, allowing scientists to build quantum computers, simulate complex materials, and measure the constants of the universe with unprecedented precision. To reach these temperatures, researchers often rely on laser cooling, a technique that uses the pressure of light to slow down particles until they are nearly stationary. While this method has been successfully applied to many atoms and simple molecules, it has remained out of reach for others, particularly those made of noble gases like helium. Helium is unique because its most stable form is a gas that refuses to freeze under normal pressure, and its molecules are notoriously difficult to trap with lasers. However, a specific version of the helium molecule, one that is stuck in a long-lived, excited state, might finally be the key to unlocking these challenges. Understanding how this fragile molecule interacts with other atoms is the first step toward cooling it down and studying its quantum secrets.

A team of researchers in France has taken the first theoretical step toward this goal by mapping out exactly how a helium molecule in this excited state behaves when it bumps into a neon or an argon atom. The helium molecule they studied, known as a dimer, consists of two helium atoms bound together in a metastable triplet state. This state is special because it lasts for a surprisingly long time—about eighteen seconds—before decaying, giving scientists a window of opportunity to manipulate it. The researchers wanted to know what happens when this molecule collides with a noble gas atom, a process that is crucial for cooling it down. Since no experiments have yet been able to measure these specific collisions, the team used powerful computer simulations to build a detailed map of the forces at play. They calculated the potential energy surface, which is essentially a topographical map showing how the energy between the molecules changes as they move closer or farther apart and rotate relative to one another.

The results revealed that the interaction between the excited helium molecule and a neon atom is incredibly weak. The two form a "van der Waals complex," a loose association held together by faint electrical forces, with a binding energy so shallow it is only about 4.612 inverse centimeters. To put this in perspective, this is a very fragile bond, easily broken by the slightest thermal jostle. The researchers found that the shape of this interaction is quite simple and symmetrical, meaning the helium molecule does not feel much difference in force depending on how it is oriented relative to the neon atom. When they simulated collisions at extremely low temperatures, they discovered that the molecules do not just bounce off each other randomly; instead, they get temporarily trapped in a kind of quantum limbo. This happens because the centrifugal force, which pushes the atoms apart as they spin, creates a barrier that, combined with the weak attraction, forms a temporary cage. This leads to a phenomenon called a resonance, where the collision probability spikes at specific energies. The team identified that these spikes are caused by the formation of quasi-bound states, where the helium and neon dance together in a fleeting embrace before separating again.

The study also looked at what happens when the helium molecule collides with an argon atom instead of neon. Argon is a heavier and more polarizable atom, which means it interacts more strongly with the helium molecule. The simulations showed that the potential well for the helium-argon pair is much deeper, about 33.518 inverse centimeters, and the interaction is more complex and directional. Because of this stronger pull and the heavier mass of the argon atom, the collision dynamics are far richer. The researchers observed a much more intricate pattern of resonances in the helium-argon system compared to the helium-neon system. This difference highlights how sensitive these low-energy collisions are to the specific properties of the atoms involved, such as their mass and how easily their electron clouds can be distorted. The team also found that the helium molecule has internal structures called fine-structure levels, which arise from the interaction between its spin and rotation. They discovered a clear rule for how these levels change during a collision: transitions that keep the fine-structure state the same are more likely to happen than those that change it.

By constructing these detailed maps of interaction and simulating the collisions, the researchers have provided a reliable benchmark for future experiments. Their work suggests that while the helium-neon complex is extremely weakly bound, it is still possible to observe specific quantum behaviors like resonances and bound states. The data they generated, including the precise energy levels of the bound states and the cross-sections for different types of collisions, serves as a guide for experimentalists who hope to eventually cool these molecules using lasers. If successful, this could open a new avenue for studying noble gas molecules at ultracold temperatures, allowing scientists to explore quantum chemistry and fundamental physics in a regime that has remained largely uncharted. The study confirms that while the forces involved are subtle, the quantum mechanical rules governing them are precise and predictable, offering a solid foundation for the next generation of experiments in cold matter physics.

Technical Summary: Interactions and Dynamics of Metastable Triplet-State Helium Dimer with Ne and Ar

Problem Statement
While ultracold molecular physics has advanced significantly for alkali and alkaline-earth systems, interactions and collision dynamics involving noble gas molecules remain largely unexplored in both ultracold ( $T < 1$ mK) and cold ( $T < 1$ K) energy regimes. Specifically, the metastable triplet-state helium dimer, He $_2(a\ ^3\Sigma^+_u)$ , represents a promising candidate for direct laser cooling and precision measurements due to its dipole-allowed transitions to high-lying levels. However, prior to this work, the intermolecular interactions and collisional properties of He $_2(a\ ^3\Sigma^+_u)$ with noble gas atoms (specifically Ne and Ar) had not been theoretically or experimentally investigated. The lack of accurate interaction potentials and scattering data hindered the interpretation of future experimental spectra and the design of collision experiments for this system.

Methodology
The authors employed state-of-the-art ab initio quantum chemistry methods to compute potential energy surfaces (PES) and subsequent quantum scattering calculations.

Electronic Structure Calculations:
- He $_2$ +Ne: The ground electronic state ( $X\ ^3A'$ ) was modeled using a partially spin-restricted coupled cluster method with single, double, and non-iterative triple excitations (RCCSD(T)). Calculations were performed on a grid of intermolecular distances ( $R$ ) and angles ( $\theta$ ) for five different He $_2$ bond lengths ( $r$ ) to account for vibrational motion up to $v=2$ . A vibrationally averaged 3D PES was constructed by averaging over the ground vibrational state ( $v=0$ ) of He $_2$ .
- He $_2$ +Ar: Due to convergence issues with RCCSD(T) at short distances for certain geometries, a multireference configuration interaction method with single and double excitations plus a Davidson correction (MRCISD+Q) was employed. A 2D PES was computed treating He $_2$ as a rigid rotor at its equilibrium bond length.
- Basis Sets: Correlation-consistent quadruple- $\zeta$ basis sets (aug-cc-pVQZ for Ne/Ar and aug-cc-pCVQZ for He $_2$ ) were used to accurately describe the metastable dimer.
- Analytical Fit: The computed interaction energies were fitted to an analytical functional form using Wigner rotation matrix elements and Legendre polynomials to facilitate scattering calculations.
Collision Dynamics:
- Scattering Calculations: Full close-coupling calculations were performed using the MOLSCAT package. The Hamiltonian included the relative kinetic energy, centrifugal terms, and the molecular Hamiltonian for He $_2(a\ ^3\Sigma^+_u)$ , explicitly incorporating fine-structure levels arising from spin-spin and spin-rotation interactions.
- Bound States: Bound-state energies were calculated using the BOUND package, solving coupled-channel equations within the energy range of $-5$ to $2$ cm $^{-1}$ .
- Parameters: Calculations covered collision energies from the ultracold regime ( $10\ \mu$ K) to the high-energy regime ($350$ K). The nuclear-spin statistics theorem was applied, restricting allowed rotational levels of $^4$ He $_2$ to odd values of $N$ .

Key Contributions and Results

Potential Energy Surfaces:
- The study presents the first theoretical investigation of the He $_2(a\ ^3\Sigma^+_u)$ +Ne and He $_2$ +Ar van der Waals complexes.
- He $_2$ +Ne: The interaction potential exhibits an extremely shallow well with a depth of $4.612$ cm $^{-1}$ at a linear geometry ( $\theta = 0^\circ$ , $R = 11.170$ bohr). The potential is weakly anisotropic.
- He $_2$ +Ar: The potential well is significantly deeper ($33.518$ cm $^{-1}$ ) and exhibits stronger angular anisotropy compared to the Ne system, attributed to the higher polarizability of Argon.
- The analytic fits reproduce the ab initio energies with a mean relative difference of less than $1.5\%$ .
Bound States:
- Bound-state energies for the He $_2$ +Ne complex were calculated, with the lowest state at $-1.832$ cm $^{-1}$ (relative to the $F_2$ fine-structure level of He $_2$ ).
- The inclusion of He $_2$ fine-structure coupling was found to have only a weak effect on the binding energies.
- Rotational constants ( $B = 0.053$ cm $^{-1}$ ) and centrifugal distortion constants ( $D = 0.003999$ cm $^{-1}$ ) were derived for the complex based on the fit to the rigid rotor energy expression excluding fine-structure coupling.
Scattering Dynamics and Resonances:
- Propensity Rules: A propensity rule was established where fine-structure conserving transitions are slightly more favorable than fine-structure changing transitions.
- He $_2$ +Ne: Scattering cross sections were computed for quenching and excitation transitions. At ultracold energies, the $F_3 \to F_1$ transition dominates, while $F_3 \to F_2$ is strongly suppressed. A distinct two-peak resonance structure was observed near $0.75$ K. Partial wave analysis identified these as shape resonances supported by the centrifugal barrier of the $J=6$ partial wave, corresponding to quasi-bound states near $0.85$ K.
- Vibrational Averaging: Comparisons between the 3D vibrationally averaged PES and a 2D rigid-rotor PES for He $_2$ +Ne showed that while qualitative features (resonance positions) are similar, quantitative differences in cross-section magnitudes can be significant (up to $\sim 66\%$ in the ultracold regime), highlighting the necessity of vibrational averaging for quantitative accuracy.
- He $_2$ +Ar: The He $_2$ +Ar system displayed a richer resonance structure at low energies compared to He $_2$ +Ne. This is attributed to the deeper potential well, stronger anisotropy, and higher reduced mass.

Significance and Claims
The authors state that this work provides the first theoretical benchmark for the description of the He $_2(a\ ^3\Sigma^+_u)$ +Ne van der Waals complex. The calculated PES and scattering properties are intended to serve as a reliable reference for the interpretation of future experimental spectra and collision measurements, such as those using crossed molecular-beam or spectroscopic techniques. The study establishes the sensitivity of low-energy scattering to both the interaction potential and reduced mass by contrasting the Ne and Ar systems. The results are presented as a foundational step toward understanding and potentially controlling ultracold noble-gas molecules, though the paper does not propose specific new experimental setups beyond referencing existing experimental efforts toward laser cooling of He $_2$ .

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