Interatomic Coulombic decay initiated by electron removal and excitation processes in helium ion and argon dimer collisions

This study investigates interatomic Coulombic decay (ICD) in helium ion–argon dimer collisions using a coupled-channel two-center basis generator method, revealing that electron excitation to the $3d$ state is the dominant ICD pathway and that lower-energy He$^+$ projectiles significantly enhance this decay process.

The Gist

The Big Picture: A Cosmic Game of "Hot Potato"

Imagine two noble gas atoms (Argon) holding hands very loosely, like two people standing on a slippery ice rink holding a single, fragile balloon between them. This pair is called an Argon Dimer.

Now, imagine a fast-moving projectile (a Helium ion) zooming past them like a speeding car. The scientists in this paper wanted to know: What happens when this "car" bumps into the "balloon-holders"?

Specifically, they were looking for a very specific, ultra-fast reaction called Interatomic Coulombic Decay (ICD).

What is ICD? (The "Domino Effect")

In the world of atoms, ICD is like a game of musical chairs where the music stops, and one person has to give their seat to a neighbor.

1. The Setup: One of the Argon atoms gets hit and loses an electron (or gets excited). It's now in a state of high energy, like a person holding a hot potato.
2. The Transfer: Instead of cooling down on its own, that "hot potato" (energy) is instantly thrown to the neighboring Argon atom.
3. The Result: The neighbor gets so much energy that it kicks its own electron out. The two atoms, now both positively charged, repel each other and fly apart.

This is important because these low-energy electrons flying around can damage DNA in living things. Understanding how they are made helps us understand radiation damage.

The Experiment: The "Speed Trap"

The researchers simulated this collision on a computer. They used two types of "projectiles" (Helium ions) and sent them at the Argon pair at different speeds:

• Slow Speed: 10 keV/amu (Like a car driving through a school zone).
• Fast Speed: 150 keV/amu (Like a car on a highway).

They also tested two different "charge" scenarios for the projectile:

1. He²⁺: A helium nucleus with no electrons (a bare, heavy charge).
2. He⁺: A helium nucleus with one electron still attached (a slightly softer charge).

The Two Models: "Frozen" vs. "Dynamic"

To predict what happens, the scientists used two different ways of thinking about the Argon atoms:

• The "Frozen" Model (No-Response): Imagine the Argon atoms are made of stone. When the projectile hits, they don't change shape or react until the very end. They are rigid.
• The "Dynamic" Model (Response): Imagine the Argon atoms are made of jelly. When the projectile gets close, the jelly wobbles and shifts while the collision is happening. The scientists found that at slow speeds, this "wobbling" (dynamic response) matters a lot. At high speeds, the projectile passes so fast the jelly doesn't have time to react, so the "frozen" model works fine.

The Key Findings

Here is what they discovered, translated into everyday terms:

1. The "Excitation" Shortcut
In Neon atoms (a simpler gas), ICD happens easily. But Argon is trickier. For ICD to happen in Argon, the atom needs to be in a very specific, excited state (like a 3d orbital).

• Analogy: Think of the Argon atom as a lock. You can't just pick it with any key. You need a very specific "3d" key to open the door to ICD. The study found that hitting the atom just right to create this "3d" state is the most common way to trigger the decay.

2. The Speed Matters

• At High Speeds (150 keV): The projectile is so fast that it mostly just rips electrons away (ionization). The difference between the "frozen" and "jelly" models disappears because the collision is over too quickly for the jelly to wobble.
• At Low Speeds (10 keV): The projectile moves slowly enough that the "jelly" (the electron cloud) has time to react. The "Dynamic" model shows very different results here. The interaction is more complex and sensitive.

3. The "He⁺" Surprise
This was the most interesting part.

• When they used the He²⁺ (bare nucleus), the results were mixed. Sometimes it caused ICD, sometimes it caused other things.
• When they used the He⁺ (the one with an electron), something magical happened at low speeds.
• The Analogy: Imagine the He⁺ projectile is a thief who steals a balloon (an electron) from the first Argon atom. Because it's now carrying a balloon, it becomes "neutral" and can't steal another one. However, in the process of stealing that first balloon, it accidentally kicks the second Argon atom into a state where it must explode (ICD).
• The Result: At low speeds, using a He⁺ projectile resulted in a nearly 100% success rate for triggering ICD. It was almost a guaranteed "domino effect."

Why Does This Matter?

This paper is like a map for a very dangerous neighborhood.

• For Science: It tells us exactly how energy moves between atoms in rare gases.
• For Biology: Since these low-energy electrons can break DNA strands, understanding how they are created (especially in complex environments like water or biological tissue) helps us understand radiation risks and how to protect living cells.

Summary in One Sentence

The study found that when a slow-moving helium ion hits an argon pair, it acts like a master key that almost always triggers a chain reaction (ICD), but only if you account for the fact that the argon atoms "wobble" and react in real-time during the slow collision.

Technical Summary

1. Problem Statement

The paper investigates the mechanisms of Interatomic Coulombic Decay (ICD) in argon dimers ($Ar_2$) following collisions with helium ions ($He^{2+}$ and $He^+$).

• Context: ICD is an ultrafast decay process where an ionized atom relaxes by transferring energy to a neighboring atom, causing its ionization. While well-studied in neon dimers (where inner-shell ionization provides sufficient energy), ICD in argon dimers is more complex.
• The Challenge: In argon, removing a single inner-valence $3s$ electron does not release enough energy to ionize a neighbor (requiring ~19.6 eV). Therefore, ICD in argon dimers requires specific, higher-energy electron configurations, specifically $Ar^+(3p^{-2}nl)$ states (two $3p$ vacancies and one excited electron).
• Gap: Previous experimental data (e.g., Kim et al.) showed less defined ICD signals in argon compared to neon. There was a need for a theoretical framework to map the electron dynamics preceding fragmentation, specifically distinguishing between direct ionization, electron capture, and the specific excitation pathways that enable ICD across a range of impact energies (10–150 keV/amu).

2. Methodology

The authors employed a semi-classical, independent-atom, and independent-electron model to simulate the collision dynamics.

• Collision System:

  • Target: Argon dimer ($Ar_2$) fixed at equilibrium bond length ($R_e = 3.76$ a.u.).
  • Projectiles: $He^{2+}$ and $He^+$ ions traveling parallel to the dimer axis.
  • Energy Range: 10 keV/amu to 150 keV/amu.
  • Impact Parameters: 0.2 to 10 a.u.

• Theoretical Framework:

  • Hamiltonian: Time-dependent Schrödinger equation using a time-dependent Hamiltonian $H(t)$ with a target potential ($\upsilon_T$) and projectile potential ($\upsilon_P$).
  • Potentials:
    • No-Response Model (Static): Assumes the target electron density does not change during the brief collision (valid at high velocities).
    • Response Model (Dynamic): Accounts for time-dependent screening effects where the target potential adjusts based on fractional ionic character as electrons are removed (crucial at low/intermediate energies).
  • Basis Set: Two-Center Basis Generator Method (TC-BGM) using target orbitals ($2s$–$4f$) and projectile orbitals ($1s$–$4f$) plus pseudo-states.

• Analysis Techniques:

  • Determinantal Analysis (DA): A statistical method using Slater determinants to calculate transition probabilities while strictly enforcing the Pauli exclusion principle.
  • Inclusive Probabilities: Calculated for specific electron removal and excitation channels (e.g., $3p^{-2}nl$) without fixing the state of all other electrons.
  • Scaling Factors: Applied to account for the fact that not all $LS$-coupled states of a configuration ($Ar^+(3p^{-2}nl)$) possess sufficient energy to trigger ICD. For example, only 42 out of 90 accessible $3d$ states exceed the energy threshold.
  • Model Variations:
    • Fixed-Charge Model (FCM): Assumes no change in projectile charge (pure ionization).
    • Modified Capture Models (MCMI/MCMII): Account for electron capture by the projectile, which changes the interaction dynamics with the second atom. These models are weighted by the ratio of ionization to capture probabilities derived from the simulation.

3. Key Contributions

1. Extension of Determinantal Analysis: The study extends the DA framework (previously used for neon) to include electron excitation channels essential for ICD in argon, specifically the $3p^{-2}nl$ configurations.
2. Dynamic vs. Static Potentials: A systematic comparison of static (frozen) and dynamic (response) potential models across a wide energy range, quantifying the significance of time-dependent screening effects.
3. Projectile Charge Dependence: A comparative analysis of $He^{2+}$ (doubly charged) vs. $He^+$ (singly charged) projectiles, revealing distinct ICD mechanisms and yields.
4. Energy-Dependent Mechanism Transition: Detailed mapping of the transition from electron capture dominance (low energy) to ionization dominance (high energy) and its effect on ICD pathways.

4. Key Results

• Dominant Channels: The $3d$ excited state ($Ar^+(3p^{-2}3d)$) is the overall dominant channel for facilitating ICD. Other significant contributors include $4s$ through $4f$ states.
• Energy Dependence ($He^{2+}$):
  • At 150 keV/amu, the Modified Capture Models (MCMI/MCMII) converge with the Fixed-Charge Model, as ionization dominates over capture.
  • At 10 keV/amu, significant differences exist between models. The $4p$ excitation channel is dominant at low energies, whereas $3d$ and $4d$ dominate at high energies.
  • Response vs. No-Response: The dynamic response model yields different probabilities than the static model, particularly at lower energies. The discrepancy narrows as energy increases (approaching 150 keV/amu) because the projectile passes too quickly for significant target relaxation.
• ICD Yield:
  • For $He^{2+}$, the ICD yield (fraction of $Ar^+-Ar^+$ fragmentation arising from ICD channels) plateaus at high energies but remains lower than some previous experimental indirect estimates, likely due to the inclusive nature of the calculation (summing all final charge states).
  • For $He^+$, the behavior is drastically different. At 10 keV/amu, the ICD yield approaches unity (100%). This is because $He^+$ is limited to single-electron capture; it cannot strip two electrons to cause Coulomb Explosion (CE) or Radiative Charge Transfer (RCT) in the same way $He^{2+}$ can. Thus, the $Ar^+-Ar^+$ fragmentation channel is almost exclusively populated by ICD-facilitating configurations at low energies.
• Model Convergence: The differences between static and dynamic potential models decrease as impact energy increases, validating the use of static models for high-energy collisions but highlighting the necessity of dynamic models for low-energy regimes.

5. Significance

• Mechanistic Insight: The paper clarifies the complex electron dynamics required to initiate ICD in argon, moving beyond the simpler "single-hole" mechanism seen in neon. It identifies specific excited configurations ($3p^{-2}nl$) as the gateway to ICD.
• Biological Relevance: Understanding ICD in argon (a noble gas) serves as a proxy for understanding similar processes in biological systems (e.g., water dimers) where low-energy electron production via ICD can damage DNA.
• Experimental Guidance: The results suggest that experiments using $He^+$ projectiles at low energies (10 keV/amu) offer a "clean" environment to study ICD, as competing fragmentation mechanisms (CE/RCT) are suppressed, leading to a near-pure ICD signal.
• Theoretical Validation: The study validates the use of the Determinantal Analysis combined with dynamic response models for predicting electron removal and excitation in multi-electron collision systems, providing a robust tool for future investigations into orientation dependence and more complex molecular targets.