Observation of Thermal Deuteron-Deuteron Fusion in Ion Tracks

A direct observation of the deuteron-deuteron (DD) fusion reaction at thermal meV energies, although theoretically possible, is not succeeded up to now. The electron screening effect that reduces the repulsive Coulomb barrier between reacting nuclei in metallic environments by several hundreds of eV and is additionally increased by crystal lattice defects in the hosting material, leads to strongly enhanced cross sections which means that this effect might be studied in laboratories. Here we present results of the 2H(d,p)3H reaction measurements performed on a ZrD2 target down to the lowest deuteron energy in the center mass system of 675 eV, using an ultra-high vacuum accelerator system, recently upgraded to achieve high beam currents at very low energies. The experimental thick target yield, decreasing over seven orders of magnitude for lowering beam energies, could be well described by the electron screening energy of 340 eV, which is much higher than the value of about 100 eV for a defect free material. At the energies below 2.5 keV, a constant plateau yield value could be observed. As indicated by significantly increased energies of emitted protons, this effect can be associated with the thermal DD fusion. A theoretical model explains the experimental observations by creation of ion tracks induced in the target by projectiles, and a high phonon density which locally increases temperature above the melting point. The nuclear reaction rate taking into account recently observed DD threshold resonance agrees very well with the experimental data.

💡 Research Summary

The authors report the first direct observation of thermal deuterium‑deuterium (DD) fusion occurring in ion tracks within a deuterated zirconium (ZrD₂) metal target. Using an upgraded ultra‑high‑vacuum accelerator capable of delivering high‑current beams at sub‑keV energies, they measured the 2H(d,p)³H reaction down to a center‑of‑mass (CMS) deuteron energy of 0.625 keV (lab energy 1.25 keV). Thick‑target yields were recorded for atomic (D⁺), molecular (D₂⁺) and tri‑atomic (D₃⁺) deuteron beams over the range 0.625–12.5 keV CMS.

The experimental yield decreases by seven orders of magnitude as the beam energy is lowered, following a theoretical curve that incorporates an electron‑screening energy (Uₑ) of 340 ± 30 eV. This value is substantially larger than the ~100 eV typical for defect‑free metals and matches the upper range previously reported for heavily defected lattices. Below a CMS energy of ≈2.5 keV the yield no longer follows the exponential screening trend but instead forms a constant “plateau”.

Simultaneously, the energy of the detected protons deviates from the kinematic expectation. For D₂⁺ beams the proton peak shifts to lower energies in the plateau region, consistent with a neutral‑atom contribution that is not decelerated by the electrostatic lens. For D₃⁺ beams, however, the proton peak lies at significantly higher energies than predicted by simple kinematics, indicating that the protons are emitted from a CMS that is essentially at rest (E_CMS ≈ 0). This observation is interpreted as evidence of thermal DD fusion: the incident deuterons generate dense collision cascades (ion tracks) that locally heat the ZrD₂ lattice above its melting point, creating a nanometer‑scale region of high temperature where deuterons can move thermally and fuse.

The authors model this process using a thermal‑spike (elastic‑collision spike) framework. Stopping‑power calculations (SRIM/TRIM) show that at deuteron energies between 0.5 and 4 keV the nuclear stopping power becomes comparable to the electronic stopping power, depositing energy both via atomic collisions and electronic excitations. Assuming about 10 % of the electronic energy is transferred to the lattice through electron‑phonon coupling, the resulting phonon density in the ion track is essentially constant across the investigated energy range. This constant phonon density translates into a quasi‑steady local temperature that can reach several thousand kelvin, sufficient to activate the 0⁺ threshold resonance in the DD system (located at ≈1 eV above the 4He ground state).

Using the Breit‑Wigner formula for a narrow resonance together with a Maxwell‑Boltzmann distribution for deuteron velocities, the authors derive a thermal reaction rate (Eq. 4) that depends exponentially on both the screening energy and the local temperature. Substituting Uₑ = 340 eV and the estimated local temperature yields a reaction rate that reproduces the measured plateau yield within experimental uncertainties.

Key insights from the work include:

1. Enhanced electron screening – Defect‑rich ZrD₂ provides a screening potential of ~340 eV, confirming that lattice vacancies and localized conduction‑electron density can dramatically lower the effective Coulomb barrier.

2. Ion‑track induced heating – Collision cascades generate nanometer‑scale hot zones (thermal spikes) where the lattice temperature exceeds the melting point, effectively creating a transient plasma‑like environment inside a solid.

3. Thermal DD fusion – In these hot zones, deuterons can fuse at thermal energies, producing a reaction yield that is orders of magnitude larger than would be expected from bare‑nucleus cross sections at meV energies.

4. Threshold resonance contribution – The recently identified 0⁺ resonance in the DD system amplifies the low‑energy cross section, and its inclusion is essential for quantitative agreement between theory and experiment.

5. Implications for low‑energy nuclear physics – The findings demonstrate that solid‑state effects (screening, defects, ion‑track heating) can enable observable nuclear reactions at energies far below the conventional Coulomb barrier, opening new avenues for laboratory astrophysics, materials‑science studies of radiation damage, and potentially for compact fusion concepts that exploit solid‑state environments.

Overall, the paper provides a comprehensive experimental and theoretical demonstration that thermal DD fusion can be realized in metallic deuterides through the combined action of strong electron screening and ion‑track induced local heating, thereby establishing a novel platform for studying low‑energy nuclear processes in condensed matter.