Historical research guide · 0533 · 2022

Deuteron-deuteron nuclear reactions at extremely low energies

Konrad Czerski

In one minute

Two deuterium nuclei repel each other, and the wall between them is about 350 keV high. Konrad Czerski, at the University of Szczecin, works on what happens when you put the deuterium inside a metal instead of a gas: the metal’s own electrons crowd around the nuclei and shield the charge, so the wall gets shorter and the nuclei tunnel through it far more often. In clean ultrahigh vacuum the shielding he measures for zirconium matches theory. But the shape of the measured curve needs one more ingredient, and this Letter argues for it: a narrow resonance in the helium-4 nucleus sitting just a few electron-volts above the point where two deuterons meet. Czerski assembles the evidence — a fit to metal and gas data that agrees, a nuclear-structure argument for why the level was missed, and an estimate that this resonance decays mostly by making an electron-positron pair rather than a proton. If he is right, deuterium in a metal at room temperature makes helium, and he puts a number on the power.

Connection

Chapter 12 is about opening the fusion door from the material side rather than by brute heat, and this is the clearest published statement of the mechanism: a lattice changes the effective barrier, and a threshold resonance changes which way the reaction goes. It also supplies the site’s cleanest answer to the oldest objection in the field — why the branching ratios at room temperature look nothing like the accelerator ones — and it names the measurement that would settle it, an experiment looking for internal electron-positron pair production. Chapter 1 gets the reproducibility question turned into physics: if the resonance is that narrow, the local screening energy of the material sets both its position and its width, which is exactly why two laboratories with different targets get different answers.

From the source

Shielding of nuclear charges by the surrounding electrons lowers the Coulomb barrier and raises its penetrability exponentially as the projectile energy falls, and the effect is especially strong in metals. Once ultrahigh vacuum removes oxygen and carbon contamination from the target surface, the measured screening energy for a zirconium target is 120 plus or minus 7 electron-volts, very close to the 110 electron-volts predicted by self-consistent dielectric function theory.Introduction; Eqs. (1) and (2)
The energy dependence of the measured enhancement cannot be described by electron screening alone. Adding a threshold zero-plus resonance in the compound nucleus helium-4, at an excitation energy of about 23.85 million electron-volts and only a few electron-volts above the deuteron-deuteron threshold, fits the zirconium thick-target data with a proton partial width of 40 plus or minus 15 milli-electron-volts, a nuclear phase shift of 116 plus or minus 40 degrees and a screening energy of 109 plus or minus 30 electron-volts.Observation of the DD threshold resonance; Eq. (6); Fig. 1(a)
The same resonance appears in the gas-target data taken by Greife and colleagues in 1995: fixing the screening energy at 20 electron-volts and including destructive interference of the threshold resonance gives a proton partial width of 10 plus or minus 2 milli-electron-volts and a phase shift of 105 plus or minus 5 degrees. The characteristic shape of the zirconium curve is therefore not a crystal lattice effect but relates to individual atoms.Observation of the DD threshold resonance; Fig. 1(b)
Because the zero-plus to zero-plus gamma transition to the ground state is strictly forbidden and the nucleon partial widths are very small, the total width of the resonance should be dominated by internal electron-positron pair creation. Four-nucleon calculations with realistic forces bracket that partial width between about 1.6 milli-electron-volts and 3.1 electron-volts, with a realistic middle estimate of 29 milli-electron-volts.Resonance decay width; Eq. (9)
The consequence is a reversal of the branching ratios at thermal energies. Where accelerator experiments see the helium-4 channel suppressed by seven orders of magnitude, at room temperature the pair-production width should exceed the proton width by two orders of magnitude, so the deuteron-deuteron reaction predominantly makes helium-4 — which is what room-temperature observations of heat correlated with helium and no gamma radiation require.Extrapolation to room temperature; Conclusions
Taking a screened cross section of ten to the minus fifteen barns at 25 milli-electron-volts for the helium-4 channel gives a reaction rate of 2.9 times ten to the minus nine per second, or 0.59 watts per gram of palladium at a metal-to-deuteron ratio of one — large enough, Czerski writes, for commercial applications. The effectiveness depends critically on the screening energy of the material, and raising the effective electron mass through crystal lattice defects is the named lever.Extrapolation to room temperature, Eq. (10); Conclusions

The way in

https://doi.org/10.1103/PhysRevC.106.L011601

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

LICENCE. The statement is printed on the first page of the paper itself: published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license, further distribution to maintain attribution to the author and the published article’s title, journal citation and DOI. The Crossref licence record for the DOI names the same licence and the Unpaywall record reports the article as open access under CC BY. TEXT. The publisher’s own server declines automated retrieval, so the version of record was taken from a repository copy of the published PDF at lenr-canr.org and converted with pdftotext; it is the American Physical Society typeset article, carrying the PHYSICAL REVIEW C 106, L011601 (2022) running head, the received, revised, accepted and published dates and the licence line. The complete Letter is reproduced below. Running heads, page numbers and figure captions are dropped, the forty-three-item reference list is omitted and is at the source, and bracketed reference numbers are removed from the prose. The three figures — the thick-target enhancement factor for zirconium and the S factor for the gas target, the schematic four-nucleon energy surface, and the resonant and non-resonant cross sections — are plots that cannot be reproduced as text. The displayed equations reached the library with Greek letters, subscripts and minus signs damaged in extraction, so they are given as named results in plain words with their original numbers, and negative exponents are written out. Published as Konrad Czerski, Physical Review C 106, L011601 (2022), from the Institute of Physics, University of Szczecin; received 15 January 2022, revised 2 May 2022, accepted 24 May 2022, published 12 July 2022.

How to cite it

Konrad Czerski (2022) Deuteron-deuteron nuclear reactions at extremely low energies doi:10.1103/PhysRevC.106.L011601

Where it sits in the curriculum

Lattice confinement fusion