Pycnonuclear fusion

Pycnonuclear fusion (from

The term "pycnonuclear" was coined by A.G.W. Cameron in 1959, but research showing the possibility of nuclear fusion in extremely dense and cold compositions was published by W. A. Wildhack in 1940.[5]^[6]

Pycnonuclear reactions can occur anywhere and in any matter, but under standard conditions, the speed of the reaction is exceedingly low, and thus, have no significant role outside of

Pycnonuclear reactions are observed in

Black dwarfs

White dwarfs

In

with energy at the energy ${\displaystyle E_{0}}$ at

Gamow's peak

equal to ${\displaystyle E_{0}\thicksim \hbar w}$ can overcome the

Some studies indicate that the contribution of pycnonuclear reactions towards instability of white dwarfs is only significant in

While most studies indicate that at the end of their lifecycle, white dwarfs slowly decay into

black dwarfs

, where pycnonuclear reactions slowly turn their cores into ${\displaystyle {\ce {^56Fe}}}$, according to some versions, a collapse of

black dwarfs

is possible: M.E. Caplan (2020) theorizes that in the most massive black dwarfs (1.25 M_☉), due to their declining electron fraction resulting from ${\displaystyle {\ce {^56Fe}}}$ production, they will exceed the Chandrasekhar limit in the very far future, speculating that their lifetime and delay time can stretch to up to 10¹¹⁰⁰ years.^[14]

This section needs expansion with: need expansion on energy release per nucleon reaction in magnetars. It requires an explanation of the arbitrary unit B* that the study has built upon. You can help by adding to it. (August 2022)

As the

threshold. As the electron capture threshold (${\displaystyle \rho =1.455*10^{12}}$ g cm⁻³) is exceeded, it allows for the formation of light nuclei from the process of double electron capture (${\displaystyle {\ce {^40Mg + 2e -> ^34Ne + 6n +}}}$
ν
_e), forming the light Since the core of neutron stars was approximated to be ${\displaystyle 3*10^{14}}$ g cm⁻³, at such extreme densities, pycnonuclear reactions play a large role as demonstrated by Haensel & Zdunik, who showed that at densities of ${\displaystyle \rho =10^{12}-10^{13}}$ g cm⁻³, they serve as a major heat source.[17]^[18][19] In the fusion processes of the inner crust, the burning of neutron-rich nuclei (${\displaystyle {\ce {^{34}Ne + ^{34}Ne -> ^68Ca}}}$)^[10][15] releases a lot of heat, allowing pycnonuclear fusion to perform as a major energy source, possibly even acting as an energy basin for gamma-ray bursts.^[1][2]

Further studies have established that most magnetars are found at densities of ${\displaystyle \rho =10^{10}-10^{11}}$g cm⁻³, indicating that pycnonuclear reactions along with subsequent electron capture reactions could serve as major heat sources.^[20]

This section needs expansion. You can help by adding to it. Relevant discussion may be found on the talk page. (August 2022)

In Wolf–Rayet stars, the triple-alpha reaction is accommodated by the low-energy of ${\displaystyle {\ce {^8Be}}}$ resonance. However, in neutron stars the temperature in the core is so low that the triple-alpha reactions can occur via the pycnonuclear pathway.^[21]

This section needs expansion with: The article should expand on the ideas of the rate of pycnonuclear fusion in MCP in various conditions which depend on the temperature, screening and also the reaction of the lattice to tunneling. You can help by adding to it. Relevant discussion may be found on the talk page. (August 2022)

As the density increases, the

increases in height and shifts towards lower energy, while the potential barriers are depressed. If the potential barriers are depressed by the amount of ${\displaystyle E_{0}}$, the Gamow peak is shifted across the origin, making the reactions density-dependent, as the Gamow peak energy is much larger than the thermal energy. The material becomes a

Pycnonuclear reactions can proceed in two ways: direct (${\displaystyle {\ce {^{34}Ne + ^{34}Ne}}}$ or ${\displaystyle {\ce {^{40}Mg + ^{40}Mg}}}$) or through chain of electron capture reactions (${\displaystyle {\ce {^25N + ^40Mg}}}$).[23]

The current consensus on the rate of pycnonuclear reactions is not coherent. There are currently a lot of uncertainties to consider when modelling the rate of pycnonuclear reactions, especially in spaces with high numbers of free particles. The primary focus of current research is on the effects of crystal lattice deformation and the presence of free neutrons on the reaction rate. Every time fusion occurs, nuclei are removed from the crystal lattice - creating a defect. The difficulty of approximating this model lies within the fact that the further changes occurring to the lattice and the effect of various deformations on the rate are thus far unknown. Since neighbouring lattices can affect the rate of reaction too, negligence of such deformations could lead to major discrepancies.

, making it either taller or thicker. A study published by D.G. Yakovlev in 2006 has shown that the rate calculation of the first pycnonuclear fusion of two ${\displaystyle {\ce {^{34}Ne}}}$ nuclei in the crust of a neutron star can have an uncertainty magnitude of up to seven. In this study, Yakovlev also highlighted the uncertainty in the threshold of pycnonuclear fusion (e.g., at what density it starts), giving the approximate density required for the start of pycnonuclear fusion of ${\displaystyle \rho _{pyc}\thickapprox 10^{12}-10^{13}}$g cm⁻³, arriving at a similar conclusion as Haesnel and Zdunik.[10]^[19][25] According to Haesnel and Zdunik, additional uncertainty of rate calculations in neutron stars can also be due to uneven distribution of the crustal heating, which can impact the thermal states of neutron stars before and after accretion.^[19]

In white dwarfs and neutron stars, the nuclear reaction rates can not only be affected by pycnonuclear reactions but also by the plasma screening of the Coulomb interaction.^[2][10] A Ukrainian Electrodynamic Research Laboratory "Proton-21", established that by forming a thin electron plasma layer on the surface of the target material, and, thus, forcing the self-compression of the target material at low temperatures, they could stimulate the process of pycnonuclear fusion. The startup of the process was due to the self-contracting plasma "scanning" the entire volume of the target material, screening the Coulomb field.^[26]

Before delving into the mathematical model, it is important to understand that pycnonuclear fusion, in its essence, occurs due to two main events:

• A phenomenon of quantum nature called quantum diffusion.
• Overlap of the wave functions of zero-point oscillations of the nuclei.

Both of these effects are heavily affected by screening. The term screening is generally used by nuclear physicists when referring to plasmas of particularly high density. In order for the pycnonuclear fusion to occur, the two particles must overcome the electrostatic repulsion between them - the energy required for this is called the Coulomb barrier. Due to the presence of other charged particles (mainly electrons) next to the reacting pair, they exert the effect of shielding - as the electrons create an

Quantum tunnelling is the foundation of the quantum physical approach to pycnonuclear fusion. It is closely intertwined with the screening effect, as the transmission coefficient ${\displaystyle T}$ depends on the height of the

On top of the other various jargon related to pycnonuclear fusion, the papers also introduce various regimes, that define the rate of pycnonuclear fusion. Specifically, they identify the zero-temperature, intermediate, and thermally-enhanced regimes as their main ones.[10]

The pioneers to the derivation of the rate of pycnonuclear fusion in one-component plasma (OCP) were Edwin Salpeter and David Van-Horn, with their article published in 1969. Their approach used a semiclassical method to solve the

$${\displaystyle P={8 \over 2}{\rho \over \mu _{A}H}\langle p\rangle _{A_{v}}}$$ where ${\displaystyle \rho }$ is the density of the plasma, ${\displaystyle \mu _{A}}$ is the mean molecular weight per electron (atomic nucleus), ${\displaystyle H}$ is a constant equal to ${\displaystyle 1.66044*10^{-24}}$ and serves as a conversion factor from atomic mass units to grams, and ${\displaystyle \langle p\rangle _{A_{v}}}$ represents the thermal average of the pairwise reaction probability.

However, the big fault of the method proposed by Salpeter & Van-Horn is that they neglected the dynamic model of the lattice. This was improved upon by Schramm and Koonin in 1990. In their model, they found that the dynamic model cannot be neglected, but it is possible that the effects caused by the dynamicity can be cancelled out.[10]^[21]

• Cold fusion
• Thermonuclear reaction
• Accretion (astrophysics)
• Plasma (physics)
• Quantum tunnelling