[Paper Review] Nuclear Reaction Rates in Dense Plasmas

В. И. Савченко|arXiv (Cornell University)|Apr 21, 1999

Astro and Planetary Science3 citations

TL;DR

This paper investigates nuclear reaction rates in dense plasmas by solving the quasiclassical tunneling problem under conditions of frequent particle collisions, showing that the resulting Lorentzian spectral density of states leads to a quantum tail in the momentum distribution. This tail significantly enhances reaction rates—by many orders of magnitude—compared to standard Maxwellian averaging, challenging conventional astrophysical reaction rate calculations.

ABSTRACT

We solve the quasiclassical problem of tunneling through an external potential barrier in a dense plasma, where the tunneling particles undergo simultaneous collisions with other particles in thermodynamic equilibrium. Under such conditions the spectral density of states available to the particle has a Lorentz shape, rather than the delta function, which leads to a quantum tail in the particle momentum distribution function. We show that, this tail indeed significantly alters the average nuclear reaction rates, which supports earlier suggestions. This rate can be many orders of magnitude higher than would be normally calculated by averaging over the Maxwell distribution of energies.

Motivation & Objective

• To understand how frequent collisions in dense plasmas alter the standard calculation of nuclear reaction rates.
• To investigate the impact of a Lorentzian-shaped spectral density of states on particle tunneling through potential barriers.
• To assess whether the resulting quantum tail in the momentum distribution leads to measurable enhancements in reaction rates.
• To provide a theoretical framework that corrects traditional Maxwellian averaging in dense plasma environments.
• To resolve discrepancies in nuclear reaction rate predictions for astrophysical environments such as stellar interiors.

Proposed method

• Formulates the quasiclassical tunneling problem in a dense plasma with thermodynamically equilibrated particles.
• Models the spectral density of states as a Lorentzian function due to collisional broadening, replacing the delta function in free-space models.
• Derives the momentum distribution function including the quantum tail induced by the Lorentzian density of states.
• Calculates the average nuclear reaction rate by integrating over the modified momentum distribution, accounting for the tail contribution.
• Compares the resulting reaction rate to the standard Maxwell-Boltzmann average to quantify enhancement.
• Applies the formalism to dense plasma conditions relevant to stellar interiors and other high-density astrophysical environments.

Experimental results

Research questions

• RQ1 How does collisional broadening of the spectral density of states affect the momentum distribution of tunneling particles in a dense plasma?
• RQ2 To what extent does the resulting quantum tail in the momentum distribution enhance nuclear reaction rates?
• RQ3 Can the standard Maxwellian averaging of reaction rates be invalidated in dense plasmas due to non-thermal momentum distributions?
• RQ4 What is the magnitude of the enhancement in reaction rates when Lorentzian spectral broadening is included?
• RQ5 How do these corrections affect nuclear reaction rate predictions in stellar and dense astrophysical environments?

Key findings

• The spectral density of states in a dense plasma takes a Lorentzian shape due to frequent collisions, rather than a delta function.
• This Lorentzian shape induces a long quantum tail in the momentum distribution function, extending into the classically forbidden region.
• The presence of this quantum tail leads to a substantial increase in the average nuclear reaction rate.
• The enhancement in reaction rates can be many orders of magnitude higher than predictions based on standard Maxwellian averaging.
• The results support earlier theoretical suggestions that non-Maxwellian effects in dense plasmas significantly alter nuclear reaction kinetics.
• The findings imply that conventional reaction rate calculations in dense astrophysical plasmas may systematically underestimate the true rates.