Dynamic screening in solar and stellar nuclear reactions

Abstract

In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates.Comment: Astrophysics and Space Science, Special Issue Solar & Stellar Modelling Corrected sign error. Now consistent with final published versio

Prospects for asteroseismology

“…However, it has been pointed out that the underlying mean-field approximation may be invalid under stellar conditions (see, for example, Shaviv 2004, for a review). As discussed by Mussack and Däppen (2010, this volume; see also Mao et al 2009) this has motivated calculations of the properties of stellar plasmas using the techniques of molecular dynamics. The results indicate that the effects of electron screening are weaker than in the Salpeter formulation and that the interactions between the charged particles may in fact lead to a reduction in the reaction rates.…”

Dynamical screening effects on big bang nucleosynthesis

“…This indicates a ∼10% increase of the enhancement factor in the third column and a reduction by the dynamical screening in the fourth column. Although opinions vary in the literature on the adopted method and result [14,16,17,20], if the dynamical screening effects are visible under the solar condition as suggested in references [18,22] as well as [11], those effects leave several issues worth discussing for related plasma properties in other astrophysical environments. First, a plasma state can be characterized with the plasma coupling parameter, classically defined as Γ = n 1/3 e (Ze) 2 /T , which means a ratio of mean Coulomb energy to averaged kinetic energy.…”

“…However, whether they are realized in astrophysical conditions or not is currently an open question. Hence, for the dynamical screening effects, subsequent studies in solar fusion have investigated various methods such as molecular dynamic simulation [18][19][20], kinetic equation [21], and field theoretical approaches [22].…”

Prospects for asteroseismology

“…However, it has been pointed out that the underlying mean-field approximation may be invalid under stellar conditions (see, for example, Shaviv 2004, for a review). As discussed by Mussack & Däppen (2010, this volume) (see also Mao et al 2009) this has motivated calculations of the properties of stellar plasmas using the techniques of molecular dynamics. The results indicate that the effects of electron screening are weaker than in the Salpeter formulation and that the interactions between the charged particles may in fact lead to a reduction in the reaction rates.…”