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Screening of Reaction Rates

.. index:: SCREEN_METHOD

Introduction

Plasma screening is the enhancement of nuclear reaction rates, R due to the Coulomb coupling of the surrounding plasma and electrons and ions. The enhancement of the reaction rates is done via the form:

R_{\mathrm{scr}} = R \exp{(h)}

where R_{\mathrm{scr}} is the screened reaction rate and h characterizes the magnitude of the screening. Plasma screening can be broken up to different regimes depending on the Coulomb coupling parameter, \Gamma, of the reaction rate reactants. Generally, \Gamma \ll 1 and \Gamma \gtrsim 1 correspond to weak and strong screening regimes, respectively. \Gamma is defined as:

\Gamma = \alpha(Z_1, Z_2) \Gamma_e

where \alpha(Z_1, Z_2) characterizes the Coulomb strength of the reactants, its definition can vary slightly depending on the screening routine. \Gamma_e is the Coulomb coupling parameter depending only on the thermodynamic conditions.

\Gamma_e= e^2 \frac{\sqrt[3]{4 \pi n_e / 3}}{k_B T}

where e is the electron charge and n_e is the electron number density.

Screening Options

The screening enhancement factor can be can be computed using several different methods, controlled by the make parameter SCREEN_METHOD. For example,

.. prompt:: bash

   make SCREEN_METHOD=screen5

Any of the available screening methods can be used with any reaction network.

The options are:

  • screen5 :

    This is the screening routine from the Kepler stellar evolution code and is the default used with the distributed versions of the "aprox" family of reaction networks. In the weak screenng regime, \Gamma < 0.3, it uses screening described in :cite:`graboske:1973`. In the strong screening regime, \Gamma > 0.8, it uses screening described in :cite:`jancovici:1977, alastuey:1978, itoh:1979`. For the intermediate screening regime, 0.3 < \Gamma < 0.8, a weighted blending between the weak and strong screening are used. The overall procedure is described in :cite:`Wallace:1982`.

    This is the default screening method.

  • chugunov2007 :

    This implements the screening of :cite:`chugunov:2007`, following :cite:`yakovlev:2006` to extend to binary mixtures. It is suitable for \Gamma \lesssim 600.

  • chugunov2009 :

    This implements the screening of :cite:`chugunov:2009`. The main difference is that the 2007 one calculates an effective coupling parameter based on the two ions and then treats it as a one-component plasma, while this version (2009) treats it fully as a multi-component plasma (which is significantly more expensive)

    This includes the portion in the appendix that blends in the weak screening limit.

  • chabrier1998 :

    This implements the screening of :cite:`Chabrier_1998` as well as the quantum corrections for strong screening according to screen5, which is suggested in the appendix of :cite:`Calder_2007`. This screening is compatible with NSE calculations unlike screen5, chugunov2007, and chugunov2009. This screening is valid in the weak screening regime, \Gamma < 0.1, and strong screening regime, 1 \lesssim \Gamma \lesssim 160.

.. index:: screening.enable_debye_huckel_skip, screening.debye_huckel_skip_threshold

  • debye_huckel :

    This is just the Debye-Hückel weak-screening limit from :cite:`chugunov:2009`.

    While it can be used on its own (by building with SCREEN_METHOD=debye_huckel, it is really meant to be used as a test to determine whether a more extensive screening approximation should be used. By setting screening.enable_debye_huckel_skip, we first compute this weak-screening approximation and then, if it is larger than screening.debye_huckel_skip_threshold, the full screening factor is computed (using the method specified via SCREEN_METHOD).

  • null :

    This disables screening by always returning 1 for the screening enhancement factor.

Runtime Options

.. index:: screening.enable_chabrier1998_quantum_corr
  • screening.enable_chabrier1998_quantum_corr = 1 in the input file enables an additional quantum correction term added to the screening factor when SCREEN_METHOD=chabrier1998. This is disabled by default since chabrier1998 is often used along with USE_NSE_NET=TRUE, and the NSE solver doesn't include quantum corrections.