EMPIRE
19
3 Reaction Modeling
A low-to-intermediate-energy nuclear reaction can be approximately divided into
an initial stage, during which direct reactions occur or the projectile (or a part
of it) fuses with the target, and a subsequent stage, during which the compound
nucleus fissions or de-excites by particle and gamma-ray emission. Pre-equilibrium
emission, which consists predominantly of multistep direct reactions, tends to blur
the distinction between the two stages, but is traditionally considered as part of
the emission rather than the formation stage of the reaction. We discuss below the
models and codes used in EMPIRE to describe each of the stages.
3.1 Fusion and Direct Reactions
EMPIRE uses the optical model to calculate transmission coefficients and absorption cross sections for light particles. Spherical optical model calculations are
performed using ECIS-2006 [3, 4], while deformed optical model calculations are
performed using ECIS-2006 or OPTMAN [5–7]. For heavy-ion induced reactions,
the simplified coupled channels code CCFUS [8] or a distributed barrier model can
be used. The photoabsorption cross section is used to initiate a gamma-induced
reaction. If desired, absorption cross sections or transmission coefficients can also
be input directly.
Direct reaction cross sections can be calculated using coupled channels with the
codes ECIS-2006 or OPTMAN or the distorted wave Born approximation (DWBA)
using ECIS-2006. The two methods can be mixed when ECIS-2006 is used. That is,
strongly coupled channels can be calculated using coupled channels, while weaker
channels can be calculated using the DWBA.
Deuteron breakup and its incomplete fusion have recently been included in
EMPIRE [9]. The breakup is calculated in the DWBA approximation and the
formation and decay of the compound nuclei involving the remaining deuterons
and the breakup protons and neutrons are taken into account consistently.
3.2 Compound Nucleus and Pre-equilibrium Emission
The basic compound nucleus decay model in EMPIRE is a multi-emission HauserFeshbach decay model [10] with a full γ -cascade and dynamical deformation
effects. Width fluctuations can be included using the HRTW [11, 12] or Moldauer
[13] formalisms. Direct channel coupling can be included in the statistical emission
through the Engelbrecht-Weidenmüller transformation [14]. Both cross sections
and angular distributions can be calculated for elastic and resolved inelastic states.
Cross sections, spectra, angular distributions, and double differential energy-angular
19
3 Reaction Modeling
A low-to-intermediate-energy nuclear reaction can be approximately divided into
an initial stage, during which direct reactions occur or the projectile (or a part
of it) fuses with the target, and a subsequent stage, during which the compound
nucleus fissions or de-excites by particle and gamma-ray emission. Pre-equilibrium
emission, which consists predominantly of multistep direct reactions, tends to blur
the distinction between the two stages, but is traditionally considered as part of
the emission rather than the formation stage of the reaction. We discuss below the
models and codes used in EMPIRE to describe each of the stages.
3.1 Fusion and Direct Reactions
EMPIRE uses the optical model to calculate transmission coefficients and absorption cross sections for light particles. Spherical optical model calculations are
performed using ECIS-2006 [3, 4], while deformed optical model calculations are
performed using ECIS-2006 or OPTMAN [5–7]. For heavy-ion induced reactions,
the simplified coupled channels code CCFUS [8] or a distributed barrier model can
be used. The photoabsorption cross section is used to initiate a gamma-induced
reaction. If desired, absorption cross sections or transmission coefficients can also
be input directly.
Direct reaction cross sections can be calculated using coupled channels with the
codes ECIS-2006 or OPTMAN or the distorted wave Born approximation (DWBA)
using ECIS-2006. The two methods can be mixed when ECIS-2006 is used. That is,
strongly coupled channels can be calculated using coupled channels, while weaker
channels can be calculated using the DWBA.
Deuteron breakup and its incomplete fusion have recently been included in
EMPIRE [9]. The breakup is calculated in the DWBA approximation and the
formation and decay of the compound nuclei involving the remaining deuterons
and the breakup protons and neutrons are taken into account consistently.
3.2 Compound Nucleus and Pre-equilibrium Emission
The basic compound nucleus decay model in EMPIRE is a multi-emission HauserFeshbach decay model [10] with a full γ -cascade and dynamical deformation
effects. Width fluctuations can be included using the HRTW [11, 12] or Moldauer
[13] formalisms. Direct channel coupling can be included in the statistical emission
through the Engelbrecht-Weidenmüller transformation [14]. Both cross sections
and angular distributions can be calculated for elastic and resolved inelastic states.
Cross sections, spectra, angular distributions, and double differential energy-angular