138
C. Hartnack et al.
profiles of protons and neutrons are described in IQMD model. Afterwards we will
recall the influence of neutron skin on the isospin ratios of pions and study whether
other observables might be affected as well.
11.1.1 Pion Production in IQMD
IQMD decomposes, as many other microscopic transport models [3–5] do similarly, the interaction of nucleons into a long-range part described by local two-body
potentials and a short-range part related to the effect of stochastic collisions. The
long-range term leads to nuclear potentials, which become important for the stability
of the nucleus and also touch topics like the nuclear equation of state [6]. We will
shortly summarize the important part of the collision term and refer for a detailed
description of both parts and their application in IQMD on [7]. Particles in IQMD
are described as Gaussian wave packages in coordinate and momentum space, where
the centroides of these packages are propagated by Hamilton’s equation of motion.
Two particles collide if their minimum distance d, i.e., the minimum relative distance
of the centroids of the Gaussians during their motion, in their centre of mass (CM)
frame fulfills the requirement:
d ≤ d 0 =
σ tot
π
,
σ tot = σ (
√
s, type).
(11.1)
The total cross section is assumed to be the free cross section of the regarded collision
type (N − N , N − , …). The cross sections for elastic and inelastic collisions are
obtained by a table lookup using experimentally measured cross sections (when
available) or derived from available cross sections using symmetry assumptions and
detailed balance.
The pion production in IQMD is done via the -channel, where deltas can be
produced in nucleon-nucleon (N N) collisions but also be reabsorbed in N collisions. The decays and produces a free pion, which can be reabsorbed in collisions
with a nucleon and form a again:
N N ↔ N
↔ N π.
(11.2)
These reactions have to comply with detailed balance and isospin effects have to
be taken into account by the use of Clebsch-Gordon coefficients. For more details
see [8].
The production of pions in IQMD has successfully been tested by various comparisons with experimental measurements performed by the FOPI collaboration at GSI
[9]. Giving an example taken from [10], Fig. 11.1 compares the excitation function
of the total pion yield in Au+Au collisions measured by FOPI to IQMD calculations
(left-hand side). For this purpose, the events calculated by IQMD have undergone
the same analysis procedures as the experimental data. The multiplicities calculated
C. Hartnack et al.
profiles of protons and neutrons are described in IQMD model. Afterwards we will
recall the influence of neutron skin on the isospin ratios of pions and study whether
other observables might be affected as well.
11.1.1 Pion Production in IQMD
IQMD decomposes, as many other microscopic transport models [3–5] do similarly, the interaction of nucleons into a long-range part described by local two-body
potentials and a short-range part related to the effect of stochastic collisions. The
long-range term leads to nuclear potentials, which become important for the stability
of the nucleus and also touch topics like the nuclear equation of state [6]. We will
shortly summarize the important part of the collision term and refer for a detailed
description of both parts and their application in IQMD on [7]. Particles in IQMD
are described as Gaussian wave packages in coordinate and momentum space, where
the centroides of these packages are propagated by Hamilton’s equation of motion.
Two particles collide if their minimum distance d, i.e., the minimum relative distance
of the centroids of the Gaussians during their motion, in their centre of mass (CM)
frame fulfills the requirement:
d ≤ d 0 =
σ tot
π
,
σ tot = σ (
√
s, type).
(11.1)
The total cross section is assumed to be the free cross section of the regarded collision
type (N − N , N − , …). The cross sections for elastic and inelastic collisions are
obtained by a table lookup using experimentally measured cross sections (when
available) or derived from available cross sections using symmetry assumptions and
detailed balance.
The pion production in IQMD is done via the -channel, where deltas can be
produced in nucleon-nucleon (N N) collisions but also be reabsorbed in N collisions. The decays and produces a free pion, which can be reabsorbed in collisions
with a nucleon and form a again:
N N ↔ N
↔ N π.
(11.2)
These reactions have to comply with detailed balance and isospin effects have to
be taken into account by the use of Clebsch-Gordon coefficients. For more details
see [8].
The production of pions in IQMD has successfully been tested by various comparisons with experimental measurements performed by the FOPI collaboration at GSI
[9]. Giving an example taken from [10], Fig. 11.1 compares the excitation function
of the total pion yield in Au+Au collisions measured by FOPI to IQMD calculations
(left-hand side). For this purpose, the events calculated by IQMD have undergone
the same analysis procedures as the experimental data. The multiplicities calculated