IAP GITLAB

Commit 57a3ab03 authored by Felix Riehn's avatar Felix Riehn

extended descritption

parent add3a091
......@@ -140,32 +140,54 @@ TEST_CASE("SibyllInterface", "[processes]") {
/*
Interactions between hadrons (h) and nuclei (A) in Sibyll are treated in the
hadron-nucleon center-of-mass frame (hnCoM). In addition the incoming hadron (h) and
nucleon (n) are assumed massless, such that the energy and momentum in the hnCoM are
hadron-nucleon center-of-mass frame (hnCoM). The incoming hadron (h) and
nucleon (N) are assumed massless, such that the energy and momentum in the hnCoM are
: E_i_cm = 0.5 * SQS and P_i_cm = +- 0.5 * SQS where i is either the projectile
hadron or the target nucleon and SQS is the hadron-nucleon center-of-mass energy.
Any hadron-nucleus event can contain several nucleon interactions. In case of Nw
(number of wounded nucleons) in the hadron-nucleus interaction the total energy and
momentum in the hadron-nucleon center-of-mass frame are: momentum: p_projectile +
p_nucleon_1 + p_nucleon_2 + .... p_nucleon_Nw = -(Nw-1) Pcm with center-of-mass
momentum Pcm = p_projectile = - p_nucleon_i energy: E_projectile + E_nucleon_1 + ...
E_nucleon_Nw = (Nw+1) / 2 * SQS with SQS the hadron-nucleon center-of-mass energy.
The true energies and momenta, accounting for the hadron masses, are: E_i = ( S +
m_i**2 - m_j**2 ) / (2 * SQS) and Pcm = +-
sqrt( (S-(m_j+m_i)**2) * (s-(m_j-m_i)**2) ) / (2*SQS) where m_i is the projectiles
mass and m_j is the target particles mass. In terms of lab. frame variables Pcm =
m_j * Plab_i / SQS, where Plab_i is the momentum of the projectile (i) in the lab.
and m_j is the mass of the target, i.e. the particle at rest (usually a nucleon).
In case of a single interaction (Nw=1), by definition, the total momentum is zero in
the hadron-nucleon frame. After the boost to the lab. frame the lab. momentum of the
projectile before the interaction is recoverred.
Any hadron-nucleus event can contain several nucleon interactions. In case of Nw
(number of wounded nucleons) nucleons interacting in the hadron-nucleus interaction,
the total energy and momentum in the hadron(i)-nucleon(N) center-of-mass frame are:
momentum: p_projectile + p_nucleon_1 + p_nucleon_2 + .... p_nucleon_Nw = -(Nw-1) *
Pcm with center-of-mass momentum Pcm = p_projectile = - p_nucleon_i. For the energy:
E_projectile + E_nucleon_1 + ... E_nucleon_Nw = E_projectile + Nw * E_nucleon.
Using the above definitions of center-of-mass energies and momenta this leads to the
total energy: E_tot = SQS/2 * (1+Nw) + (m_N**2-m_i**2)/(2*SQS) * (Nw-1) and P_tot
= -m_N * Plab_i / SQS * (Nw-1).
A Lorentztransformation of these quantities to the lab. frame recovers Plab_i for
the total momentum, so momentum is exactly conserved, and Elab_i + Nw * m_N for the
total energy. Not surprisingly the total energy differs from the total energy before
the collision by the mass of the additional nucleons (Nw-1)*m_N. In relative terms
the additional energy is entirely negligible and as it is not kinetic energy there
is zero influence on the shower development.
Due to the ommission of the hadron masses in Sibyll, the total energy and momentum
in the center-of-mass system after the collision are just: E_tot = SQS/2 * (1+Nw)
and P_tot = SQS/2 * (1-Nw). After the Lorentztransformation the total momentum in
the lab. thus differs from the initial value by (1-Nw)/2 * ( m_N + m_i**2 / (2 *
Plab_i) ) and momentum is NOT conserved. Note however that the second term quickly
vanishes as the lab. momentum of the projectile increases. The first term is fixed
as it depends only on the number of additional nucleons, in relative terms it is
always small at high energies.
For this reason the numerical precision in these tests is limited to 5% to still
pass at low energies and no absolute check is implemented, e.g.
In case of multiple interactions (Nw>1), the momentum is not zero and the total
momentum in the lab. frame after the boost is different from the original projectile
(momentum violation).
CHECK(pSum.GetComponents(cs).GetX() / P0 == Approx(1).margin(0.05));
CHECK((pSum - plab).norm()/1_GeV == Approx(0).margin(plab.norm() * 0.05/1_GeV));
The level of violation of momentum conservation is further enhanced due to the
approximation of massless hadrons. At low energies (~10GeV), where the masses can
not be neglected the violation is at the level of percent.
/FR'2020
For this reason the numerical precision in these tests is limited to 5% at low
energies. see also:
See also:
Issue 272 / MR 204
https://gitlab.ikp.kit.edu/AirShowerPhysics/corsika/-/merge_requests/204
......@@ -181,6 +203,36 @@ TEST_CASE("SibyllInterface", "[processes]") {
[[maybe_unused]] const GrammageType length = model.GetInteractionLength(particle);
}
SECTION("InteractionInterface - high energy") {
setup::Stack stack;
const HEPEnergyType E0 = 60_EeV;
HEPMomentumType P0 =
sqrt(E0 * E0 - particles::Proton::GetMass() * particles::Proton::GetMass());
auto plab = corsika::stack::MomentumVector(cs, {P0, 0_eV, 0_eV});
geometry::Point pos(cs, 0_m, 0_m, 0_m);
auto particle = stack.AddParticle(
std::tuple<particles::Code, units::si::HEPEnergyType,
corsika::stack::MomentumVector, geometry::Point, units::si::TimeType>{
particles::Code::Proton, E0, plab, pos, 0_ns});
particle.SetNode(nodePtr);
corsika::stack::SecondaryView view(particle);
auto projectile = view.GetProjectile();
Interaction model;
model.Init();
[[maybe_unused]] const process::EProcessReturn ret = model.DoInteraction(projectile);
auto const pSum = sumMomentum(view, cs);
CHECK(pSum.GetComponents(cs).GetX() / P0 == Approx(1).margin(0.05));
CHECK(pSum.GetComponents(cs).GetY() / 1_GeV == Approx(0).margin(1e-4));
CHECK(pSum.GetComponents(cs).GetZ() / 1_GeV == Approx(0).margin(1e-4));
CHECK((pSum - plab).norm() / 1_GeV == Approx(0).margin(plab.norm() * 0.05 / 1_GeV));
CHECK(pSum.norm() / P0 == Approx(1).margin(0.05));
[[maybe_unused]] const GrammageType length = model.GetInteractionLength(particle);
}
SECTION("NuclearInteractionInterface") {
setup::Stack stack;
......
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