From 68ef9aa489dc58ec0af1978310f0bb07757b847f Mon Sep 17 00:00:00 2001
From: Felix Riehn <felix@matilda>
Date: Sat, 1 Aug 2020 14:01:22 +0100
Subject: [PATCH] extended descritption
---
Processes/Sibyll/testSibyll.cc | 96 ++++++++++++++++++++++++++--------
1 file changed, 74 insertions(+), 22 deletions(-)
diff --git a/Processes/Sibyll/testSibyll.cc b/Processes/Sibyll/testSibyll.cc
index 23c9eb043..a35cf8ea7 100644
--- a/Processes/Sibyll/testSibyll.cc
+++ b/Processes/Sibyll/testSibyll.cc
@@ -143,38 +143,90 @@ 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.
+ 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).
+
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.
+ (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.
+
+ 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));
+
+ /FR'2020
+
+ See also:
- 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.
+ Issue 272 / MR 204
+ https://gitlab.ikp.kit.edu/AirShowerPhysics/corsika/-/merge_requests/204
- 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).
+ */
- 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.
+ 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));
- For this reason the numerical precision in these tests is limited to 5% at low
- energies. see also:
+ 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);
+ }
- Issue 272 / MR 204
- https://gitlab.ikp.kit.edu/AirShowerPhysics/corsika/-/merge_requests/204
+ 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));
@@ -183,7 +235,7 @@ TEST_CASE("SibyllInterface", "[processes]") {
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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