Version: SMASH-3.1
Collision term

The Collision_Term section in the input file can be used to configure SMASH interactions. Before describing each possible key in detail, it is useful to give some taste with a couple of examples.

A real life example

The following section in the input file configures SMASH to include all but strangeness exchange involving 2 ↔ 2 scatterings, to treat N + Nbar processes as resonance formations and to not force decays at the end of the simulation. The elastic cross section is globally set to 30 mbarn and the \( \sqrt{s} \) cutoff for elastic nucleon + nucleon collisions is 1.93 GeV. All collisions are performed isotropically and 2 ↔ 1 processes are forbidden.

Collision_Term:
    Included_2to2: ["Elastic","NN_to_NR","NN_to_DR","KN_to_KN","KN_to_KDelta"]
    Two_to_One: true
    Force_Decays_At_End: false
    NNbar_Treatment: "resonances"
    Elastic_Cross_Section: 30.0
    Elastic_NN_Cutoff_Sqrts: 1.93
    Isotropic: true

If necessary, all collisions can be turned off by adding

    No_Collisions: True

in the configuration file.

Configuring deuteron multi-particle reactions

The following example configures SMASH to include deuteron multi-particle reactions scatterings.

Collision_Term:
    Collision_Criterion: Stochastic
    Multi_Particle_Reactions: ["Deuteron_3to2"]

Note, that the that the fake baryon resonance d' should not be included in the particles.txt file, otherwise PiDeuteron_to_pidprime and NDeuteron_to_Ndprime have to be excluded from Included_2to2 by listing all 2-to-2 reactions except those two.


In this page many generic keys are described. For information about further tuning possibilities, see the following pages:


Additional_Elastic_Cross_Section — double, optional, default = 0.0

Add an additional constant contribution in mb to the elastic cross section.

Warning
Most elastic cross sections are constrained by experimental data. Adding an additional contribution to them will therefore lead to nonphysical results and is only meant for explorative studies.

Collision_Criterion — string, optional, default = "Covariant"

The following collision criterions can be used.

  • "Geometric"Geometric collision criterion
    The geometric collision criterion calculates the two-particle impact parameter as the closest approach distance in the two-particle center-of-momentum frame by boosting to the respective frame. The collision time used for the ordering is calculated as the time of the closest approach in the computational frame. For further details, see Bass:1998ca [1].
  • "Stochastic"Stochastic collision criterion
    The stochastic collision criterion employs a probability to decide whether particles collide inside a given space-time cell. The probability is derived directly from the scattering rate given by the Boltzmann equation. The stochastic criterion is the only criterion that allows to treat multi-particle reactions. For more details, see Staudenmaier:2021lrg [14].
    Note
    The stochastic criterion is only applicable within limits. For example, it might not lead to reasonable results for very dilute systems like pp collisions. Futhermore, the fixed time step mode is required. The assumption for the criterion is that only one reaction per particle per timestep occurs. Therefore, small enough timesteps (Delta_Time) have to be used. In doubt, test if the results change with smaller timesteps. Since the probability value is not by defintion limited to 1 in case of large timesteps, an error is thrown if it gets larger than 1.
  • "Covariant"Covariant collision criterion
    The covariant collision criterion uses a covariant expression of the two-particle impact parameter in the two-particle center-of-momentum frame, which allows for its calculation in the computational frame without boosting. Furthermore, it calculates the collision times used for the collision ordering in the two-particle center-of-momentum frame. Further details are described in Hirano:2012yy [6].

Cross_Section_Scaling — double, optional, default = 1.0

Scale all cross sections by a global factor.

Warning
Most cross sections are constrained by experimental data. Scaling them will therefore lead to nonphysical results and is only meant for explorative studies.

Elastic_Cross_Section — double, optional, default = -1.0

If a non-negative value is given, it will override the parametrized elastic cross sections (which are energy-dependent) with a constant value in mb. This constant elastic cross section is used for all collisions.


Elastic_NN_Cutoff_Sqrts — double, optional, default = 1.98

The elastic collisions between two nucleons with \(\sqrt{s}\) below the specified value (in GeV) cannot happen.

  • Elastic_NN_Cutoff_Sqrts < 1.88 → Below the threshold energy of the elastic collision, no effect.
  • Elastic_NN_Cutoff_Sqrts > 2.02 → Beyond the threshold energy of the inelastic collision \(NN\rightarrow NN\pi\), not suggested.

Total_Cross_Section_Strategy — string, optional, default = "TopDownMeasured"

Which strategy to use when evaluating total cross sections for collision finding. Currently, possible options are

  • "BottomUp" → Partial cross sections of a given initial state are summed up. This matches most inclusive experimental cross sections with the 3- and 4-star hadronic list from PDG2018, but is susceptible to changes once new resonances are added in the particles file.
  • "TopDown" → The total cross section of measured processes is parametrized, and the partial cross sections are rescaled to match it. Unmeasured processes use the high energy parametrization even in low energies, ignoring possible resonance peaks, and scaled with AQM. This is then insensitive to changes in the input hadronic list.
  • "TopDownMeasured" → Mixes the options above, with parametrizations only for \(NN, N\bar{N}, NK, N\pi,\) and \(\pi\pi\). Remaining processes use sum of partial cross sections.
Note
In a box calculation, using the "BottomUp" strategy is recommended to preserve detailed balance.

Pseudoresonance — string, optional, default = "LargestFromUnstable"

Due to the lack of known high-mass resonances for several processes, the energy region between resonances and strings might lack inelastic processes, which is referred to as “inelastic gap”. To mitigate this, “pseudo-resonances” based on existing resonances can be extended to fill said gap, using the difference between the high energy parametrization of the total cross section and the sum of cross sections from all processes as a proxy for how large it is. Candidates are resonances that decay into the incoming pair. Possible options for this key are

  • "None" → No pseudo-resonance is created.
  • "Largest" → Use the resonance with largest mass.
  • "Closest" → Select the resonance that has the closest pole mass to the available energy ( \(\sqrt{s}\) of the incoming pair).
  • "LargestFromUnstable" → Same as "Largest" but a pseudo-resonance is used only for processes that have at least one incoming unstable particle.
  • "ClosestFromUnstable" → Same as "Closest" but a pseudo-resonance is used only for processes that have at least one incoming unstable particle.

Fixed_Min_Cell_Length — double, optional, default = 2.5

The (minimal) length in fm used for the grid cells of the stochastic criterion, only. Collisions are searched within grid cells only. Cell lengths are scaled up so that grid contains all particles if fraction of a cell length would remain at end of the grid.


Force_Decays_At_End — bool, optional, default = true

  • true → Force all resonances to decay after last timestep.
  • false → Don't force decays (final output can contain resonances).

Include_Weak_And_EM_Decays_At_The_End — bool, optional, default = false

Enable to also perform weak and electro-magnetic decays at the end of the simulation. If enabled, all decays in the decaymodes.txt file are considered at the end, even for hadrons usually considered stable (i.e. with an on-shell width larger than the width_cutoff), for example \(\Sigma\), \(\pi\) or \(\eta\). Note that for isospin violating decay modes all possible isospin combination have to be manually specified in the decaymodes.txt file.

Warning
If true, this option removes the particles that decay from the evolution, so the Dileptons output will not contain final state decays. Therefore we do not recommend its usage for dilepton studies. Because the key name is somewhat misleading, it is for now deprecated and will be renamed in the next release.

Decay_Initial_Particles — bool, optional, default = true

Allow or prohibit initial state particles from decaying before their first collision. This is relevant when, for instance, studying the interactions a resonance can go through.


Included_2to2 — list of strings, optional, default = ["All"]

List that contains all possible 2 ↔ 2 process categories. Each process of the listed category can be performed within the simulation. Possible categories are:

  • "Elastic" → elastic binary scatterings
  • "NN_to_NR" → nucleon + nucleon ↔ nucleon + resonance
  • "NN_to_DR" → nucleon + nucleon ↔ delta + resonance
  • "KN_to_KN" → kaon + nucleon ↔ kaon + nucleon
  • "KN_to_KDelta" → kaon + nucleon ↔ kaon + delta
  • "Strangeness_exchange" → processes with strangeness exchange
  • "NNbar" → annihilation processes, when NNbar_treatment is set to resonances; this is superseded if NNbar_treatment is set to anything else
  • "PiDeuteron_to_NN" → deuteron + pion ↔ nucleon + nucleon and its CPT-conjugate
  • "PiDeuteron_to_pidprime" → deuteron + pion ↔ d' + pion
  • "NDeuteron_to_Ndprime" → deuteron + (anti-)nucleon ↔ d' + (anti-)nucleon, and their CPT-conjugates
  • "All" → include all binary processes, no necessity to list each single category

Detailed balance is preserved by these reaction switches: if a forward reaction is off then the reverse is automatically off too.

Warning
If "Elastic" is the only process allowed, the "Total_Cross_Section_Strategy" must be set as "BottomUp", otherwise SMASH fails. See user guide description for more information.

Isotropic — bool, optional, default = false

Do all collisions isotropically.


Maximum_Cross_Section — double, optional, default = 200 or 2000

The maximal cross section in mb that should be used when looking for collisions. This means that all particle pairs, whose transverse distance is smaller or equal to \(\sqrt{\sigma_\mathrm{max}/\pi}\), will be checked for collisions. The default value is usually set to 200 mb and this value occurs in the Delta peak of the \(\pi+p\) cross section. Many SMASH cross sections diverge close at the threshold; these divergent parts are effectively cut off. If deuteron production via d' is considered, then the default is increased to 2000 mb to function correctly (see Oliinychenko:2018ugs [9]). The maximal cross section is scaled with Cross_Section_Scaling factor.


Multi_Particle_Reactions — list of strings, optional, default = []

List of reactions with more than 2 in- or outgoing particles that contains all possible multi-particle process categories. Multi particle reactions only work with the stochastic collision criterion. Possible categories are:

  • "Meson_3to1" → Mesonic 3-to-1 reactions:
    \(\strut\pi^0\pi^+\pi^-\leftrightarrow\omega\) \(\strut\pi^0\pi^+\pi^-\leftrightarrow\phi\) \(\strut\eta\pi^+\pi^-\leftrightarrow\eta'\) \(\strut\eta\pi^0\pi^0\leftrightarrow\eta'\)
    Since detailed balance is enforced, the corresponding decays also have to be added in decaymodes.txt to enable the reactions.
  • "Deuteron_3to2" → Deuteron 3-to-2 reactions:
    \(\strut \pi pn\leftrightarrow\pi d\) \(\strut Npn\leftrightarrow Nd\) \(\strut \bar{N}pn\leftrightarrow\bar{N}d\)
    The deuteron has to be uncommented in particles.txt as well. Do not uncomment d' or make sure to exclude 2-body reactions involving the d' (i.e. no "PiDeuteron_to_pidprime" and "NDeuteron_to_Ndprime" in Included_2to2). Otherwise, the deuteron reactions are implicitly double-counted.
  • "A3_Nuclei_4to2" → Create or destroy A = 3 nuclei (triton, He-3, hypertriton) by 4 ↔ 2 catalysis reactions such as \(X NNN \leftrightarrow X t\), where \(X\) can be a pion, nucleon, or antinucleon.
  • "NNbar_5to2" → 5-to-2 back-reaction for NNbar annihilation: \(\pi^0\pi^+\pi^-\pi^+\pi^- \rightarrow N\bar{N}\). Since detailed balance is enforced, NNbar_Treatment has to be set to "two to five" for this option.

NNbar_Treatment — string, optional, default = "strings"

  • "no annihilation" → No annihilation of NNbar is performed.
  • "resonances" → Annihilation through \(N\bar{N}\rightarrow\rho h_1(1170)\); combined with \(\rho\rightarrow\pi\pi\) and \(h_1(1170)\rightarrow\pi\rho\), which gives 5 pions on average. This option requires "NNbar" to be enabled in Included_2to2.
  • "two to five" → Direct Annhilation of NNbar to \(5\pi\), matching the resonance treatment: \(N\bar{N}\rightarrow\pi^0\pi^+\pi^-\pi^+\pi^-\). This option requires "NNbar_5to2" to be enabled in Multi_Particle_Reactions.
  • "strings" → Annihilation through string fragmentation.

No_Collisions — bool, optional, default = false

Disable all possible collisions, only allow decays to occur if not forbidden by other options. Useful for running SMASH as a decay afterburner, but not recommended in general, because it breaks the detailed balance.


Only_Warn_For_High_Probability — bool, optional, default = false

Only warn and not error for reaction probabilities higher than 1. This switch is meant for very long production runs with the stochastic criterion. It has no effect on the other criteria. If enabled, it is user responsibility to make sure that the warning, that the probability has slipped above 1, is printed very rarely.


Resonance_Lifetime_Modifier — double, optional, default = 1.0

Multiplicative factor by which to scale the resonance lifetimes up or down. This additionally has the effect of modifying the initial densities by the same factor in the case of a box initialized with thermal multiplicities (see Box: Use_Thermal_Multiplicities).

Warning
This option is not fully physically consistent with some of the other assumptions used in SMASH; notably, modifying this value will break detailed balance in any gas which allows resonances to collide inelastically, as this option breaks the relationship between the width and lifetime of resonances. Note as well that in such gases, using a value of 0.0 is known to make SMASH hang; it is recommended to use a small non-zero value instead in these cases.

Strings — bool, optional, default = (Modus!="Box")

  • true → String excitation is enabled
  • false → String excitation is disabled

Strings_with_Probability — bool, optional, default = true

  • true → String processes are triggered according to a probability increasing smoothly with the collisional energy from 0 to 1 in a certain energy window. At energies beyond that window, all the inelastic scatterings are via strings, while at the energies below that window, all the scatterings are via non-string processes. One should be careful that in this approach, the scatterings via resoances are also suppressed in the intermediate energy region, and vanishes at high energies, e.g. \(p\pi\rightarrow\Delta\rightarrow\Sigma K\) can't happen at a collisional energy beyond 2.2 GeV in this approach. Therefore, the cross sections of the scatterings to the certain final states, which might be crucial for the production of the rare species, will be reduced at the high energies.
  • false → String processes always happen as long as the collisional energy exceeds the threshold value by 0.9 GeV, and the parametrized total cross section is larger than the sum of cross sections contributed by the non-string processes. The string cross section is thus obtained by taking the difference between them.

Two_to_One — bool, optional, default = true

Enable 2 ↔ 1 processes (resonance formation and decays).


Use_AQM — bool, optional, default = true

Turn on AQM cross-sections for exotic combination of particles (baryon-baryon cross-sections are scaled from proton-proton high energy parametrization, for example). This includes both elastic and non-elastic contributions; non-elastic contributions go through string fragmentation. Turning off strings or elastic collisions while leaving this on will result in the corresponding part of the AQM cross-sections to also be off. Cross-sections parametrization are scaled according to

\[ \frac{\sigma^{\mathrm{AQM}}_{\mathrm{process}}} {\sigma^{\mathrm{AQM}}_\mathrm{ref\_process}} \sigma^{\mathrm{param}}_\mathrm{ref\_process} \]

where \( \sigma^{\mathrm{AQM}}_x = 40 \left( \frac{2}{3} \right)^{n_\mathrm{meson}} (1 - 0.4 x^s_1) (1 - 0.4 x^s_2) \), with \(n_\mathrm{meson}\) being the number of mesons in the process, \(x^s_{1,2}\) the fraction of strange quarks in the participant. "process" is then a generic process and "ref_process" a reference process such as PP for which solid parametrizations exist. (Bass:1998ca [1])