Adding New Collisions

Adding New Binary Collisions

Users may add their own binary interaction cross sections to the /src/commom/DifferentialCrossSectionFunctions.jl file of DiplodocusCollisions.jl by forking the repository and using their local version of the package. Once verifying that their addition functions they may then submit a pull request to have the interaction added to the main branch. Functions should be named in the following format: "sigma_name1name2name3name4" and "dsigmadt_name1name2name3name4" where the names are three letter abbreviations of the particles involved (see Particles, Grids and Units). The named pairs name1name2 and name3name4 should be in alphabetical order. Both the total cross section and differential cross sections must be provided for a single interaction.

All cross sections are to be defined in terms of the Mandelstram variables $s=(p_1^{\mu }+p_2^{\mu }{)}^2$, $t=(p_1^{\mu }-p_3^{\mu }{)}^2$ and $u=(p_2^{\mu }-p_3^{\mu }{)}^2$. To maintain accuracy of cross sections and avoid DivZero issues when momenta is small compared to the mass of the particles (at Float64 precision), each Mandelstram variable in the cross sections should be split into two components:

• s=sSmol+sBig where $sBig=(m_1+m_2{)}^2$

• t=tSmol+tBig where $tBig=(m_1-m_3{)}^2$

• u=uSmol+uBig where $uBig=(m_2-m_3{)}^2$

The "Big" part typically cancels with terms in the cross sections, leading to better accuracy. Therefore the function should defined as follows:

function sigma_name1name2name3name4(sSmol::Float64,sBig::Float64,tSmol::Float64,tBig::Float64,uSmol::Float64,uBig::Float64)
    ... 
end

function dsigmadt_name1name2name3name4(sSmol::Float64,sBig::Float64,tSmol::Float64,tBig::Float64,uSmol::Float64,uBig::Float64)
    ... 
end

where all of sSmol, sBig, tSmol, tBig, uSmol, and uBig must be included in the function definition irrespective of if they actually appear in the cross section. It is also important to define a normalisation for the cross sections to avoid emission and absorption terms becoming small compared to the Float64 minimum.

WARNING

Total cross sections may typically be defined/derived in textbooks and other sources to include division by $1/2$ if output states are identical. This factor should NOT be included here as this factor is included separably in the code.

Adding New Emissive Interactions

Coming soon