Changes between Version 2 and Version 3 of perWeight

Timestamp:

Mar 6, 2016, 12:10:18 AM (9 years ago)

Author:

gallmei

Comment:

Adding some explanation for the perWeight

perWeight

@@ -3 +3 @@
 == 'perturbative' and 'real' particles ==
 
-(following text is taken from: O.Buss, PhD thesis, [http://www.uni-giessen.de/cms/fbz/fb07/fachgebiete/physik/einrichtungen/theorie/theorie1/publications/dissertation/buss_diss pdf], Appendix B.1) 
+(following text is taken - slightly modified - from: O.Buss, PhD thesis, [http://www.uni-giessen.de/cms/fbz/fb07/fachgebiete/physik/einrichtungen/theorie/theorie1/publications/dissertation/buss_diss pdf], Appendix B.1) 
 
 For some calculations, e.g. low-energetic πA or γA collision, it is a good assumption, that the
@@ -20 +20 @@
 
 Furthermore, since the ''perturbative'' particles do not react among each other or modify the ''real''
-particles in a reaction, one can also split a ''perturbative'' particle in \(n\) pieces (several ''perturbative''
-particles) during a run. Each piece is given a corresponding weight \(1/n\) and one simulates like
-this \(n\) possible final state scenarios of the same ''perturbative'' particle during one run.
+particles in a reaction, one can also split a ''perturbative'' particle in \(N_{test}\) pieces (several ''perturbative''
+particles) during a run. Each piece is given a corresponding weight \(1/N_{test}\) and one simulates like
+this \(N_{test}\) possible final state scenarios of the same ''perturbative'' particle during one run.
 
 
 
-== the perturbative weigth ==
+== The perturbative weigth 'perWeight' ==
 
-the variable `perWeight` in the [//Documentation2016/code/typeDefinitions/particleDefinition_f90.html#robo688 definition of the particle type] 
+Usually, in the cases mentioned above, where ou use the seperation into ''real'' and ''perturbative'' particles like this, you want to calculate some final quantity like \(d\sigma^A_{tot}=\int_{nucleus}d^3r\int \frac{d^3p}{(2\pi)^3} d\sigma^N_{tot}\,\times\,\dots \). Here we are hiding all medium modifications, as e.g. Pauli blocking, flux corrections or medium modifications of the cross section in the part "\(\,\times\,\dots \)". Now, solving this via the testparticle ansatz (with \(N_{test}\) being the number of test particles), this quantity is calulated as \(d\sigma^A_{tot}=\frac{1}{N_{test}}\sum_{j=1}^{N_{test}\cdot A}d\sigma^j_{tot}\,\times\,\dots \), with \(d\sigma^j_{tot}=d\sigma^N_{tot}(\vec r_j,\vec p_j)\) standing for the cross section of the \(j\)-th test-particle.
+
+The internal implementation of calculations like this in GiBUU is, that a loop runs over all \(N_{test}\cdot A\) target nucleons and creates some event. Thus all these events have the same probability. But since they should be weighted according \(d\sigma^j_{tot}\), this is corrected by giving all (final state) particles coming out of event \(j\) the weight \(d\sigma^j_{tot}\).
+
+This information is stored the variable `perWeight` in the [//Documentation2016/code/typeDefinitions/particleDefinition_f90.html#robo688 definition of the particle type].
+
+Thus, in order to get the correct final cross section, one has to '''sum the perWeight''', and not the particles.
+
+As an example: if you want to calculate the inclusive pion production cross section, you have to loop over all particles and sum the perWeights of all pions. Simply taking the number of all pions would give false results. 
+