Some remarks on the normalisation issues Joanna Stepaniak NCBJ Warsaw

Outlines 1.What is meant by : sigma inelastic, sigma absorption, sigma quasi-el, sigma production in h-A interactions. 2. Difference between our  inel and „Denisov” results. Small but still exist. Possible explanation. 3. On the LT discrepancy with FLUKA

Possible final states after p-A interactions 1.Both p and nucleus A without change (coherent elastic scattering) 2.Nucleus excited, photon emission possible ( quasi-elastic?) 3.Proton knocked-out one or more nucleons ( quasi-elastic? production in FLUKA??) 4.New particle(s) produced (fraction of inelastic, production) In the Glauber papers calculated using „sum rule” = scattering 2+3 = quasi elastic In Denisov paper =  absorption =  total – „1” =inelastic In our paper production = „4”, inelastic = but QE sometimes generated in GEANT4

In the Glauber paper QE=2+3 The sum rules (or closure approximation) was used in the Glauber paper. The sum over all possible final states of the nucleus gives 1 Dependence on the final state disapeared in the square of the amplitude of the nucleon-nucleus scattering process (without production).

pC small angle scattering p=21.5 GeV/c |t| ~= p 0 2 Θ 2

The sum rules (or closure approximation) was used in the Glauber and Matthiae paper (1970). In that approach the sum over all possible final states of the nucleus was taken and the dependence on the final state disapeared in the square of the amplitude of the nucleon-nucleus scattering process (without production).

The comparison of the inelastic cross section from the draft of our paper

Tanimoto,Wakaizumi (1974) pn pHe 1+ReA/ImA term

Summary 1.The QE differential cross section is expected to decrease at small |t|. We should not use the MC with exponential increase. 2.The presently small (~2 sigma) difference with the previous measurement can be explained by the 1+(Re/Im) 2 = 1 assumed in there. 3. We should check the definition of „inelastic” cross section in FLUKA. It is a possibility that the process „2” has been included in „inelastic”.

Backup

One should calculate the quasi-elastic scattering as a difference  QE =  scatt -  elastic ~= A |F| 2 [ [1-S(g) 2 ] where F is the nucleon-nucleon elastic amplitudes and the simplified approximate formula does not take into account the multiple scatterings, two nucleon correlation and the spin effects but works quite well.

Some more problems with naming components of the cross section In the fundamental paper by Glauber and Matthiae, High-energy Scattering of Protons by Nuclei, Nucl.Phys.B21 (1970) 135 Inelastic scattering = in page 142 „sum over all final nuclear states in which no particle production takes place” – from which the elastic scattering must be subtracted, It means that all type of nucleus break-up in included. In the calculation the „completness relation” was used. The sum over all nucleus final states gives 1. It is what we call „quasi-elastic scattering”.