EGS4_AUSGAB.

The EGS4_AUSGAB subroutine is responsible for doing the `scoring' for the EGS code, although the work is handled by EGS4_AUSGAB1. Its primary duty is to calculate the number of Cerenkov photons for each step (assuming the code is currently tracking a charged particle), which it does by assuming the theory of Frank and Tamm [9], see Jelley [8], which predicts the mean yield, $N$, of Cerenkov photons created in a track of length $\delta x$ is

$$N = \delta x \; \frac{\alpha}{c} \int \limits _{\omega_{1}}^... ...ega_{2}} \left(1 - \frac{1}{\beta^{2} n^{2}} \right)\; d\omega$$ (13.9)

where $\omega_{1}$ and $\omega_{2}$ are the frequency cutoffs, $n$ is the (currently frequency independent) refractive index and $\beta$ is the relativistic factor. In order to minimize the tracking of excess Cerenkov photons, the peak quantum efficiency of the PMTs can be renormalized to one, and the number of Cerenkov photons generated is reduced by a compensating factor (CERFAC). This effectively eliminates photons which would have been thrown out anyway and, thus, only throws those with a chance of being detected. This reduces the execution time but, unless taken ito account, may produce errors in quantities derived from tracking individual photons (the statistics of the detected photons should not be affected. The user may turn this feature off if they wish by setting CERFAC=1 ($cerfac 1). The user can select between grey disk and 3-d PMT models and this gives rise to the following minor complications:-

1. There are two cerfac factors: CERFAC (grey disk) and CERFAC_II (3-d). CERFAC is smaller than CERFAC_II as the grey disk model has to fold in other losses, principally the loss due to absorbtion in the PMT glass. Photons are generated using CERFAC or CERFAC_II depending on whether the grey disk or 3-d PMT model has been selected, but see also point 3 below.

2. The technique works because those photons that do not fire the PMT are discarded. Care has to be taken with the grey disk model. An incident photon can be reflected, absorbed (without firing PMT) or can fire the PMT. If the probabilities are $P_{refl}$, $P_{abs}$, $P_{fire}$ then the CERFAC is not $P_{fire}$, even though this is the fraction that produce a hit, as not all other photons are lost. Instead CERFAC is set to $P_{fire}/(P_{abs} + P_{fire})$, as this is the probability that a photon, that is not reflected, will fire the PMT. There is no such complication in the 3-d model, where reflections are dealt with explicitly.

3. Even when the grey disk model has been selected, other particles still see the 3-d model and in particular, charged particles can deposit photons within the PMT. It is also possible to generate seed photons inside the PMT. So, if using grey disks, all photons created within PMTs must use CERFAC_II because, while they are within the 3-d model the PMT they `see' has this efficiency. If they escape from the PMT, then the only PMTs they can then strike have the lower CERFAC efficiency so it is necessary, as they leave, to discard randomly the fraction CERFAC / CERFAC_II to adjust the photon's cerfac factor to lower efficiency.

In order to further optimize the efficiency of this approach, by default the value of CERFAC is made wavelength-dependent to follow the efficiency curve of the PMT. The wavelength-independent (i.e. "single-value" approach) may be selected by setting MODE_CERFAC=1 ($mode_cerfac 1). All the details pertaining to the implementation of this are contained in the routine CER_FAC.FOR (which is also used to sample from an appropriately modified Cerenkov spectrum).

When explicitly generating photons in the detector (e.g. a ``photon bomb"), CERFAC is automatically applied by default so that the resulting number of detected photons will be independent of the specific CERFAC value used (since the detection probabilities are normalized to CERFAC). This may be overridden by setting NP_EXTERNAL_CERFAC=2 ($np_external_cerfac 2). Caution should be exercised when doing this however, as the number of detected photons will not necessarily be accurately represented!

This reduces the execution time but may produce subtle errors in the derived statistical uncertainties. Therefore, if the user is interested in the true statistical uncertainties then the program must either be run with CERFAC=1, or the output corrected to account for its effects. Because the 3-d PMT simulation uses different distributions from the grey disks model, a secondary CERFAC_II is used; it operates analogously to CERFAC. In the case of events which begin in the PMT structure, but for which the user wishes to use a grey disk approximation for all the other PMTs, CERFAC is applied on exit from the PMT bucket. This produces the requirement that CERFAC_II $\ge$ CERFAC.

nb The use of CERFAC or CERFAC_II can introduce subtle errors if used with events in which the Cerenkov photons are not produced from a charged particle governed by the above equations. The best example is if the user sets off a photon bomb with a defined number of photons and sets CERFAC to other than unity. In this case the number of photons is not renormalised, but the hit probability is. However, as of version 3.00, the this problem has been addressed, the number of photons can be renormalised using the NP_EXTERNAL_CERFAC switch.

The code uses Poisson statistics to establish the actual number of photons based on this mean and creates that number of new vertices connected to the EGS vertex by dummy tracks (the creation of these tracks and vertices is actually handled by the subroutine EGSCER). The tracks contain useful information such as the current energy and direction of the particle's current motion, however, the subsequent propagation of these tracks and vertices is discussed in the section on the propagation of Cerenkov photons. The routine also keeps track of the `primary' electron (if there is more than one electron in the shower, the primary electron is assumed to be the one with the higher energy), its range, the total energy deposited, the number of steps the code takes to deal with the electromagnetic shower and the total range of all charged particles in the shower.