5.11. [ Delta Ray ] section

In this section, you can set parameters used in the function to generate knocked-out electrons so-called \(\delta\) -rays, which are produced along the trajectory of a charged particle in materials, as secondary particles. In the PHITS calculation, an energy transfer to the material is estimated by Linear Energy Transfer (LET; \(\frac{dE}{dx}\) ), and is assumed to be deposited only on the particle trajectory. However, it is well known that owing to a high energy \(\delta\) -ray the energy deposition is spread far away from the orbit of the primary particle. You can take the effect of \(\delta\) -rays into account using this function. The production cross sections of \(\delta\) -rays from those particles in liquid water were calculated using the model proposed by Butts and Katz [1] , considering the relativistic collision dynamics.

This function shouldn’t be used together with [t-sed] tally.

You can set a threshold energy \(E_{\rm th}\) (MeV) for each region except outer void to control the production of \(\delta\)-rays. As the secondary particle, \(\delta\)-rays with energies above \(E_{\rm th}\) are explicitly generated and transported. For lower energies than \(E_{\rm th}\), the deposition energies from \(\delta\)-rays are included in LET. A minimum energy of \(E_{\rm th}\) you can set is 0.001 MeV (\(=1\ \mathrm{keV}\)). It is noted that in case of very low \(E_{\rm th}\) or setting of a material thinner than \(10\ \mu\mathrm{g/cm^2}\), a behavior of the charged particle slightly changes. This is because the effective stopping power of the charged particles becomes smaller than its real value due to too many delta-ray productions. To calculate the delta-ray productions induced by charged particles with energies less than 1 MeV, set emin(1) and emin(i=15-19)=1 keV. A default value of \(E_{\rm th}\) is \(1.0\times10^{10}\), i.e. \(\delta\)-rays are not produced in the PHITS calculation except for setting the \(E_{\rm th}\) parameter in this section. The region number and \(E_{\rm th}\) are given by reg and del, respectively.

Set these parameters as follows.

[ delta ray ]
  reg  del
  1    0.1
  11   1.0
  ...  ...
  ...  ...

You can use the format ( { 2 - 5 } 8 9 )}. But you need to close a value by ( ) if it is not a single numeric value. You cannot use the lattice and universe style as ( 6 < 10[1 0 0] < u=3 ). If you want to replace the order of region number (reg) and the threshold energy (del), set as del reg. You can use the skip operator non. Even if you use GG, use the symbol not cell but reg here.