5.12. [ 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 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 setting \(E_{\rm th}\) of 10 keV or less, or setting a material thinner than \(10\ \mu\mathrm{g/cm^2}\), a behavior of the charged particle slightly changes. Specifically, while too many \(\delta\)-rays are produced, the effective stopping power of the charged particle becomes smaller than its real value. 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 ) to write regions with the same value together. 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.