The current web calculator for **collision** electronic stopping power is based on a fit of the tables - based on ICRU Report 37 - from ESTAR code at NIST.

The fitting function is a polynomial of degree 15 and the tables are reproduced with a maximum discrepancy < 1%.

The **radiative** stopping powers are those evaluated in ESTAR (e.g., see webpage). The tables corresponding are reproduced with a maximum discrepancy < 1%.

In ESTAR webpage at NIST, the uncertanties regarding the collision and radiative stopping power are discussed as reported in the following. The uncertainties of the calculated collision stopping powers for electrons are estimated (ICRU, 1984) to be 1 % to 2 % above 100 keV, 2 % to 3 % (in low-Z materials) and 5 % to 10 % (in high-Z materials) between 100 keV and 10 keV. The increasing uncertainties at low energies are due to the lack of shell corrections which are required when the velocity of the incident electron is no longer large compared to the velocities of the atomic electrons, especially those in the inner shells. Because of this limitation, tabulations of collision stopping powers are customarily restricted to energies above 10 keV. A similar restriction is recommended in regard to the use of the ESTAR. Due to the omission of shell corrections, the stopping powers from ESTAR are expected to be too large at very low energies. It is estimated that for materials of low atomic number, such as water, air or plastics, the error will be to the order of 10 % at 1 keV. ESTAR will not run below 1 keV. Radiative stopping powers are evaluated in ESTAR with a combination of theoretical bremsstrahlung cross sections described by Seltzer and Berger (1985). Analytical formulas (using a high-energy approximation) are used above 50 MeV, and accurate numerical results of Pratt et al. (1977) below 2 MeV. Cross sections in the intermediate energy region from 2 MeV to 50 MeV are obtained by interpolation, a procedure whose accuracy was confirmed by more detailed calculations for a few cases. The uncertainties of the radiative stopping powers are estimated to be 2 % above 50 MeV, 2 % to 5 % between 50 MeV and 2 MeV, and 5 % below 2 MeV.

The following link give access to the Web Applications for the Electronic Stopping Power and Dose for Electrons:

### How to use this Electronic and Radiative Stopping Power Calculator and Ionizing Dose Converter

This tool calculates the Electronic Stopping Power curve for a particle incident on a material.

The input parameters and options for the tool are described below. When the input form has been completed, pressing the "CALCULATE" button will start the calculation and open the "Results" page (allow for pop-up in your browser settings). The result page will be also linked at the bottom of the calculator page.

This web calculator has been complemented by an ionizing dose converter which allows one a quick estimate of the ionizing dose absorbed by a materiel or a compounds. However, for the conversion from electronic stopping power to dose, the energy lost by the incoming electron is assumed to be fully absorbed by the medium - i.e., it is supposed to to be thick enough to fully absorb the kinetic energy of emitted delta rays - and the electron energy is almost constant while the particle traverses the absorber. In addition, radiative phenomema are assumed to be negligible - as, for instance, when the electron energy is well below that critical - e.g., see for a definition and a discussion Sect. 2.3.3.5 in Leroy and Rancoita (2016) and references therein -, and subsequent interactions of emitted photons are not taken into account. The discussion on the relevance of ionization energy loss (e.g, see Sects. 2.1-2.1.3.6 in Leroy and Rancoita (2016) and references therein) with respect to radiative emission of electrons can be found, for instance, in Sects. 3.1-3.1.3.3 and 3.2 of Leroy and Rancoita (2016) and references therein.

### Input Parameters:

- Target material (Single Element or Compound)

- Calculator energy limits.

- Particle fluence for dose calculation.

### Target Material

In the section "Target Selection" it is possible to specify a **Single Element** target material or a predefined **Compound** material. Fraction by weight, mean excitation energy and densities of media are available here.

Following is the maximum difference percentage between the fit and ICRU tables for single elements as a functions of the target atomic number (Z):

The overall max difference for compounds is 0.36% for collision, 0.91% for radiative. The average difference is 0.17% for collision and 0.73% for radiative.

### Energy Limits

This section define the energy limits of the calculation, and the following parameters will be defined:

- Minimum Energy of the incident particle

- Maximum Energy of the incident particle

The output table will contain 20 fixed values for each decade within the above selected range.

Moreover a text box is provided for entering additional energies. The input format is one energy per line; it is also possible to copy and paste energy values.

### Particle Fluence for Dose Calculation

Here has to be inserted the particle fluence to be used to obtain the corresponding deposited Dose.

### Result

The result page contains the input parameters, the Stopping Power curve in MeV cm^{2}/g (i.e., the mass stopping power), with collision and radiative contributions, and the result table, which includes the Ionizing Dose (in [MeV g^{-1}] and [Gy]).

The upper energy limit of the ionizing dose converter is set to that of the critical energy in the medium. It has to be remarked that critical energy vales are those available from particle data group (PDG) 2018 web page on Nuclear properties. These values - based on the remarks available at the critical energy webpage in PDG web site - are expected to differ from the actual ones by a few percents.