Traceable stopping cross sections of Al and Mo elemental targets for 0.9–3.6-MeV protons

Accurate knowledge about the energy loss of ions in matter is essential in many problems, ranging from fundamental to applied nuclear physics. Indeed, there is a recent and increasing demand for new data on stopping cross sections measured with high accuracy and with a rigorous budget of their uncertainty sources. In the present paper we describe an accurate and traceable approach to determine the stopping cross sections in pure elemental materials—aluminum and molybdenum—for protons in the energy range of 0.9–3.6 MeV by the transmission method. The main sources of uncertainties here considered are (i) (random) the uncertainty in the peak positions and in the Gaussian fits and (ii) (systematic) the presence of thickness nonuniformity (a special procedure has been developed to correct it as far as possible). The accuracy in the final stopping cross section is $0.63\%$ ($0.32\%$ random and $0.54\%$ systematic) for Al and $1.5\%$ ($0.44\%$ random and $1.4\%$ systematic) for Mo, both mainly limited by the quality and homogeneity of the foils. For Al, this high accuracy represents an improvement compared to previous publications and serves as a benchmark for our procedure. For Mo, even though the uncertainty is somewhat higher, our results will help in improving the few data currently available in the energy range here considered. The data were also compared to the most commonly employed theoretical models (srim 1985, srim 2013, pstar, and casp 5.2) and Monte Carlo codes (geant 3 and geant 4). The experimental results are electronically available as supplemental material.

Figure 1

Schematic diagram of the experimental setup. (a) Relative positioning of the Au scattering foil, absorber foil, and PIPS detector. (b) Absorber foil in front of the PIPS detector.

Figure 2

Typical transmission spectra for Au-backscattered protons partially stopped in Al (top) and in Mo (bottom) foils. The energy difference of the peaks is related to the stopping power of the Au-scattered protons in the foils (see text). The peak height difference is due to variations in the position of the absorber foils in front of PIPS [see Fig. 1].

Figure 3

Record of the terminal voltage, $V_{\mathrm{GVM}}$, during one measurement of protons in aluminum.

Figure 4

Example of RBS (a) and PIXE (b) spectra of the aluminum foil. The impurity levels were obtained from these techniques with self-consistent analysis.

Figure 5

Example of the nonuniformity correction of the Al foil. The three sets of stopping powers measured in three different regions of the target are shown in (a). The same three sets of data are displayed again in (b) after correcting for the foil thickness nonuniformity.

Figure 6

Experimental stopping cross sections (solid circles) for Al (top left) and for Mo (top right) compared with all the other data (squares) of the Paul database [30]. The lower panels show the deviation of the same data to the VB model (see text for details). The vertical bars and the vertical rectangles represent the random and systematic uncertainties, respectively.

Figure 7

Comparison between the present data (solid circles) and theoretical evaluations for Al and Mo [panels (a) and (b), respectively]. The same representation of the residuals from the VB parametrization Eq. (7), as in Fig. 6, has been adopted to show small deviations. The dashed line has been calculated with the 1985 version of srim (the first version of the software available by Ziegler et al.), the solid line with the latest version of srim (2013), the dash-dotted line with pstar, and finally the thick-dashed line with the newest version of the casp code (5.2).

Figure 8

Comparison between the present data (solid circles) and evaluations performed with the geant series for Al and Mo [panels (a) and (b), respectively]. The same representation of the residuals from the VB parametrization Eq. (7), as in Figs. 6 and 7, has been adopted to show small deviations. Because of how the energy loss is parametrized in geant 4, it is interesting to include in the same figures the values calculated with pstar (dash-dotted line) and with Eq. (7) adopting the parameters from ICRU 49 (dashed line; see text for details).