Journal of the ICRU Vol 5 No 1 (2005) Report 73 Oxford University Press
doi:10.1093/jicru/ndi005
EXECUTIVE SUMMARY Accelerators for charged particles with a very wide range of masses and charge states have an increasing application range in fundamental physics research, in medical radiology, in materials science and engineering, in micro- and nanoscience and technology, in nuclear fission and fusion technology, and in mass spectrometry. The range of kinetic energies reached at existing accelerators spans from a few electron volts per particle into the 1012 electron volt regime. Effective and successful application of such particle beams requires detailed quantitative knowledge of the penetration of charged particles through matter, a field commonly categorized under the discipline of atomic physics. Early studies of charged-particle penetration were stimulated by experimental work with gas discharges toward the end of the 19th century, but experimental possibilities were greatly enhanced after the discovery of radioactivity, in particular in pioneering work by E. Rutherford and coworkers in the beginning of the 20th century. Fundamental theoretical studies of particle penetration in particular by J. J. Thomson and N. Bohr date back to the same time. Subsequently, after the development of quantum mechanics, the quantum theory of particle stopping was developed by H. Bethe, C. Møller, F. Bloch and others. Prime parameters characterizing the penetration of charged particles are the mean energy loss per unit path length, i.e., the stopping power or stopping force, and its fluctuation, called energy-loss straggling. These quantities determine the penetration depth (range) and its fluctuation (range straggling) as well as the energy-deposition profile. Since particles are more or less deflected from their initial direction of motion, also the spatial and directional distribution, the multiple-scattering profile, is of interest. With the exception of a very small part of the available parameter space, the dominating process leading to energy loss of a penetrating charged particle is electronic excitation of the atoms or molecules of the penetrated medium. Additional contributing effects are momentum transfer to recoiling nuclei and, depending on the type and energy of the penetrating particle, electronic excitation of the projectile and charge exchange with the atoms of the
penetrated medium. At high velocities, radiational processes and nuclear reactions have to be considered. Angular deflection is mainly connected to momentum transfer to recoiling nuclei. Until the mid-1960s, experimental activities in the area focused on the penetration of light charged particles such as electrons and positrons, protons and alpha particles. This was motivated by the needs of nuclear and particle physics. Moreover, options for experimental research on the penetration of particles heavier than helium were very limited in terms of available species and beam energies. This situation changed rapidly with new generations of ion sources and accelerators becoming available. Until the early 1990s, theoretical research on particle stopping likewise focused on light penetrating particles, with the exception mainly of low-energy ion implantation. The relatively weak Coulomb interaction of such particles with the electrons of the stopping medium allowed the application of well-developed concepts from quantum mechanical perturbation theory. As the stopping force on a light charged particle is proportional to the square of its charge, the range of validity of quantal perturbation theory must rapidly deteriorate with increasing atomic number of the penetrating particle. Numerous measurements have been performed on heavy-particle stopping during the past half century. The scatter between comparable data is usually considerably larger than for light particles in the same velocity range for a number of reasons. The coverage with experimental data of the entire parameter space in terms of the atomic number Z1 and the energy of the projectile, and the atomic number Z2 of the stopping medium, is necessarily fragmentary. Nevertheless, attempts have been made regularly to collect available experimental data and to systematize them by empirical scaling relations so as to allow predictions of stopping forces for systems not covered by existing data. Data compilations by Northcliffe and Schilling (1970), Ziegler (1980), Zeigler et al. (1985), and by Hubert et al. (1980, 1990) have had a lasting impact on the development of research around heavy-ion accelerators. The accuracy of specific predictions of these tables is limited as use is made of scaling laws that
ª International Commission on Radiation Units and Measurements 2005
STOPPING OF IONS HEAVIER THAN HELIUM
of pertinent theory and experiment. Although much progress has been made in light-particle stopping since the appearance of previous ICRU reports on stopping of electrons and positrons (ICRU Report 37) and of protons and alpha particles (ICRU Report 49), no attempt has been made of an update of those areas in the present report. Despite an extensive bibliography,1 no claim is made of completeness. A large collection of experimental data on heavyion stopping was established which proved to be a valuable tool both within and outside the work of the report committee. The majority of experimental data shown on graphs in this report is quoted from that database (Paul, 2003), whether stated or not. This collection was also employed in a scaling procedure similar to that of Northcliffe and Schilling (1970) allowing the prediction of stopping forces for ions with Z1 < 18 (Paul and Schinner, 2001, 2002; Paul, 2003). Comparisons between predictions of codes based either on theory or empirical interpolation were performed for a large number of ion----target combinations. An overall agreement of about 10% is found for the best available codes of both kinds. A somewhat higher accuracy is generally found in the energy range above 10 MeV/u, while at energies below 0.1 MeV/u, uncertainties increase due to increasing scatter of experimental data, increasing deficiencies in available theory and breakdown of simple scaling relationships. Tables of stopping forces listed in this report were computed by the PASS code (Sigmund and Schinner, 2002b) based on the binary stopping theory of Sigmund and Schinner (2000). The parameter range covered includes 16 ions with atomic numbers from 3 to 18 as well as iron; the range of materials covered is essentially that of ICRU reports 37 and 49 except for a single element and a few compounds, and the tabulated energy range goes from 25 keV/u to 1 GeV/u. It is planned to make updates accessible on the Internet. Such updates will report errors, improved and extended tables as well as tables for a wider variety of ion----target combinations.
lack theoretical justification and as erroneous data are not necessarily identified as such and hence enter as input. However, no feasible alternative was available until recently. This situation changed during the 1990s, when several new theoretical approaches were developed which did not hinge on quantal perturbation theory to the lowest order. An important step was made with the understanding of the Barkas----Andersen effect, sometimes called Z31 effect, in the stopping of light particles. This had been considered until then as a major hurdle that had to be overcome before a feasible theoretical approach to heavy-ion stopping. At present, four promising theoretical approaches are available, all of which go beyond or even avoid quantal perturbation theory (Arista, 2002; Grande and Schiwietz, 2002; Maynard et al., 2002b, 2001b; Sigmund and Schinner, 2000, 2002b). In order to allow predictions of stopping forces, a number of significant physical processes must be incorporated into the basic schemes, such as projectile screening and equilibrium charge state, charge exchange and projectile excitation, low- and high-speed corrections of various kinds, and reliable input on electronic properties of the penetrated material. This process has not been finished on any of the four schemes. Despite this, successful predictions have been made by all of them. With regard to straggling, the situation is quite different. Very few measurements with heavy ions have been done altogether. The number of physical processes affecting straggling exceeds those affecting stopping forces. While most of them have been identified and understood theoretically as isolated phenomena, several of them interfere, making quantitative predictions a complex task requiring further study. Angular deflection (multiple scattering), on the other hand, is well described by existing scaling laws, and despite only few systematic experiments, there is consensus that predictions on the basis of those scaling laws are reliable and accurate. The present report addresses penetrating ions heavier than helium. Extensive reviews are given
1
The bibliography was closed on 1 October, 2003.
10
doi:10.1093/jicru/ndi005
EXECUTIVE SUMMARY Accelerators for charged particles with a very wide range of masses and charge states have an increasing application range in fundamental physics research, in medical radiology, in materials science and engineering, in micro- and nanoscience and technology, in nuclear fission and fusion technology, and in mass spectrometry. The range of kinetic energies reached at existing accelerators spans from a few electron volts per particle into the 1012 electron volt regime. Effective and successful application of such particle beams requires detailed quantitative knowledge of the penetration of charged particles through matter, a field commonly categorized under the discipline of atomic physics. Early studies of charged-particle penetration were stimulated by experimental work with gas discharges toward the end of the 19th century, but experimental possibilities were greatly enhanced after the discovery of radioactivity, in particular in pioneering work by E. Rutherford and coworkers in the beginning of the 20th century. Fundamental theoretical studies of particle penetration in particular by J. J. Thomson and N. Bohr date back to the same time. Subsequently, after the development of quantum mechanics, the quantum theory of particle stopping was developed by H. Bethe, C. Møller, F. Bloch and others. Prime parameters characterizing the penetration of charged particles are the mean energy loss per unit path length, i.e., the stopping power or stopping force, and its fluctuation, called energy-loss straggling. These quantities determine the penetration depth (range) and its fluctuation (range straggling) as well as the energy-deposition profile. Since particles are more or less deflected from their initial direction of motion, also the spatial and directional distribution, the multiple-scattering profile, is of interest. With the exception of a very small part of the available parameter space, the dominating process leading to energy loss of a penetrating charged particle is electronic excitation of the atoms or molecules of the penetrated medium. Additional contributing effects are momentum transfer to recoiling nuclei and, depending on the type and energy of the penetrating particle, electronic excitation of the projectile and charge exchange with the atoms of the
penetrated medium. At high velocities, radiational processes and nuclear reactions have to be considered. Angular deflection is mainly connected to momentum transfer to recoiling nuclei. Until the mid-1960s, experimental activities in the area focused on the penetration of light charged particles such as electrons and positrons, protons and alpha particles. This was motivated by the needs of nuclear and particle physics. Moreover, options for experimental research on the penetration of particles heavier than helium were very limited in terms of available species and beam energies. This situation changed rapidly with new generations of ion sources and accelerators becoming available. Until the early 1990s, theoretical research on particle stopping likewise focused on light penetrating particles, with the exception mainly of low-energy ion implantation. The relatively weak Coulomb interaction of such particles with the electrons of the stopping medium allowed the application of well-developed concepts from quantum mechanical perturbation theory. As the stopping force on a light charged particle is proportional to the square of its charge, the range of validity of quantal perturbation theory must rapidly deteriorate with increasing atomic number of the penetrating particle. Numerous measurements have been performed on heavy-particle stopping during the past half century. The scatter between comparable data is usually considerably larger than for light particles in the same velocity range for a number of reasons. The coverage with experimental data of the entire parameter space in terms of the atomic number Z1 and the energy of the projectile, and the atomic number Z2 of the stopping medium, is necessarily fragmentary. Nevertheless, attempts have been made regularly to collect available experimental data and to systematize them by empirical scaling relations so as to allow predictions of stopping forces for systems not covered by existing data. Data compilations by Northcliffe and Schilling (1970), Ziegler (1980), Zeigler et al. (1985), and by Hubert et al. (1980, 1990) have had a lasting impact on the development of research around heavy-ion accelerators. The accuracy of specific predictions of these tables is limited as use is made of scaling laws that
ª International Commission on Radiation Units and Measurements 2005
STOPPING OF IONS HEAVIER THAN HELIUM
of pertinent theory and experiment. Although much progress has been made in light-particle stopping since the appearance of previous ICRU reports on stopping of electrons and positrons (ICRU Report 37) and of protons and alpha particles (ICRU Report 49), no attempt has been made of an update of those areas in the present report. Despite an extensive bibliography,1 no claim is made of completeness. A large collection of experimental data on heavyion stopping was established which proved to be a valuable tool both within and outside the work of the report committee. The majority of experimental data shown on graphs in this report is quoted from that database (Paul, 2003), whether stated or not. This collection was also employed in a scaling procedure similar to that of Northcliffe and Schilling (1970) allowing the prediction of stopping forces for ions with Z1 < 18 (Paul and Schinner, 2001, 2002; Paul, 2003). Comparisons between predictions of codes based either on theory or empirical interpolation were performed for a large number of ion----target combinations. An overall agreement of about 10% is found for the best available codes of both kinds. A somewhat higher accuracy is generally found in the energy range above 10 MeV/u, while at energies below 0.1 MeV/u, uncertainties increase due to increasing scatter of experimental data, increasing deficiencies in available theory and breakdown of simple scaling relationships. Tables of stopping forces listed in this report were computed by the PASS code (Sigmund and Schinner, 2002b) based on the binary stopping theory of Sigmund and Schinner (2000). The parameter range covered includes 16 ions with atomic numbers from 3 to 18 as well as iron; the range of materials covered is essentially that of ICRU reports 37 and 49 except for a single element and a few compounds, and the tabulated energy range goes from 25 keV/u to 1 GeV/u. It is planned to make updates accessible on the Internet. Such updates will report errors, improved and extended tables as well as tables for a wider variety of ion----target combinations.
lack theoretical justification and as erroneous data are not necessarily identified as such and hence enter as input. However, no feasible alternative was available until recently. This situation changed during the 1990s, when several new theoretical approaches were developed which did not hinge on quantal perturbation theory to the lowest order. An important step was made with the understanding of the Barkas----Andersen effect, sometimes called Z31 effect, in the stopping of light particles. This had been considered until then as a major hurdle that had to be overcome before a feasible theoretical approach to heavy-ion stopping. At present, four promising theoretical approaches are available, all of which go beyond or even avoid quantal perturbation theory (Arista, 2002; Grande and Schiwietz, 2002; Maynard et al., 2002b, 2001b; Sigmund and Schinner, 2000, 2002b). In order to allow predictions of stopping forces, a number of significant physical processes must be incorporated into the basic schemes, such as projectile screening and equilibrium charge state, charge exchange and projectile excitation, low- and high-speed corrections of various kinds, and reliable input on electronic properties of the penetrated material. This process has not been finished on any of the four schemes. Despite this, successful predictions have been made by all of them. With regard to straggling, the situation is quite different. Very few measurements with heavy ions have been done altogether. The number of physical processes affecting straggling exceeds those affecting stopping forces. While most of them have been identified and understood theoretically as isolated phenomena, several of them interfere, making quantitative predictions a complex task requiring further study. Angular deflection (multiple scattering), on the other hand, is well described by existing scaling laws, and despite only few systematic experiments, there is consensus that predictions on the basis of those scaling laws are reliable and accurate. The present report addresses penetrating ions heavier than helium. Extensive reviews are given
1
The bibliography was closed on 1 October, 2003.
10
