NBS Publi- Reference cations AlllOb NBSIR 82-2550 Stopping Powers and Ranges of Electrons and Positrons U.S. DEPARTMENT OF COMMERCE National Bureau of Standards Washington, DC 20234 August 1 982 Prepared for: Office of Standard Reference Data National Bureau of Standards Washington, DC 20234 Office of Health and Environmental Research Department of Energy Washington, DC 20545 fice of Naval Research lington, Virginia 22217 IJO . U56 oZ-255u «Ar»OK4X UURKAO o» 10 0 arAMDAMaa T aOUlAfiY AUG 1 9 1982 O. 'C'^f NBSIR 82-2550 Oo\Q QX Stopping Powers and Ranges of Electrons and Positrons U.S. DEPARTMENT OF COMMERCE National Bureau of Standards Washington, DC 20234 August 1982 Prepared for: Office of Standard Reference Data National Bureau of Standards Washington, DC 20234 Office of Health and Environmental Research Department of Energy Washington, DC 20545 Office of Naval Research Arlington, Virginia 22217 NBSIR 82-2550 Stopping Powers and Ranges of Electrons and Positrons M. J. Berger and S. M. Seltzer U.S. DEPARTMENT OF COMMERCE National Bureau of Standards Washington, DC 20234 August 1 982 Prepared for: Office of Standard Reference Data National Bureau of Standards Washington, DC 20234 Office of Health and Environmental Research Department of Energy Washington, DC 20545 Office of Naval Research Arlington, Virginia 22217 U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director : I ^ ^ ^ V- I' X - - ^ 2.U :• , -'1 i-rmu'.- ’u I lUV? ' <jZ r . -r v : ,-i .!<-. I ,-/i ;t,:, / , : r\ ‘J & u\ . •• r r''i ‘ . r»U -?Ofl| • './ • ViVsi't , 'V .P*J^ l»'-'‘./''l S ^O UA'jrsUS V<i> I Jk' . : . ; STOPPING POWERS AND RANGES OF ELECTRONS AND POSITRONS M. J. Berger and S. M. Seltzer Center for Radiation Research National Bureau of Standards Washington, D.C. 20234 ABSTRACT Tables of stopping powers and related data are given for electrons in 25 elements and 46 mixtures and compounds, and for positrons in 8 materials. The tables include: (1) collision stopping powers (ionization and excitation losses); (2) radiative stopping powers (bremsstrahlung losses); (3) total stopping powers; (4) ranges (rectified pathlengths computed in the continuous- slowing-down approximation) radiation yields (fraction of initial ; (5) electron energy converted to bremsstrahlung in the course of slowing down) and (6) the logarithmic derivatives of all these quantities with respect to the mean excitation energy of the medium (the key parameter of the Bethe stopping power formula). The results are tabulated at 81 energies between 1000 MeV and 10 keV. Collision stopping powers for electrons in materials of low atomic number are given also for energies down to 1 keV. The principal new ingredients in the preparation of the tables are: (1) improved values of the mean excitation energies for elements and compounds, derived from stopping-power and range measurements and from semi -empirical oscillator- strength distributions and dielectric-response functions; (2) density- effect corrections evaluated according to the method of Sternheimer, using up-to-date input parameters; and (3) use of new theoretical cross sections of Pratt and Tseng for electron-nucleus bremsstrahlung and of Haug for electron -electron bremsstrahlung Key words Collision stopping power, electrons, positrons, radiation yield, radiative stopping power, range. These tables were prepared as input for a report on stopping power to be written by a committee sponsored by the International Commission on Radiation Units and Measurements (ICRU). The ICRU sponsors of this committee are A. Allisy and R. S. Caswell. The committee members are H. H. Andersen, M. J. Berger (chairman), H. Bichsel, J. A. Dennis, M. Inokuti, D. Powers, and J. E. Turner. Consultants to the committee are S. M. Seltzer and R. M. Sternheimer. All of the above have made important contributions to this work. It should be emphasized that this report is a draft submitted to the ICRU, and may be revised before being included in an ICRU document We would like to acknowledge the financial support for this work provided by the NBS Office of Standard Reference Data, the Office of Health and Environmental Research of the Department of Energy, and the Office of Naval Research. Last but not least we would like to thank Mrs. Gloria Wiersma for her editorial help in the preparation of the manuscript. TABLE OF CONTENTS 1. ABSTRACT INTRODUCTION 1.1. Purpose and scope 1.2. Background 1.3. New features 2. FORMULAS FOR THE COLLISION STOPPING POWER 3 2.1. General Formulas 2.2. Stopping-power formulas for heavy charged particles 2.3. Stopping-power formulas for electrons and positrons 3.2.1. 3. METHODS FOR ESTIMATING MEAN EXCITATION ENERGIES 7 3.1. Use of oscillator- strength and dielectric data 3.2. Use of stopping-power and range data Bichsel's shell corrections 3.2.2. Comparisons of Bichsel's and Bonderup's shell correction 4. SELECTION OF MEAN EXCITATION ENERGIES FOR ELEMENTS 12 5. SELECTION OF MEAN EXCITATION ENERGIES FOR COMPOUNDS 13 6. DENSITY EFFECT 16 6.1. General equations 6.2. Sternheimer ' s model 6.3. Numerical evaluation 6.4. Complications for inhomogeneous media 7. RESTRICTED COLLISION STOPPING POWER 19 8. ELECTRON COLLISION STOPPING POWERS AT LOW ENERGIES 20 8.1. Calculations for gases 8.2. Calculations for solids and liquids 8.3. Comparison of stopping powers 9. RADIATIVE STOPPING POWER 23 9.1. Electron-nucleus bremsstrahlung 9.1.1. High-energy region 9.1.2. Low-energy region 9.1.3. Intermediate energy region 9.2. Electron-electron bremsstrahlung 9.2.1. High-energy region 9.2.2. Low-energy region 9.2.3. Intermediate energy region 9.3. Accuracy and comparison with experiments 10. RANGES AND RADIATION YIELDS 26 11. MISCELLANEOUS COMPARISONS 27 11.1. Positron-electron differences 11.2. Comparison of calculated and experimental stopping powers 11.3. Comparisons with previous calculations REFERENCES 29 TABLES TO ACCOMPANY TEXT 41 FIGURES 66 MAIN STOPPING-POWER AND RANGE TABLES 79 11 . 1. INTRODUCTION 1.1. Purpose and scope . In radiation physics, chemistry, biology, and medicine, it is often important to have accurate information about the stopping power of various media for charged particles, that is, the average rate at which the charged particles lose energy along their tracks. The purpose of this report is to supply up-to-date stopping -power information, with emphasis on the requirements of biomedical dosimetry. The contents of this report are the following: (a) In Sections 2 to 6, topics are reviewed which are pertinent to the evaluation of stopping powers for any charged particle within the framework of the Bethe theory. ^ These include shell corrections, the determination of mean excitation energies from experimental data, the use of the Bragg additivity rule for compounds, and the density-effect correction. Recommended values of mean excitation energies are given in Table 4.3 for elemental substances and in Table 5.5 for compounds and mixtures. (b) In Sections 7 to 11, topics are reviewed which are pertinent mainly or entirely to electrons. These include the radiative stopping power due to the emission of bremsstrahlung , and the information on electron collision stopping power at energies below 10 keV where the Bethe theory is no longer fully applicable. (c) In Section 12, electron stopping- power tables are presented for 25 elements and 46 compounds and mixtures, covering the energy region from 10 keV to 1000 MeV. These tables also include the range (rectified pathlength) and the radiation yield (fraction of electron kinetic energy converted to bremsstrahlung as the electrons slow down to rest) , both computed in the continuous-slowing-down approximation.^ Such data are also given for positrons in a few materials. 1.2. Background . For electrons it is customary to separate the total stopping power into two components: (a) the collision stopping power , which is the average energy loss per unit pathlength due to inelastic Coulomb collisions with bound atomic electrons of the medium resulting in ionization and excitation; (b) the radiative stopping power , which is the average energy loss per unit pathlength due to the emission of bremsstrahlung in the electric field of the atomic nucleus and of the atomic electrons.^ The separation of the electron stopping power into two components is useful for two reasons. First, the methods used for the evaluation of the two components are quite different. Second, the energy going into the ionization and excitation of atoms is absorbed in the medium rather close to the electron track, whereas most of the energy lost in the form of bremsstrahlung travels far from the track before being absorbed. This distinction is important when attention ^The results obtained will be applied to the tabulation of stopping powers for heavy charged particles in a future report. ^In this approximation, energy-loss fluctuations are disregarded, and the rate of energy loss at any point along the track is assumed to be equal to the stopping power. ^The nomenclature "collision stopping power" and "radiative stopping power" is that adopted by the International Commission on Radiation Units and Measurements (ICRU, 1980) In the literature, the collision stopping power is often referred to as stopping power, with the adjective "collision" omitted, especially in circumstances where the radiative stopping power is negligible. The collision stopping power is some- times also called "ionization loss." Numerically, but not conceptually, the collision stopping power is identical with the "linear energy transfer" (more precisely, the unrestricted linear energy transfer LET ) often used in radiobiology (see, e.g. , ICRU, 1970) The excitations contributing to the collision stopping power include not only electronic excitations but also vibrational and rotational excitations of molecules; however, the latter two processes are relatively unimportant above the threshold energy for electronic excitation. Charged particles also lose some energy in elastic collisions with atoms.