The stopping and range of ions in matter is physically very complex, and there are few simple approximations which are accurate. However, if modern calculations are performed, the ion distributions can be calculated with good accuracy, typically better than 10%. This review will be in several sections: 

a)

A brief exposition of what can be determined by modern calculations.




b)

A review of existing widely-cited tables of ion stopping and ranges.




c)

A review of the calculation of accurate ion stopping powers.

The stopping and range of ions in solids

The main advantages of proton therapy are the reduced total energy deposited in the patient as compared to photon techniques and the finite range of the proton beam. The latter adds an additional degree of freedom to treatment planning. The range in tissue is associated with considerable uncertainties caused by imaging, patient setup, beam delivery and dose calculation. Reducing the uncertainties would allow a reduction of the treatment volume and thus allow a better utilization of the advantages of protons. This paper summarizes the role of Monte Carlo simulations when aiming at a reduction of range uncertainties in proton therapy. Differences in dose calculation when comparing Monte Carlo with analytical algorithms are analyzed as well as range uncertainties due to material constants and CT conversion. Range uncertainties due to biological effects and the role of Monte Carlo for in vivo range verification are discussed. Furthermore, the current range uncertainty recipes used at several proton therapy facilities are revisited. We conclude that a significant impact of Monte Carlo dose calculation can be expected in complex geometries where local range uncertainties due to multiple Coulomb scattering will reduce the accuracy of analytical algorithms. In these cases Monte Carlo techniques might reduce the range uncertainty by several mm.

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Range uncertainties in proton therapy and the role of Monte Carlo simulations

(1976). Nuclear Tracks in Solids (Principles and Applications) Nuclear Technology: Vol. 30, No. 1, pp. 91-92.

Nuclear Tracks in Solids (Principles and Applications)

The projectile fragment separator FRS designed for research and applied studies with relativistic heavy ions was installed at GSI as a part of the new high-energy SIS/ESR accelerator facility. This high-resolution forward spectrometer has been successfully used in first atomic and nuclear physics experiments using neon, argon, krypton, xenon, and gold beams in the energy range from 500 to 2000 MeV/u. For the first time relativistic xenon and gold fragments have been isotopically separated. In this contribution we describe first experiments characterizing the performance of this spectrometer.

The GSI projectile fragment separator (FRS): A Versatile magnetic system for relativistic heavy ions

High-energy beams of charged nuclear particles (protons and heavier ions) offer significant advantages for the treatment of deep-seated local tumors in comparison to conventional megavolt photon therapy. Their physical depth-dose distribution in tissue is characterized by a small entrance dose and a distinct maximum (Bragg peak) near the end of range with a sharp fall-off at the distal edge. Taking full advantage of the well-defined range and the small lateral beam spread, modern scanning beam systems allow delivery of the dose with millimeter precision. In addition, projectiles heavier than protons such as carbon ions exhibit an enhanced biological effectiveness in the Bragg peak region caused by the dense ionization of individual particle tracks resulting in reduced cellular repair. This makes them particularly attractive for the treatment of radio-resistant tumors localized near organs at risk. While tumor therapy with protons is a well-established treatment modality with more than 60 000 patients treated worldwide, the application of heavy ions is so far restricted to a few facilities only. Nevertheless, results of clinical phase I-II trials provide evidence that carbon-ion radiotherapy might be beneficial in several tumor entities. This article reviews the progress in heavy-ion therapy, including physical and technical developments, radiobiological studiesmore » and models, as well as radiooncological studies. As a result of the promising clinical results obtained with carbon-ion beams in the past ten years at the Heavy Ion Medical Accelerator facility (Japan) and in a pilot project at GSI Darmstadt (Germany), the plans for new clinical centers for heavy-ion or combined proton and heavy-ion therapy have recently received a substantial boost.« less

Heavy-ion tumor therapy: Physical and radiobiological benefits

We review the theory of the electromagnetic interactions between rapidly moving charged particles and the matter through which they pass. The emphasis will be on very massive electric ($\ensuremath{-}100\ensuremath{\le}{Z}_{1}100$) and magnetic ($|g|=137e \mathrm{and} \frac{137e}{2}$) particles moving with relativistic velocities ($\ensuremath{\beta}g0.2$, $\ensuremath{\gamma}l100$). Consideration will be given to both the stopping power of the projectile and to the response of the absorbing medium to the excitation caused by the projectile.

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Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

IRIS, a telescope consisting of a large-area precision Cerenkov detector, scintillators, spark chambers, and a passive stack of Lexan polycarbonate track detectors, was exposed to the primary cosmic radiation for 6.6 sq m sr hr in a balloon flight in 1976. This measurement has yielded the isotopic composition of the iron-group elements Cr, Mn, Fe, and Ni with an average mass resolution of 0.65 amu for the energies 320-500 MeV per amu at the detector. This experiment places the most severe constraints to date on deviation from solar-system composition of the source of the cosmic radiation. Upper limits of 10 percent are placed on the ratios Fe-54/Fe-56 and Fe-58/Fe-56, which are inconsistent with large departures from solar system source composition reported by other workers. The isotopic measurements of Fe and Ni preclude the possibility that these cosmic rays were produced in a single e-process zone. The mean mass of Mn is less than 55, indicating the presence of electron-capture species produced by spallation.

Cosmic ray isotope abundances from chromium to nickel

It is pointed out that detectors of the energy loss of penetrating charged particles are widely used for particle identification. These measurements are hampered, however, by fluctuations in the amount of energy deposited within the detector. It is shown that this limitation can be overcome with a new nuclear track detector, CR-39(DOP), and that the charge resolution of this detector exceeds that of any other, including semiconductor diodes.

Energy straggling eliminated as a limitation to charge resolution of transmission detectors

A novel particle detection technique employing well established principles of high order quantum electrodynamics for searching for antimatter in cosmic rays is described, and shown to have both collecting power and resolution superior to conventional alternatives. By taking into account various estimates of the metagalactic cosmic-ray energy density, and the possible modulation of metagalactic cosmic rays by a galactic wind within the framework of the dynamical halo model, it is shown that the experiment proposed would be the first to be sensitive to the presence of extragalactic antimatter.

Can we detect antimatter from other galaxies

Using dioctyl-phthalate-doped CR-39 plastic track detectors with charge resolution ${\ensuremath{\sigma}}_{Z}\ensuremath{\approx}0.06e$, the authors have made the first dynamic search for fractionally charged particles bound to nuclei. They find, from charge measurements in the first \ensuremath{\sim} 2 cm after production, that no more than 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}3}$ (95% confidence level) of the projectile fragments of 1.85-GeV/u $^{40}\mathrm{Ar}$ interactions with $10l~Zl18$ have charges differing from an integer by as much as $0.3e$. This rules out explanations of anomalons based on models in which the anomalons have nonintegral charge in such charge range.

S. P. Ahlen

Papers

Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles

Cosmic ray isotope abundances from chromium to nickel

Energy straggling eliminated as a limitation to charge resolution of transmission detectors

Can we detect antimatter from other galaxies

Search for nonintegrally charged projectile fragments in relativistic nucleus-nucleus collisions