Are Further Cross Section Measurements Necessary for Space Radiation Protection or Ion Therapy Applications? Helium Projectiles
- 1NASA Langley Research Center, Hampton, VA, United States
- 2Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Milano, Milan, Italy
- 3German Cancer Research Center (DKFZ), Heidelberg, Germany
- 4University of Heidelberg, Heidelberg, Germany
- 5Thales Alenia Space, Torino, Italy
- 6GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany
- 7Institute for Nuclear Research of the Russian Academy of Sciences, Moscow, Russia
- 8University of New Hampshire, Durham, NH, United States
- 9Technische Universität Darmstadt, Darmstadt, Germany
- 10Heidelberg Ion Beam Therapy Center, Heidelberg, Germany
- 11University of Tennessee, Knoxville, TN, United States
- 12University of Trento, Trento, Italy
- 13Trento Institute for Fundamental Physics and Applications (INFN‐TIFPA), Trento, Italy
- 14Universita’ di Roma “Sapienza”, Roma, Italy
- 15European Space Agency, Noordwijk, Netherlands
- 16RHEA System, Noordwijk, Netherlands
- 17Technische Universität Wien, Atominstitut, Vienna, Austria
- 18Chalmers University of Technology, Gothenburg, Sweden
- 19Leidos Innovations Corporation, Houston, TX, United States
The helium (
1 Introduction and Review
The International Biophysics Collaboration1 (IBC) was recently formed at the GSI Helmholtzzentrum für Schwerionenforschung, with the aim of utilizing the future Facility for Antiproton and Ion Research (FAIR) and other accelerators for biophysics studies relevant to space radiation protection, ion therapy, and other biophysics applications. Within the IBC, a cross section working group has been formed to study what cross section measurements and modeling need to be performed to support the broad aims of the IBC. Membership of the cross section working group is open, and other colleagues are encouraged to participate: An important objective for the cross section working group is to have broad support within the international scientific community.
Previous analyses of experimental data [1–4] focused on measurement gaps for space radiation. The highest priority measurement recommendations were double differential cross sections for the following ion2 reactions,
where X is anything, thereby denoting an inclusive reaction, where a particular nuclide, say
The aim of the present study was therefore to consider whether further cross section measurements are necessary for space radiation protection or ion therapy applications, define overlaps in interest for both disciplines, and prioritize needed experiments and measurement quantities.
1.1 Importance of Light Ion Fragments
In the context of space radiation protection, light ion fragments
(1)Neutrons and light ion fragments dominate dose equivalent [8–10] for realistic spacecraft shield thicknesses (
(2)Because they have small charge and mass, neutrons and light ion fragments are scattered at large angles, and therefore require full 3-dimensional transport  methods (as opposed to 1-dimensional straight-ahead scattering approximations). Full 3-dimensional transport methods, in turn, require nuclear physics double differential cross sections [12, 13] as input.
(3)Transport code (GEANT, FLUKA, MCNP, PHITS, HZETRN, and SHIELD) comparisons  show the largest differences for light ion fragment production. The disagreements are mainly due to inaccurate light ion nuclear physics models and lack of experimental data to be used to improve these models. As an illustration of this, Figure 2 shows large disagreements for numerous transport code comparisons for the production of
(4)An experimental double differential cross section measurement program was recently completed at the NASA Space Radiation Laboratory (NSRL), located at Brookhaven National Laboratory (BNL), using oxygen and iron beams on several targets, with the production of light ion fragments . Large differences were seen between measurements and the light ion cross-section models used in the PHITS  transport code.
(5)An experimental thick target program was also recently completed at the NSRL, using unique combinations of double thick targets where incident beam particles scattered from the first target and secondary fragments subsequently scattered from a back target. This simulated the scattering geometry in a spacecraft, where fragments are produced when GCRs interact with a spacecraft wall and more scattered products are produced from the far, back, and surrounding walls. These measurements show significant discrepancies  compared to transport codes (MCNP and PHITS) for light ions. Further cross section measurements of light ion fragments have been recommended to resolve these discrepancies.
(6)Mars Science Laboratory Radiation Assessment Detector (MSL-RAD) light ion flux measurements highlight the need for improved nuclear interaction models. Light ion model results show moderate to large discrepancies [19–21] over the MSL-RAD energy range,5 with model errors mainly attributed to inaccurate light ion nuclear physics models.
(7)Calculations with the HZETRN transport code underpredict dose measurements from the International Space Station [22, 23], at high latitudes where GCRs contribute most. The cause of the discrepancy has yet to be fully clarified, but improvements to the underlying cross section models will help remove some measure of uncertainty.
(8)Light ion cross sections represent the largest physics uncertainty in space radiation.
(9)Light ion cross section measurements  are needed to improve inaccurate light ion nuclear physics models.
(10)Light ion cross section measurements represent the largest gap in the cross section database .
FIGURE 1. Calculated percent contribution to blood-forming organ (BFO) dose equivalent for free space (far left), simple spherical geometries in free space, and detector locations inside the space shuttle (STS) and the International Space Station (ISS) in free space. The vehicles included three aluminum spheres with areal densities 1, 5, and 30 g/cm
As emphasized above, light ions make large contributions to dose equivalent and are essential for treatment planning, but the physics of their production remains poorly understood. One would hope to compare theoretical nuclear physics models to cross section measurements to resolve these issues, but the largest gap in the cross section database occurs for light ions. This is why a further cross section measurement program is recommended for space radiation and ion therapy applications.
1.2 Importance of Double Differential Cross Sections
Neutrons and light ion fragments are scattered at large angles because they have small charge and mass. They therefore require full 3-dimensional transport methods, which need double differential cross sections [12, 13] as input. This is why double differential6 cross sections are highlighted in the present work, with emphasis on isotopic production cross sections,
Other reasons for emphasizing double differential isotopic cross sections are as follows. Single differential spectral,
Similar reasoning applies to isotopic fragment cross sections vs. elemental or charge changing cross sections. Consider light ions: An isotopic measurement would provide double differential production cross sections for each
All of the above discussion in this subsection has centered on measurement issues, but the same is true for theoretical modeling. At the most fundamental level, a particle physics Feynman diagram gives the quantum mechanical amplitude for a given process which is inserted directly into a formula for the double differential cross section. Spectral, angular and total cross sections are obtained by integrating as described above. Even if one is not using Feynman diagrams directly, the quantum mechanical amplitude, obtained by some theoretical model, is the most fundamental quantity. In other words, double differential cross sections are most fundamental. Another matter concerns comparing theoretical model results to experimental measurements. Comparisons of double differential cross section models with double differential cross section measurements is the most precise sort of validation test of a theoretical model. Comparing theoretical models for single differential spectral or angular cross section measurements is less precise: The models might get these correct, even though the underlying double differential cross sections might be incorrect. Comparing total cross section models with experiment is the least precise. In summary, the most precise test of a theoretical model is comparison of double differential cross sections with experiment. If these are correct, then single differential spectral and angular cross sections, as well as total cross sections, will automatically be correct. The reverse situation does not hold; for example, comparing total theoretical model cross sections with experiment will not guarantee that the double differential cross sections are correct. The considerations are the same for isotopic vs. elemental cross sections. If all the theoretical model isotopic cross sections agree with experiment, then the elemental and charge changing cross sections will automatically be correct as well. The reverse situation does not hold.
However, it is important to note that in many modern Monte Carlo transport codes, the removal of primary ions and the fragment production are treated separately. The interaction probability is typically sampled according to parameterized total reaction cross sections for which semi-empirical models fine-tuned to experimental data are used, while the fragment production and their double differential distribution is obtained from nuclear event generators and coalescence/evaporation models. Therefore, to optimize such transport codes, experimental data on both the total reaction cross section and the double differential fragment distributions are required.
The conclusion of this subsection is that the most useful and precise types of cross sections are isotopic double differential cross sections. This is true for both experimental measurements and theoretical models. If these types of cross sections give good comparisons between models and experiment, then all other types of cross sections will automatically also give good comparisons. Also, all other types of cross sections (both theoretical and experimental) can be obtained from isotopic double differential cross sections. This behavior should be exploited to cross-check total and single differential datasets.
Previous measurement studies [1–4] will now be summarized, for all types of projectiles, emphasizing double differential cross sections for light ion fragment production. Figures 3–7 show where isotopic double differential cross section data have been measured for light ion production. The following conclusions can be stated:
• In the low energy region below the pion threshold (
• In the medium energy (280–3,000 MeV/n) region, double differential cross sections for light ion production mainly exist for H, He, C, Ne, and Ar projectiles.
• In the high energy (3–15 GeV/n) and very high energy (
• Even though there are a moderate number of experimental measurement articles dealing with helium projectiles, further detailed analysis of He data below 3 GeV/n reveals significant problems and flaws with the data, leading to the conclusion that there is almost no high-quality double differential data for helium projectiles over the entire energy region.11 This is discussed in more detail later in this article.
• No double differential cross section data exist for light ion fragment production from helium projectiles above 3 GeV/n.
• No double differential cross section data exist for light ion fragment production from oxygen projectiles12 above the pion threshold (
• No double differential cross section data exist for light ion fragment production from silicon (Si) projectiles in any energy region.
• No double differential cross section data exist for light ion fragment production from iron (Fe) projectiles13 in any energy region. This is particularly surprising, given the prominent role of Fe projectiles in space radiation biophysical studies .
FIGURE 3. Available isotopic double differential cross section measurements for
FIGURE 4. Available isotopic double differential cross section measurements for
FIGURE 5. Available isotopic double differential cross section measurements for
FIGURE 6. Available isotopic double differential cross section measurements for
FIGURE 7. Available isotopic double differential cross section measurements for
1.3.1 Measurement Strategies and Experimental Setup
When planning and setting up measurements of double differential cross sections, there are a number of factors to be considered, ranging from detector system, detection efficiency, statistics, beam monitor, acceptance angles, data acquisition system, target thickness, and time resolution for TOF (time of flight) techniques.
In order to measure the angular distributions, several different configurations are possible. One standard option is a TOF setup with a fast counting detector (e.g., plastic scintillator, silicon detector, and diamond detector) that provides trigger information, that is, the start signal, before the target, and a plastic scintillator, for example, some distance downstream from the target, providing the stop of the TOF, and measurements of the energy loss. After this, a thick dense crystal calorimeter (e.g., BGO and NaI) can be located to provide the projectile fragment residual energies. Additional detector systems can be added to this general setup to improve its capabilities. Tracking detectors in front and after the target allow vertexing and different magnet configurations, and large-area drift chambers behind the target can be employed to increase particle identification performance. Silicon detectors in different configurations, for example, silicon micro-strips or silicon pixel detectors, or emulsion chambers, can also be used. Time resolution between the start detector and the stop detector and the angular acceptances are important. To obtain the double differential cross sections, in addition to the angular distributions, the energy distributions also need to be determined at each point of the angular distributions.
In principle, all cross sections should be measured in targets with infinitesimal thickness, which are, however, not optimal from the experimental point of view since targets which are too thin increase the beam time requirements and increase susceptibility to systematic errors. The target thicknesses are therefore a trade-off between thick enough to give acceptable statistics when exposed during a reasonable time, but not so thick to give rise to substantial corrections for secondary and higher-order interactions in the targets. Targets should also not be thick enough to cause a significant decrease of the projectile energies in the target, since the cross sections are energy dependent. Measured fragment yields need to be converted to cross sections and require correction for the finite depth target which is applied to the cross section values of each fragment. The corrections are typically of the order of half the fraction of an interaction length presented by the target to the primary. For example, for a target depth of 20% of an interaction length, about 20% of the incident primary particles undergo a charge-changing interaction in the target, and therefore about 10% of the fragments within a few charge units of the primary will undergo secondary charge-changing interactions. For experiments with a heavy projectile, the corrections for lighter fragments are more complicated, because they are both depleted by interactions in the target and are also produced as third- and higher-generation fragments by interactions of heavier fragments as they traverse the target.
It is always important to certify that particles created in other materials in the beam line are not measured. It is therefore essential that the beam never hits anything other than the target. When measuring neutron energy distributions, this is especially important since the neutron detectors are also picking up neutrons that scatter around the room before striking the detectors. Because their flight paths are unknown, those neutrons must be subtracted from the data. Measurements of the room-scattered neutrons should therefore be performed and subtracted from the total detected neutrons. Depending on the setup, this can be done by placing a shadow bar (a long, solid piece of iron, or other material, thick enough to stop the neutrons that enter it) directly between the target and the neutron detector, so that all neutrons originating from the target are blocked, and only room-scattered neutrons are detected. By subtracting the neutrons measured during the shadow bar run from the non-shadow bar run, the neutrons originating from the target can be determined. It is important to note that all of the previously mentioned experimental techniques do not scale well with increasing primary particle energy due to, for example, the inability to stop the light fragments in a crystal calorimeter or the increasing demands on TOF resolution and distance.
2 Importance of Helium Projectiles
2.1 Space Radiation
A discussion of the importance of helium projectiles in the galactic cosmic ray environment now follows.14 Subsequent to the analyses of measurement gaps [1–4] discussed in Section 1.3, an important work was published by Slaba and Blattnig , which analyzed the contributions of each external boundary condition GCR ion to effective dose. Not only was the charge number (Z) contribution specified but also the energy range contributing to effective dose. Previous studies [1–4] emphasized measurement gaps, but the study of Slaba and Blattnig  enabled one to prioritize which measurement gaps were the most important ones to close for space radiation. Figure 8 shows how helium projectiles dominate the effective dose contribution compared to heavier projectiles over the GCR energy region. For Al shield thickness of 20 g/cm
• 86% of effective dose is contributed from GCR ions with kinetic energy
• 50% of effective dose is contributed from GCR ions with kinetic energy
• 32% of effective dose is contributed from ions with Z
• He contribution to effective dose is 30% of the total ion (Z
• He contribution to effective dose is 12% of the total effective dose (from all Z).
FIGURE 8. Effective dose contributions as a function of external GCR energy behind 20 g/cm
For Al shield thickness of 40 g/cm
Using the calculations of reference , Table 1 shows the percent contribution of each energy range to total He effective dose from the external GCR spectrum. For a shield thickness of 20 g/cm
• More than half of the effective dose delivered by all GCR ions (including protons, i.e., Z
• Of all external GCR ions heavier than protons (Z
TABLE 1. Percent contribution of each energy range (MeV/n) to total He effective dose from external GCR spectrum for Al shield thicknesses of 20 g/cm
Also, similar results have been obtained by Bocchini et al.  obtained using Geant4. In particular, for Al thickness of 20 g/cm
However, at 40 g/cm
Extensive simulations have been performed by Bocchini et al.  to iteratively characterize the GCR contribution to the effective dose with Geant4, and here, results for He are reported. An aluminum spherical shell was modeled in GRAS , with varying thickness (i.e., from 10 up to 100 g/cm
Figure 9 shows the male effective dose deposited by primary GCR He (including its secondary particles), while the percentage contribution of the different particle species to the dose is shown in Figure 10. The increase in the dose with thickness is in line with results reported in 50 for dose reduction of 1 GeV/n He particles against different spacecraft materials. At 30 g/cm
FIGURE 9. Geant4 simulation of Male Effective dose due to GCR He (including its secondary particles), calculated using the ICRP Publication 123 fluence to dose conversion factors with NASA quality factors.
FIGURE 10. Geant4 simulation of the percent contribution to the male effective dose of He GCR, showing in percentage the radiation component responsible for the GCR HE dose (either primary He or secondary particle generated by GCR He). Total male NASA effective dose has been calculated with ICRP Publication 123 fluence to dose conversion factors. 0 g/cm
Geant4 simulations were also carried out to calculate the GCR He contribution to the dose in terms of energy range of the primary particle responsible for the dose deposition, to better prioritize testing activities. Figure 11 shows the dose delivered by GCR helium particles in Sv/y per different thicknesses, considering both primary He and its generated secondary particles. For all thicknesses, the majority of the dose delivered by He is in the following energy ranges: 200–500 MeV (20–28% of total He dose) and 1.5–3 GeV/n (17–25% of total He dose), contributing overall to about 50% of the dose. Based on these results, availability of nuclear interaction cross section data for He in the 500 MeV/n–3 GeV/n energy range interacting with spacecraft materials should be a priority for space research, allowing transport code optimization.
FIGURE 11. GCR He energy ranges contributing to the 1 year NASA male effective dose for different thickness, using fluence to dose conversion factors from ICRP Publication 123.
2.2 Heavy Ion Therapy
After the treatment of more than 2000 patients with
• The availability of high-quality
2.3 Required Cross Section Measurements
Having discussed the importance of He projectiles for space radiation and ion therapy, the question of which reactions are necessary to meet requirements is now addressed. A variety of low to medium mass targets are needed as well as a range of projectile energies.
• Inclusive, isotopic, double differential cross sections should be measured for the complete set of neutron and light ion fragments,
for projectile kinetic energies ranging over 50 MeV/n–50 GeV/n and fragment angles ranging over 0
3 Present Status
Section 1.3 discussed the availability of measurements for all types of projectiles. However, previous work [1–4] did not discuss the quality or usefulness of the measurements, and it will be seen below that when measurement quality is considered, there is an even more pressing need for a new set of cross section data. Another aspect that should be considered when the quality of a cross section dataset is evaluated is the target that was used for the measurement. Thinner targets give better data (better defined projectile kinetic energy, less elastic scattering, and less probability of multiple reactions) but increase the required beam time to collect data with appropriate statistical uncertainty. There is no universal definition what is a thin target. This should be judged based on the accuracy requirements for the measured cross sections as well as the ion species and energy used (see also section 1.3.1).
3.1.1 Total Cross Sections
Concerning total reaction cross sections for
FIGURE 12. Overview of
The energy range of the
The measurement of helium fragments produced from the fragmentation of heavier ions interacting with different target materials is important for nuclear models developed for space radiation transport models. NASA has specifically been interested in these data for validation of the nuclear fragmentation model NUCFRG. With this in mind, NASA collected experimental total cross sections, as NUCFRG only models the total cross section for production of isotopic fragments. This data gathering effort was restricted to projectiles with charge less than or equal to nickel. A total of 157 cross section values were found in the open literature at the time that work was performed [82–88]. The data are concentrated in the medium projectile energy range (280–3,000 MeV/n) with 135 cross sections. In the low projectile energy range (
3.1.2 Light Ion Fragment Production
Partial (Non-Differential) Cross Sections
Cross sections for
Additional cross sections for
Differential cross sections
The available helium projectile double differential data are listed in Table 2. A high-quality data set is required, and therefore some data are not useful. For example, many data do not include error bars [92, 97], and other data have not been published in refereed journals. Also, many data are for proton fragments only [91, 96, 99]. In addition, many data sets measured only large angles or only very small angles. There are certainly no data sets covering all the requirements of the necessary reactions of Eq. 2. Given these problems, it is recommended that a new experimental program be initiated that covers all the reactions listed in Eq. 2. There might be a small amount of overlap with some of the reactions on Table 2, but that will serve as a very useful benchmark to check the accuracy of new measurements.
TABLE 2. He projectile double differential cross section measurement details.
Some recent investigations in the scope of helium ion therapy [102, 103] provided experimental data about double differential fragment yields behind thick water and PMMA targets which can also be useful for nuclear model validation.
3.1.3 Neutron Production
From Figure 10, it is possible to see how the neutron contribution increases with spacecraft shielding thickness. From 104, discrepancies are found when comparing neutron ambient dose with PHITS and Geant4 simulations results. There is a need to have better models to simulate neutron production from space GCR.
Differential Cross Sections
There is a limited set of inclusive double differential cross-sectional data available on neutron production from medium and high energy
While it is relatively easy to develop accurate models for total cross sections and more difficult to develop accurate single differential spectral or angular cross sections, it is most difficult to develop accurate double differential models. And again, charge changing or elemental production models are easiest, while isotopic models are the most difficult. Accurate isotopic double differential cross section models are the most difficult of all to develop, but once available, they automatically generate accurate total and single differential cross sections including charge-changing and elemental cross sections.
3.2.1 Applications in Ion Therapy and Space Radiation Research
Treatment planning systems (TPS) are standard applications in ion therapy. The first TPS for scanned ion beams was the GSI code TRiP98 [29, 107]. It has been used clinically in the carbon ion pilot project at GSI . Special emphasis has not only been on dose calculation but also on dose optimization including radiobiological effects. It features a built-in deterministic transport model to create the base data necessary for treatment planning, that is, depth dose profiles and particle spectra which are necessary for radiobiological modeling. TRiP98 is now further developed as a research prototype for use with ion beams other than carbon, in particular oxygen  and helium . TPS predictions have been validated in dosimetric and radiobiological experiments at HIT and KVI Groningen.
TRiP98 is a deterministic code based on a set of tables comprising single particle energy loss (dE/dx) for primary and secondary ions, nuclear reaction cross sections describing the loss of the primary ion beam, and fragmentation cross sections to compute the build up of the produced secondary ions. In this respect, it needs the same basic physics data as the various Monte Carlo codes.
For space radiation research, TRiP98 is being extended to SpaceTRiP, in the framework of the ESA ROSSINI project. The latter is designed to calculate the dose reduction due to different space radiation shielding materials. The native TRiP98 transport model is extended to more types of ion projectiles than in ion therapy. This extension will allow the simulation of the multitude of HZE particles found in GCR spectra, of which
3.2.2 Total Reaction Cross Sections
An important quantity for light and heavy ion transport codes is the total reaction cross section
Figure 13 shows a collection of total cross section data for
FIGURE 13. Experimental data of total cross sections for
The modified Hybrid Kurotama model  for proton + nucleus and nucleus + nucleus total reaction cross sections can handle complex targets containing different target nuclei with both natural and unnatural abundances, for projectile energies from below 5 MeV/n to well above 10 GeV/n, where limiting fragmentation occurs. The model is based on the Black Sphere (BS) cross section formula for proton + nucleus reactions and extended to nucleus + nucleus reactions. However, the BS model requires that the de Broglie wavelength of the proton is considerably smaller than the nuclear size, and the BS model therefore breaks down below around 100 MeV/n. In addition, the Coulomb repulsion causes resonance features and a sharp increase at energies below 100 MeV/n, at which an energy dependent transparency parameter and the influence of the Fermi motion and Coulomb effects should be included. To solve the limitations of the BS model at low energies and to create a general purpose total reaction cross section model which can also be used for reactions with projectile energies below around 100 MeV/n, the BS model has been connected to the parameterization developed by Tripathi et al. [108, 109, 113]. The Hybrid Kurotama model has been extensively benchmarked against experimental total reaction cross section data, and an overall better agreement has been found than for earlier published models. The model is used in the PHITS transport code .
3.2.3 Partial (Non-Differential) Cross Sections
In addition to total reaction cross sections, models for partial (elemental and isotopic) cross sections are also required for calculation of the production of different fragment species.
The total reaction cross section model shown in Figure 14 is the parameterization by Tripathi et al. , and modified by Horst et al. [42, 43], based on recent experimental cross sections. These modifications result in a significant improvement of the agreement between calculated and measured
3.2.4 Double Differential Cross Sections
Heavy ion production isotopic double differential cross sections can be modeled with relatively simple physical ideas because the ions are mostly produced from simple abrasion–ablation processes, and because the ions are heavy, they proceed mostly in the forward direction. The abrasion–ablation model  assumes that the dominant source of heavy ion production is from the incident projectile. On the other hand, neutron, proton, and composite light ions are scattered at large angles because they are relatively light. Also, composite light ions have a complicated production mechanism, often involving not only abrasion–ablation but also coalescence.
The general picture for high-energy heavy ion projectile collisions is the following: The projectile and target nuclei collide and form a central fireball overlap region, together with deformed and excited projectile and target pre-fragments, which decay into lighter fragments. The fireball is very hot and decays quickly with the emission of pions, other mesons, and baryons such as neutrons, protons, and other particles. The cooler excited projectile and target pre-fragments decay more slowly, generally by emitting nucleons, which may coalesce into light ions. There are therefore three different sources of particles, the projectile and target pre-fragments and the central fireball. Each of these three sources can produce the same type of particle that eventually reaches detectors in the lab frame (or an astronaut’s body in a spacecraft). Because the fireball is very hot, light ion fragments cannot survive and will be broken up into baryons and mesons. However, what happens when the fireball cools? The answer is similar to what happened in the very early Universe. After a rapid period of inflation, the Universe started as a quark-gluon plasma, which then cooled and formed hadrons such as pions, kaons, other mesons, nucleons, deltas, and other baryons. After further cooling the baryons decayed to nucleons, which later coalesced into light ions: H, He, and some Li. Then, the density dropped too rapidly to form heavier ions, which were made much later in stellar interiors, supernovae , and binary neutron star mergers . As the Universe cooled further, electrons and light ions coalesced into atoms. Aspects of the nuclear fireball cooling are similar to the early Universe scenario. As the fireball cools and decays and emits neutrons and protons, these are cool enough to coalesce into the light ion isotopes of H and He (and also some Li). As with the early Universe, the fireball density drops very rapidly, and nucleons are unable to coalesce to form heavier ions, which come from projectile and target pre-fragments. Of course, the projectile and target pre-fragments also emit nucleons (neutrons and protons), and these can also coalesce. Thus, light ions are produced from nucleon coalescence [12, 13, 119] of all three sources: projectile, fireball, and target. This is in contrast to the simpler mechanism of abrasion–ablation of heavy ions, where the dominant source is the incident projectile. Another complicating factor for neutron, proton, and composite light ion production is that there are two production mechanisms from each of the three sources, namely, direct production vs. thermal emission of nucleons with subsequent coalescence.
Despite all these complications, models for neutron, proton, and composite light ion production have been recently developed [12, 13, 119, 120] and compared to a variety of data. DDFRG is a double differential fragmentation model based on Lorentzian parameterizations of the projectile, fireball, and target sources including direct and thermal/coalescence production. Results for helium projectiles producing fragments at 0
• Experimental double differential cross section results  for light ion production from He projectiles need to be confirmed, including angles 0
• SHIELD double differential cross section results for light ion production from He projectiles need to be confirmed by comparing to other cross section models.
Other approaches to nuclear cross section modeling are under development. A deterministic Serber nuclear model was developed for use in the radiation transport code, HZETRN, with the aim of improving nucleon spectral and angular distributions. Various implementations of the Serber nuclear models have been employed successfully in Monte Carlo codes for internuclear cascade processes. The underlying theory describes the propagation of an incident nucleon through target media modeled with a characteristic density and potential well. The target nucleus is composed of nucleons that are bound within a Fermi sea. When a projectile nucleon strikes a target nucleon, the kinetic energy of the struck nucleon must exceed the Fermi energy to escape the target. Both the spectra of the projectile nucleon and the recoil nucleons are tracked. The primary nucleon is assumed to traverse in the straight-forward direction, whereas the recoil spectra are assumed to have an angular dependence . This model is being extended to nucleus–nucleus reactions for the evaluation of nucleon double differential and spectral distributions. Primary nucleons and nucleons resulting from internuclear processes, including abrasion and de-excitation, are among the most consequential reactions for the projection of radiation risk. Additional nucleon and light ion fragmentation data for space radiation relevant reactions are needed to validate the nuclear models. The current process of validating models (when data are not available) is to compare transport code results in thin target simulations, which ultimately is a comparison of the different cross section models. Ideally, the nuclear cross section models would be compared directly to nuclear data, but additional experiments are needed to support these efforts and is the subject of the current work.
4 Review of Accelerators
The aim of this section is to summarize the availability of accelerators for helium ion beams. The ideal accelerator facility for the intended cross section measurements would provide helium ions in an energy range from typically 50 MeV/n up to 50 GeV/n. These conditions can only be met by large-scale research facilities like GSI/FAIR, the Joint Institute for Nuclear Research (JINR, Dubna), and the NASA Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory (BNL). However, since beam time at these accelerators is relatively expensive and has to be planned on a long time scale, it might be convenient to supplement the use of high-energy accelerators with medium-energy accelerators, which are more readily available. Especially, medical facilities often provide experimental beam during the night after finishing quality assurance. Thus, medium to high energies (100–800 MeV/n) could be delivered by some medical facilities for ion beam therapy like the HIMAC accelerator in Chiba or the HIT facility in Heidelberg. In some cases, low-energy facilities, such as the KVI in Groningen, could be a cost effective addition for the helium cross-section measurement program. However, in order to meet the requirements for space radiation research and ion beam therapy, a minimum energy of 50 MeV/n is specified that should be reached by the accelerator. This limit defines a subset of existing accelerators that will be presented for this study. Table 3 comprises the eligible accelerators corresponding to the above mentioned requirements.
GSI/FAIR. GSI Helmholtzzentrum für Schwerionenforschung plays a special role among the facilities listed in Table 3 because it fulfills all requirements for a comprehensive cross section measurement program. During FAIR‐phase‐0, the current project phase until completion of the SIS100 synchrotron cross section, experiments can be conducted at different irradiation sites with different profiles. Cave M and Cave A, which are used by the GSI biophysics group, can accommodate compact experiments such as the FOOT  experiment. Cave C provides space for experiments with larger detectors , while the fragment separator (FRS)  allows high precision charge-changing cross-section and double differential measurements at small angles (
NSRL/BNL. NSRL is a multidisciplinary center for space radiation research funded by NASA and located at the Brookhaven National Laboratory (BNL). Operational since 2003, the scope of NSRL is to provide ion beams in support of NASA programs in radiobiology, physics, and engineering . Recently, it has also been recognized as the only facility in the United States currently capable of contributing to heavy ion therapy research. The facility provides a large room (10 m long from exit window to beam dump), well suited for time of flight (TOF) and double differential cross section measurements .
Nuclotron. The Dubna Nuclotron was the world’s first superconducting synchrotron, built by the Joint Institute for Nuclear Research (JINR), Russia. In the past, the accelerator was used to extract ion beams with Z = 1–36 up to energies of 2.2 GeV/n. As part of the upgrade for the NICA project , the beam energy can be increased up to 4.5 GeV/n in future. The nuclotron facility comprises various large experimental rooms and would enable the full spectrum of cross section measurements with helium beams.
Clinical facilities: HIT, HIMAC, MedAustron, and CNAO. Clinical facilities with medium to high energy can complement the measurements at the large-scale research facilities and can decrease the costs and effort for the whole cross section program. The Heavy Ion Medial Accelerator in Chiba (HIMAC) in Japan is part of the National Institute of Radiological Sciences (NIRS) and has been operational since 1993 as a medical facility for treating cancer patient with protons and carbon ions. The center has also served as a multi-user facility for medical, biological, and physics research. It can accelerate all ions between
AGOR/KVI-CART and LNS. In case of difficulty obtaining helium beams at large-scale and medical facilities, the AGOR cyclotron facility (KVI-Centre, Groningen) could provide
5 FOOT Program
5.1 Description of Program
FOOT (FragmentatiOn Of Target) [140–142] is an experiment funded by the INFN (Istituto Nazionale di Fisica Nucleare, Italy), aiming at the measurement of double differential cross sections for the production of charged particles in nuclear fragmentation which are of interest for medicine (hadron therapy) and radioprotection in space missions. The experiment has been originally designed with the main goal of investigating target fragmentation in proton therapy by means of an inverse kinematic approach, using beams of
The accuracy goal of FOOT is to identify charge and mass of the produced fragments with an accuracy of 3% and 5%, respectively, and to measure their energy spectra with a resolution of 2 MeV. Taking into account these goals, the idea is to realize a “portable” experimental setup in order to operate it in different facilities and to have some flexibility to optimize its configuration for different energy ranges. The detector design has been guided by Monte Carlo simulations, based on the FLUKA code [143, 144]. It shows that in the whole energy range under consideration, light (Z
FIGURE 16. Cross section differential in energy, integrated in the forward hemisphere, for inclusive production of secondaries of
FIGURE 17. Cross section differential in solid angle (forward hemisphere), integrated in energy, for inclusive production of secondaries of
On the basis of the experimental goals summarized above, the FOOT experiment has been conceived considering two complementary experimental configurations:
This approach of employing two complementary detection techniques is particularly useful in the measurement of
(1) Upstream/target region: A thin plastic scintillator counter provides the start signal of the TOF and the trigger system, and downstream, a drift chamber operates as a beam monitor, tracking the direction and the position of the beam. The target is positioned beyond the beam monitor.
(2) Magnetic region: It is composed of three stations of pixel and strip detectors allocated between and downstream of the magnets providing the vertex reconstruction and the initial tracking of the produced fragments; two permanent dipole magnets supply the magnetic field (up to 1.4 T).
(3) Identification region: It is the distal part of the detector, located at least 1 m away from the target (more for higher energies). It is composed of two orthogonal planes of plastic scintillator rods, providing the stop of the TOF and the measurement of the energy loss. A BGO calorimeter provides the fragment kinetic energy measurements.
FIGURE 18. Pictorial view of the FOOT electronic apparatus as obtained from the FLUKA graphical interface.
The TOF, measured by the start counter and the scintillator, has an estimated resolution at the level of 70–100 ps. The silicon detectors, in the magnetic region, are able to perform momentum measurements with an expected resolution of about 5%, while the resolution supplied by the scintillator and by the calorimeter is about 3 and 2%, respectively, in the measurement of the energy loss and kinetic energy. The emulsion spectrometer is built using Emulsion Cloud Chamber (ECC) technology, alternating nuclear emulsion films with passive material . A sketch of the ECC is shown in Figure 19.
The ECC acts as a micrometric tracking device, ionization chamber, and a spectrometer for isotope separation. The nuclear emulsion films consist of two 50-μm thick sensitive emulsion layers deposited on both sides of a plastic base, 200 μm thick, resulting in a total thickness of 300 μm. AgBr crystals, dispersed in a gelatine matrix, are sensitive to ionizing particles and record their trajectory acting as latent image centers. A chemical process of development produces the latent image as silver grains recorded as dark pixels by an optical microscope. A dedicated software recognizes aligned clusters of dark pixels producing a track related to the path of the charged particle. The present design of the experiment does not allow for an efficient measurement of neutron production, which however is considered a relevant issue in radioprotection for space missions. Different ideas to extend the capability of FOOT to neutron detection are under study.
5.2 Present Status of the Experiment
Data have been taken using the ECC setup at GSI, in 2019 with O ions at 200 and 400 MeV/n on C and C
6 Future Recommendations
6.1.1 Total Reaction Cross Sections
Total reaction cross section data for
Very low energy data are missing. They are important for modeling the energy dependence of the cross sections below and at the Coulomb barrier, which seems to be shifted toward to high energies for very heavy targets in the currently used parameterizations (see Figure 20). An appropriate modeling of the Coulomb barrier is important to accurately predict nuclear reaction thresholds.
FIGURE 20. Experimental data of total reaction cross sections for
6.1.2 Light Ion Production
Given the sparseness of the present data set and the need for a uniform set of data covering all energies appropriate to ion therapy and space radiation, new set of inclusive, isotopic, double differential cross sections should be measured for a complete set of neutron and light ion fragments for the reactions
6.1.3 Neutron Production
Given the limited set of direct measurements taken to date, there are a number of recommendations for additional neutron production data. Data are needed for He energies above 230 MeV/n, at all angles, especially angles beyond the existing measurements at 110
The ultimate use of new cross section measurements is the development of accurate theoretical cross section models that can be used in modern transport codes. As mentioned previously in the text, isotopic production double differential cross section will give more detailed information about the nuclear reactions, so measurements of these cross sections are important to verify the theoretical models. Some models have been developed previously, but often they are compared to only a limited data set. Ion therapy and space radiation applications require models to be accurate for a wide range of projectiles, energies, and targets. Therefore, a cross section modeling program proceeding in parallel with the measurement program needs to be initiated. The cross section models should be compared to all available cross section data, including previously measured total and single differential cross sections.
A special emphasis will be given to modeling the high energy
Some modeling approaches for
Recent experiments pointed out problems with dose calculation in the beam halo of
Although double differential cross section models are preferred for comparisons to experimental data, accurate total reaction and fragmentation cross sections are also needed by radiation transport codes for prediction of particle fluences. Moreover, total fragmentation cross section models can be used for normalizing and anchoring parametric models, such as DDFRG [12, 13, 119]. Werneth et al. [146–150] developed a relativistic (kinematics) multiple scattering theory (RMST) for the prediction of reaction, elastic, total, and elastic differential cross sections for space radiation–relevant reactions. The fundamental nuclear constituents of the MST are defined as the nucleons, and the quark structure of individual nucleons is not considered. Consequently, the interaction of nucleon–nucleus and nucleus–nucleus reaction is modeled as the sum of nucleon–nucleon interactions, which may be parameterized to free nucleon–nucleon transition amplitudes. Elastic differential, total, reaction, and elastic cross sections may be found by solving the Lippmann–Schwinger (LS) equation or with a high-energy, small angle approximation known as the Eikonal approximation. Relativistic kinematics are easily incorporated into the momentum–space formulation of the LS equation [146, 147], and a large shift toward small angles and with larger magnitude is observed in the elastic differential cross sections. Another interesting result is that relativistic kinematic effects will depend on both energy and relative mass of the projectile and target . A comprehensive validation effort  showed that the relativistic three dimensional LS model (LS3D) agrees best with experimental data. Additional model improvements led to LS3D predictions of the reaction cross sections that were of the same fidelity to data as the Tripathi parameterizations . In order to improve computational efficiency, a momentum–space formulation of the Eikonal approximation was developed.
The relativistic abrasion–ablation de-excitation fragmentation (RAADFRG) model has been formulated for fragments produced from nucleus–nucleus collisions by coupling the highly efficient Eikonal model for nuclear abrasion to a de-excitation model described by the Weisskopf–Ewing mechanism. Relativistic kinematics may be incorporated by renormalizing the sum of the Eikonal abrasion cross sections to the reaction cross section produced from the LS3D theory. As the projectile nucleus collides with a target nucleus, nucleons are sheared away from the projectile and target during a very short time scale, leaving the pre-fragment (remaining projectile nuclear constituents) in an excitation state. The pre-fragment is assigned an excitation energy, which may include multiple scattering and energy depositions from nucleon–nucleon collisions. After a much longer time scale, the excited pre-fragment will emit light ions and neutrons with probabilities described by the Weisskopf–Ewing formalism until all available excitation energy is exhausted. Nuclear structure is manifested in the fragmentation cross sections with proper choice of the nuclear partition function and excitation energy model. Furthermore, RAADFRG may be used to anchor parametric double differential cross section models such as DDFRG [12, 13, 119]. The dearth of experimental light ion fragmentation data makes it difficult to fully validate the RAADFRG model and other nuclear models that are needed for space radiation applications.
Finally, another modeling activity required in future is to confirm the SHIELD double differential cross section results for light ion production from He projectiles, shown in Figure 15. Comparisons need to be made with other cross section models.
7 Summary and Conclusion
Helium projectile double differential cross sections for the production of neutrons and light ions are of great importance to space radiation and ion therapy studies. However, transport codes and cross section models display significant problems when compared with limited data on both thick and thin targets. Also, there is a very significant lack of high-quality experimental data available that could resolve these problems. The following recommendations are made:
• A new set of inclusive, isotopic, double differential cross sections should be measured for a complete set of neutron and light ion fragments for the reactions
• for projectile kinetic energies ranging over 50 MeV/n–50 GeV/n and fragment angles ranging over 0
• Those experiments should be accompanied by measurements of total reaction and single differential fragment production cross sections for
• A parallel program of cross section model development needs to be initiated in order to develop accurate models for these new measurements.
• A parallel program of transport code validation needs to be undertaken.
The present work has focused on helium projectiles because they represent the highest priority. Nevertheless, other projectiles, such as C, O, Si, and Fe are important for both ion therapy and space radiation, as discussed in Section 1.3. A program similar to that described above would be very worthwhile for these other projectiles, as summarized by Eq. 1.
All authors contributed to the planning, ideas, debating, writing, and editing of the manuscript.
Conflict of Interest
Author CZ was employed by the company “Leidos Innovations Corporation”. Authors MG and LB were employed by the company “Thales Alenia Space”.
The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We wish to thank Laura Bagnale (Federico II University, Naples, Italy) for help with data analysis and collection, and Dr. Steve Smith (NASA Langley) for reviewing the manuscript. Bocchini, Giraudo, and Santin were partially supported by the European Space Agency under contract Number 4000125785 (“ROSSINI 3”). Experiments with He ions are performed in Cave A at GSI in the framework of FAIR Phase-0 supported by the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt (Germany).
1Spokesperson: Vincenzo Patera (Universita’ di Roma “Sapienza”, Roma, Italy).
2The very first ion collision experiments  were carried out more than 100 years ago by Ernest Rutherford, who scattered helium (He) projectiles (alpha particles) from gold (Au) targets. Of course, no accelerators were available, and the helium projectiles were produced from the radioactive decay of radium. The helium projectile kinetic energy was only 5 MeV (about 1 MeV/n) and the scattering was elastic (no fragments could be produced), but some of the helium projectiles suffered large deflections from the incident direction, which indicated scattering from a tiny atomic core. This was the discovery of the atomic nucleus, with a size of order 10 m. Helium projectiles are also the subject of the present work.
3An exclusive measurement would mean that
4He(Z = 2), C(Z = 6), O(Z = 8), Si(Z = 14), Fe(Z = 26).
5In this particular case, the observed discrepancies did not contribute significantly to dose-equivalent, but improvements would yield better agreement with MSL-RAD.
6Other double differential cross sections, such as Lorentz-invariant double differential cross sections or double differential cross sections written in terms of momentum, transverse momentum, etc., are equivalent to
7Unless specified otherwise, standard particle physics units are used in the text, with the speed of light defined as unity,
9Ne(Z = 10), Ar(Z = 18).
10Except for proton + target
14Helium projectiles are absent from the geomagnetically trapped radiation environment. They are present in solar particle events , but are of insufficient flux to make any significant contribution to the space radiation field.
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Keywords: helium projectile cross section measurements, space radiation cross sections, ion therapy cross sections, helium projectile ion therapy, helium projectile space radiation
Citation: Norbury JW, Battistoni G, Besuglow J, Bocchini L, Boscolo D, Botvina A, Clowdsley M, de Wet W, Durante M, Giraudo M, Haberer T, Heilbronn L, Horst F, Krämer M, La Tessa C, Luoni F, Mairani A, Muraro S, Norman RB, Patera V, Santin G, Schuy C, Sihver L, Slaba TC, Sobolevsky N, Topi A, Weber U, Werneth CM and Zeitlin C (2020) Are Further Cross Section Measurements Necessary for Space Radiation Protection or Ion Therapy Applications? Helium Projectiles. Front. Phys. 8:565954. doi: 10.3389/fphy.2020.565954
Received: 26 May 2020; Accepted: 21 August 2020;
Published: 30 November 2020.
Edited by:Federico Giove, Centro Fermi - Museo storico della fisica e Centro studi e ricerche Enrico Fermi, Italy
Reviewed by:Loredana G. Marcu, University of Oradea, Romania
Giacomo Cuttone, Laboratori Nazionali del Sud (INFN), Italy
Copyright © 2020 Norbury, Battistoni, Besuglow, Bocchini, Boscolo, Botvina, Clowdsley, de Wet, Durante, Giraudo, Haberer, Heilbronn, Horst, Kraemer, La Tessa, Luoni, Mairani, Muraro, Norman, Patera, Santin, Schuy, Sihver, Slaba, Sobolevsky, Topi, Weber, Werneth and Zeitlin. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: John W. Norbury, firstname.lastname@example.org