Quasi-free proton-proton scattering in light nuclei at 460 MeV

Tyrén, H.

doi:10.1016/0375-9474(68)90268-6

Cited by 6 publications

(7 citation statements)

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“…However, the binding energy and most likely nuclear recoil momentum (4 parameters) are known from (p,2p) experiments e.g. [23], so we can then proceed as in the (p,p) case.…”

Section: Size Of the Halomentioning

confidence: 99%

“…Focusing for the moment on the (p,2p) reaction, by measuring the total kinetic energy of the outgoing protons one can measure the binding energy of protons in each shell, and from their angular distributions one can infer the momentum distributions. See [2] for more details and [23] for the best (p,2p) measurement on O.…”

Section: Incoherent Reactionsmentioning

confidence: 99%

“…Fig. 3 is a plot of the results for reactions with parameters given in the caption and justified by [2,23]. Because these only represent most likely values, and the core itself has some size, we must imagine a fairly broad band of maximum radii.…”

Section: Size Of the Halomentioning

confidence: 99%

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On the nuclear halo of a proton pencil beam stopping in water

et al. 2015

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The dose distribution of a proton beam stopping in water has components due to basic physics and may have others from beam contamination. We propose the concise terms core for the primary beam, halo (cf. Pedroni et al. [1]) for the low dose region from charged secondaries, aura for the low dose region from neutrals, and spray for beam contamination.We have measured the dose distribution in a water tank at 177 MeV under conditions where spray, therefore radial asymmetry, is negligible. We used an ADCL calibrated thimble chamber and a Faraday cup calibrated integral beam monitor so as to obtain immediately the absolute dose per proton. We took depth scans at fixed distances from the beam centroid rather than radial scans at fixed depths. That minimizes the signal range for each scan and better reveals the structure of the core and halo.Transitions from core to halo to aura are already discernible in the raw data. The halo has components attributable to coherent and incoherent nuclear reactions. Due to elastic and inelastic scattering by the nuclear force, the Bragg peak persists to radii larger than can be accounted for by Molière single scattering. The radius of the incoherent component, a dose bump around midrange, agrees with the kinematics of knockout reactions.We have fitted the data in two ways. The first is algebraic or model dependent (MD) as far as possible, and has 25 parameters. The second, using 2D cubic spline regression, is model independent (MI). Optimal parameterization for treatment planning will probably be a hybrid of the two, and will of course require measurements at several incident energies.The MD fit to the core term resembles that of the PSI group [1], which has been widely emulated. However, we replace their T (w), a mass stopping power which mixes electromagnetic (EM) and nuclear effects, with one that is purely EM, arguing that protons that do not undergo hard single scatters continue to lose energy according to the Beth-Bloch formula. If that is correct, it is no longer necessary to measure T (w), and the dominant role played by the 'Bragg peak chamber' (BPW) vanishes.For mathematical and other details we will refer to [2], a long technical report of this project.

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“…However, the binding energy and most likely nuclear recoil momentum (4 parameters) are known from (p,2p) experiments e.g. [23], so we can then proceed as in the (p,p) case.…”

Section: Size Of the Halomentioning

confidence: 99%

Section: Incoherent Reactionsmentioning

confidence: 99%

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On the nuclear halo of a proton pencil beam stopping in water

et al. 2015

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“…Quasi-elastic p-p scattering 16 O(p,2p) 15 N is nonelastic. Kinematics resemble scattering on free hydrogen, somewhat modified by the binding energy E B required to extract the target proton and by the initial momentum of the target proton [45]. Quasi-elastic protonneutron 16 O(p,pn) 15 O scattering is similar except, of course, that one secondary is neutral and travels much farther on average.…”

Section: Contributing Reactionsmentioning

confidence: 99%

Radiotherapy Proton Interactions in Matter

Gottschalk¹

2018

Preprint

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Radiotherapy protons interact with matter in three ways. Multiple collisions with atomic electrons cause them to lose energy and eventually stop. Multiple collisions with atomic nuclei cause them to scatter by a few degrees. Occasional hard scatters by nuclei or their constituents throw dose out to large distances from the beam. Unlike the first two processes, these hard scatters or 'nuclear interactions' do not obey any simple theory, but they are rare enough to be treated as a correction. We discuss the three interactions (stopping, multiple Coulomb scattering, and hard scatters) in turn.We begin, however, with the fundamental formula relating dose (energy deposited per unit mass) to fluence (areal density of protons) and mass stopping power (their rate of energy loss).Concerning stopping, we define range experimentally, noting that the clinical and physics definitions are different. We present in simplified form the 'Bethe-Bloch' theory of energy loss, how it leads to range-energy tables, how to interpolate these, and two simple 2-parameter approximations to the range-energy relation. Finally we discuss range straggling, the fact that protons in a monoenergetic beam stop at slightly different depths.Concerning multiple Coulomb scattering (MCS), we present a short reading list and point out some incorrect or unhelpful aspects of the standard literature. We outline a simplified form of Molière theory, the accepted theory for protons and correct to 1% as far as is known. We explain the Gaussian approximation to Molière theory, which suffices for almost all radiotherapy calculations, and discuss Highland's formula, vastly simpler than the full theory. We discuss scattering power, an approximation to Molière theory required by transport calculations.We treat hard scatters by focusing on the 'nuclear halo' acquired by a bundle of protons (a 'pencil beam') as it stops in matter. We emphasize recent experimental results and their implications for the most efficient parameterization of the halo.All three interactions combine in the Bragg curve, the depth-dose distribution of a monoenergetic beam stopping in water and the signature property of charged (as distinct from neutral) radiotherapy beams. For computation, the Bragg curve should be converted to an effective mass stopping power. We discuss two limiting cases.Looking ahead, we sketch how stopping theory and MCS combine in 'Fermi-Eyges' transport theory when, as is normally the case, both processes occur at once. We present three very general properties of beams spreading in a homogeneous medium, found by Preston and Koehler at the dawn of proton radiotherapy. Finally, we sketch a dose algorithm which outperforms those in current use and may ultimately prove useful.Five appendices contain supporting material: acronyms and symbols, a review of 1D and 2D Gaussians, relativistic single particle kinfematics and finally, a few problems that occur in beam line design.

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“…Using the energy level schemes as reported byLauritsen and 12 Ajzenberg-Selove (29,30) for the neighboring nuclei of C , one obtains the positions of the bound proton and neutron states as given inFigure 1. The proton Is^yg state at -34 neV was taken from (p, 2p) and (e, e'p) data(31,32,33). The position of the neutron Is^yg state at -37 MeV is deduced from the energy separation of the Ip -Id states In the bound neutron spectrum.…”

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confidence: 99%

Soluble model calculations of the continuum structure of closed-shell nuclei in the eigenchannel reaction theory

Gieraltowski

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Quasi-free proton-proton scattering in light nuclei at 460 MeV

Cited by 6 publications

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On the nuclear halo of a proton pencil beam stopping in water

On the nuclear halo of a proton pencil beam stopping in water

Radiotherapy Proton Interactions in Matter

Soluble model calculations of the continuum structure of closed-shell nuclei in the eigenchannel reaction theory

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