Scattering Of Protons Research Articles

Erratum to: Amplitude of Scattering of Protons on the Bounded Nuclear Nucleons from Analysis of the Proton-Nucleus Scattering

Erratum to: Amplitude of Scattering of Protons on the Bounded Nuclear Nucleons from Analysis of the Proton-Nucleus Scattering

The Neutron Skin-Thickness of 208Pb Determined by Electron and Proton Scattering

Abstract Electron as well as proton elastic scattering is not able to determine the point proton and point neutron densities, $\rho _\tau (r), (\tau =p,n)$, separately. If both scatterings are analyzed consistently, those densities would be determined uniquely, since the two densities are observed by different combinations from each other. Previous experiments have not provided $\rho _\tau (r)$ uniquely, but the values of the mean square radii of $\rho _p(r)$, $\langle \, r^2\, \rangle _p$, and of $\rho _n(r)$, $\langle \, r^2\, \rangle _n$, are shown to be determined consistently through the fourth moment of the observed charge density, $\langle \, r^4\, \rangle _c$, in 208Pb. The previous analyses of $(\gamma , \pi ^0)$ and $\bar{p}$-nucleus obtained a similar value of $\langle \, r^2\, \rangle _n$, but they do not yield the experimental value of $\langle \, r^4\, \rangle _c$ observed in electron scattering.

Amplitude of Scattering of Protons on the Bounded Nuclear Nucleons from Analysis of the Proton-Nucleus Scattering

Amplitude of Scattering of Protons on the Bounded Nuclear Nucleons from Analysis of the Proton-Nucleus Scattering

Low-Energy Theorems for Neutron–Proton Scattering in χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi $$\\end{document}EFT Using a Perturbative Power Counting

Low-energy theorems (LETs) for effective-range parameters in nucleon-nucleon scattering encode properties of the long-range part of the nuclear force. We compute LETs for S-wave neutron–proton scattering using chiral effective field theory with a modified version of Weinberg power counting. Corrections to the leading order amplitude are included in distorted-wave perturbation theory and we incorporate contributions up to the third order in the power counting. We find that LETs in the 1S0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^1S_0$$\\end{document} and 3S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3S_1$$\\end{document} partial waves agree well with empirical effective-range parameters. At the same time, phase shifts up to laboratory scattering energies of about 100 MeV can be reproduced. We show that it is important to consider the pion mass splitting in the one-pion exchange potential in the 1S0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^1S_0$$\\end{document} partial wave while the effect is negligible in the 3S1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^3S_1$$\\end{document} partial wave. We conclude that pion exchanges, as treated in this power counting, accurately describe the long-range part of the S-wave nuclear interaction.

The Impact of Dose Calibration Point Differences Between the Treatment Plan and Patient-specific Quality Assurance in Passive Scattering Proton Beam Therapy.

Passive scattering proton beam therapy (PSPT) is performed by taking actual measurements of all pre-designated fields in a treatment plan followed by appropriate adjustments to the prescribed dose. For this reason, it is necessary to ensure precision management of the measurements (patient-specific calibration) in the administration of a planned dose. Therefore, this study investigated the impact on dose distribution in treatment planning when the patient calibration point differs from the normalized point in a treatment plan. A total of 16 cases were selected, where the patient calibration point and normalized point did not match, and the normalized point used in the treatment plan was changed to the patient calibration point using a treatment planning system (VQA ver. 2.01, HITACHI). At this point, the displacement of the relative dose at the isocenter was estimated as an error owing to the difference compared to the patient calibration point. Overall, the error was within the range of ±1.5%, with the exception of orbit cases. Calibrated points also tended to be lower than the normalized points in the treatment plan. In terms of treatment sites, a greater deviation was observed for head cases. Cases with a large deviation in sites other than the head were attributed to poor flatness within the radiation field owing to a narrower opening of the patient collimator. Dose measurement errors in PSPT due to differing calibration points were generally within ±1.5%, with higher deviations observed in head treatments because of complex structures and narrow collimator openings. A γ analysis for significant deviations showed a 98.7% passing rate, suggesting limited overall impact. It is important to select stable calibration points in dosimetry to ensure high precision in dose administration, particularly in complex treatment areas.

Optical-Model Analysis of the Elastic Scattering of Protons on a 7Li Nucleus, Including the Resonant Contribution

Optical-Model Analysis of the Elastic Scattering of Protons on a 7Li Nucleus, Including the Resonant Contribution

Refinement of the Optical Potential Parameters of the Elastic Scattering of Protons on a 6Li Nucleus

Refinement of the Optical Potential Parameters of the Elastic Scattering of Protons on a 6Li Nucleus

Optical-Model Analysis of the Elastic Scattering of Protons on a 9Be Nucleus, Including the Resonant Contribution

Optical-Model Analysis of the Elastic Scattering of Protons on a 9Be Nucleus, Including the Resonant Contribution

Abstract P1-10-08: Incidence of rib fracture following treatment with proton therapy for breast cancer

Abstract Purpose: To determine the rate of rib fracture in a cohort of patients with breast cancer treated with proton therapy and enrolled on a prospective registry. In series investigating photon therapy for breast cancer, the rib fracture rate ranges from 0.3-13% Methods: From a prospective database, we identified patients treated with proton therapy for breast cancer at our institution between January 1, 2012 and December 31, 2020. Clinical and dosimetric data was extracted from the electronic medical record. The cumulative incidence method assessed rib fracture rate; the Fine-Gray test statistic assessed prognostic significance select variables. Results: 225 patients were identified, 223 women and 2 men. Median age at the time of radiation was 57.8 years (range, 25 – 87). 26% of patients were black, 69% white and 5% were other races or race not disclosed. 5% were Hispanic. 74% of patients had left-sided breast cancer, 5% bilateral, and 21% right-sided. DEXA scan was normal in 20%, showed osteopenia in 34%, osteoporosis in 6%, and not performed in 40%. 57% of patients received antiendocrine therapy with an aromatase inhibitor. For 16% of patients, the breast +/- internal mammary nodes (IMN) were treated, while 32% underwent proton therapy to treat the breast and comprehensive regional lymphatics. 1% of patients had chest wall +/- IMN treated, while 51% underwent proton therapy to treat the chest wall and comprehensive regional lymphatics. 41% of patients were treated with passive scatter proton therapy (n=92); 52% of these had mastectomy. 58% of patients received treatment with pencil beam scanning (PBS) proton therapy (n=131); 53% of these had mastectomy. A combination of passive scatter and PBS was used for 2 patients (1%). 85% of patients received a boost. Median follow-up was 3.1 years (range, 0.2 – 9.1). 97% of patients had > 12 months of follow-up. The 3 year cumulative incidence of in-field rib fracture was 3.7% (95%CI: 1.6%-7.1%). In total, 8 patients developed in-field rib fractures, one symptomatic and 7 identified incidentally on surveillance imaging, for a 0.4% rate of symptomatic rib fracture. Median time from completion of radiation to identification of rib fracture was 1.8 years (range, 0.4-7.4 years). Rib fractures occurred within 2.2 years from radiotherapy completion for seven of the eight patients who experienced this side effect. Three patients developed rib fractures outside of the radiation field, for a cumulative incidence of out-of-field rib fracture of 0.9% (95%CI: 0.2-3.0%). No variables were associated with rib fracture on univariate analysis. Of those with in-field rib fractures, 3 had low and 3 had normal bone density while 2 had not undergone testing; of those with out-of-field rib fractures, 2 had osteopenia and 1 did not have testing. Conclusions: Although a proton beam has higher biological dose deposition at end-of-range than the assumed constant RBE=1.1, the 3 year rate of any in-field rib fractures in our series remains low at 3.7%, with a 0.4% rate of symptomatic rib fracture. Contouring ribs as an OAR and establishing a dose constraint warrants further investigation as a means to maintaining a low rate of rib fracture with proton therapy. Citation Format: Julie Bradley, Xiaoying Liang, Raymond Mailhot Vega, Chunbo Liu, Eric Brooks, Teena Burchianti, Emma Viviers, Roi Dagan, Oluwadamilola Oladeru, Christopher Morris, Nancy Mendenhall. Incidence of rib fracture following treatment with proton therapy for breast cancer [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P1-10-08.

Clinical outcomes and toxicities of 100 patients treated with proton therapy for chordoma on the proton collaborative group prospective registry

BackgroundWe present efficacy and toxicity outcomes among patients with chordoma treated on the Proton Collaborative Group prospective registry. MethodsConsecutive chordoma patients treated between 2010–2018 were evaluated. One hundred fifty patients were identified, 100 had adequate follow-up information. Locations included base of skull (61%), spine (23%), and sacrum (16%). Patients had a performance status of ECOG 0–1 (82%) and median age of 58 years. Eighty-five percent of patients underwent surgical resection. The median proton RT dose was 74 Gy (RBE) (range 21–86 Gy (RBE)) using passive scatter proton RT (PS-PBT) (13%), uniform scanning proton RT (US-PBT) (54%) and pencil beam scanning proton RT (PBS-PBT) (33%). Rates of local control (LC), progression-free survival (PFS), overall survival (OS) and acute and late toxicities were assessed. Results2/3-year LC, PFS, and OS rates are 97%/94%, 89%/74%, and 89%/83%, respectively. LC did not differ based on surgical resection (p = 0.61), though this is likely limited by most patients having undergone a prior resection. Eight patients experienced acute grade 3 toxicities, most commonly pain (n = 3), radiation dermatitis (n = 2), fatigue (n = 1), insomnia (n = 1) and dizziness (n = 1). No grade ≥ 4 acute toxicities were reported. No grade ≥ 3 late toxicities were reported, and most common grade 2 toxicities were fatigue (n = 5), headache (n = 2), CNS necrosis (n = 1), and pain (n = 1). ConclusionsIn our series, PBT achieved excellent safety and efficacy outcomes with very low rates of treatment failure. CNS necrosis is exceedingly low (<1%) despite the high doses of PBT delivered. Further maturation of data and larger patient numbers are necessary to optimize therapy in chordoma.

Data on the Neutron–Proton Scattering Length from the $$nd$$-Breakup Reaction at Low Energies

Data on the Neutron–Proton Scattering Length from the $$nd$$-Breakup Reaction at Low Energies

Model-independent Odderon Results Based on TOTEM data on Elastic Proton–Proton Scattering at 8 TeV

Model-independent Odderon Results Based on TOTEM data on Elastic Proton–Proton Scattering at 8 TeV

Analysis of Early Outcomes of Pencil Beam Proton Therapy Compared with Passive Scattering Proton Therapy for Clival Chordoma

To assess the early outcomes of the following 2 types of proton therapy: passive scattering proton therapy (PSPT) and pencil beam proton therapy (PBPT). The consecutive patients who had surgery in our facility were retrospectively reviewed. Thirty-two patients were identified (PBPT 22 patients [69%]). The mean (±standard deviation [SD]) tumor size was 3.8±1.8cm, and the most common location was the upper clivus (41%). Four cases (13%) were revision surgeries referred from elsewhere, and 2 cases underwent additional surgery elsewhere to achieve near-total resection before radiation. The cerebrospinal fluid leak occurred in 3 patients (9%). The mean (±SD) prescribed dose of PSPT and PBPT was 74±3Gy and 72±3Gy, respectively (P= 0.07). The mean (±SD) fractionation of PSPT and PBPT was 39±2 and 36±2, respectively (P= 0.001). Radiation toxicities were recorded in endocrine (11 patients [34%]), ophthalmic (3 patients [9%]), otologic (7 patients [22%]), and radiation necrosis (4 patients [13%]). PSPT was associated with endocrinopathy (odds ratio [OR], 10.5; 95% confidence interval, 1.86-59.4, P= 0.008), and radiation dose was associated with otologic toxicity (OR 1.57; 95% confidence interval, 1.02-2.44; P= 0.04). The gross-near total resection group had better progression-free survival than the subtotal resection group regardless of radiation therapy (P= 0.01). Overall, 3-year progression-free survival was 73%, and 5-year overall survival was 93%. The PBPT group showed comparable outcome to the PSPT group. The degree of resection was more important than the modality of proton therapy. Further follow-up and cases are necessary to evaluate the benefit of PBPT.

Modeling Variable Proton Relative Biological Effectiveness (RBE) Using Voxel-Level Image Density Change for Non-Small Cell Lung Cancer (NSCLC) Patients Treated with Passive Scattering Proton Therapy (PSPT) or Intensity Modulated Photon Therapy (IMRT)

<h3>Purpose/Objective(s)</h3> To test the hypothesis that radiation damage measured via lung image density change is a function of variable RBE for protons with a coefficient of determination (R²) greater than 0.8. <h3>Materials/Methods</h3> Data from 61 NSCLC patients previously treated on a prospective clinical trial with PSPT (N = 24) or IMRT (N = 37) to 74 Gy(RBE) (proton RBE of 1.1) were acquired. Patients with noticeable atelectasis or pleural effusion were excluded. For each patient, a ∼5-month post-treatment PETCT was obtained to assess response and was deformed to the planning exhale phase of the 4DCT (exCT) via a biomechanical model-based image registration algorithm. Subsequently, voxel-level image density change (IDC) within the normal ipsilateral lung was obtained by subtracting the exCT from the deformed PETCT, as a signal of biological damage. IMRT dose (D_x) was recalculated on the exCT using a commercial treatment planning system while the PSPT dose (D_p) and dose-averaged linear energy transfer (LET_d) were recalculated on the exCT using a commissioned track-repeating Monte-Carlo system. The fitted variable RBE models included a linear model (RBE = 1 + λ•LET_d) and a linear-quadratic (LQ) model (RBE = 1/(2D_p)•{√[(α/β)² + 4D_p(α/β)(p₀+(p₁•LET_d)/(α/β) + 4D_p²(p₂ + p₃•√(α/β)•LET_d)] - α/β}) with α/β = 3 Gy for lung tissue. <b>RBE was modeled against the ratio between D_x and D_p at given IDC levels.</b> We adapted Lyman-Kutcher-Burman normal tissue complication probability (NTCP) model to fit the dose-IDC relationship for each cohort by averaging the dose and IDC of voxels in 5-Gy dose intervals (adaptations: n = 1, effective dose = voxel dose, and complication probability = IDC normalized against global min and max IDC). LET_d corresponding to each D_p was approximated by averaging the LET_d of voxels that received D_p with a margin of 0.001Gy. All NTCP and RBE models were fitted using non-linear least squares with the Python SciPy package. <h3>Results</h3> For NTCP fitting, min and max IDC were 2.7 HU and 136.3 HU, respectively, and TD₅₀ and m were fitted to be 31.5 Gy and 0.51 for PSPT (R² = 0.99) and 44.4 Gy and 0.40 for IMRT (R² = 0.98). The table shows the IDC levels, the corresponding LET_d (SD), and the fitted D_x and D_p. The linear model resulted in λ = 0.154 µm/keV (R² = 0.27), and the LQ model resulted in p₀ = -0.72, p₁ = 10.02, p₂ = 1.51, and p₃ = -0.08 (R² = 0.999). <h3>Conclusion</h3> The study demonstrates that voxel-level radiation damage and image changes for proton therapy are functions of dose and LET and, thus, variable RBE.

Clinical Outcomes of Medulloblastoma Patients Treated with Proton Radiotherapy: A Systematic Review

<h3>Purpose/Objective(s)</h3> The aim of this study was to comprehensively review all studies examining clinical outcomes of proton therapy for craniospinal irradiation of medulloblastoma, to determine whether theoretical dosimetric advantages of proton therapy have translated into superior clinical outcomes, including survival and toxicities. <h3>Materials/Methods</h3> We performed a systematic review based on the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines, using the PubMed (Medline), EMBASE, and Cochrane Library databases (inception to December 2021). The study was registered with PROSPERO, CRD42022302455. Articles in the English language reporting on clinical outcomes of pediatric and/or adult medulloblastoma patients treated with proton therapy were included. Two independent authors screened all titles/abstracts, reviewed full texts and extracted relevant data, with discrepancies resolved by consensus. Individual study quality was scored using Newcastle Ottawa Scale and overall evidence base by GRADE scale. <h3>Results</h3> Thirty-five studies were included, representing 629 unique patients. Publication dates ranged from 2011 to 2021, with the majority (n=32) from the United States. None of the studies were randomized, 12 were comparative, 9 were prospective, 3 mixed and 22 retrospective. Average mean/median follow up was 5.0 years (range = 4 weeks to 12.6 years). The majority of studies (n=19) reported on treatment with passive scatter proton beams exclusively. Average study quality score was 6.08 out of 9 (SD 0.688, median 5). Seven studies scored ≥8/9 on the Newcastle Ottawa Scale; an overall "moderate" GRADE score was assigned. Well-designed comparative cohort studies with adequate follow-up demonstrate superior neurocognitive outcomes, lower incidence of hypothyroidism (23% vs 69%) and reduced acute toxicities (including myelosuppression, esophagitis, diarrhea, weight loss and nausea/vomiting) in patients treated with protons compared to photons. The 10-year cumulative incidence of secondary malignancy is also lower for proton cohorts (2.1-4.9% vs 8%), but did not reach statistical significance in any individual study. Overall survival (10-yr) (85.3-86.9% for standard-risk disease), progression-free survival (10-yr), patterns of failure, and other endocrine outcomes such as incidence of GH deficiency, adrenal insufficiency and precocious puberty were similar to those reported for photon therapy. Quality of life, ototoxicity and incidence of CNS injury were also found to be comparable between proton and photon cohorts, albeit with lower quality of evidence. Overall, quality of evidence was most robust in the domains of intellectual outcomes, endocrinopathies and acute toxicity. <h3>Conclusion</h3> Moderate grade evidence supports proton beam therapy as a preferred treatment for craniospinal irradiation of medulloblastoma based on equivalent disease outcomes and comparable-to-improved toxicity versus photon beam radiotherapy.

A Simple Model for Describing the Minimum Differential Cross-Section of Elastic Proton Scattering on Protons at High Energies

Relevance. The most modern and widely applied phenomenological theory, which well describes an entire range of physical characteristics of such processes as elastic and inelastic proton-proton and antiproton-proton scattering at high energies, is the Regge poles method in relativistic theory. Based on a simple amplitude, such as the dipole pomeron, where the pomeron is the Regge pole, the researchers add different terms to it. Using such more complex amplitudes, it is possible to explain well or satisfactorily together not only the experimental data for these reactions obtained at the end of the last century, but also the latest ones obtained at the Large Hadron Collider. Purpose. The purpose of this study is to find numerical values of the amplitude parameters at which the circumferences of the differential cross-sections of elastic proton scattering on protons at high energies are satisfactorily described, and to answer whether the parameters satisfy the obtained constraints. Methods. To find the amplitude parameters, the least squares method is used and minima equations are obtained for the squares of differences between the experimental and theoretical values of these cross-sections. These equations are transcendental, and therefore, they are solved by approximation. Within the framework of successive approximations, a method is selected that ensures fast convergence of the process, namely: the faster descent method or the gradient method. Parameter errors are calculated using a covariance matrix. The statistical acceptability of the model is determined according to the Fischer criterion. Results. Numerical calculations from experimental data of differential cross-sections of elastic pp-scattering were used to find the values of the parameters and the scale multiplier of the amplitude. Differential cross-sections are calculated from the amplitude near the minima. The corresponding graphs of these cross-sections are presented. The coincidence with the experiment is satisfactory in most cases, and in some cases, it is of high quality. A covariance matrix is obtained, from which the errors of the model parameters are found. Under general conditions, restrictions on the found approximate values of parameters are derived. It is shown that they satisfy the constraint. According to the Fischer criterion, the statistical acceptability of the model was verified, which turned out to be positive. Conclusions. The proposed simple amplitude ensures that the Froissard constraint and unitarity are met. It will serve as a seed for constructing more complex amplitudes that will describe a wide range of experiments on proton-proton and antiproton-proton scattering at high energies.

The Effects of Quantum Entanglement in Low-Energy Proton–Proton Scattering

The Effects of Quantum Entanglement in Low-Energy Proton–Proton Scattering

Radiative correction to lepton proton scatterings in manifestly Lorentz-invariant chiral perturbation theory

Manifestly lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at next-to-leading order with nonzero lepton mass, in which both are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model, but somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry.

Hyperon–Proton Scattering Experiment and Recent Progress of Strangeness Nuclear Physics at J-PARC

Hyperon–Proton Scattering Experiment and Recent Progress of Strangeness Nuclear Physics at J-PARC

Effects of Hot Protons on the Pitch Angle Scattering of Ring Current Protons by EMIC Waves

AbstractVia cyclotron resonant interactions, electromagnetic ion cyclotron (EMIC) waves play an important role in the loss of ring current protons. In this study, by calculating the proton bounce‐averaged pitch angle diffusion coefficients using both the cold and hot plasma dispersion relations, we investigate the effects of hot protons on the EMIC wave‐induced scattering loss of ring current protons. Our results show that, for H+ band (He+ band) EMIC waves, inclusion of hot protons results in significant decrease of pitch angle diffusion coefficients of ∼10–60 keV (4–30 keV) protons, while the scattering efficiency of higher energy protons increases at low pitch angles and decreases at relatively high pitch angles. We also find that the cold plasma approximation seriously underestimates the loss timescales of protons at energies from a few keV to tens of keV but overestimate that of higher energy protons. The differences in proton loss timescales caused by hot protons are generally less than a factor of ∼5 for H+ band but can exceed an order of magnitude for He+ band, showing a strong dependence on the hot proton concentration and temperature anisotropy and L‐shell. This study confirms that effects of hot protons play a crucial role in the EMIC wave driven loss of ring current protons and should be included in future modeling of ring current dynamics.