No abstract

The low-energy N interaction is investigated with the use of a relativistic isospin-symmetric N model based on scalar-isoscalar and vector-isovector exchanges in the t channel, and the nucleon and ⌬-isobar contributions in the s and u channels; the small contributions from the well-established s and p higher ͑baryon͒ resonances are also taken into account. In the region of elasticity, the model provides a firm basis for analyzing the experimental data. The analysis of all ͑recent and old͒ N measurements between ͑pion laboratory kinetic energy of͒ 20 and 100 MeV has been achieved with the implementation of robust statistics. Provided the correctness of the bulk of the experimental data and the completeness of the electromagnetic corrections applied to the scattering problem, this work provides overwhelming evidence for isospin-symmetry breaking of the strong interaction in the N system. ͓S0556-2813͑97͒03212-3͔ PACS number͑s͒: 13.75.Gx, 11.30.Hv, 25.80.Dj *Electronic address: evangelos.matsinos@psi.ch; Tel.: ϩ41 56 310 32 77, FAX: ϩ41 56 310 43 62.

Using electromagnetic corrections previously calculated by means of a potential model, we have made a phase-shift analysis of the π ± p elastic-scattering data up to a pion laboratory kinetic energy of 100 MeV. The hadronic interaction was assumed to be isospin invariant. We found that it was possible to obtain self-consistent databases by removing very few measurements. A pion-nucleon model, based on sand u-channel diagrams with N and ∆ in the intermediate states, and σ and ρ t-channel exchanges, was fitted to the elastic-scattering database obtained after the removal of the outliers. The model-parameter values showed an impressive stability when the database was subjected to different criteria for the rejection of experiments. Our result for the pseudovector πN N coupling constant (in the standard form) is 0.0733 ± 0.0014. The six hadronic phase shifts up to 100 MeV are given in tabulated form. We also give the values of the s-wave scattering lengths and the p-wave scattering volumes. Big differences in the s-wave part of the interaction were observed when comparing our hadronic phase shifts with those of the current GWU solution. We demonstrate that the hadronic phase shifts obtained from the analysis of the elastic-scattering data cannot reproduce the measurements of the π − p charge-exchange reaction, thus corroborating past evidence that the hadronic interaction violates isospin invariance. Assuming the validity of the result obtained Preprint submitted to Elsevier Science within the framework of chiral perturbation theory, that the mass difference between the u-and the d-quark has only a very small effect on the isospin invariance of the purely hadronic interaction, the isospin-invariance violation revealed by the data must arise from the fact that we are dealing with a hadronic interaction which still contains residual effects of electromagnetic origin. PACS: 13.75.Gx; 25.80.Dj; 25.80.Gn

No abstract

In a previous paper, we reported the results of a partial-wave analysis (PWA) of the pion–nucleon (πN) differential cross-sections (DCSs) of the CHAOS Collaboration and came to the conclusion that the angular distribution of their π+p data sets is incompatible with the rest of the modern (meson factory) database. The present work, re-addressing this issue, has been instigated by a number of recent improvements in our analysis, namely regarding the inclusion of the theoretical uncertainties when investigating the reproduction of experimental data sets on the basis of a given "theoretical" solution, modifications in the parametrization of the form factors of the proton and of the pion entering the electromagnetic part of the πN amplitude, and the inclusion of the effects of the variation of the σ-meson mass when fitting the ETH model of the πN interaction to the experimental data. The new analysis of the CHAOS DCSs confirms our earlier conclusions and casts doubt on the value for the πN Σ term, which Stahov, Clement and Wagner have extracted from these data.

We give the conversion equations which lead from experimental values of the 3p → 1s transition energy in pionic hydrogen and the total width of the 1s level to values of the s-wave threshold scattering parameters for the processes π − p → π − p and π − p → π 0 n respectively. Using a three-channel potential model, we then calculate the electromagnetic corrections to these quantities, which remove the effects of the Coulomb interaction, the external mass differences and the presence of the γn channel. We give the s-wave scattering parameters obtained from the present experimental data and these electromagnetic corrections. Finally we discuss the implications for isospin invariance.

We calculate the electromagnetic corrections to the isospin invariant mixing angle and to the two eigenphases for the s-, p 1/2 -and p 3/2 -partial waves for π − p elastic and charge exchange scattering. These corrections have to be applied to the nuclear quantities in order to obtain the two hadronic phase shifts for each partial wave. The calculation uses relativised Schrödinger equations containing the sum of an electromagnetic potential and an effective hadronic potential. The mass differences between π − and π 0 and between p and n are taken into account. We compare our results with those of previous calculations and estimate the uncertainties in the corrections. PACS: 13.75. Gx,25.80.Dj

The well-known Bragg-Kleeman rule R CSDA = A·E 0 p has become a pioneer work in radiation physics of charged particles and is still a useful tool to estimate the range R CSDA of approximately monoenergetic protons with initial energy E 0 in a homogeneous medium. The rule is based on the continuous-slowing-down-approximation (CSDA). It results from a generalized (nonrelativistic) Langevin equation and a modification of the phenomenological friction term. The complete integration of this equation provides information about the residual energy E(z) and dE(z)/dz at each position z (0 ≤ z ≤ R CSDA ). A relativistic extension of the generalized Langevin equation yields the formula R CSDA = A·(E 0 +E 0 2 /2M·c 2 ) p . The initial energy of therapeutic protons satisfies E 0 << 2M·c 2 (M·c 2 = 938.276 MeV), which enables us to consider the relativistic contributions as correction terms. Besides this phenomenological starting-point, a complete integration of the Bethe-Bloch equation (BBE) is developed, which also provides the determination of R CSDA , E(z) and dE(z)/dz and uses only those parameters given by the BBE itself (i.e., without further empirical parameters like modification of friction). The results obtained in the context of the aforementioned methods are compared with Monte-Carlo calculations (GEANT4); this Monte-Carlo code is also used with regard to further topics such as lateral scatter, nuclear interactions, and buildup effects. In the framework of the CSDA, the energy transfer from protons to environmental atomic electrons does not account for local fluctuations. Based on statistical quantum mechanics, an analysis of the Gaussian convolution and the Landau-Vavilov distribution function is carried out to describe these fluctuations. The Landau tail is derived as Hermite polynomial corrections of a Gaussian convolution. It is experimentally confirmed that proton Bragg curves with E 0 ≥ 120 MeV show a buildup, which increases with the proton energy. This buildup is explained by a theoretical analysis of impinging proton beamlets. In order to obtain a complete dose calculation model for proton treatment planning, some further aspects have to be accounted for: the decrease of the fluence of the primary protons due to nuclear interactions, the transport of released secondary protons, the dose contribution of heavy recoil nuclei, the inclusion of lateral scatter of the primary and secondary protons based on Molière's multiple-scatter theory, and the scatter contributions of collimators. This study also presents some results which go beyond proton dose calculation models; namely, the application of the relativistic generalization of the Bragg-Kleeman rule to electrons, the influence of detectors to the profiles of narrow photon beams, and the application of deconvolution kernels to scatter problems in image processing. E Mc W and c M c p W z + = + = The use of the invariant variable s accounts for the length contraction besides the relativistic mass dependence. The initial energy E 0 has the same meaning as previo...