Improved optical potential for low and medium energy π−-4He elastic scattering

Effects of the second-order correction in multiple scattering theory and the nucleon binding correction to the optical potential are investigated in π^?-⁴He elastic scattering and total reaction cross-sections. The second-order correction includes not only nucleon-nucleon correlation effects but also the contribution from spin (isospin) double-flip processes. It is found that the latter has an ascendency over the former. We have also shown that the nucleon binding effect is very important to reproduce the energy dependence of the total elastic cross section and the total reaction cross section, especially in the low energy and resonance energy regions.     

Binding and pauli principle corrections in subthreshold pion-nucleus scattering

In this investigation I develop a three-body model for the single scattering optical potential in which the nucleon binding and the Pauli principle are accounted for. A unitarity pole approximation is used for the nucleon-core interaction. Calculations are presented for the π−⁴He elastic scattering cross sections at energies below the inelastic threshold and for the real part of the π−⁴He scattering length by solving the three-body equations. Off-shell kinematics and the Pauli principle are carefully taken into account.

The binding correction and the Pauli principle correction each have an important effect on the differential cross sections and the scattering length. However, large cancellations occur between these two effects. I find an increase in the π−⁴He scattering length by 100%; an increase in the cross sections by 20–30% and shift of the minimum in π−⁴He scattering to forward angles by 10°.     

Pion and eta photoproduction in nuclei

We calculate the quasifree photoproduction of pions and eta mesons on nuclei from¹²C to²⁰⁸Pb. Assuming that for the quasifree process the cross sections forπ/η photoproduction on a nucleon in medium are — besides a lowering due to Pauli blocking — identical to those on a free nucleon, we use these as an input. The produced mesons or resonances then propagate through the nucleus where they can undergo several scattering and absorption processes. This final state interaction, which leads to a lowering of the initial meson yield up to 70%, we simulate in a coupled channel Boltzmann-Uehling-Uhlenbeck transport model. It allows us to study in detail the influence of Fermi motion, Pauli blocking and of the additional decay channels for nucleon resonances in medium on the photoproduction cross section. The calculated total and differential cross sections are compared to experimental data and the influence of the different medium effects on the cross sections is discussed in detail.     

Pion scattering from a bound nucleon at medium energies

In order to examine the validity of the impulse approximation for pion-nucleus scattering in the 33-resonance energy region, we consider pion-scattering from a “nucleus” which consists of a single nucleon bound in a harmonic oscillator potential. A separable πN interaction is assumed. The oscillator parameter is chosen such that the nuclear sizes are fitted for ⁴He ～ ¹⁶O. The binding effect is found to result in a downward shift of the resonance energy (by about 20 MeV), and an increase (by 50 ～ 70%) of the total cross section near the resonance. The angular distribution is also strongly modified. In connection with the binding effect, the importance of a careful treatment of nucleon recoil is emphasized. It is pointed out that the closure approximation which is often used to sum over intermediate nuclear states leads to very misleading results. The effect of the Pauli principle is also examined by excluding some intermediate states.     

Medium corrections to the first order optical potential for low-energy pion-4He scattering

We study the Pauli-principle corrections for low energy π-⁴He elastic scattering. In our approach we take into account explicitly the spin and isospin dependence of the Pauli-principle effect. Furthermore we discuss the combined effect of the Pauli-principle correction and the nuclear binding. Contrary to the Pauli principle we treat the binding corrections in an approximate way, using an effective mass for the residual nucleus. In our calculations we use the first-order optical potential of Celenza, Liu and Shakin. The Pauli-principle correction is found to have a considerable effect on the differential cross section. Our results indicate that the Pauli-principle corrections are largely compensated by the nuclear binding.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

Isobar-hole doorway states and π-16O scattering

We describe and apply the isobar-hole approach to intermediate energy pion-nucleus reactions. Pion propagation, nucleon and isobar binding, Pauli restrictions and Δ propagation are calculated explicitly within a shell model framework. Intermediate coupling to multihole channels, for example through pion absorption, is treated phenomenologically through an isobar spreading potential. We find strongly collective Δ-hole states, leading to a reformulation of the approach in an extended schematic model. This entails systematic construction of a Δ-hole doorway state basis within which the Δ-hole propagator is evaluated. We find that this doorway space can be truncated at very low dimensionality while preserving accuracy, thereby simplifying the calculations appreciably. We make a detailed comparison between the theoretical results and recent data for π⁺ — ¹⁶O scattering in the pion energy range 50–340 MeV. Nonresonant πN interactions and the π-nucleus Coulomb interaction are included in the calculations. The data is reproduced quite well both below and in the resonance region, and we discuss in detail the role of various dynamical mechanisms. Above the resonance, the calculations are far less successful. We discuss possible shortcomings, stressing the role of inclusive pion-nucleus reactions for revealing the important dynamics. As a test of the Δ spreading potential used for describing elastic scattering, we calculate the total cross section for pion absorption. The result agrees reasonably well with the available data.     

Isobar-hole description of the pion-nucleus single-charge-exchange reaction

The charge-exchange reaction in pion-nucleus scattering is analysed in the framework of the isobar-hole model. Calculations are performed for the ¹⁵N(π⁺, π⁰)¹⁵O reactions. The cross section proves very sensitive to the different medium corrections which account for Pauli, binding, true pion absorption and reflection effects.A flat-angle integrated cross section of around σ = 0.4 mb is obtained in the resonance region once all these medium corrections are included.     

Violations of the Pauli principle and the interior of the sun

The consequences of a violation of the Pauli principle for the physics of the solar interior are explored. It is found that a bound state of two protons becomes possible. This leads to an increase in the rate of hydrogen burning in the sun. Because a very large cross section for this reaction is in clear contradiction with the theory of stellar structure when compared with observations of solar luminosity, radius and mechanical oscillations, stringent limits on a violation of the Pauli principle in the two nucleon system can be given. However, a very small violation of the Pauli principle in the two nucléon system might solve the longstanding solar neutrino problem.     

Experimental Results on Ultrahigh-Energy Cosmic Rays and Asymptotic Behavior of the Total Cross Section for Nucleon–Nucleon Interaction

Results obtained by studying the energy dependence of the total cross section for nucleon–nucleon interaction are presented. The analytic parametrization proposed within axiomatic quantum field theory describes quantitatively a unified set of experimental data on proton–proton and antiproton–proton scattering. At collision energies above 86 GeV, the parameter values fitted to subsets of all available data and accelerator data alone were found to deviate from the respective asymptotic values. This indicates that the Froissart–Martin limit for the total cross section has not yet been reached in the case of these subsets. An approximation of the total nucleon–nucleon cross section measured in cosmic rays leads for some parameters to fitted values that, within 1.0 to 1.3 standard deviations, agree with the respective asymptotic values. This resultmay be viewed as an indication of the beginning of the asymptotic functional behavior of the total nucleon–nucleon cross section measured in cosmic rays of ultrahigh energy O(100 TeV). This is confirmed within the color glass condensate approach.     

dd → 3 Hen Reaction at Intermediate Energies

The dd → ³ Hen reaction is considered at the energies between 200 and 520?MeV. The Alt–Grassberger–Sandhas equations are iterated up to the lowest order terms over the nucleon–nucleon t-matrix. The parameterized ³ He wave function including five components is used. The angular dependence of the differential cross section and energy dependence of tensor analyzing power T ₂₀ at the zero scattering angle are presented in comparison with the experimental data.     

Measurement of the 2H(p,n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A _y of the ²H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD₂) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the ²H(p, p) inclusive breakup reaction at 250 MeV.     

Study of Different Forms of Density Distributions in Proton–Nucleus Total Reaction Cross Section and the Effect of Phase in NN Amplitude

Proton total-reaction cross-section (σR), measurements for about five nuclei in the range ¹²C to ²⁰⁸Pb at beam energies spanning 40–800 MeV have been analyzed in a systematic way by using the optical limit approximation of the Coulomb-modified Glauber multiple scattering theory. Two different phenomenological nuclear density distributions of the target nucleus in addition to the realistic one have been used in the present analysis. By applying the energy dependence in the slope parameter of nucleon–nucleon (NN) scattering amplitude, it is found that in general, the predictions of σ _R with the phenomenological Gambhir and Patil density distribution agree fairly well with the experimental data. The inclusion of phase in the NN amplitude improves the theoretical results. Our analysis shows that the calculated total reaction cross sections closely reproduce the measured data over the whole range of energy considered in this work. To validate our analyses, we have also obtained a fairly good representation of elastic p-nucleus differential scattering cross section data. The effect of a Coulomb energy shift in the proton beam has also been studied.     

Measurements of the Cross Sections and A y for D(p, n) Inclusive Breakup Reaction at 170 MeV

The effects of three-nucleon force (3NF) has been actively studied by using the nucleon–deuteron (Nd) scattering states. The differential cross sections of the elastic Nd scattering at the energy below 150 MeV can be well reproduced by incorporating 3NF in the Faddeev calculation based on modern nucleon–nucleon (NN) interactions. On the other hand, the differential cross sections of Nd elastic and inelastic scatterings at 250 MeV show large discrepancies between the data and the Faddeev calculations with 3NF. It indicates the presence of the missing features of the three nucleon system at this energy region. For the systematic study about the energy dependence of this large discrepancies, we measured the differential cross sections and the vector analyzing power A _y for the ²H(p, n) inclusive breakup reaction at 170 MeV. The experiment was carried out at RCNP by detecting scattered neutrons by using the neutron detector NPOL3. The data was compared with the results of the Faddeev calculations with and without the 3NF.     

用高能核子非弹性散射研究核力有效势

本文用扭曲波玻恩近似法及多体高能近似法,处理了原子核对高能核子的非弹性散射现象。在具有可靠的靶核激发态波函数的情况下,可利用这些理论处理方法研究核内两核子间的有效势,本文具体就碳核对185MeV入射核子的非弹性散射进行了计算。在计算中利用了粒子-空穴模型核波函数。在采用了具有各种交换性质并包含自旋轨道耦合项的有效势后,用一组合理的位阱参数,由多体高能近似法计算的理论值可与几个微分截面及极化实验曲线同时符合。     

Inelastic interactions of fast nucleons with nuclei and fission of nuclei

The cross section for the fission of actinide nuclei that is induced by fast neutrons is considered as a fraction of the cross section for inelastic nucleon interaction with nuclei. In turn, inelastic nucleon interaction with a nucleus is treated as scattering on intranuclear nucleons. It is shown that this interaction model describes satisfactorily the cross section for the inelastic interaction of 60- to 2200-MeV nucleons for a broad set of nuclei and that the energy dependence of the cross section for the fission of actinide nuclei that is induced by 400- to 1000–MeV protons replicates the energy dependence of the cross section for inelastic interactions with respective nuclei. From the model used, it follows that the cross sections for proton-nucleus interactions exceed cross sections for respective neutron-nucleus interactions in the energy range extending up to 550 MeV; at higher energies neutron cross sections are larger than proton cross sections.     

Analysis of intermediate energy nucleon-deuteron elastic scattering

We present a theoretical analysis of a broad range of aspects of intermediate energy nucleon-deuteron scattering. This analysis is based on a multiple scattering approach using knowledge of the deuteron's structure and nucleon-nucleon interactions. Conversely, comparison of this theory with experiment can yield information about low and intermediate energy strong interactions. The relationship of this multiple scattering type of approach to the complementary Faddeev equation approach is discussed. Our program consists of calculating the single scattering and one nucleon exchange contributions in a realistic way then parametrizing the remaining contributions as an S-wave. We argue that the largest error in this analysis is the P-wave part of the double scattering and we give estimates of its size. The single scattering integral is evaluated numerically. Coulomb effects are neglected. We derive the relativistic expressions for single scattering and nucleon exchange and discuss the approximations made, including the off-mass-shell extrapolation of the nucleon-nucleon scattering amplitude. Fits are made to experimental measurements of differential cross sections, nucleon polarizations, and total elastic cross sections. Unitarity is maintained. We tabulate the partial waves for $\text{J ?}\text{5}\text{2}$, L ? 2. They are consistent with recent Faddeev calculations. We argue that with the additional calculation of double scattering the deuteron D-state percentage can be determined to the same relative uncertainty as the differential cross section. Even without the calculation of double scattering, our results indicate a D-state percentage around 8%. In an effort to provide benchmarks for future work, we have tried to be conscientious in describing our techniques and in tabulating numerical results. Comparisons are also made with earlier analyses.     

K+ nucleon elastic scattering at 180° between 1.0 and 1.5 GeV/c incident momentum

We have measured the cross section at 180° for K⁺p and K⁺n elastic scattering in the momentum range 1.0 to 1.5 GeV/c. The K⁺n cross section was measured on deuterium and the K⁺p on hydrogen and deuterium. We were thus able to measure directly the difference between free nucleon (proton) scattering and bound nucleon (proton) scattering at large angles. This difference was found to be small and within our experimental accuracy the K⁺p(n) cross section should be equal to the K⁺p (free) cross section at 180°. We found no evidence for an s-channel resonance Z¹ in either the K⁺p or K⁺n system. A comparison of our data and those of other groups with theoretical predictions is given.     

Classical many-body model for heavy-ion collisions incorporating the Pauli principle

A classical model for heavy-ion collisions, introduced previously, has been extended to include certain effects of the Pauli principle. All nucleons are treated equally. They obey classical dynamics and interact through an ordinary two-body force and through a momentumdependent two-body “Pauli core” which satisfies, approximately, that $\text{p}{}_{\mathrm{ij}}\text{r}{}_{\mathrm{ij}}\text{≧ξ}\text{h}\text{?}$, where ξ is a dimensionless constant. A form for the Pauli core is presented. The ordinary two-body force has been adjusted to fit bulk properties of nuclei and to reproduce that moment of nucleon nucleon scattering cross sections which is relevant to hydrodynamics. The parameters of the forces are given.