Elastic and charge exchange scattering of pions on3He in the (3,3)-resonance region

The elastic scattering of pions from³He and the single charge exchange reaction³He(π ^?,π ⁰)³H are calculated in the energy domain of the (3,3)-resonance within the framework of Glauber's theory, including spin and isospin degrees of freedom in all orders. It is pointed out that, from the first minimum on, the differential cross section strongly depends on the parametrization of theπN amplitude, especially on its continuation into the unphysical region of momentum transfer. Single and double spin flip contributions prove to be very important in the charge exchange reaction. Within a modified version of Glauber's formalism, directly usingπN phase shifts rather than amplitudes, the³He charge exchange scattering is reexamined. Whereas the shape of the angle-integrated cross section as a function of pion energy is confirmed, the magnitude is still uncertain within a factor of 2.     

Analyzing power measurements for p-3He elastic scattering from 1.75 to 4.50 MeV

Analyzing powers for p-³He elastic scattering have been measured at 12 energies between 1.75 and 4.50 MeV for θ_c.m. = 40° to 150°. A comparison of our results with earlier data of Drigo et al. shows substantial differences at all energies. The R-matrix fits to our data that were included in the global search calculations of Hale and Dodder are shown. These calculations established the ordering of the lowest-lying T = 1 levels of ⁴He as J^π = 2^?, 1^? (triplet), 0^?, and 1^? (singlet), which is the WMI (MHI) ordering.     

Pionic deuterium

The strong-interaction shift ε _1s ^πD and broadening Γ _1s ^πD in pionic deuterium have been determined in a high statistics study of the πD(3p-1s) X-ray transition using a high-resolution crystal spectrometer. The pionic deuterium shift will provide constraints for the pion-nucleon isospin scattering lengths extracted from measurements of shift and broadening in pionic hydrogen. The hadronic broadening is related to pion absorption and production at threshold. The results are ε _1s ^πD = (?2356 ± 31) meV (repulsive) and Γ _1s ^πD meV yielding for the complex πD scattering length a _πD = [?(24.99±0.33)+i(6.22 _?0.26 ^+0.12 )] × 10^?3 m _π ^?1 . From the imaginary part, the threshold parameter for pion production is obtained to be α = (251 _?11 ⁺⁵ ) μb. This allows, in addition, and by using results from pion absorption in ³He at threshold, the determination of the effective couplings g ₀ and g ₁ for s-wave pion absorption on isoscalar and isovector NN pairs.     

Meson exchange contributions to electron-3He scattering

Theoretical calculations have been done corresponding to Ω-, σ-, π°-meson exchange between pairs of nucleons in ³He for e-³He inelastic scattering and compared with the experimental data for 14.6 GeV incident electrons. The purpose of these calculations was to see if these calculations could account for the experimental cross sections on either side of the quasi-elastic peak, where the impulse approximation calculations gave results less than 10% of the experimental cross sections. Meson exchange calculations account impressively for the experimental cross sections on the left side of the quasi-elastic peak, whereas the contribution of the meson exchange calculations on the right side of the quasi-elastic peak was found to be negligible.     

On mesonic interference phenomena in deep inelastic scattering

Possible effects of a π′ contribution to lepton deep-inelastic scattering (DIS) are analyzed. The exchange of the first radial excitation of the pion (π′(0^?)) has been advocated recently to solve the notorious problem of hard vertex form factors innucleon-nucleon scattering. The π′-meson exchange contribution is calculated in addition to the well known pionic (Sullivan) contribution. Interference between π and π′ contributions and their possible influence on the cut-off mass parameter of the πNN form factor extracted from DIS on the nucleon are examined. It is shown that the orthogonality relation between the π and π′ wave functions, in conjunction with number and momentum sum rules, put strong restrictions on the size of the interference effect. The interference effect between π and π′ is found to be negligible for the nucleon quark distributions and to modify only higher moments of the quark distributions. The interference effects of a pionic contribution with other mesons are discussed.     

Chiral symmetry probed with pionic atoms

Study of pionic atom has been revisited by a recent discovery of deeply bound pionic states in the context of possible sensitivity to the partial chiral restoration in the nuclear medium. Precisely measured binding energies and widths of the deeply bound π^? Is states in ^115,119,123Sn in ^116,120,124Sn(d,³He) reactions at recoil-free conditions are used to deduce the medium-modified isovector scattering amplitude as b₁ = 0.115 ± 0.007m _π ^?1. The observed enhancement of b ₁ over the free πN value infers 34% reduction of $\left\langle {\bar qq} \right\rangle $ at the normal nuclear density, ρ = 0.17 fm^?3.     

Empirical formula for energy level shifts of pionic atoms

An empirical formula for energy level shifts of pionic atoms is proposed. Numerical results show remarkably good agreement with experimental data. We predict energy level shifts and widths for pionic deuterium, tritium and helium. With these values, scattering lengths of π-d, π-t and π-³He are also calculated. The results are (in fm) ?0.083 + 0.024 i, ?0.287 + 0.028 i and 0.067 + 0.035 i, respectively.     

N1−3H configurations in 4He

Wavefunctions for N¹?³H configurations in ⁴He are calculated using NN → N¹N transition potentials V and ³HN → N¹³H transition potentials from a two-nucleon exchange mechanism. The radial N¹?³H momentum distributions peak at ～ fm^?1 which is much lower than the short-ranged V. For (πN) S-wave isobars, e.g. N¹(1535) and N¹(1700), N¹?³H probabilities are estimated to be ～2‰ each, while those for N¹'s in higher (πN) partial waves are much smaller.     

Formation of Deeply Bound Pionic Atoms in Sn Isotopes

We study the formation of deeply bound pionic atoms in the (d,³He) reaction theoretically. At different scattering angles, we find that the different subcomponents dominate the formation spectra because of the matching condition of the reaction. We also find that the pionic 1s state which is free from the residual interaction effects appears clearly in ¹¹⁷Sn(d, ³He) spectra. We conclude that the observation of the (d,³He) reaction for these new cases will provide more systematic and accurate information on the pionic bound states, and it will help to develop the study of the pion properties and the partial restoration of chiral symmetry in nuclei.     

Towards a high-precision calculation for the pion-nucleus scattering lengths

We calculate the leading isospin-conserving few-nucleon contributions to pion scattering off ²H, ³He, and ⁴He. We demonstrate that the strong contributions to the pion-nucleus scattering lengths can be controlled theoretically to an accuracy of a few percent for isoscalar nuclei and of 10% for isovector nuclei. In particular, we find the π-³He scattering length to be (62 ± 4 ± 7) × 10⁻³ m _π⁻¹ where the uncertainties are due to ambiguities in the π-N scattering lengths and few-nucleon effects, respectively. To establish this accuracy we need to identify a suitable power counting for pion-nucleus scattering. For this purpose we study the dependence of the two-nucleon contributions to the scattering length on the binding energy of ²H. Furthermore, we investigate the relative size of the leading two-, three-, and four-nucleon contributions. For the numerical evaluation of the pertinent integrals, a Monte Carlo method suitable for the momentum space is devised. We observe that, so far, no power counting is able to provide a quantitative understanding of the relative strength of N- and (N + 1)]]-nucleon operators. Empirically, we find a relative suppression by a factor of 5 compared to a factor of 50 predicted from dimensional analysis. On the other hand, the relative importance of different contributions within each class of N-nucleon operators can be understood within Weinberg counting. The relevance of our findings for the extraction of the isoscalar π-N scattering length from pionic ²H and ⁴He is outlined. We also discuss the applicability of heavy pion effective field to the π-²H system.     

Pionic contribution to the muon magnetic moment

A procedure is developed to derive an optimal lower bounds for the pionic contribution to the muon magnetic moment from analyticity of the pion form factor F(t), its normalization F(0)=1 and from experimental information from both the processes e^?p → e^?π⁺n and e⁺e^? → π⁺π^?. It represents essentially the solution of a certain kind of optimization problem in Hilbert space. Numerical results are presented and compared to the recent data for the muon magnetic moment; we find a_μ(π⁺π^?) ? 42 × 10^?9.     

Ω− non-leptonic decays

Non-leptonic decay rates for Ω^? are calculated in a model where strong interactions introduce new ΔI = 1/2 operators in the effective hamiltonian. Both Ω^?→Ξ^0,?π^?,0 and Ω^?→Λ⁰K^? are predicted to be nearly parity conserving. ΔI = 1/2 contributions are found to dominate the sum of the pionic rates, while ΔI = 3/2 contributions are non-negligible in each of them. Rough agreement in magnitude with experimental data is obtained.     

Formation of Essential Kaonic Nuclei, “K − pp”

We have reviewed our theoretical calculations of the formation of a deeply bound K ^? pp state with I = 1/2, J ^π  = 0^? by the ³He(in-flight K ^?, n) reaction at ${p_{K^-} = 1.0}$ rm GeV/c and θ _lab = 0° for the forthcoming J-PARC E15 experiment. The expected inclusive and semiexclusive spectra have been calculated within the framework of a distorted-wave impulse approximation using the Green’s function method. The advantage of the use of the ³He target for the ³He(K ^?, N) reactions are emphasized.     

Meson-exchange currents in thermal n-3He radiative capture

The cross section for radiative capture of thermal neutrons by ³He arising from 1π, 1ρ and 1ω meson-exchange processes is calculated using oscillator and exponential wave functions for ³He (including a D-wave component) and oscillator wave functions for ⁴He (also including a D-wave component). A correlation function with a range of 0.25 fm is incorporated in the wave function to describe the short-range behaviour. Results are sensitive to the assumed range of the correlation function and to the triplet scattering length in the neutron scattering wave function, which are not known accurately. For a reasonable set of parameter choices, a combination of one-body impulse approximation (between D-states) and two-body meson-exchange current processes can explain the entire experimental cross section.     

Electromagnetic contributions to proton- and neutron-4He scattering

A proper treatment of various electromagnetic contributions toN-⁴He scattering enables one to determinen(p)-⁴He observables fromp(n)-⁴He data. Several calculations ofn-⁴He observables considering different electromagnetic effects are presented. It is shown that the contribution of thep-⁴He Coulomb corrections ton-⁴He polarizations and differential cross sections dominates over other electromagnetic effects forθ _c.m.≧30°. For smaller scattering angles, neutron magnetic scattering is important and produces a divergingn-⁴He differential cross section atθ=0° and a large peak (Mott-Schwinger effect) in the polarization. The influence of thep- andn-⁴He vacuum polarizations on then-⁴He observables is found to be small.     

Pionic fusion study of the halo nucleus 6He, the reaction d+4He→6He+π + at CELSIUS

The halo nucleus ⁶He has been studied in a pionic fusion experiment at the CELSIUS storage ring facility in Uppsala. The ⁶He nuclei were produced in reactions with a deuteron beam incident on a ⁴He jet target 0.9–5.4 MeV above threshold in the center-of-mass frame. The ⁶He ions were detected in a ΔE-E solid-state detector telescope inserted into the CELSIUS ring. The aim of the experiment was to investigate, in particular, the high-momentum part of the halo wave function by measuring the total and differential cross sections of the reaction d+⁴He→⁶He+π ⁺.     

Angular-momentum analysis of pionic nucleon capture

The pionic capture reaction A(N, π)(A + 1) is analyzed in terms of the Mandelstam model for pion production by two nucleons. The results are applied to the proton-capture reactions ¹²C(p, π⁺)¹³C and ⁴He(p, π⁺)⁵He, and comparisons are made with experiments.     

Binding corrections for reactions on the deuteron in the 3-3 resonance region

Binding corrections evaluated to all orders in a phenomenological nucleon-nucleon potential are compared with the leading term and with a double scattering correction in the Watson expansion for breakup and for coherent reactions on the deuteron at intermediate pion or photon energies. As principal result, we establish that for charged pion photoproduction, and for certain pion induced “spectator” reactions, the binding correction remains sufficiently small that truncation of the Watson expansion at terms of second order in the projectile-nucleon amplitudes is justifiable, but sufficiently large that it cannot be neglected in comparison with multiple scattering corrections. For the reactions π⁺d → π⁺p + spectator neutron and π^?d → π^?n + spectator proton, our theory predicts deviations from the simplest impulse approximation which become very large in well-defined kinematical regions, and should be easily accessible to experimental investigation.