Contribution of the two-nucleon pion absorption-emission mechanism to the pion-nucleus double-charge-exchange reaction

The two-nucleon pion absorption-emission mechanism 1) and its contribution to the pioni-induced double-charge-exchange (DCX) reaction at energies T_π 300 MeV is studied. By combiing this new mechanism with the conventional sequential mechanism, the 0° excitation functions for the DCX reactions to the isobaric analog states on the ¹⁴C, ¹⁸O, ²⁶Mg, and ⁴²Ca are calculated and compared with the experimental data. We find that the theoretical results are much improved after considering the contribution of the new mechanism, especially at low energies.     

Energy spectra of neutrons emitted following muon capture in O and C

The energy spectra of neutrons emitted following muon capture in ¹⁶O and ¹²C are investigated using the continuum shell model. Nuclear wave functions, which have been shown by Ohtsubo and the author to describe the radiative pion capture reaction in the above nuclei well, are adopted. The calculated neutron energy spectra explain well the observed main peaks, at 5 MeV for ¹⁶O and 4 MeV for ¹²C, which are considered to be the giant resonances excited in the muon capture reaction. These peaks are interpreted as the 2⁻ state at 20.3 MeV for ¹⁶O and the 1⁻ state at 22.5 MeV for ¹²C. Comparisons with photon spectra in radiative pion capture reactions are also made. The calculated total capture rates exceed the experimental values by a factor of 2.5 for ¹⁶O and by 30–40% for ¹²C.     

The asymmetry in π−He scattering

We show that the π⁺−³He asymmetry data obtained in a recent TRIUMF experiment at T_π = 100 MeV can be understood in terms of the elementary πN amplitudes. Through a comparison to a full optical-potential calculation that employs realistic Faddeev wave functions for the trinucleon we show that all nuclear-structure dependence cancels for at lower energies. At higher pion energies around the Δ-resonance region the sign flip of offers the possibility of extracting information about the smaller partial waves.     

Microscopic description of the A(p, π)A + 1 reaction

We have developed a flexible and thoroughly tested computer program for microscopic calculations of proton-induced pion production in nuclei at bombarding energies up to 500 MeV. The model used includes explicitly both the one-nucleon (pionic stripping) mechanism and the resonant p-wave rescattering part of the two-nucleon mechanism. Initial and final state interactions are included through proton-nucleus and pion-nucleus optical model distortions, with careful consideration of the multiple scattering series. The intermediate delta in the two-nucleon mechanism is treated as static with possible inclusion of a local density approximation for the delta-nucleus interaction. We explain the philosophy of the model, detail the parametrization of the microscopic dynamics, and give the formalism for the calculation of experimental observables. We also describe the testing of the computer program and present preliminary results for the ³He(p, π⁺)⁴He reaction.     

Coupled-channels calculations of intermediate energy π−C inelastic scattering and charge exchange

Coupled-channels calculations have been carried out for pion inelastic scattering and charge exchange on 1p-shell nuclei at pion energies between 120 and 226 MeV. A momentum space technique is used, with the 1p-shell shell-model wavefunctions of Cohen and Kurath. Results are presented here for A=13. Channel-coupling effects are negligible in the strong 3/2^- and 5/2^- inelastic excitations of ¹³C, but enhance the analog charge-exchange cross sections by 7 to 20%.     

Nuclear Fermi Motion Effect on Pion Double Charge Exchange

The influence of nuclear Fermi motion on the conventional mechanism of pion double charge exchange (DCX) is examined.Concrete calculations of the 0° excitation function over the energy region 0—300MeV are performed for the double isobaric analog DCX transition on ¹⁴C.The calculated results coincide very well with the experimental data for the energies above 100MeV,but are about a factor of 2—3 smaller than the experimental data around 50MeV.It indicates that the pure conventional mechanism seems incapable to fully explain the anomalous behavior of the low energy DCX,and some new mechanisms are needed.     

Inclusive (p, π) reactions at 201 and 180 MeV

Inclusive proton-induced charged pion production was studied on ¹²C, ⁸⁹Y and ^natPb at 201 and 180 MeV. A QQD spectrometer was used for forward angles and a plastic scintillator range spectrometer for backward angles. The angular dependence, variation with the pion energy, and total cross sections are deduced from doubly differential cross section measurements.     

Pion-transfer (n, d) and (d, He) reactions leading to deeply bound pionic atoms

Theoretical studies are given on the (n, d) and (d, ³He) reactions leading to deeply bound pionic atoms in heavy nuclei of configuration [(nl)_π·j_n⁻¹]J. The cross sections for various pionic and neutron-hole configurations in the case of a ²⁰⁸Pb target are calculated at incident energies 300–1000 MeV/u by using the effective number approach and the eikonal approximation for distortion. The effective number with a pion in the 1s or 2p state and a neutron hole in the orbit peaks around the same incident energy (T_n = 600 MeV) as the elementary cross section n+n→d+π⁻, where the momentum transfer matches the angular-momentum transfer of L = 5–7. The DWIA cross section for (n,d) producing a pion in the 1s or 2p orbit at T_n = 600 MeV is found to be around 42 or 75 μb/sr, respectively. At T_n = 350 MeV, where the momentum transfer is small, quasi-substitutional states of configurations and are preferentially populated with (n, d) cross sections of 95 and 190 μb/sr, respectively. The (d, ³He) cross sections are estimated to be an order of magnitude smaller than the (n, d) cross sections. Thus, the (n, d) and (d, ³He) reactions are found to be suited for the production of deeply bound pionic atoms.     

Effect of the adiabatic process on the absorption in heavy-ion scattering

We have succeeded in obtaining the optical model potential for ¹²C---¹²C scattering at low incident energies (10 MeV E_cm 20 MeV), by applying the adiabatic approximation to the coupled channels equation. As for this potential inelastic channels of single and mutual excitations of ¹²C^*(2⁺, 4.43 MeV) make a contribution to the real part and not to the imaginary part.     

Excitation function of (p, pn) reactions at high energy

A closed theoretical formula for the (p, pn) reaction cross section at high energies in light, medium and heavy nuclei has been derived, and a comparison of the calculated cross sections with the experimental datais made for ¹²C, ¹⁹F, ⁵⁴Fe, ⁵⁸Ni, ⁵⁹Co, ⁶⁴Zn, ⁶⁵Cu, ¹⁰⁰Mo, ¹²⁷I, ¹⁴²Ce, ¹⁸²Ta and ²³⁸U at incident energies above 50 MeV. Good agreement between experimental and calculated cross sections is obtained in the entire energy range considered. In deducing the formula a direct reaction with a pure knock-out mechanism has been assumed.     

ON THE REACTION MECHANISM AND THE SELECTION RULE IN THE DOUBLE CHARGE EXCHANGE REACTION OF PIONS ON NUCLEI (DCX)-A STUDY OF THE CONNECTION BETWEEN THE 2β-DECAY AND DCX ON jP=O+ NUCLEI

It is shown that in the pion induced double charge exchange reaction on J^p=O⁺→O⁺ nuclei,there exists a possible new reaction mechanism π⁺(Δ⁰,Δ⁺⁺)π^- or π⁺(Δ^-,Δ⁺)π^- in so-called single step process,while that old speculative mechanism π⁺(N,Δ)π^- or π⁺(N,Δ)π^- is firbidden by a well-known selection rule which has been indicated in the theory of the nuclear 2β-decay.     

Self energies of the pion and the Δ isobar from the He(e,e′π)H reaction

In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the ³He(e,e′π⁺)³H reaction have been measured in the excitation region of the Δ resonance to determine the longitudinal (L), transverse (T), and the LT interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and Δ-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the π⁺ mass of MeV/c² in the neutron-rich nuclear medium at a density of fm⁻³. Our data are consistent with the Δ self energy determined from measurements of π⁰ photoproduction from ⁴He and heavier nuclei.     

Reanalysis of Elastic Scattering of 6Li + 209Bi Reaction Using a New Density Distribution of 6Li Nucleus

In the present paper, the elastic scattering of ⁶Li + ²⁰⁹Bi system is reanalyzed by using the double folding model (DFM) at energies near the Coulomb barrier (E_Lab=29.9 and 32.8 MeV). With this goal, a new density distribution of ⁶Li nucleus, the no-core full configuration (NCFC) density distribution (DD), is used to obtain the real potentials in DFM calculations. The NCFC DD results are compared with the results of both gaussian shape (GS) DD and an earlier study as well as the experimental data. This comparison provides information about the similarities and differences of the models used in calculations.     

π Meson interaction on He at 120, 145 and 165 MeV

The total cross sections and the differential cross sections of π⁺-⁴He elastic and inelastic reactions at E_π=120, 145 and 165 MeV have been measured using a 38 cm diffusion cloud chamber in a magnetic field exposed to the Frascati Laboratories' pion beam. Total π⁺ track lengths of (2141 ± 10) × 10³ cm, (3435 ± 10) × 10³ cm and (2413 ± 10) × 10³ cm were measured at the three considered energies, respectively. The elastic cross-section data are in good agreement with the results of the Dubna-Torino collaboration. The total inelastic cross sections have been obtained taking into account the contributions from all the inelastic channels. The analysis of the various inelastic processes has allowed us to distinguish five main reaction mechanisms, which compare reasonably with the existing data and with the models for pion-light-nuclei interactions.     

Spectroscopy of C

The ¹⁴C(t, p)¹⁶C reaction locates five new states in ¹⁶C, at excitation energies of 3120 ± 15, 3983 ± 10, 4136 ± 10 and 6109 ± 15 keV, in addition to the g.s. and 1.76 MeV states. The 3.02 and 3.98 MeV states appear to be the second 0⁺ and 2⁺ 2p-2h states, respectively. The 4.14 MeV state has J^π = 4⁺ and the 6.11 MeV state has J^π = 2⁺, 3⁻, or 4⁺.     

Pauli exchange effects in the elastic scattering of O + O

The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.     

Further Analysis of Neutron Double-Differential Cross Section of n ＋ ^16O at 14.1 MeV and 18 MeV

By using a new reaction model for light nuclei, the double-differential cross section of total outgoing neutron with LUNF code for n＋^16O reactions at En=14.1 MeV and 18 MeV have been calculated and analyzed. In this paper the opened reaction channels, which have contribution to emitting the neutrons, are listed in detail. To improve the fitting results the direct inelastic scattering mechanism is involved. The calculating results agree fairly well with the experimental data at E,~ = 14.1 MeV and the deviation from calculated results and experimental data in low energy region at En= 18 MeV has been analyzed. Since the possibility of 5He has been affirmed theoretically [J.S. Zhang, Sci. Chin. G 47 （2004） 137], so 5He emission from n＋ ^16O reaction is taken into account, which plays an important role at the region of the outgoing neutron energy εn〈3 MeV in total outgoing neutron energy-angular spectrum. The calculated results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil effect in light nuclear reactions is essentially important.     

An energy-independent multipole analysis of pion photoproduction on protons below 450 MeV

In this paper results are presented of a multipole analysis of pion photoproduction on protons at 27 energies below a photon lab energy of 450 MeV, using almost all existing data. The analysis gives rise to one continuous solution. It is shown, however, that when omitting certain asymmetry ratio data, another solution is possible. The latter is closer to certain dispersion-theoretic predictions. A comparison of the solutions to the data and predictions for unmeasured quantities are given. In addition, the solutions are used to evaluate total cross sections for π⁺ and π⁰ photoproduction. As a byproduct of certain fits, the πN coupling constant is evaluated from forward π⁺ differential cross sections. A comparison of the solutions is made to two other multipole analyses.     

Inelastic Pion Scattering from 12C at 800 MeV/c

The differential cross section of the inelastic scattering of pion at 800 MeV/c fir the 3^- excited states of ¹²C is calculated by making use of eikonal approximation and the collective coordinate. The calculation indicates that the 3_- state of ¹²C is octupole vibrational state.The results are in agreement with experimental data.     

Electroproduction of π from C leading to low-lying residual states in B

Energy distributions of π⁺ produced from ¹²C by electrons of total energy 195 MeV were measured at various angles. The results show large contributions from transitions leaving the residual nucleus in the ground (1⁺), first (2⁺) excited state and states at around 4.5 MeV. The angular distributions of ¹²C(γ, π⁺)¹²B leading to these residual states are deduced from the energy distributions by the unfolding method with the virtual photon theory. Theoretical results with the Helm model and the shell model are compared with the experimental results. Their relative shapes are in good agreement. A better agreement in the absolute value is found for the theoretical results which include the final-state interaction estimated with a pion optical potential. The surface production model shows better agreement with the experimental (γ, π⁺) cross sections than the volume production model.