Coincidence cross sections for coherent pion electroproduction on He and H

We have calculated coincidence cross sections for coherent pion electroproduction on ³He and ³H using Faddeev wave functions obtained with the Reid soft-core potential. The four coincidence structure functions, corresponding to unpolarized and polarized transverse, interference and longitudinal terms differ substantially in their energy dependence. Effects of Fermi motion and off-shell ambiguities are more pronounced for virtual than for real photons. The correct treatment of Fermi motion in the production operator decreases the maximum transverse cross section by up to 50% and lowers the peak energy by up to 50 MeV. Ratios of coherent pion production on ³He and ³H differ significantly for the four structure functions. Finally, the theoretical calculations have been compared with existing experimental data on inclusive pion electroproduction.     

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.     

Charged Pion Form Factor Determination in the Range of Q^2= 0.6-1.6 （GeV／c）^2

Using the most recent differential cross section data for e-p quasi-elastic scattering, the charged pion formation and its form factor Fπ is calculated in the energy range of 2.4-4 GeV at Q^2 = 0.6-1.6 (GeV/c)^2. The functional dependence of the charged pion form factor to the separated cross section aL is investigated and compared to the previously determined result.     

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.     

Photoproduction of positive pions from hydrogen with PHOENICS at ELSA

The differential cross section of the reaction γp→π⁺n has been measured with the PHOENICS detector at ELSA in Bonn. For the first time this cross section has been determined simultaneously over a large range of photon energies (E_γ = 220−900 MeV) and pion angles (Θ^c.m._pi = 35°−135°) with a tagged photon facility. The experimental set-up allowed a considerable kinematic overdetermination of the investigated reaction. Accordingly, the background contributions have been suppressed to below 1%. The measured differential cross section is in good agreement with existing data. The comparison with different model calculations is presented.     

COHERENT π0 PHOTOPRODUCTION IN THE QUASI-Δ33 DOORWAY STATE MODEL

The quasi-Δ, doorway state model, previously developed to describe pion-nucleus scattering, ^[1] is applied to the study of cohe-rent π photoproduction on nuclei.The unifying features of this approach for pion elastic scattering and photoproduction are briefly discussed. The relationship to W. Weise's isobar-hole model calculation and plane wave impulse approximation calculations are examined. The results are presented for ¹⁶O(γ, π⁰)¹⁶O and ¹²C(γ, π⁰)¹²C, and compared with the available experimental data. It has a large suppression of cross section from the impulse approximation prediction.     

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.     

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.     

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.     

π-electroproduction on hydrogen near threshold at four-momentum transfers of 0.2, 0.4 and 0.6 GeV

The reaction e + p → e + π⁰ + p was measured near the one pion threshold, detecting the final electron and proton in coincidence for values of q² = 0.2, 0.4 and 0.6 GeV². The slope of the cross section at threshold is determined. The data are compared with those of the e + p → e + π⁺ + n reaction, measured simultaneously, and with the results of pseudovector Born approximation and with dispersion theoretical calculations.     

Pion Induced Double Charge Exchange Reaction at Pure Nucleonic Level

The two pure nucleonic mechanisms (the conventional sequential mechanism and the two-nucleon pion absorption-emission mechanisml^[1]) are studied within a unified framework of Distorted Wave Impulse Approximation (DWIA). The distorted pion waves are obtained by solving the Klein-Gordon equation with the first-order optical potential. The difference between this approach and the eikonal approximation is showed. For the two-nucleon pion absorption-emission mechanism the effective Landau-Migadal interaction of Pines, et al.^[2] is used for the two bound nucleons, the result is compared with that by using the Paris force. By combining theee two mechanism the O⁰ 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.     

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%.     

Analyzing power in the reaction pp→dπ for beam momenta from 1.17 to 1.96 GeV/c

The analyzing power A_y0 in the reaction p↑p→dπ⁺ has been measured using the polarized proton beam at Argonne National Laboratory's zero gradient synchrotron. Data were taken at beam momenta of 1.17, 1.47, 1.70, and 1.96 GeV/c and for pion center of mass angles from 8° to 163°.     

HOW TO DETERMINE THE NUCLEAR MATRIX ELEMENT IN 2β-Decay?-A DISCUSSION OF PCAC, 2β-DECAY AND DOUBLE-CHARGE EXCHANGE REACTION OF PIONS ON NUCLEI

It is shown that by applying PCAC, the 2β-decay process can be directly related to double-charge-exchange reaction. Therefore, by studying double-charge-exchange reactions one is able to determine the nuclear matrix element of the relevant 2β-decay experimentally. A preliminary analysis has indicated that if the experimental data of forward-angle cross section on Ca⁴⁰ with pion beam at 164 Mev^[9] are used and extrapolated to Ca⁴⁸, then the squared nuclear matrix element thus determined is smaller than that calculated for Ca⁴⁰→Ti⁴⁸+2e^-+2v^[11] by 10⁵～10⁶.     

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.     

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.     

Intermediate Energy Pion-20Ne Elastic Scattering in the α+16O Model of 20Ne

We present an analysis of π-²⁰Ne elastic scattering at intermediate energy basing on the α+¹⁶O model of the ²⁰Ne nucleus and in the framework of Glauber multiple scattering theory. Satisfactory agreement with the general features of the experimental data of pion elastic scattering on the neighboring 4N-type nuclei is obtained without any free parameters. Compared with the experimental angular distributions of pion elastic scattering on ¹²C, ¹⁶O, ²⁴Mg, and ²⁸Si nuclei, the diffractive patterns and the positions of the dips and peaks in the angular distributions of π-²⁰Ne elastic scattering are reasonably predicted by the calculations.     

Effects of meson exchange currents on pion absorption

The effect of the π exchange current on the pion absorption process π⁺ + d → p + p has been investigated. The absorption cross section is significantly enhanced particularly in the energy region above the 33 resonance.     

Nuclear reactions between oxygen isotopes

Elastic and inelastic cross sections have been measured for the system ¹⁶O + ¹⁷O at c.m. energies from 12.5 to 15.5 MeV, and for ¹⁶O + ¹⁸O at c.m. energies from 12 to 20 MeV, at angles between 60° and 125°. Position-sensitive detectors were employed, using the kinematic coincidence technique. The data have been analyzed with particular attention to the contributions of multiple-exchange processes.     

轻奇特核结构中的核心激发--以11Be为例

近年来,越来越多的实验表明,很多轻奇特核结构中都有核心激发成分。本研究以丰中子晕核11Be为例,介绍核心激发成分的实验和理论研究进展,重点阐述核心激发成分对直接核反应微分截面的影响。实验上,1n移除反应及11Be（p,d）和10Be（d,p）转移反应是测量11Be核心激发成分比例的典型实验类型。理论上,发展了能够包括11Be核心激发成分的Faddeev AGS方法,XDWBA方法以及XCDCC方法。加入核心激发成分后,这些模型的计算结果可以更加合理地描述11Be在各种靶上的弹性散射和碎裂微分截面。通过对比是否包含核心激发成分的计算结果,发现其影响主要体现在弹散微分截面的大质心系角度,以及（p,d）转移反应角分布的小质心系角度。另外,对E_x=0:5s3 MeV的激发能区的碎裂反应,核心激发的影响不可忽略;对E_x=3s5:5 MeV的碎裂反应,核心激发的贡献非常重要。It was found that many light exotic nuclei have the core-excitation components. In this paper, taking one-neutron halo nucleus 11Be for example, the experimental and theoretical research progress, as well as the influences on the direct nuclear reaction differential cross sections of this exotic component were reviewed. The 1n removal, 11Be(p, d) and 10Be(d, p) transfer reactions are typical experimental methods to investigate this component. The Faddeev AGS, the XDWBA, and the XCDCC methods are developed to include this constituent in various theoretical models. With the core-excitation component, the calculated results can more reasonably describe the elastic scattering and breakup differential cross sections of 11Be impinging on various targets. Comparing the full XCDCC calculation with that omitting core-excitation effect, we found that this component mainly affects the elastic scattering differential cross sections at large center-of-mass angles, and the (p, d) transfer reaction angular distributions at small center-of-mass angles. In addition, its effect is non-negligible for the breakup reaction within the excitation energy interval of E_x = 0:5~3 MeV, and is remarkable for E_x =3 5:5 MeV.