Building light nuclei from neutrons,protons, and pions

In these lectures I first explain, in a rather basic fashion, the construction of effective field theories. I then discuss some recent developments in the application of such theories to two- and three-nucleon systems.     

Polarization of recoil neutrons from single-pion photoproduction off protons in the resonance region

The polarization of the recoil neutrons from the reaction γp→π⁺n was measured at a c.m. angle of 105° for incident photon energies between 675 and 1125 MeV. A scattered π⁺ meson and a recoil neutron were detected in coincidence with a magnetic spectrometer and a neutron polarimeter system using liquid hydrogen. Results are compared with recent phenomenological analyses and the other existing data measured by the double polarization measurement technique.     

Evidence for nucleon-resonance excitation in omega-meson photoproduction

The photoproduction of the omega meson has been studied at GRAAL from threshold up to a photon energy of 1.5 GeV. The differential cross sections and beam asymmetries have been measured precisely at all angles. The total cross section is also obtained. Systematic enhancements of the differential cross section at large angles and nonzero beam asymmetries at intermediate angles provide clear evidence for s- and u-channel resonant processes. The data are compared to the results of hadron and quark models.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Forward photoproduction of neutral pions on protons in the third resonance region

Four angular distributions of the differential cross section of the reaction γ + p → π⁰ + p have been measured at the Bonn 2.5 GeV Synchrotron at pion c.m. angles between 3° and 63° in the photon energy range from 0.9 GeV to 1.2 GeV. The π⁰ mesons were detected by their two decay photons. The data are compared with data of other laboratories and predictions of two recent partial-wave analyses.     

Production of neutrons in thick targets by high-energy protons and nuclei

This article is dedicated to the physics of spallation neutron production by high-energy particles and applications thereof. This field of research is related to the rapidly developing branch of nuclear physics that is high-energy neutron physics. The central part of this article is a review of experimental results obtained in different laboratories of the world during the last more than a quarter of a century. Analysis of the characteristics of multiple neutron production in targets induced by protons and nuclei with energies higher than several hundreds of mega-electronvolts per nucleon is performed. The results of measurements that were carried out at the Joint Institute for Nuclear Research with beams of protons, deuterons, and light nuclei are discussed. Natural and artificial sources of spallation neutrons and their role in up-to-date studies are considered.     

Forward photoproduction of neutral pions on polarized protons in the third resonance region

Angular distributions of the target symmetry for the reaction γ + p → π⁰ + p have been measured at the Bonn 2.5 GeV Electron Synchrotron at pion c.m. angles between 13° and 63° and photon energies of 1.0 and 1.1 GeV. The π⁰ mesons were detected by their two decay photons with total absorption lead-glass ?erenkov counters. Butanol was used as target material in a continuous flow ³He cryostat operating at 0.5 K and 25 kG. The π⁰ counting rate from free protons in the butanol target was derived from the measurements of the differential cross section on hydrogen. The data are compared with data of other laboratories and the results of two recent partial-wave analyses.     

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of?ω for neutrons and protons separately, as functions of the neutron numberN and the proton numberZ respectively, are derived. The dependence ?ω_n(?ω_p) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of?ω show “discontinuities in the slope” at the closed shells throughout the periodic table. The difference ?ω_n — {ie17-01} is also discussed.     

Possibility of observation of hidden-bottom pentaquark resonances in bottomonium photoproduction on protons and nuclei near threshold

We study the \begin{document}$\Upsilon(1S)$\end{document} meson photoproduction on protons and nuclei at near-threshold center-of-mass energies below 11.4 GeV (or at the corresponding photon laboratory energies \begin{document}$E_{\gamma}$\end{document} below 68.8 GeV). We calculate the absolute excitation functions for the nonresonant and resonant photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons off protons at incident photon laboratory energies of 63-68 GeV by considering direct (\begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}) \begin{document}$\Upsilon(1S)$\end{document} production channels within different scenarios for the nonresonant total cross section of the elementary reaction \begin{document}${\gamma}p \to {\Upsilon(1S)}p$\end{document} and for branching ratios of the decays \begin{document}$P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}$P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, and \begin{document}$P^+_b(11130) \to {\Upsilon(1S)}p$\end{document}. We also calculate an analogous function for the photoproduction of \begin{document}$\Upsilon(1S)$\end{document} mesons on the ¹²C and ²⁰⁸Pb target nuclei in the near-threshold center-of-mass beam energy region of 9.0-11.4 GeV by considering the respective incoherent direct (\begin{document}${\gamma}N \to {\Upsilon(1S)}N$\end{document}) and two-step (\begin{document}${\gamma}p \to P^+_b(11080) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11125) \to {\Upsilon(1S)}p$\end{document}, \begin{document}${\gamma}p \to P^+_b(11130) \to {\Upsilon(1S)}p$\end{document} and \begin{document}${\gamma}n \to P^0_b$\end{document}\begin{document}$ (11080) \to{\Upsilon(1S)}n $\end{document}, \begin{document}${\gamma}n \to P^0_b(11125) \to {\Upsilon(1S)}n$\end{document}, \begin{document}${\gamma}n \to P^0_b(11130) \to {\Upsilon(1S)}n$\end{document}) \begin{document}$\Upsilon(1S)$\end{document}) production processes using a nuclear spectral function approach. We demonstrate that a detailed scan of the\begin{document}$\Upsilon(1S)$\end{document} total photoproduction cross section on proton and nuclear targets in the near-threshold energy region in future high-precision experiments at the proposed high-luminosity electron-ion colliders EIC and EicC in the US and China should provide a definite result for or against the existence of the nonstrange hidden-bottom pentaquark states\begin{document}$P_{bi}^+$\end{document} and \begin{document}$P_{bi}^0$\end{document} (\begin{document}$i$\end{document}=1, 2, 3) as well as clarify their decay rates.     

Pion production by 600 MeV protons on light nuclei

The forward cross section at E_p=600 MeV is calculated for the reaction $\text{p}\text{+(N, Z)→(N+1, Z)}{}^1\text{+π}{}^{\mathrm{+}}$ using a single-nucleon mechanism, distorted pion and proton wave functions and bound-state nucleon wave functions with realistic asymptotic behavior. Good agreement with experiment is found for ⁴He, ¹²C, and ¹⁴N.     

Polarization of protons formed in the electrodisintegration of light nuclei

It is shown that the protons arising from the electrodisintegration of light nuclei may be considerably polarized. Relationships are obtained between the degree of polarization and the escape angle of the protons in the coplanar case. The polarization is extremely sensitive to the choice of the distorted wave function of the proton in its final state.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 7, pp. 31–34, July, 1973.     

Evaluation of the photoproduction of negative pions on neutrons in the region of the first resonance

In this paper we extend our systematic investigation of pion photoproduction to the case of negative pion production on neutrons. In our approach two phenomenological parameters occur in the electric and magnetic dipole amplitudesE ₀₊ andM _1?. These constants have been determined by a least squares fit of the total cross section data of the ABBHHM collaboration. We obtain a very good fit, also the prediction of the asymmetry ratio for polarized photons agrees with experiment at energies below and at the resonance. Serious discrepancies between theory and experiment are found for theπ ^?/π ⁺ ratio, moreover the relationship between the electric dipole at threshold, the Panofsky ratio and the difference ofs-waveπN-scattering lengths is fulfilled only within 20%. These discrepancies are discussed thoroughly.     

The photoproduction of neutral pions from protons at forward angles in the resonance region

Differential cross sections for the photoproduction of pi-zero mesons from protons have been measured at angles between 10° and 70° c.m. in the energy range 0.85 GeV to 1.30 GeV. The values are compared with the fits to pion photoproduction data from three recent partial-wave analyses.     

Photofission of actinide nuclei in the nucleon-resonance region: First photonuclear experiment at the Siberia-2 storage ring

Results of an experiment performed to study ²³⁸U photofission with the aid of the initial section of the GAMMA channel of the Siberia-2 storage ring at the Kurchatov Institute are presented. These results are predominantly of a methodological value, because a photonuclear experiment was conducted for the first time in this channel. However, the data obtained in this way allowed us to evaluate an upper limit on the probability of the fast fission (fragmentation) of ²³⁸U nuclei that was induced by photons of energy up to 2.5 GeV. This is pertinent to the problem of the deviations of the total photoabsorption cross sections for actinide nuclei from a “universal curve.”     

Subthreshold and near-threshold K +-meson production on light nuclei by protons

Inclusive K ⁺-meson production in proton-nucleus collisions in the near-threshold and subthreshold energy regimes is analyzed with respect to the one-step (pN → K ⁺ YN, Y=Λ, Σ) and two-step (pN → NNπ, NN2π; πN → K ⁺ Y) incoherent production processes. An appropriate folding model is used that properly takes into account the struck-target-nucleon-removal energy and the momentum distribution (nucleon spectral function), novel elementary cross sections for proton-nucleon reaction channel close to threshold, as well as nuclear-mean-field-potential effects on the one-step and two-step kaon-creation processes. A detailed comparison of the model calculations of the K ⁺ total and differential cross sections for the p+⁹Be and p+¹²C interactions with the existing experimental data is given, which displays both the relative role of the primary and secondary production channels at considered incident energies and those features of the cross sections that are sensitive to the high-momentum and high-removal-energy parts of the nucleon spectral function. It is found that, contrary to previous studies known in the literature, the pion-nucleon production channels do not necessarily dominate in pA collisions at subthreshold energies and that the relative strength of the proton-and pion-induced reaction channels for light target nuclei in the subthreshold energy regime is governed by the kinematics of the experiment under consideration.     

Role of two-nucleon mechanisms in pion photoproduction on nuclei in the region of high momentum transfers

The role of two-nucleon mechanisms in pion photoproduction on nuclei was studied in the region of high momentum transfers to the residual nucleus. The process in which the photoproduction of negative pions on a ¹²C nucleus is accompanied by proton emission was considered by way of example. The results of the calculations were compared with available experimental data.     

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.     

Polarization in the quasielastic scattering of 1-GeV/c protons on light nuclei

Polarization measurements in the A(p, 2p)B reactions on ⁶Li, ⁷Li, and ²⁸Si nuclei at a proton-beam energy of 1 GeV were performed in a kinematically complete experiment. By using a two-arm magnetic spectrometer, two secondary protons were recorded in coincidence at asymmetric scattering angles of θ₁=15°?26° and θ₂=58.6° for residual-nucleus momenta in the range K _B=0–150 MeV/c. Either arm of the spectrometer was equipped with polarimeters based on proportional chambers. The data coming from this experiment are analyzed within the distorted-wave impulse approximation. It is shown that the polarization of recoil protons formed at angle θ₂ in the interaction featuring a proton from the P shell of the ⁷Li nucleus can be described under the assumption of an effective intranuclear-proton polarization by using the single-particle shell-model wave function of the nucleus. Our data on the polarizations of the two protons from the reaction (p, 2p) on a ²⁸Si nucleus also suggest the effective polarization of the protons in the D shell of the ²⁸Si nucleus. It is found that, for high recoil-nucleus momenta of K _B≥90 MeV/c, the effective polarization of the protons in the P shell of the ⁶Li nucleus—this polarization was discovered in studying the polarization of recoil protons in the reaction ⁶Li(p, 2p)⁵He—cannot be described within the shell model assuming LS coupling. As might have been expected, the polarization of recoil protons knocked out from the S shells of the ⁶Li and ⁷Li nuclei comply well with the predictions obtained in the impulse approximation with allowance for the depolarization effect alone.     

πo photoproduction on quasi-free neutrons in the reaction γd → πo np in the Δ region

The possibility of obtaining information about the reaction γn → π^on in the Δ resonance region from the reaction γd → π^onp is analyzed. To this aim, the differential cross sections d³σ/dE_ndΩ_πdΩ_n both for unpolarized particles and in case of polarized photons and deuterons as well as the asymmetry Σ for linearly-polarized photons are calculated at photon energies from 250 to 400 MeV in the diagrammatic approach. The contributions from the pole diagrams as well as one-loop diagrams both with n-p and π-N-rescattering are taken into account. The main contribution to the differential cross sections of π^o photoproduction on the neutron in the quasi-free kinematics arises from the neutron pole diagram. The correction due to n-p rescattering decreases with increasing pion angle and becomes to be less than 8% at Θ_π ≥ 90°. The contributions of the proton pole diagram and the one of π -N rescattering were found to be negligible. Background effects are more pronounced in the case of the asymmetry Σ. However, they are also strongly suppressed in the neutron quasi-free kinematics at photon energies above 300 MeV.