The study of the binding energy of nuclear matter in the relativistic σ− ω− π model with Δ isobar degree of freedom

The relativistic σ?ω?π model is proposed and used to calculate the binding energy of relativistic nuclear matter. By coupling Δ isobar to the σ meson, the zero-point fluctuation energy of the Δ isobar in the one loop approximation is derived. We calculate the effective mass of nucleon and Δ isobar, exchange and correlation energies, pressure and incompressibility of nuclear matter. The density dependence correction to σNN ωNN coupling constants is a very important mechanism to saturate the binding energy. The pion propagator is nuclear matter is constructed by the relativistic particle-hole, delta-hole and short-range correlation. The pion dispersion relation is calculated we find it’s very sensitive to the effective mass of nucleon and Δ isobar.     

Treatment of the Δ current in electromagnetic two-nucleon knockout reactions

The contribution of the Δ(1232) isobar to the electromagnetic current of the two-nucleon system and its role in (γ,NN) processes is investigated. The difference between the genuine Δ-excitation current and that part of the current connected to the deexcitation of a preformed Δ in the target nucleus is stressed. The latter cannot lead to a resonant behaviour of matrix elements for energies in the Δ region. The reaction ¹⁶O(γ, pp)¹⁴C, where the Δ contribution is dominant at intermediate energies, is considered. The large variations found in the cross sections for different treatments stress the need for a proper treatment of the Δ current for a clear understanding of the reaction mechanism of two-nucleon emission processes.     

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.     

Soft-pion limits of the inclusive pion distributions in NN → π± + anything at rest

The PCAC hypothesis of extrapolating off mass shell is used to show that the invariant pion distributions in the reactions $\text{N}\text{N}\text{→ π}{}^{\mathrm{\pm }}\text{+}$ anything at rest must vanish as the pion momentum tends to zero, a behavior which is supported by recent data on $\text{p}\text{n}\text{→ π}{}^{\mathrm{\pm }}\text{+}$ anything.     

The ϱNN vertex in vector-dominance models

A new πN amplitude analysis and experimental data for the pion form factor have been used in order to determine the $\text{I = J = 1 ππ}\text{N}\text{N}$ partial waves and properties of the ?NN vertices. The results are compared with earlier determinations of ?NN coupling constants from πN and NN scattering and from nucleon for, factor data.     

A t-channel isospin analysis of the chew-low plot for NN → N(Nπ) interactions at 5.7 GeV/c

A new approach to the t-channel isospin analysis of ZN → Z′(Nπ) reactions is presented. This approach, useful for $\text{Z = N,}\text{N}\text{, K}{}^{\mathrm{?}}$ when only five independent sets of data are availables, is used to analyse data of $\text{N}\text{N →}\text{N}\text{(Nπ)}$ reactions obtained in a $\text{p}\text{p →}\text{N}\text{N}\text{π}$ experiment at $\text{5.7}\text{GeV}\text{/c}\text{and a}\text{p}\text{d →}\text{N}\text{Nπp}{}_{\mathrm{s}}$ experiment at 5.5 GeV/c. the t behaviour of the different isospin exchange amplitudes, suggests their exchange mechanism production. The mass spectrum, M_πN, of the contributions produced by exchanged isospin I_ex = 1, shows enhancements corresponding to N(1490) N(1670) and Δ(1230) isobars, while the mass spectrum for I_ex = 0 presents only a large bump at ～1350 MeV commonly identified as N¹(1400).     

Photoexcitation of the quasi-bound Δ nuclear state in the <Superscript>12</Superscript>C(γ, π<Superscript>−</Superscript>pp) reaction

Photoproduction of negative pions on the carbon nucleus in the (γ, π^?p) and (γ, π^?pp) reactions was experimentally studied. The measurement results are explained within the framework of a model which supposes formation of an intermediate quasi-bound Δ nuclear state (Δ nucleus) decaying with emission of a pion and a nucleon. The mass and width of the Δ nucleus ¹¹B_Δ are evaluated.     

Four-nucleon system with Δ-isobar excitation

The four-nucleon bound state and scattering below three-body breakup threshold are described based on the realistic coupled-channel potential CD Bonn+Δ$\text{Bonn}+\mathrm{\Delta }$ which allows the excitation of a single nucleon to a Δ isobar. The Coulomb repulsion between protons is included. In the four-nucleon system the two-baryon coupled-channel potential yields effective two-, three- and four-nucleon forces, mediated by the Δ isobar and consistent with each other and with the underlying two-nucleon force. The effect of the four-nucleon force on the studied observables is much smaller than the effect of the three-nucleon force. The inclusion of the Δ isobar is unable to resolve the existing discrepancies with the experimental data.     

A non-relativistic operator convenient for analysis of pion photoproduction on nuclei in the Δ(1236) region

In view of its application to the analysis of medium energy photonuclear reactions we have obtained an operator valid, to order $\text{(}\text{p}\text{m}\text{)}{}^2$, in any frame of reference. We have started from a model where the pion photoproduction on a nucleon is described by the Born terms and the s-channel Δ(1236) formation amplitude and we have deduced the non-relativistic limit of the corresponding matrix elements. Both pseudo-scalar and pseudo-vector pion-nucleon couplings are compared. The Δ(1236) parameters are chosen so as to lead to a good account of pion-nucleon reaction cross sections. The agreement with the charged photoproduction data is very good from threshold through the Δ(1236) energy region, whereas the addition of ω⁰ exchange in the t-channel is necessary to reproduce the neutral pion photoproduction cross sections. As an example this operator is used to derive the cross section of the γD → ppπ^? reaction in the spectator nucleon model when the undiscernability of the two outgoing protons is taken into account.     

Pion production and the higher resonances in pion-nucleon scattering

The reaction π + N → 2π + N has been studied in the vicinity of the higher resonances in the pion-nucleon cross section. The Low equation for the production amplitude is transformed into an integral equation by isolating the true one-meson intermediate states and discarding higher order contributions. The only part kept in the inhomogeneous term corresponds to the collision of a pion in the nucleon cloud with the incident pion in the resonant T = J = 1 state, which is simulated by an unstable vector Boson. Crossed terms are neglected and the 2π-N state is described by the static model. The terms kept in the sum over states describe the rescattering (off the nucleon) of one of the outgoing pions. The required off-the-energy-shell elastic scattering amplitude is approximated by the 3-3 resonance formula of Chew and Low. With these simplifications the Low equation for the production amplitude reduces to an easily soluble linear integral equation. The rescattering amplitude, which dominates the inhomogeneous term in the resonance region, is proportional to the 3-3 scattering amplitude of one of the outgoing pions. Although the result provides some support for the conventional isobar model, it is important to note that the largeness of the rescattering term arises from scattering far off the energy shell, rather than by “real” excitation as in the phenomenological isobar model. Quantitative calculations for the $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ channel leading to a p-wave ($\text{J =}\text{3}\text{2}$) and an s-wave pion produce a maximum in the cross section near 600 Mev incident pion lab energy. For a π-π resonance energy squared S = 10, agreement with experiment is obtained with a width about one third that suggested by nucleon electromagnetic structure. In our approximation, the well known 600 Mev $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ isospin $\text{1}\text{2}$ resonance occurs at the same energy as the 800 Mev $\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ isospin $\text{3}\text{2}$ resonance. It is assumed, but not proved, that the neglected terms are responsible for the splitting of the resonance energies. When this splitting is taken into account, the predicted charge state ratios near the second resonance agree well with existing data. The “third” resonance occurs for the state having two p-wave pions, according to the present theory, although no numerical calculations were made for this case. This point of view suggests that the $\text{F}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, and $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ incident channels contribute to the third resonance.     

The YN interactions and K− reactions on deuterium at low energies

The K^?d → π^?Λp reaction, as well as the other three-body K^? reactions on deuterium, are considered for s-wave kaons in the Faddeev formalism for charge-independent separable two-body coupled-channel interactions fitted to the available low-energy data. In particular we study the effect of a hypothetical $\text{I =}\text{1}\text{2}\text{, S = 1, Σ}\text{N}$ unstable bound state near the πΣN threshold on the shape of the calculated Λp invariant mass distribution near the ΣN threshold. This calculated distribution always exhibits a cusp behavior at the ΣN threshold, but considerable structure and broadening may be reached by varying the parameters of the YN interaction. Multiple scatterings in the initial K?NN and intermediate πΣN channels play a dominant role at low energy. The calculation compares favorably with the measurements at rest and at low energies. This comparison suggests that a ΣN bound state does not exist near the ΣN threshold.     

Determination of the one-pion exchange potential from pn and pp charge exchange scattering

The πNN vertex function is determined from $\text{d}\text{σ}\text{d}\text{t}$ for pn → np and $\text{p}\text{p →}\text{n}\text{n}$ at 8 GeV/c in the interval 0 < ? t < 0.1 GeV². A “regularor mass” of 3.5m_π=488 MeV is found, corresponding to an “extension” of 0.40 fm of the πNN vertex. The resulting OPE potential is discussed.     

SU(6) symmetry breaking effects in deep inelastic scattering

The fact that the N and Δ states of the $\text{56}$ baryons are not degenerate in mass is shown to imply that the deep inelastic scattering ratio F_2n(x)/F_2p(x) should approach $\text{1}\text{4}$ as x → 1. The rate of approach is predicted to be approximatel linear in x. The possibility of observing analogous effects in other large momentum transfer processes is also discussed.     

Antiproton annihilations in deuterium at rest into two pions: Evidence for pN bound states near threshold

The charged pion spectra in $\text{p}$d→π⁻π⁰p_s, π⁻π⁺n_s have been measured. The Doppler broadening of the pion mom entum due to the spectator neutron recoil is at least a factor of two larger than that due to the proton and in disagreement with that expected from the deuteron wave function. This effect and earlier observations on spectators are well described by assuming narrow $\text{N}$N bound states near threshold.     

The Δ mass dependence of the M matrix and its influence on the NΔ→NN cross-sections

TheΔmass dependence of the M matrix and its influence on the NΔ→NN cross-sections are investigated in the one-boson exchange model.Our calculations show that theΔmass dependence of the momentum of the outgoingΔand the M matrix affects the calculations ofσNΔ→NN,especially around the threshold energy.     

Calculation of baryon masses in quantum chromodynamics

The polarization operator of quark currents with baryon quantum numbers is considered in quantum chromodynamics. The non-zero mean vacuum values of the field operator products are taken into account. The sum rules are obtained assuming that in the virtuality region ～1 GeV, among the mean vacuum values violating the chiral invariance, the most important is $\text{〈0|}\text{ψ}\text{ψ|0〉}$. Saturating these sum rules by the lowest baryonic states one is able to calculate the masses of the isobar Δ and nucleon N, M_Δ = 1.4 GeV, M_N = 1 GeV, up to 15% through the known value $\text{〈0|}\text{ψ}\text{ψ|0〉}$. The mass splitting in the baryonic decuplet $\text{M}{}_{\mathrm{\Sigma 1}}\text{?M}{}_{\mathrm{\Delta }}\text{= 125}\text{MeV}$ is calculated in first order in the current strange quark mass m_s = 150 MeV. Certain results for other baryonic resonances have also been obtained.     

Analysis of two-prong events in antiproton-proton interactions at 5.7 GeV/c

A study of elastic scattering, one-pion production and annihilation reactions in $\text{p}$p interactions at 5.7 GeV/c was carried out, from the two-prong events, obtained in the hydrogen bubble chamber exposed at CERN.Single particle distributions for the reactions $\text{pp}\text{→}\text{pp}\text{π}{}^0\text{,}\text{p}\text{p}\text{→}\text{p}\text{n}\text{π}{}^{\mathrm{+}}$ and $\text{p}\text{p}\text{→}\text{p}\text{n}\text{π}{}^{\mathrm{?}}$ are presented. The study of the squared momentum transfer distributions with and without charge exchange in the cross channel shows different behavior of the slope parameters versus the mass of the produced (Nπ) system. The cross sections for isobar production and for diffractive dissociation in the one-pion production reactions are obtained from a detailed Dalitz plot analysis. The results of the analysis of the decay angular distributions for the N(1510) and for the N(1680) produced in these reactions are in agreement with $\text{J =}\text{3}\text{2}\text{and}\text{J =}\text{5}\text{2}$ assignment, respectively. The cross sections of the annihilation reactions $\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{and}\text{p}\text{p}\text{→ π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{π}{}^0$ are determined. Finally, we give some as aspects of the mass distributions for the last reaction.     

Double-charge-exchange and inelastic scattering in π−+3He

The reactions π^?+³He→⁺+3n and π^?+³He→^?+³He were studied to investigate the $\text{T=}\text{3}\text{2}$ three-nucleon system. The differential cross sections were measured at scattering angles from 20 to 40 degrees. The secondary pion was momentum analyzed in a magnetostrictive-readout wire-chamber spectrometer. The double-charge-exchange reaction yielded a secondary pion energy distribution, the features of which can be due to either a $\text{T=}\text{3}\text{2}$ three-nucleon resonance or a resonace of the nucleons in the ³He nucleus. The inelasticc scaterring reaction yielded a secondary pion energy distribution peaked near threshold, consistent with resonances in both the $\text{T=}\text{3}\text{2}$ and $\text{T=}\text{1}\text{2}$ three-nucleon systems.