Pion Absorption Cross Section Research Articles

The short-range correlation of asymmetric nucleonic matter at finite temperature: The LOCV approach

The short-range correlation of the asymmetric nucleonic matter (ASM) is perused at finite temperature in the lowest order constrained variational (LOCV) method. It is observed that, by increasing the temperature, the LOCV ASM static non-central distribution functions become weak. For small inter-particle distances, a universal behavior is found for the LOCV ASM state-dependent density distributions. Using the expectation value of the one-pion exchange part of the AV18 interaction, the scaling factor of the pion absorption cross section (the number of quasideuterons), for the different proton to neutron ratios R, is also estimated in the LOCV formalism. It is shown that, by increasing (decreasing) the ratio R (the temperature), the number of quasideuterons grows. Considering the scaling factor, the Bethe-Levinger (BL) factor for the ASM is also investigated. It is demonstrated that, at the saturation density and temperature 20 MeV, the BL factor for the ASM with R=1(0.5) becomes 4.3 (4.5).

Spin–Isospin Modes in Heavy-Ion Collisions: II. Transport Simulations

Transport simulations including in-medium properties derived in a microscopic π+NN−1+ΔN−1 model in infinite nuclear matter are presented. In-medium pion dispersion relations, partial Δ decay widths, pion absorption cross sections, and Δ cross sections are incorporated into the transport description by means of a local density approximation. Comparisons between standard and medium-modified transport simulations are presented. Large changes of π and Δ production and absorption rates are found, but the effect on the resulting pion observables is relatively small.

Transport simulations with π and Δ in-medium properties

Transport simulations including in-medium properties derived in a microscopic π+ NN −1+ ΔN −1 model in infinite nuclear matter are presented. In-medium pion dispersion relations, partial Δ decay widths, pion absorption cross sections and Δ cross sections are incorporated into the transport description by means of a local-density approximation. Strong modifications of π and Δ production and absorption rates are found, but only small effects on pion observables.

Total and partial pion absorption cross sections on4Hein the Δ resonance region

This paper presents a large solid angle measurement of the positive pion absorption cross section on 4He and its decomposition into partial channels. The total absorption cross sections at incident pion kinetic energies of Tπ+=70, 118, 162, and 239 MeV are 35±5, 52±4, 51±5, and 27±2 mb, respectively. These values are lower than those reported in some previous experiments. At all pion energies a large fraction of the absorption cross section is due to multinucleon channels.Received 2 September 1997DOI:https://doi.org/10.1103/PhysRevC.58.942©1998 American Physical Society

Pion absorption reaction on 2H and 3He in the Δ-isobar region

By using Faddeev equations the absorption of π + on 3He in the Δ-isobar region is investigated with the final state three-nucleon interaction. We calculated the NN - NΔ t-matrix and πN → Δ vertex from a phenomenological model for NN and πd reactions. In case of neglecting the initial pion scattering effects the theoretically predicted peaks of the pion absorption cross sections for 2H and 3He occur at too high an energy with respect to the data. It is shown that the final state three-nucleon interactions have a negligible effect on the magnitude and the shift of the peak position. By a small modification of the Δ bare mass and the πNΔ coupling strength the peak positions of the absorption cross sections of 2H and 3He are simultaneously brought to the correct peak position. The Dalitz plots of the outgoing three protons are shown and compared to the recent PSI measurements using kinematics cuts which almost eliminate the contribution from quasi free pion absorption.

Pion absorption cross section for2H and3He in theΔ-isobar region: A phenomenological connection

The absorption of ${\ensuremath{\pi}}^{+}$ on ${}^{3}$He in the $\ensuremath{\Delta}$ region is evaluated with exact inclusion of the final state interaction among the three emerging protons. The absorption is described by a $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\Delta}$ vertex and an $N\ensuremath{\Delta}$-$\mathrm{NN}$ transition $t$ matrix which are calculated from a phenomenological model for $\mathrm{NN}$ and $\ensuremath{\pi}d$ reactions. In a calculation where the initial pion scattering effects are neglected, the predicted peaks of the pion absorption cross sections for ${}^{2}$H and ${}^{3}$He lie too high in energy in relation to the data. The effect of the final-state three-nucleon interaction turns out to be too small for changing the magnitude and shifting the peak position of the total absorption cross section for ${}^{3}$He. We demonstrate that the adjustment of the peak position for the deuteron cross section by small modifications of the $\ensuremath{\Delta}$ parameters automatically leads to the correct peak position in ${}^{3}$He.

Pion vs. photon absorption on the deuteron

Using an NN → ΔN transition potential fixed by the reaction pp ↔ dπ + a good agreement can be obtained also for the reaction γd → pn in the Δ region. Further it is seen that the πNΔ and ϱNΔ parameters of the widely used Bonn potential, fitting the NN sector, yield a transition potential too weak to reproduce the pion production or absorption cross section.

Neutrino-induced nuclear excitations.

We present an improved, compared to that of Belusevic and Rein, theoretical value of the cross section for the neutrino-induced nuclear excitation of iron. This result is based on a measurement of the photoabsorption cross section on the same nucleus, which can be related to the transverse part of the neutrino cross section via the conserved vector current hypothesis. The longitudinal part is related to the pion absorption cross section through the partial conservation of the axial-vector current, and thus reflects the spontaneous breaking of chiral symmetry. A general formula for the excitation cross section is derived, which is valid for both low and high incident neutrino energies. When caused by a weak neutral current, this process may play an important role in core-collapse supernovae. It can also be detected using low-temperature techniques with the purpose of cosmological and weak-interaction studies. A new estimate of the cross sections for neutrino-induced nonscaling processes described by Belusevic and Rein is discussed in the context of two experiments using iron targets, but at very different beam energies.

Statistical model of three nucleon pion absorption.

In this paper we present a model for three nucleon pion absorption based on the assumption that pion absorption on three nucleons is a one-step process. In the assumption that the square of the effective matrix element is proportional to the probability that three nucleons are contained inside a certain volume V, this model is equal to the Fermi statistical model. The construction of the volume V is different from the Fermi model. Very good agreement between this simple model and experimental data for the energy dependence of the three-nucleon pion absorption cross section on $^{3}\mathrm{He}$ and $^{3}\mathrm{H}$ opens a new possibility for the explanation of multinucleon effects in pion absorption.

Pion-nucleus reactions in a microscopic transport model

We analyse pion-nucleus reactions in a microscopic transport model of the BUU type, which propagates nucleons, pions, deltas and N(1440) resonances explicitly in space and time. In particular we examine pion absorption and inelastic-scattering cross sections for pion kinetic energies Tπ = 85–315 MeV and various target masses. In general, the mass dependence of the experimental data is well described for energies up to the Δ-resonance (≈ 160 MeV), while the absorption cross sections are somewhat overestimated for the higher energies. In addition we study the possible dynamical effects of delta and pion potentials in the medium on various observables as well as alternative models for the in-medium Δ-width.

Effect of isospin on three nucleon pion absorption in light nuclei.

In this paper we present a model based solely on isospin for the determination of ratios of pion absorption cross sections on three nucleons. We then compare the results with the available experimental data for pion absorption on $^{3}\mathrm{He}$ and $^{4}\mathrm{He}$, at the energies 120 and 165 MeV, and for $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ at 50, 100, 140, and 180 MeV. Good agreement was found between this simple model and experiment, suggesting that pion absorption on three nucleons in light nuclei may be described as a one step process.

Energy dependence of the total 12C(π +, 2p) cross section

Measurements have been made of the excitation function for π + absorption on 12C at energies from 19 to 140 MeV using a large solid angle bismuth germanate multi-element detection system. These measurements show a smooth energy dependence of the pion absorption cross sections contradicting a previously reported dip in the energy dependence at 28 MeV.

Three-nucleon processes and the total pion absorption cross section in 3He

Pion absorption processes involving three nucleons have been investigated in 3He with positive and negative pions of 64, 119, 162 and 206 MeV kinetic energy. The most important of these processes is characterized by a constant phase-space density and has comparable integrated cross sections for π + and π − with a Δ-resonance-like dependence on the pion energy. This process constitutes up to one third of the total absorption cross section. The total absorption cross section has been determined by adding up the measured cross sections for all the observed absorption channels.

Inclusive inelastic scattering of 96.5-MeV pi + and pi - by the hydrogen and helium isotopes.

Spectra, angular distributions, and integrated cross sections for inclusive inelastic scattering of 96.5-MeV {pi}{sup +} and {pi}{sup {minus}} from {sup 2}H, {sup 3}He, and {sup 4}He are presented. The measurements were made using a high-pressure gas cell, which permits an accurate determination of relative cross sections for all targets. The data are compared with distorted-wave impulse-approximation calculations and with a modified plane-wave impulse-approximation calculation. In addition, by combining the total inelastic cross sections from this work with estimates of single-charge-exchange cross sections and with published values and reasonable estimates of the other {pi}{sup +} cross sections at the same energy, values for total reaction and pion absorption cross sections are obtained for all the targets. The dependence of these cross sections on {ital Z}, {ital N}, nuclear density, and nuclear binding energy is discussed in terms of a simple model.

Pion spectra in a hadronic transport model for relativistic heavy ion collisions.

A set of coupled transport equations for the phase-space distribution functions of nucleons, deltas, and pions is solved with the test particle method to study pion production in relativistic heavy ion collisions. The experimentally observed concave shape of the pion spectra is well reproduced. The mechanism that causes the concave shape of the pion spectra is found to be due to the different contributions of the delta resonance produced during the early and the late stages of the heavy ion collision and due to the energy dependence of the pion and delta absorption cross sections. The dependence of the shape of the pion spectra on beam energy, target and projectile mass, and impact parameter is also studied. An approximate scaling function for the shape parameter of the pion spectra is found.

Three-nucleon pion absorption in carbon.

We have performed an experiment in which we have detected three protons in coincidence, following the absorption of positive pions in carbon. Data were collected with twelve plastic scintillator detectors, covering a fairly large region of the available phase space, at three incident pion kinetic energies: ${T}_{\ensuremath{\pi}}$=130, 180, and 228 MeV. Comparisons are made with phase space calculations which simulate quasifree three-nucleon and four-nucleon absorption mechanisms. The first of these provides an excellent description of the bulk of the data. Some of the observed events appear to come from quasideuteron absorption, followed by a final-state interaction of one of the outgoing protons. There is no evidence for absorption mechanisms involving more than three nucleons. Estimates are made for the contributions of the three-nucleon absorption mechanisms to the total pion absorption cross section. These are relatively small.

67Li( pi +,pd)3,4He reactions at 59.4 MeV.

The (..pi../sup +/,pd) reactions on /sup 6/Li and /sup 7/Li have been studied at T/sub ..pi../ = 59.4 MeV. Triple- and single-differential cross sections for these reactions are presented. The data are fitted to a T matrix and compared to the /sup 3/H(..pi../sup +/,p)/sup 2/H reaction. A model in which the pion interacts and is absorbed on a ''quasi-triton'' cluster describes the main features of the data very well. An extrapolation of our data into unmeasured regions of phase space suggests that about 8% of the pion absorption cross section on /sup 6/Li at 59.4 MeV goes into the (..pi../sup +/,pd) channel. The /sup 7/Li(..pi../sup +/,pd)/sup 4/He(2 /sup -/) transition at 22.1 MeV excitation appears to be strongly populated. This is a surprise because it is not seen in the /sup 7/Li(p,..cap alpha..)/sup 4/He reaction.

Pion absorption on nuclei at 65 MeV.

Proton-proton and proton-neutron angular correlations as well as proton and deuteron inclusive spectra from pion absorption on C, Al, Cu, and Ta were measured at ${T}_{\ensuremath{\pi}}$=65 MeV. We compared the results with the prediction of the intranuclear cascade model, assuming that pion absorption proceeds only through two-nucleon absorption processes. The differential cross sections of the (${\ensuremath{\pi}}^{+}$,p) and (${\ensuremath{\pi}}^{+}$,pp) reactions were fairly well reproduced by the calculation in a wide angular range. Ratios R of the pion absorption cross section on a pn pair to that on a pp or nn pair, were in agreement between the inclusive and exclusive measurements for C and Al, but for Cu, the inclusive measurement gave a smaller R value. The internuclear cascade calculations for the (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,pn) and (${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$,pp) reactions revealed the importance of the pion charge exchange process before absorption, even at ${T}_{\ensuremath{\pi}}$=65 MeV.

Triple-differential cross sections of the ( pi +,pp) reaction on lithium isotopes.

The ( ,pp) reactions on WLi and XLi have been studied at T/sub / = 59.4 MeV with high resolution. The first triple-differential cross sections for these reactions are presented. The data are fitted to a T matrix and compared to the d pp reaction. A model in which the pion is absorbed on a TS1 (pn) pair in the lithium nucleus describes many features of the data very well. An extrapolation of our data into unmeasured regions of phase space suggests that about 60% of the pion absorption cross section on WLi at 59.4 MeV goes into the ( ,pp) channel. One surprising feature of the data is that the WLi( ,pp)UHe (2 ) transition at 22.1 MeV excitation is strongly populated, similar to what is observed in the WLi(d, ) UHe reaction. This transition involves removing one nucleon from the 1p shell and one from the 1s shell.

Isospin dependence of pion absorption on nucleon pairs

The suppressed ratio of (${\ensuremath{\pi}}^{\ensuremath{-}},\mathrm{pn}$) to (${\ensuremath{\pi}}^{+},\mathrm{pp}$) pion absorption cross sections on $^{3,4}\mathrm{He}$ has an important contribution from NN\ensuremath{'} intermediate states, where N\ensuremath{'} denotes a ${P}_{11} \ensuremath{\pi}\mathrm{N}$ interaction. The order-of-magnitude energy variation of this ratio, from stopped pions to pions above the (3,3) resonance, is reproduced in calculations using a unitary isobar model. We predict a strong asymmetry in the angular distribution of the ratio of higher pion energies.