Radiative Pion Research Articles

Radiative pion capture on 13C.

It is found that the differential cross sections for $^{13}({\ensuremath{\pi}}^{+}$,\ensuremath{\gamma}${)}^{13}$N $_{\mathrm{g}.\mathrm{s}.}$ for 115.5 MeV kinetic energy pions can be understood within the framework of a distorted wave impulse approximation, suggesting that core polarization and precursor effects give small contributions. It is further found that, within the limits of current nuclear photopion theory, the data for the radiative capture process are incompatible with earlier measurements for the inverse reaction $^{13}(\ensuremath{\gamma}$,${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$${)}^{13}$N $_{\mathrm{g}.\mathrm{s}.}$. It is shown that the reconciliation of the two sets of data places stringent demands on possible modifications to the theory.

First observation of the decay π + → e +νe +e − and a determination of the form factors FV, FA, R

The radiative pion decay π + → e + νe +e - has been observed for the first time. Information on the form factors was obtained from the kinematical distribution of 79 events. The vector form factor has the same sign as the pion decay constant f π . The ratios of axial-vector form factors to the vector form factor are γ = F A F V = 0.7 ± 0.5 and ξ = R F V = 2.3 ± 0.6. The value for γ is in agreement with the small positive value (0.53 ± 0.06) and excludes the large negative value (−2.49 ± 0.06) of γ obtained in π + → e +νγ experiments.

Chiral symmetry and radiative pion decay.

Within the context of chiral symmetry we analyze the radiative pion-decay process ${\ensuremath{\pi}}^{+}$\ensuremath{\rightarrow}${e}^{+}$${\ensuremath{\nu}}_{e}$\ensuremath{\gamma}. The interrelationship of various approaches is demonstrated, and we show that present phenomenology is consistent with the value \ensuremath{\gamma}=${h}_{A}$/${h}_{V}$\ensuremath{\simeq}+0.5. .AE

Isovector transitions in 1p-shell nuclei induced by radiative pion capture

A systematic study of radiative pion capture transitions in 1p-shell nuclei has been performed. High-resolution photon spectra measured with a pair spectrometer for 6Li, 7Li, 9Be, 10B, 11B, 12C and 14N targets show transitions to low-lying bound states of 6He, 7He, 9Li, 10Be, 11Be, 12B and 14C respectively. The observed levels are predominantly analogs of isovector M1 states in the target nucleus. The measured branching ratios are compared to various shell-model calculations using nuclear wave functions constrained to fit other electromagnetic and weak properties of the same levels or their analogs. The data are found to be consistent with existing electron scattering data where they exist.

Inclusive radiative pion capture by N = Z nuclei in the 1p shell

A study of inclusive radiative pion capture by means of sum rules is given for the case of self-conjugated nuclei in the 1p shell. The sum rules M 0 and M 1 are evaluated for the dominant Kroll-Rudermann term in the effective hamiltonian. Total branching ratios and mean photon energies are determined from the calculated sum rules. These quantities compare reasonably well with experiment.

On the role of complicated shell-model configurations in the description of radiative pion capture on16O

The importance of np-nh configurations in the description of the ( pi -, gamma ) reaction on closed-shell nuclei is investigated. The numerical results obtained for the target nucleus 16O show that the influence of complicated ground-state configurations can be described approximately by a renormalisation factor ( alpha 0)2, where alpha 0 is the amplitude of the 0p-0h component of the target wavefunction.

Constituent-quark and baryon loops in pseudoscalar-meson transitions

Predictions for the ..pi gamma gamma.. coupling, the pion charge radius , the q/sup 2/ dependence of the pion decay constant near q/sup 2/ = 0 (f/sub ..pi..//sup prime/(0)), and the ratio ..gamma.. describing radiative pion decay are obtained in the context of two related models: the constituent-quark model and a baryon-loop model with n/sub f/ = 2, 3, or 4 flavors. All these models lead to two relations among the four above-mentioned parameters, which are satisfied by the data. A sort of equivalence or duality for the two models is observed, particularly for n/sub f/ = 4.

Decayπ+→e+e+e−νand theγparameter

A possible way to extract the value for the $\ensuremath{\gamma}$ parameter in the radiative pion decay is presented through the study of the decay process ${\ensuremath{\pi}}^{+}\ensuremath{\rightarrow}{e}^{+}{e}^{+}{e}^{\ensuremath{-}}\ensuremath{\nu}$. A particular kinematic configuration is suggested to select those events dominated by the structure-dependent contribution without having to perform the difficult measurement on particle polarizations, but retaining the favored picture from the study of a polarized electron in the radiative pion decay ${\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{e}^{\ensuremath{-}}\overline{\ensuremath{\nu}}\ensuremath{\gamma}$. A specific positron spectrum is given for this particular configuration to serve as a tentative way of determining an exact value for $\ensuremath{\gamma}$ between the existing two possible ones.

Impulse approximation versus elementary particle method: Pion photoproduction and radiative muon capture

General differences between the impulse approximation and the elementary particle method in the treatment of two-step processes like pion photoproduction and radiative muon and pion capture are discussed. Important numerical differences arise, exemplified by pion photoproduction on /sup 3/He. The reason is that the Born approximation with low-energy theorems leaves terms undetermined in the elementary particle method. In particular it is shown that in pion photoproduction in pseudo- p scalar coupling the impulse approximation accounts for numerically sizable contributions of intermediate nuclear excited states not contained in the elementary particle method. In pseudovector coupling no unique and unambiguous relation between the pion-nucleus coupling constant and pion photoproduction holds. An earlier calculation of radiative muon capture by /sup 3/He is improved by including in a semiempirical way exchange contributions to the muon radiating diagram.

Importance of the orbital magnetization for isovectorM1transitions of nuclei in thesdshell

The spin and orbital-current contributions to isovector M1 transitions in light nuclei are studied using shell model wave functions. An impressive effect of the orbital magnetization is predicted for /sup 20/Ne and demonstrated by comparing the M1-strength distributions for inelastic electron scattering with the distribution for radiative pion capture and (p,n) reactions.

M2states inA=15:N15(π−, γ)C15

Radiative pion capture in a liquid $^{15}\mathrm{N}$${\mathrm{H}}_{3}$ target has been measured with a high-resolution photon detector. Evidence for ${J}^{\ensuremath{\pi}}={\frac{5}{2}}^{+}$, $T=\frac{3}{2}$ giant magnetic quadrupole states has been found. Results of a shell model calculation are given which represent the experimental spectrum satisfactorily. For the ${J}^{\ensuremath{\pi}}={\frac{5}{2}}^{+}$, ${E}^{*}(^{15}\mathrm{C})=0.75$ MeV level and the total spectrum the measured branching ratios are (9.6\ifmmode\pm\else\textpm\fi{}2.4) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ and (2.4\ifmmode\pm\else\textpm\fi{}0.6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$, respectively.NUCLEAR REACTIONS $^{15}\mathrm{N}({\ensuremath{\pi}}^{\ensuremath{-}}, \ensuremath{\gamma})^{15}\mathrm{C}$, (${E}_{x}<25$ MeV), ${E}_{\ensuremath{\pi}}=0$ MeV, measured photon spectra, pair spectrometer, compared with shell model calculations.

Analysis of radiative pion decayπ−→e−νγ

We give a quantitative account of radiative pion decays. By the chiral structure of the interaction and the fact of the low mass ratio between an electron and a pion, one can suppress the inner-bremsstrahlung contribution and correspondingly enhance the structure-dependent contribution by looking at decays with the emission of a negative-helicity electron. By this observation, we examine a way of determining the value of the structure-dependent parameter $\ensuremath{\gamma}$, giving particular attention to the decay spectra with this electron helicity. We also investigate the effects of a neutrino mass in this process.

An exact operator solution of the quantum liouville field theory: Eric Braaten, Thomas Curtright, and Charles Thorn. Physics Department, University of Florida, Gainesville, Florida 32611

The present-day status of the giant dipole resonance (GDR) in light nuclei is discussed with main emphasis on the supermultiplet and configurational splitting of GDR, which are its most important features. A great wealth of experimental data, which confirm the existence of the above phenomenon are presented. Consideration is also given to the related problems, such as radiative pion capture and muon capture, spin-isospin dipole excitations, the role of the supermultiplet structure of nuclear levels in the formation of hypernuclear states in processes of the coherent substitution of hyperons for nucleons.

Electroproduction ofπ+fromB10and its relation to electron scattering

The electroproduction of 12.3 +- 0.7 MeV positive pions from /sup 10/B, leading to low-lying states in /sup 10/Be, has been measured in the angular range theta/sub ..pi../ = 30/sup 0/--140/sup 0/ for incident electron energies E/sub e/ = 158.5--165.0 MeV. The unique character of M3 transitions in the p shell permits a direct comparison of d/sup 2/sigma/dE/sub ..pi../d..cap omega../sub ..pi../ with the analog electron scattering form factors in /sup 10/B, assuming the strong ..pi..-nucleus interaction can be neglected. For the two lowest T = 1 states, the (e,..pi../sup +/) angular distributions agree with the M3 form factors. The convective term in the M1 form factor for the third T = 1 state is deduced from a comparison of the (e,..pi../sup +/) and (e,e') data and is in good agreement with recent radiative pion capture results. The photoproduction cross section leading to the /sup 10/Be ground state is estimated.

The QCD non-perturbative contribution to the axial form factor in radiative pion decay

We show that QCD non-perturbative terms à la Shifman-Vainshtein-Zakharov are crucial for understanding the radiative pion decay. We obtain for the axial-vector form factor γ = 0.0 ± 0.3 which is in very good agreement with one of the two experimental values γ exp = 0.15 ± 0.11 and excludes the other one γ exp = −2.1 ± 0.11.

Some comments on the π-3He-3H coupling constant

Some comments are made on recent determinations of the π-3He-3H coupling constant. It is pointed out how the impulse approximation and the elementary particle method treat differently two step processes like radiative pion or muon capture and photo pion production.

Energy spectra of neutrons emitted following muon capture in 16O and 12C

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.

Gauge invariance and nucleonic Fermi motion in radiative pion capture on16O

Partial transition rates and the gamma -ray spectrum for the radiative pion capture reaction on 16O have been evaluated using the gauge-invariant effective Hamiltonian which also contains the nucleonic Fermi motion effects. Compared with the results obtained for the conventional effective Hamiltonian, a 15-25% reduction in the yield of the gamma -ray spectrum is observed. This is almost completely related to a new energy term and kinematic renormalisation of the constants of the effective Hamiltonian results in essential changes in the weak partial transitions.

The observation of charge exchange of pions captured in several nuclei

We have measured for the first time the branching ratios of the charge exchange of stopped negative pions in targets of 6Li, Al, Ti, Cu, Nb and Pb. These branching ratios are of the order of 10 −6, about an order of magnitude smaller than the upper limit previously established. Using the branching ratio for radiative pion capture in 6Li to the ground state of 6He we obtain the Panofsky ratio in 6Li, P 6 = (8.7 ± 2.3) × 10 −4.

Parity violation: Radiative pion capture in hydrogen

We investigate radiative pion capture in hydrogen, π − → n γ, as a means of determining the parity-violating πNN coupling constant ƒ π. We include contributions from the lightest baryon resonance [Δ(1232)] and the light vector mesons [ρ, ω, φ]. Our results indicate that, despite their negligible role in parity-conserving amplitudes, the effects of the Δ and ρ may hamper the determination of ƒ π.