Pionic States Research Articles

Pion–nucleon sigma term σπNand deeply bound pionic atoms

AbstractWe investigate the possibility of determining the value of the pion–nucleon sigma term σπN precisely by the experimental observables of deeply bound pionic atoms. We discuss the sensitivity of the observables to σπN and take into account the typical errors of up-to-date experiments on deeply bound pionic atoms. We find that the gap in the binding energies and the width of the deeply bound pionic states are good observables for σπN value determination with experimental data. We also discuss the expected difficulties for the accurate determination of the value of σπN due to the correlation between the σ term and the potential parameter in the pion–nucleus optical potential.

Confining density functional approach for color superconducting quark matter and mesonic correlations

We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Beyond the mean field, quark correlations in the pseudoscalar channel are described within the Gaussian approximation. This explicitly introduces pionic states into the model. Their contribution to the thermodynamic potential is analyzed within the Beth–Uhlenbeck framework. The modification of the meson mass spectrum in the vicinity of thee (de)confinement transition is interpreted as the Mott transition. Supplemented with the vector repulsion and diquark pairing the model is applied to construct a hybrid quark-hadron EoS of cold compact-star matter. We study the connection of such a hybrid EoS with the stellar mass-radius relation and tidal deformability. The model results are compared to various observational constraints including the NICER radius measurement of PSR J0740+6620 and the tidal deformability constraint from GW170817. The model is shown to be consistent with the constraints, still allowing for further improvement by adjusting the vector repulsion and diquark pairing couplings.

Structure of double pionic atoms

Abstract We study theoretically the structure of double pionic atoms, in which two negatively charged pions ($\pi^-$) are bound in the atomic orbits. The double pionic atom is considered to be an interesting system from the point of view of the multi-bosonic systems. In addition, it could be possible to deduce valuable information on the isospin $I = 2$$\pi\pi$ interaction and the pion–nucleus strong interaction. In this paper, we take into account the $\pi\pi$ strong and electromagnetic interactions, and evaluate the effects on the binding energies by perturbation theory for the double pionic atoms in heavy nuclei. We investigate several combinations of two pionic states and find that the order of magnitude of the energy shifts due to the $\pi\pi$ interaction is around 10 keV for the strong interaction and around 100 keV for the electromagnetic interaction for the ground states.

Spectroscopy of Pionic Atoms in ^{122}Sn(d,^{3}He) Reaction and Angular Dependence of the Formation Cross Sections.

We observed the atomic 1s and 2p states of π^{-} bound to ^{121}Sn nuclei as distinct peak structures in the missing mass spectra of the ^{122}Sn(d,^{3}He) nuclear reaction. A very intense deuteron beam and a spectrometer with a large angular acceptance let us achieve a potential of discovery, which includes the capability of determining the angle-dependent cross sections with high statistics. The 2p state in a Sn nucleus was observed for the first time. The binding energies and widths of the pionic states are determined and found to be consistent with previous experimental results of other Sn isotopes. The spectrum is measured at finite reaction angles for the first time. The formation cross sections at the reaction angles between 0° and 2° are determined. The observed reaction-angle dependence of each state is reproduced by theoretical calculations. However, the quantitative comparison with our high-precision data reveals a significant discrepancy between the measured and calculated formation cross sections of the pionic 1s state.

Formation of Deeply Bound Pionic Atoms and Pion Properties in Nuclei

We study theoretically the formation of the deeply bound pionic atoms in various cases to deduce the pion properties in nuclei precisely from the observables. We show the angular dependence of the pionic atom formation spectra of the 122 Sn(d, 3 He) reactions in the forward angles. At each scattering angle, a different combination of the pion-bound and neutron-hole states dominates the spectrum because of the kinematical condition. We conclude that we can obtain information on the deeply bound pionic 2p state in addition to the 1s and 2s states by observing the spectra in finite angles. We also consider the neutron-odd nucleus as a target nucleus of the formation reaction, because it has an advantage that the pionic atom is formed in the even-even nucleus, of which the ground state has no neutron-hole states. In the 117 Sn(d; 3 He) reaction, we find that we can see clearly the peak structure of the pionic 1s state formation with the ground state of the even-even nucleus 116 Sn. The pionic atom in the even-even nucleus will not have additional shifts induced by the effects of the residual interaction between pion-bound and neutron-hole states. The observation of these pionic states is preferable for extracting the accurate information on the pion properties from data.

Status and future plan of the spectroscopy of pionic atoms

The spectroscopy of deeply bound pionic atoms provides a way to understand the restoration of chiral symmetry breaking at finite density. We have been performing a series of experiments of missing-mass spectroscopy of the (d,3He) reaction at RIBF to investigate pionic atoms of several Sn isotopes. As a first step, we conducted a pilot experiment to measure deeply bound pionic states of 121Sn and successfully observed the deeply bound pionic states. In addition to the experiment at RIBF, we are planning the spectroscopy of deeply bound pionic atoms in inverse kinematics and conducted a feasible study by simulations. We showed that by using a deuterium gaseous active target TPC and silicon detectors, the Q-value resolution is about 500 keV (FWHM) and the yield of the pionic 1s state is 20 counts/day, indicating the experiment is feasible.

The first precision measurement of deeply bound pionic states in121Sn

We performed a precision missing-mass spectroscopy experiment of the deeply bound pionic states in a 121 Sn atom using the (d, 3 He) reaction near the ! emission thresh- old. The experiment serves as a pilot experiment for our new 'pionic atom factory project' at RIBF, which aims at precision spectroscopy of the energy spectrum of the pionic atom of isotopes and isotones. The result of the pilot experiment demonstrated the potentiality of BigRIPS and of the RIBF facilities for the project. The current status of the analysis is reported.

Pion-nucleus elastic scattering, double-charge-exchange reactions, and subthreshold resonances

In the scattering of positive pions by nuclei the double-charge-exchange (DCX) reaction creates the possibility of the formation of pionic atom states in the vicinity of the threshold of the reaction. These quasistationary states can manifest themselves as resonances in the elastic scattering cross section. The strength and shape of these resonances are strongly affected by the instability of the nucleus created in the DCX channel. It is shown that this mechanism can explain oscillation structures in the excitation function observed in scattering of low-energy positive pions from ${}^{12}\mathrm{C}$.

(d,3He) reaction on an odd-neutron nuclear target for the formation of deeply bound pionic atoms

We consider the pionic atom spectroscopy by the (d,3He) reaction on an odd-neutron nuclear target in this article, which has not been investigated so far. In the (d,3He) reaction on the odd-neutron nuclear target, we can observe the pionic states in the even-neutron nucleus with spin-parity 0+. We expect that this pionic state does not have the additional shifts due to the effects of the residual interaction between neutron-hole and pionic states. For the even-neutron nuclear target cases, we may have to take into account the residual interaction effects to deduce the binding energies of the pionic states precisely from the high precision experimental data since the final pionic states are the pion-particle plus neutron-hole states. Thus, in addition to widening the domain of the pionic atom spectroscopy in nuclear chart, the present study of the (d,3He) reaction on the odd-neutron target is considered to be important to deduce extremely precise information on the binding energies of the observed pionic states, and to know the pion properties and aspects of the symmetries of the strong interaction at finite density. We modify the formula of the even-even nuclear target case to study the pionic atom formation spectra on the even-odd nuclear target and show the numerical results of 117Sn target case. This experiment will be performed at RIBF/RIKEN in near future.

Precision Spectroscopy of Deeply Bound Pionic Atoms and Partial Restoration of Chiral Symmetry in Medium

We study theoretically the formation spectra of deeply bound pionic atoms expected to be observed by experiments with high energy resolution at RIBF/RIKEN, and we discuss in detail the possibilities to extract new information on the pion properties at finite density from the observed spectra, which may provide information on partial restoration of chiral symmetry in medium. We find that the non-yrast pionic states such as 2s are expected to be seen in the (d,3He) spectra, which will be helpful to reduce uncertainties of the theoretical calculations in the neutron wave functions in nucleus. The observation of the 2s state with the ground 1s state is also helpful to reduce the experimental uncertainties associated in the calibration of the absolute excitation energy. We find that the nuclear densities probed by atomic pions are quite stable and almost constant for various atomic states and various nuclei. Effects of the pion wave function renormalization to the formation spectra are also evaluated.

Pionic atom factory project in the RIBF

We are preparing for a high resolution spectroscopy of the 1s and 2s pionic states of 121Sn in the 122Sn(d,3He) reaction at the incident deuteron energy of ~500 MeV. The measurement will provide accurate information on the strong interaction between the pion and the nucleus, which leads to quantitative determination of the magnitude of the quark condensate at the normal nuclear density.

A pionic hadron explains the muon magnetic moment anomaly

A significant discrepancy exists between experiment and calculations of the muon's magnetic moment. We find that standard formulas for the hadronic vacuum polarization term have overlooked pionic states known to exist. Coulomb binding alone guarantees π+π− states that quantum mechanically mix with the ρ meson. A simple 2-state mixing model explains the magnetic moment discrepancy for a mixing angle of order α∼10−2. The relevant physical state is predicted to give a tiny observable bump in the ratio R(s) of e+e− annihilation at a low energy not previously searched. The burden of proof is reversed for claims that conventional physics cannot explain the muon's anomalous moment.

Chiral Symmetry Probed with Pionic Atoms

Study of pionic atom has been revisited by a recent discovery of deeply bound pionic states in the context of possible sensitivity to the partial chiral restoration in the nuclear medium. Precisely measured binding energies and widths of the deeply bound π− Is states in 115,119,123Sn in 116,120,124Sn(d,3He) reactions at recoil-free conditions are used to deduce the medium-modified isovector scattering amplitude as b1 = 0.115 ± 0.007m π −1. The observed enhancement of b 1 over the free πN value infers 34% reduction of $$\left\langle {\bar qq} \right\rangle $$ at the normal nuclear density, ρ = 0.17 fm−3.

A spectrometer for seeking exotic states of pionic atoms of xenon

The parameters of a spectrometer for searching for deeply bound pionic states of xenon are presented. The main component of the spectrometer is a multilayer semiconductor telescope based on high-purity germanium detectors. A technique for calibrating the spectrometer and measuring its energy resolution using reactions p(d, 3He)π0 and 14N(d, 3He)13C is described. The energy resolution of the setup is shown to be 0.85 MeV for 3He ions with an energy of ∼360 MeV.

Residual interaction effects on deeply bound pionic states in Sn and Pb isotopes

We have studied the residual interaction effects theoretically on the deeply bound pionic states in Pb and Sn isotopes. We need to evaluate the residual interaction effects carefully in order to deduce the nuclear medium effects for pion properties, which are believed to provide valuable information on nuclear chiral dynamics. The s- and p-wave $\pi-N$ interactions are used for the pion-nucleon residual interactions. We show that the complex energy shifts are around [(10-20)+i(2-7)]keV for 1s states in Sn, which should be taken into account in the analyses of the high precision data of deeply bound pionic $1s$ states in Sn isotopes.

A search for deeply bound pionic states of xenon produced in the 136Xe(d, 3He)135Xeπ-bound reaction

A search for deeply bound pionic states of xenon produced in the 136Xe(d, 3He)135Xeπ-bound reaction at Ed = 500 MeV is reported. The population of the 1s pionic-atom state of 135Xe is observed on the predicted level of the cross section ∼ 40 μb/sr. The binding energy of the 1s state, B = 2.9 ± 0.5 MeV, however, is lower than theoretically predicted.

Hadron-nucleus bound-state spectroscopy

To investigate the behavior of hadrons in nuclear media we are developing new type of nuclear spectroscopy for hadron-nucleus bound states. The domain of deeply bound pionic states is well matured, and new precision experiments on the 1s π − states in 205Pb and in Sn isotopes have indicated an evidence for partial restoration of chiral symmetry in a well-defined nuclear medium. In the K sector we have predicted possible existence of deeply bound K states in few-body systems, which are characterized by dense nuclear systems formed due to the strong attraction of the I = 0 K N interaction.

The observation of deeply bound pionic states of xenon produced in the d + Xe nat → Xe π−bound + 3He reaction

We report on a search at the CELSIUS accelerator for deeply bound pionic states of xenon produced in the Xe nat. (d, 3He)Xe π−bound reaction at E d = 500 MeV. In the 3He energy spectrum two peaks are observed corresponding to the production of pionic atoms in the 1s state in even and odd isotopes respectively.

Pionic atom formation in halo nuclei by(d,3He)reactions

We investigate the formation cross sections of the deeply bound pionic atoms on halo nuclei theoretically. We consider one-neutron pick-up (d,3He) reaction for the pionic atom formation and find that the formation rate is significantly increased by the existence of the halo neutron with long tail of the wave function. This enhancement is expected to increase the experimental feasibility for the formation of the deeply bound pionic states on beta-unstable nuclei.

Chiral Symmetry and Meson-Nucleus Bound States

We summarize current research activities on the deeply bound pionic states, η-mesic nuclei, and σ-mesic nuclei, and their relation to the chiral dynamics in hadron physics.