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

Abstract

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 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 πN 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./2 1.7 + 0.8i −6.0i J = 11/2 1.5 + 0.7i −5.1i J = 11/2 1.4 + 0.6i J = 13/2 −6.2 − 3.3i J = 13/2 −5.6 − 2.8i J = 13/2 −5.1 − 2.5i d −1 5/2 −15.1 J = 3/2 −7.6 − 2.6i −13.6 J = 3/2 −7.1 − 2.2i −12.2 J = 3/2 −6.5 − 1.9i −4.8i J = 5/2 1.0 + 0.6i −3.7i J = 5/2 0.9 + 0.4i −2.8i J = 5/2 0.8 + 0.3i J = 7/2 −5.0 − 1.7i J = 7/2 −4.6 − 1.4i J = 7/2 −4.3 − 1.2i

Formation of Deeply Bound Pionic Atoms in the (d,3He) Reaction

“…Consequently, there exists a neutron-hole state j −1 n in the daughter nucleus which couples to pionic atom states (n π π ) to make total spin J state [ j −1 n ⊗ π ] J . In these states, we generally expect the existence of the residual interaction effects and of the level splittings between different J states [3,4]. The experimental errors of the pion binding energies and widths reported in Ref.…”

“…The experimental errors of the pion binding energies and widths reported in Ref. [2] are approaching the magnitude of the estimated level shifts due to the residual interaction [3,4]. Thus, the observation of the pionic states free from these effects is very important to obtain more accurate information on pion properties in nucleus from the data, which will be necessary to deduce the density dependence of the chiral condensate qq beyond the linear density approximation [5,6].…”

Formation of Deeply Bound Pionic Atoms and Pion Properties in Nuclei

“…We expect that this pionic state does not have additional shifts due to the effects of the residual interaction between neutron-hole and pionic states [12,13]. 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 pion-particle plus neutron-hole [π ⊗ n −1 ] states.…”

Formation of deeply bound pionic atoms and pion properties in nuclei

“…So far, all theoretical and experimental studies have been concentrated on the even-even nuclear target cases. For the even-neutron nuclear target cases, since the final pionic states are the pion-particle plus neutron-hole [π ⊗ n −1 ] states, we will have to take into account the residual interaction effects [3,4] to deduce the pion-nucleus interaction precisely from the high precision experimental data. On the other hand, for the odd-neutron nuclear target cases, we expect to observe the pionic states with the ground state of the even-even nucleus with J P = 0 + , which will not be affected by the additional shifts induced by the residual interaction effects.…”