Formation of Deeply Bound 1s Pionic States of Intermediate Mass Nuclei in (d,3He) Reactions

Abstract

We study the formation cross sections of the deeply bound 1s pionic states in (d, 3 He) reactions at intermediate energies. We investigate the reaction spectra for the three target nuclei 136 Xe, 116 Sn and 112 Cd, which involve the (s 1/2 ) n neutron orbit in outer shell. We conclude that the (d, 3 He) reactions at T d = 500 MeV with 136 Xe and 116 Sn targets are the best candidates to observe the deepest 1s pionic states with very high accuracy. §1. IntroductionPionic atoms have been studied for a long time to investigate the behavior of pions in nuclei. In particular, deeply bound pionic atoms have attracted much attention, since they provide us with valuable information on the behavior of "real" pions in the interior of the nucleus. These states, however, cannot be observed in conventional pionic X-ray experiments due to the strong absorption of pions. Despite of this, deeply bound pionic states are predicted to have rather narrow widths due to the repulsive pion-nucleus optical potential that pushes the pion wave function outwards. 1) Toki and Yamazaki pointed out the possibility of observing deeply bound pionic atoms using pion-transfer reactions such as (n, p) and (d, 2 He). 1), 2) Following their suggestions, deeply bound pionic states were searched for by using the (n, p) reaction at T n = 420 MeV at TRIUMF 3) and the (d, 2 He) reaction at T d = 1000 MeV at SATURNE. 4) No positive evidence was found in these experiments. After these experiments, it was pointed out that the charge-exchange pion-transfer reactions at large momentum transfer are quite sensitive to the initial-and finalstate interactions, and the distortion effects reduce the cross section by about two orders of magnitude 3), 5) compared with the predictions of the plane-wave approximation. 1), 2) Thus the pion-transfer reactions of this type turned out to be not suited for the formation of deeply bound pionic atoms. 3), 5)Other kinds of reactions, such as the single nucleon pick-up pion-transfer reactions (n,d) 6) and (d, 3 He), 7) were studied theoretically for the formation of deeply bound pionic states. Since the angular momentum matching condition is satisfied under these reactions, we can expect to have smaller distortion effects than in the (n,p) and the (d, 2 He) cases. Following these theoretical expectations, there were experimental attempts using (n,d) 8) and (p,pp) 9) reactions. In both cases, some extra strength was observed in the pion subthreshold region, which suggests the existence of deeply bound pionic states. However, due to weak neutron intensity or difficulty in observing the two unbound protons, we could not find clear evidence of deeply

Formation of Deeply Bound Pionic Atoms in Sn Isotopes

“…We refine the theoretical model used in Refs. [5,6,13] to study the angular dependence of the (d, 3 He) spectra by including the kinematical correction factors K in Eq. (1) as explained below.…”

“…We introduce the distortion effects to the wavefunctions χ * He and χ d by Eikonal approximation as described in Refs. [5,6,13]. The kinematical correction factor K is defined as,…”

“…The (d, 3 He) spectra have been obtained in near recoilless kinematics to observe the peaks of the pionic state formation with a neutron hole in the quasi-substitutional configurations [2][3][4]. The Pb and Sn isotopes were used as the target nuclei in the experiments [2][3][4] since the spectra were expected to show the peak structures owing to one dominant [π ⊗ n −1 ] configuration based on the theoretical evaluations [5,6]. The simple structure of the observed peak is important and effective to deduce the pion binding energies precisely from the observed spectra.…”

Formation of σ mesic nuclei in (d, t) and (d,3He) reactions

“…The σ wave functions φ lσ used to calculate the effective number N eff are obtained by solving the Klein-Gordon equation (1). N eff is calculated in exactly the same way as the pion production [20] at the resonance energy ω nl and is known to give a good account of the relative contributions of bound states for the pionic atoms [5].…”

“…We remark that (14) can be reduced to the same formula used in Ref. [20] with non-relativistic energies by identifying Γ = −ImΣ/m σ , E σ = (ω 2 − m 2 σ )/2m σ and E nl = (ω 2 nl − m 2 σ )/2m σ , where Γ, E σ and E nl are the σ width, nonrelativistic σ energy induced by the reaction and non-relativistic σ eigenenergy of the (nl) state, respectively. From Eq.…”