Formation of Deeply Bound 1s Pionic States in the Pb(d,He) Reaction

Recently, deeply bound pionic states were found experimentally in (d,He) reactions on Pb. The observed spectrum showed an excellent agreement with the DWIA calculation and the dominant peak was attributed to the pionic 2p state contribution. We studied theoretically Pb(d,He) reactions within the same model, and found that it is very likely to observe the pionic 1s state as an isolated peak in the Pb(d,He) reaction with feasible energy resolution and statistics. Since the suggestion of Toki and Yamazaki for the formation of deeply bound pionic atoms such as 1s and 2p states in heavy nuclei by direct reactions , there have been a number of efforts to find these states both experimentally and theoretically . It is worth mentioning that (n,d) reactions 8 and (p,pp) reactions 9 on the Pb target were able to identify some strength in the excitation function below the pion production threshold. It was, however, not yet convincing to claim for pionic atom formation due to the lack of good resolution and statistical accuracy. Very recently, Yamazaki et.al. performed an experiment of (d,He) reactions on Pb with better resolution and statistical accuracy , and succeeded in identifing clearly a peak structure in the bound pion region. We found also that the theoretical predictions 6 made before the experiment agree almost perfectly with the experiment. This agreement provides a strong confidence on the predictability of the theoretical model used. We have analyzed the latest data in more detail using our model 11 and found that the experimental peak structure consists of several contributions. The largest contributions are due to [lπ⊗j n ] = [2p⊗p −1 1/2] and [2p⊗p −1 3/2]. Contributions from the deepest pionic 1s state, which is the most interesting, can be found only as a skewed shape of the experimental peak because the contributions from the pionic 1s state and 2p state could not be separated with the experimental energy resolution. We expect to identify the pionic 1s contribution as a shoulder with much better energy resolution (FWHM ≈ 200keV ) as shown in Fig. 1 (a). However, it is very difficult to realize such high resolution experimentally. At higher incident energies, because of the matching condition of the momentum transfer, the [1s ⊗ i 13/2] configuration makes an isolated peak. In this case, however, the excitation strength is small and the peak identification will be difficult . In this paper we study the spectral shape and the excitation function of the Pb(d,He) reaction instead in order to observe the pionic 1s contribution as a peak with feasible experimental energy resolution. Since the contribution of the [2p⊗ p 1/2] configuration in the case of Pb makes an additional peak between the [2p⊗p 3/2] and the [1s⊗ p 3/2] peaks, we may be able to remove this if we do not have contributions from the p 1/2 neutron hole. It is expected that the valence two neutron holes in the ground state of Pb are dominantly p1/2. Hence, the assumption that the p1/2 orbital in the ground state of Pb is empty may hold. This is the reason why we consider Pb as a target nucleus to observe the pionic 1s contributions as an isolated peak. First we consider the Pb(d,He)πPb reaction as the Pb(d,He)πPb without contributions from two neutrons in the p1/2 orbital for qualitative discussions. We will calculate realistic spectra later. We have used the effective number approach for the theoretical calculation . In Fig.1 (a), the calculated spectrum of Pb(d,He)πPb is shown. This calculated spectrum agrees with the data very well . We show the spectrum without the contribution from the p1/2 neutron orbital in Fig.1 (b). Clearly we can see the pionic 1s state contributions as an isolated peak at Q ≈ −134MeV which consists of [1s⊗ f 5/2] and [1s⊗ p −1 3/2]. We improve, then, the calculation by taking into account the realistic ground state configuration of Pb , and the realistic excitation energies and strengths of Pb. The experimental data show that the Pb ground state is not a pure p 1/2 state but contains admixtures of other two neutron hole configurations and can be written as ; Ψ(Pb)g.s. = a(2p1/2) −2 + b(1f5/2) −2 + c(2p3/2) −2 + d(0i13/2) −2 (1)