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We have studied the isotope dependence of deeply bound pionic states in Sn and Pb in order to examine the possibility of obtaining important information on neutron density distribution and the modification of the pion decay constant f in a nuclear medium. Formation cross sections of the pionic states are calculated in the (d, 3 He) reactions. The present results indicate that the isotope dependence of the pionic states can be deduced from the experimental data with accessible energy resolution. The effects of the neutron skin for the formation cross sections are also examined and are found to affect the (d, 3 He) spectra significantly.

We investigate the formation cross sections of the deeply bound pionic atoms on halo nuclei theoretically. We consider one-neutron pick-up (d, 3 He) 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 β-unstable nuclei.

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

Singular spectrum analysis is a nonparametric and adaptive spectral decomposition of a time series. This method consists of the singular value decomposition for the trajectory matrix constructed from the original time series, followed with the subsequent reconstruction of the decomposed series. In the present paper, we show that these procedures can be viewed simply as complete eigenfilter decomposition of the time series. The eigenfilters are constructed from the singular vectors of the trajectory matrix and the completeness of the singular vectors ensure the completeness of the eigenfilters. The present interpretation gives new insight into the singular spectrum analysis.