Formation spectra of pionic atoms in the Green's function method

Structure of double pionic atoms

“…Especially, we like to mention the existence of two threshold energies in the energy spectrum of two pion state, which are the quasi-free one-pion production energy and the quasi-free two-pion production energy. The quasi-free one-pion production threshold energy is defined as B π = B 1s π + 0 and is B 1s π = 3850.0 keV for 121 Sn case [26]. The quasi-free two-pion production threshold energy is B π = 0.…”

“…The energy shift ∆E s can be evaluated as, To obtain the energy shift ∆E em by the ππ electromagnetic interaction V em ππ , we evaluate the expectation value defined in Eq. (26). For the ground state (1s, 1s) of the double pionic atom, the energy shift can be evaluated by using the wave function of Eq.…”

“…2, we explain the formulation for the study of the structure of single and double pionic atoms based on the theoretical methods reported in Refs. [3,[23][24][25][26]. For the double pionic atoms, we evaluate the energy shifts of the bound states of two pions by the ππ interaction using the perturbation theory with the realistic wave functions of the single pionic atoms.…”

Formation of Deeply Bound Pionic Atoms and Pion Properties in Nuclei

“…Here, we study the formation spectra of deeply bound pionic atoms in the (d, 3 He) reactions using the Green's function method [10], stimulated by recent developments in experimental techniques. The Green's function method is considered to be a better theoretical formalism than the effective number approach to evaluate the formation rate of unstable systems.…”

“…In order to find out the appropriate procedure to obtain more precise information on chiral symmetry restoration from the observables, we have developed theoretical studies of the formation spectra of the pionic atoms [7][8][9][10]. On the other hand, the new experiment at RIBF/RIKEN was also performed and the observed spectra were reported in Ref.…”