Let X and Y be Hilbert spaces and T a bounded linear operator from X into Y with a separable range. In this note, we prove, without assuming the closeness of the range of T , that the Moore-Penrose inverse T + of T ca...Let X and Y be Hilbert spaces and T a bounded linear operator from X into Y with a separable range. In this note, we prove, without assuming the closeness of the range of T , that the Moore-Penrose inverse T + of T can be approximated by its bounded outer inverses T n# with finite ranks.展开更多
The ^7Be（p, γ）8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars. Study of this reaction requires the asymptotic normalization coeffici...The ^7Be（p, γ）8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars. Study of this reaction requires the asymptotic normalization coefficient （ANC） for the virtual decay ^8Bg.s. → ^7Be ＋ p. By using the charge symmetry relation, we obtain this proton ANC with the single neutron ANC of ^8Lig.s.→^7Li ＋ n, which is determined with the distorted wave Born approximation （DWBA） and adiabatic distorted wave approximation （ADWA） analysis of the ^7Li（d, p）^8Li angular distribution. The astrophysical S-factors and reaction rates of the direct capture process in the 7Be（p, y）SB reaction are further deduced at energies of astrophysical relevance. The astrophysical S-factor at zero energy for direct capture, S 17（0）, is derived to be （19.9 ± 3.5） eV b in good agreement with the most recent recommended value. The contributions of the 1 ^＋ and 3^＋ resonances to the S-factor and reaction rate are also evaluated. The present result demonstrates that the direct capture dominates the ^7Be（p, γ）8B reaction in the whole temperature range. This work provides an independent examination to the current results of the ^7Be（p, γ）8B reaction.展开更多
基金Project supported by the National Science Foundation of China (Grant No. 10571150 and No. 10271053).
文摘Let X and Y be Hilbert spaces and T a bounded linear operator from X into Y with a separable range. In this note, we prove, without assuming the closeness of the range of T , that the Moore-Penrose inverse T + of T can be approximated by its bounded outer inverses T n# with finite ranks.
基金supported by the National Natural Science Foundation of China(Grant Nos.11321064,11490560,11475264,11375269 and11275272)the National Basic Research Program of China(Grant No.2013CB834406)
文摘The ^7Be（p, γ）8B reaction plays a central role not only in the evaluation of solar neutrino fluxes but also in the evolution of the first stars. Study of this reaction requires the asymptotic normalization coefficient （ANC） for the virtual decay ^8Bg.s. → ^7Be ＋ p. By using the charge symmetry relation, we obtain this proton ANC with the single neutron ANC of ^8Lig.s.→^7Li ＋ n, which is determined with the distorted wave Born approximation （DWBA） and adiabatic distorted wave approximation （ADWA） analysis of the ^7Li（d, p）^8Li angular distribution. The astrophysical S-factors and reaction rates of the direct capture process in the 7Be（p, y）SB reaction are further deduced at energies of astrophysical relevance. The astrophysical S-factor at zero energy for direct capture, S 17（0）, is derived to be （19.9 ± 3.5） eV b in good agreement with the most recent recommended value. The contributions of the 1 ^＋ and 3^＋ resonances to the S-factor and reaction rate are also evaluated. The present result demonstrates that the direct capture dominates the ^7Be（p, γ）8B reaction in the whole temperature range. This work provides an independent examination to the current results of the ^7Be（p, γ）8B reaction.
