We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general fe...We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.展开更多
The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the ...The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in- teraction （MRCI） approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification （MRCI＋Q）. These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.展开更多
We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interac...We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly,it yields the momentum spectrum of the emitted photons and the photon-photon correlations.展开更多
文摘We present an approach to solve Bethe-Salpeter (BS) equations exactly withoutany approximation if the kernel of the BS equations exactly is instantaneous, and take positroniumas an example to illustrate the general features of the exact solutions. The key step for theapproach is from the BS equations to derive a set of coupled and well-determined integrationequations in linear eigenvalue for the components of the BS wave functions equivalently, which maybe solvable numerically under a controlled accuracy, even though there is no analytic solution. Forpositronium, the exact solutions precisely present corrections to those of the correspondingSchrodinger equation in order υ~1 (υ is the relative velocity) for eigenfunctions, in order υ~2for eigenvalues, and the mixing between S and D components in J~(PC) = 1~(--) states etc.,quantitatively. Moreover, we also point out that there is a questionable step in some existentderivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, weemphasize that one should take the O(υ) corrections emerging in the exact solutions into accountaccordingly if one is interested in the relativistic corrections for relevant problems to the boundstates.
文摘The potential energy curves （PECs） of three low-lying electronic states （X^3∑, a^1△, and a^3△） of SO radical have been studied by ab initio quantum chemical method. The calcula- tions were carried out with the full valence complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration in- teraction （MRCI） approach in combination with correlation-consistent basis sets. Effects of the core-valence correlation and relativistic corrections on the PECs are taken into account. The core-valence correlation correction is carried out with the cc-pCVDZ basis set. The way to consider the relativistic correction is to use the second-order Douglas-Kroll Hamiltonian approximation, and the correction is performed at the level of cc-pV5Z basis set. To obtain more reliable results, the PECs determined by the MRCI calculations are also corrected for size-extensivity errors by means of the Davidson modification （MRCI＋Q）. These PECs are extrapolated to the complete basis set limit by the two-point energy extrapolation scheme. With these PECs, the spectroscopic parameters are determined.
基金Supported by National Natural Science Foundation of China under Grant Nos.11434011,11674334,11421063,and 11674393National Key Basic Research Special Foundation of China under Grant No.2012CB922104+1 种基金the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China under Grant Nos.16XNLQ03 and 17XNH054
文摘We investigate the quantum dynamics of the decay of a multiple-component positronium condensate into pairs of photons. A positronium atom has four internal spin states which are interconvertible through s-wave interactions. The quantum fields of all spin states of positroniums and photons are simulated from first principle in quasi-one-dimensional system using the truncated Wigner method. This method warrants us a full treatment of the depletion of positronium fields and the spin mixing induced by s-wave collisions between positronium atoms. Particularly,it yields the momentum spectrum of the emitted photons and the photon-photon correlations.
