标题： 多体理论和正电子湮灭的高斯基组实现 多原子分子的$γ$-射线光谱 显示英文标题

标题： Many-body theory and Gaussian-basis implementation of positron annihilation $γ$-ray spectra on polyatomic molecules

摘要： 多普勒展宽的$\gamma$射线谱对于分子正电子湮灭是通过多体理论计算得到的。 通过采用高斯基组来表示电子和正电子波函数，在独立粒子模型近似下，得到了一个涉及两个湮灭光子动量的四中心积分的可计算表达式，用于$\gamma$谱，并在开源{\tt 激子+}代码中实现。 通过\textit{从头计算}处理正电子波函数，研究了电子-正电子相关性对$\gamma$谱的影响，而对湮灭顶点的修正则通过之前计算出的增强因子[ D. G. Green 和 G. F. Gribakin, Phys.~Rev.~Lett.~{\bf 114}, 093201 (2015)] 近似处理，该增强因子针对原子已精确计算。 给出了呋喃和丙腈的$\gamma$谱，这些谱对应于正电子结合态与单个分子轨道电子的湮灭。 对于来自正电子-分子束缚态的湮灭，发现单个分子轨道对$\gamma$谱的分量贡献的大小不仅取决于轨道能量，还取决于分子对称性，更准确地说是正电子和电子密度的相对定位。 显示英文摘要

摘要： Doppler-broadened $\gamma$-ray spectra for positron annihilation on molecules are calculated using many-body theory. By employing Gaussian bases for the electron and positron wavefunctions, a computable expression that involves a four-centre integral over the two-annihilation-photon momenta is derived for the $\gamma$ spectra in the independent particle model approximation to the annihilation vertex, and implemented in the open-source {\tt EXCITON+} code. The influence of electron-positron correlations on the $\gamma$ spectra is examined through \textit{ab initio} treatment of the positron wavefunction, whilst corrections to the annihilation vertex are treated approximately via enhancement factors previously calculated [D. G. Green and G. F. Gribakin, Phys.~Rev.~Lett.~{\bf 114}, 093201 (2015)] exactly for atoms. Calculated $\gamma$ spectra for furan and acetonitrile are presented for annihilation from the positron bound state with electrons of individual molecular orbitals. For such annihilation from the positron-molecule bound state, it is found that the magnitude of the partial contribution to the $\gamma$ spectra from individual molecular orbitals depends not just on the orbital energies, but also on the molecular symmetry, more precisely the relative localisation of the positron and electron densities.