Accurate Calculations On Positron State And Tests On Several Physical Models

With the rapid development of numerical analysis method and computer technol-ogy, computational physics has become an important intermediate branch between the-oretical and experimental physics. Developed computational methods are applied to many physics problems without analytical solution and data analysis for experimental measurements. In this thesis, we firstly investigate what is important to accurately and quickly calculate the positron state based on three electronic structure calculation meth-ods including the full-potential linearized augmented plane wave (FLAPW) plus local orbitals approach, the atomic superposition (ATSUP) approach and the projector aug-mented wave (PAW) approach. Then, based on the Bayesian statistics, we probe the methods for precise positron annihilation lifetime spectrum analysis. Next, we apply the positron state calculation to some specific physics problems. At last, by using chi-squared analysis and experimental data, we test several physical models and constrain their parameter spaces. The achievements are as followings:We find that a well implemented PAW method can give near-perfect agreement on both the positron lifetimes and affinities with the FLAPW method. The differences between calculated lifetimes using the ATSUP and FLAPW methods are clearly in-terpreted in the view of positron and electron transfers, and the competitiveness of the ATSUP method against the FLAPW/PAW method is reduced when using the best positron-electron correlation scheme. We make two new gradient correction to the positron-electron correlation approximation. By comparing with experimental data, the new introduced gradient corrected correlation forms are proved competitive for positron lifetime and affinity calculations. Especially, one of these forms gives the best perfor-mance.Based on the Bayesian statistics, chi-squared analysis and Markov Chain Monte Carlo methods, we probe various factors in detail during the positron annihilation life-time spectrum analysis. We find that the widespread dependent phenomena between free parameters are important and can be well handled by using the marginalization method.We find that the latest approximation of positron-electron correlation energy can lead to reasonable positron surface state and related lifetime, which have chances to be another convenient and effective DFT method beyond the WDA (weighted density approximations) approach. Moreover, a calculation method combining the molecular dynamics simulation and the ATSUP calculation for the positron lifetime in He bubble is developed and is found feasible. Based on the chi-squared analysis and a reliable dataset containing172experi-mental values of positron bulk lifetime, we perform an initiatory statistical assessment on the reliability level of theoretical positron lifetime of bulk material. We found the widely used original generalized gradient approximation (GGA) form of the enhance-ment factor and correlation potentials overestimates the effect of the gradient factor, while for other GGA forms no assured overestimation is appeared. In addition, one of the new GGA forms of the correlation scheme we suggested gives the best performance with the root mean squared deviation (RMSD) being3.5ps. Furthermore, an excellent agreement between model and data with the difference being the noise level of the data is found in this work.This statistical analysis demonstrates that a brand-new reliability level is achieved for the theoretical prediction on positron lifetime of bulk material, and the accuracy of the best theoretical scheme can be independent on the type of materials. So, it is rea-sonable to conclude that the accuracy of the solo experimental value with a deviation from the best theoretical value being larger than10ps (3RMSD) should be questioned. This fact implies that the current combined theoretical calculation and valid experimen-tal measurement on positron lifetime can validate the quality of prepared single crystal, such as ZnO, etc.Based on the chi-squared analysis and above lifetime data, we constrain the positron-electron enhancement factor by using two parameterized model with two and three pa-rameters respectively, which provide the experiment evidence for further progress on theoretical models. Meanwhile, this analysis indicates that current experimental data are unable to make exact judgment on the enhancement behavior in low electron den-sity region. In addition, the fitted experiential enhancement factor can be used in future positron state calculations.Based on the chi-squared analysis and the recent cosmological observational data, we also test five modified gravity (MG) models and find that MG models can not lead to an appreciable reduction of the minimal chi-squared. The standard cosmological constant model is still the most preferred by the current data. We also find that current available growth factor data are not enough to distinguish these MG models from the standard model, so further accurate data is needed.