Confined Variational Calculation Of Low-energy Ps-H₂ Elastic Scattering

The physical properties of few-body systems have always been one of the focuses of quantum mechanics research.However,due to the extremely complicated correlation effects between particles,it is impossible to accurately solve the Schrodinger equation of the system,and a series of approximate theories calculation have emerged.The number of particle that different numerical calculation methods focus on is also different.The explicitly correlated Gaussian basis functions selected in this paper can perform highprecision calculations for four-body and more-particle systems.Positronium(Ps)is a metastable system consisting of an electron and a positron bound together.Its unique properties and interactions with other atoms and molecules are the object of interest in many fields of scientific research.In atomic and molecular physics,the properties of o-Ps scattering by various atoms and molecules(H,He,Ne,Ar,N2)have been studied.In the calculation of Ps-molecules scattering,the Ps-H2 system is the simplest one.In this thesis,the specific derivation procedure and expression form of the explicitly correlated Gaussian basis function are introduced in detail,as well as its application in Ps-H2 system;the theoretical method for solving the scattering properties of the system-the confined variational method-is sorted out in detail;the optimization strategy of the explicitly correlated Gaussian basis function is also described in detail.Based on the explicitly correlated Gaussian function,this thesis treats the finite mass effects of leptons and protons equally;and the confined variational method is used to study in the range of incident energy less than 0.13 eV,the low-energy S-wave elastic scattering of Ps-H2.The S-wave scattering phase shifts,scattering length,scattering cross sections and distortion effects of the system are accurately calculated,and compared with other theoretical and experimental methods.When we remove the fixed nuclear approximation,the S-wave phase shifts of the system increase;and the phase shifts calculated only by the pseudopotential method are closer to our calculated results than those calculated by the pseudopotential method with van der Waals potential are.Using the effective range formula modified by van der Waals force,which is more in line with the fitting of the phase shift to the scattering length under low incident energy,the scattering length of the S-wave is determined to be 1.97 Bohr radius,and it is compared with the values obtained by other theoretical methods.This result is about 2.5%smaller than the S-wave scattering length calculated by the confined variational method using the fixed nuclear approximation,and 5.6%smaller than the scattering length obtained by the commonly used effective range formula.And this result is closer to the scattering length value obtained by the pseudopotential method without van der Waals potential;the scattering length values obtained by the above methods are all within the error bars of the results obtained by the annihilation angle correlation experiment method.The value of the scattering cross section is calculated by the partial-wave expansion.In lowenergy elastic scattering,the S-wave dominates,and the value of the P-wave is already much smaller than the S-wave,so we only compare the values of the S-wave scattering cross section.The results of the calculated scattering cross section are consistent with the results obtained from the annihilation angle correlation experiment,and the results measured by the Doppler-broadened spectroscopy method are quite different from our results,indicating that the results of the Doppler-broadened spectroscopy method may be inaccurate.In addition,the distortion of Ps and H2 is also studied,and the results show that the distortion distance decreases with the increase of the incident momentum.The research result of this thesis is of great help to the in-depth understanding of the scattering process between Ps and H2;at the same time,the successful application of the confined variational method under finite nuclear mass developed by our group has laid a good foundation for the future calculation of vibration excitation problem.The obtained calculation results also lay a benchmark for the theoretical and experimental research of this system.