The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the interior part of the Coulomb potential is left in the Hamiltonian and, secondly, when the long range tail is considered as the potential. The partial wave results are summed up to obtain the wave function in three dimensions. It is shown that in the domains where the wave function is expected to be proportional to the known solutions, the proportionality is given by an operator acting on the angular part of the wave function. The explicit representation for this operator is obtained in the basis of Legendre polynomials. We proposed a driven Schrödinger equation including an inhomogeneous term of the finite range with purely outgoing asymptotics for its solution in the case of the three dimensional scattering problem with long range potentials.
The triple alpha reaction is a key to $^{12}$C production and is expected to occur in weakly-coupled, thermal plasmas as encountered in normal stars. We investigate how Coulomb screening affects the structure of a system of three alpha particles in such a plasma environment by precise three-body calculations within the Debye-Hückel approximation. A three-alpha model that has the Coulomb interaction modified in the Yukawa form is employed. Precise three-body wave functions are obtained by a superposition of correlated Gaussian bases with the aid of the stochastic variational method. The energy …
The first excited $J^π=0^+$ state of $^{12}$C, the so-called Hoyle state, plays an essential role in a triple-$α$ ($^4$He) reaction, which is a main contributor to the synthesis of $^{12}$C in a burning star. We investigate the Coulomb screening effects on the energy shift of the Hoyle state in a thermal plasma environment using precise three-$α$ model calculations. The Coulomb screening effect between $α$ clusters are taken into account within the Debye-Hückel approximation. To generalize our study, we utilize two standard $α$-cluster models, which treat the Pauli principle between the $α$ pa…
Proton-proton scattering without Coulomb force renormalization
我们数值证明了质子-质子（pp）散射观测值可以直接确定的标准短程方法使用屏蔽pp库仑力没有重整化。在示例中给出了适当的屏蔽半径。我们还数值研究了3维Lippmann-Schwinger（LS）方程的解决方案的屏蔽库仑势单独在大屏蔽半径的限制，并确认分析预测的性能为壳外，半壳和壳库仑t-矩阵。这些3维的解决方案将形成一个新的方法，包括PP库仑相互作用到3 N Faddeev框架的基础。
Comment on ``Exact three-dimensional wave function and the on-shell t matrix for the sharply cut-off Coulomb potential: Failure of the standard renormalization factor''
Exact three-dimensional wave function and the on-shell t-matrix for the sharply cut off Coulomb potential: failure of the standard renormalization factor
Coulomb screening and weak interactions in a hot, magnetized plasma are investigated. Coulomb screening is evaluated in a relativistic thermal plasma in which electrons and positrons are in equilibrium. In addition to temperature effects, effects on weak screening from a strong external magnetic field are evaluated. In high fields, the electron transverse momentum components are quantized into Landau levels. The characteristic plasma screening length at high temperatures and at high magnetic fields is explored. In addition to changes to the screening length, changes in weak interaction rates a…
