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arXiv 1206.3155nucl-th
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算符形式的双核子T矩阵的不同方法

Different Methods for the Two-Nucleon T-Matrix in the Operator Form

J. Golak, R. Skibinski, H. Witala, K. Topolnicki, W. Gloeckle, A. Nogga, H. Kamada

摘要:

我们比较了三种计算核子-核子t-矩阵的方法,这些方法是基于J. Golak等人的三维公式,Phys. Rev. C 81,034006,(2010)。首先,我们直接求解一个复线性非齐次方程组的t-矩阵。我们的第二种方法是基于迭代和Lanczos算法的变体。在第三种情况下,我们得到的t-矩阵在两个步骤中,解决一个系统的实线性方程组的k-矩阵的展开系数,然后解决一个壳方程,它连接的k-和t-矩阵的标量系数。一个非常好的协议之间的三种方法被证明为选定的核子-核子散射观测使用手征下一个下一个领先的顺序中子-质子势。我们也适用于我们的三维框架的要求质子-质子散射的问题,使用相应版本的核子-核子势和补充(屏蔽)库仑力,也采取了三维形式。我们收敛的结果,两个不同的屏蔽功能,并找到一个非常好的协议与其他方法处理质子-质子散射。

英文摘要:

We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.

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