Exact nuclear pairing solution for large-scale configurations: I. The EP (v1.0) program at zero temperature

In this work, we present the “EP code” (version 1.0), a user-friendly and robust computational tool. It computes the exact pairing eigenvalues and eigenvectors directly from the general nuclear pairing Hamiltonian, represented using SU(2) quasi-spin algebra with basis vectors in binary representation, at zero temperature for both odd and even deformed nucleon systems. In this initial release, the sparsity and symmetry of the pairing matrix are exploited for the first time to quickly construct the pairing matrix. The ARPACK and LAPACK packages are employed for the diagonalization of large- and small-scale sparse matrices, respectively. In addition, the calculation speed for odd-nucleon systems is significantly improved by employing a novel technique to accurately identify the block containing the ground state in such odd-nucleon configurations. To ensure the high numerical stability, the Kahan compensation algorithm is employed. The current version of the EP code can efficiently expand the computational space to handle up to 26 doubly folded (deformed) single-particle levels and 26 nucleons on a standard desktop computer in approximately 10^2 s with double precision. With sufficient computational resources, the code can process up to 63 deformed single-particle levels, which can accommodate from 1 to 63 nucleon pairs. The EP v1.0 code is also designed for future extensions, including the finite-temperature and parallel computations.本研究中，我们推出了EP代码（EP code）版本1.0，一款易用且鲁棒的计算工具。该工具可直接从广义核配对哈密顿量出发，计算精确的配对本征值与本征向量；该哈密顿量采用SU(2)准自旋代数进行表征，基矢采用二进制表示，适用于零温条件下的奇数与偶数形变核子系统。在此次首个正式版本中，我们首次利用配对矩阵的稀疏性与对称性，实现配对矩阵的快速构建。本工具分别采用ARPACK与LAPACK数值库，完成小规模与大规模稀疏矩阵的对角化运算。此外，本工具通过一种新颖的技术精准识别奇核子组态中包含基态的矩阵块，大幅提升了奇核子系统的计算速度。为保障极高的数值稳定性，本工具采用了Kahan补偿算法。在标准台式机上，当前版本的EP代码可高效拓展计算空间，在双精度模式下，约100秒内即可处理最多26个二重折叠（形变）单粒子能级与26个核子的计算任务。若配备充足的计算资源，该代码可处理最多63个形变单粒子能级，可容纳1至63个核子对。EP v1.0代码还预留了未来扩展空间，可支持有限温度计算与并行计算等功能。