Perturbation expansion from an extended model space

Perturbation expansion from an extended model space 

MBPT starts with the partition of the Hamiltonian into H = H0 + V. The basic idea is to use the known eigenstates of H0 as the starting point to find the eigenstates of H. The most advanced solutions to this problem, such as the coupled-cluster method, are iterative well-defined classes of contributions are iterated until convergence, meaning that the perturbation is treated to all orders. Iterative MBPT methods have many advantages. First, they are economical and still capable of high accuracy. Only a few selected states are treated and the size of a calculation scales thus modestly with the basis set used to carry out the perturbation expansion. Radial basis sets that are complete in some discretized space can be used [112, 120, 121], and the basis 

Unfortunately, there are still systems where problems are encountered, and the main reason is that it is not possible to find a suitable model space, i.e., one with the properties mentioned above. Relativistic and nonrelativistic 

In spite of the intruder state problem, there is a range a systems where (relativistic) MBPT can produce reliable and accurate results for energies and width of resonance states. A few examples are given below. 

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