TiSc

DUSM-Novosleky-Vallières

Ti and Sc Nuclei


Using the DUPSM code we were able to calculate spectra and transition rates in the full fp-shell for nuclei beyond A=50. We completed such calculations for 51 Sc [Novoselsky,97] as well as for 52 Sc [Novoselsky,98]. For these nuclei the largest matrix we diagonalized was 39,420 ( for the J=9/2 states in 51 Sc). To obtain the 5 lowest eigenvalues we need only 10 minutes on a 32 nodes MOSIX computer. The diagonalization of a matrix of dimension 63,757 (for the J=4 states of 48 Ti) takes less than one hour. This demonstrates the high efficiency of our algorithm. These calculations are among the largest calculations we can do when the Hamiltonian matrix is stored in RAM.

Recently, by using the new option of the code, we have calculated and diagonalized Hamiltonian matrices of order of hundreds of thousands. For example, we have diagonalized the Hamiltonian matrix of the J=4 states in 50 Ti whose dimension is 204,425 (with only 14\% of the matrix elements being non-zero) in about 4 days running on 52 nodes for 48 iterations (each iteration took less than 2 hours.) Another example is 51 Ti where the largest dimension is 278,034 for J=9/2. In this case each iteration is completed in about 4 hours on 52 nodes.

We also were able to complete a few iterations required for the Lanczos diagonalization for a matrix of order of 576,934. This is the Hamiltonian matrix of 51 VV for J=3/2 states, and is one of the largest calculated so far in the nuclear shell model.

Our main goal is to calculate and diagonalize matrices of the order of a few million. These matrices are encountered in nuclei in the iron region which have important physical applications. Algorithmic development alone will not be sufficient to reach these sizes, and access to larger parallel systems will be crucial.


References


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