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
- [Novoselsky,97] A. Novoselsky, M. Vallières and O. La'adan,
Phys. Rev. Lett. 79, 4341 (1997).
- [Novoselsky,98] A. Novoselsky and M. Vallières,
Phys. Rev. C 57, R19 (1998).