"The Density Matrix Renormalization Group and the Nuclear Shell Model"
Stuart Pittel, University of Delaware
(id #184)
Seminar: NoPoster: No
Invited talk: Yes
In this presentation, I will review our recent efforts to develop
the Density Matrix Renormalization Group method into a
practical approach for carrying out large-scale shell model
calculations of atomic nuclei. I will begin with an overview of the essential features of the method [1] and will then turn to some of the issues specific to its use in atomic nuclei.
I will then summarize the principal results we have obtained to date [2-3].
Our primary applications have been to nuclei in the 2p-1f
shell, where our focus has been to test the method by comparison with
the results of exact shell-model diagonalization. We have carried
out calculations for both even-even and odd-mass nuclei, ranging
from A=48-56.
We find that the method converges rapidly to the exact results for
all nuclei considered. Most importantly, the fraction of the full
space required for a high level of accuracy goes down rapidly with
the size of the full shell-model space, suggesting that the method
may prove useful for heavier nuclei where exact diagonalization is not feasible.
[1] See e.g. J. Dukelsky and S. Pittel, Rep. Prog. Phys. 67 (2004) 513.
[2] B. Thakur, S. Pittel and N. Sandulescu, Phys. Rev. C 78 (2008) 041303.
[3] B. Thakur, Ph.D. thesis, University of Delaware (2010), unpublished.
the Density Matrix Renormalization Group method into a
practical approach for carrying out large-scale shell model
calculations of atomic nuclei. I will begin with an overview of the essential features of the method [1] and will then turn to some of the issues specific to its use in atomic nuclei.
I will then summarize the principal results we have obtained to date [2-3].
Our primary applications have been to nuclei in the 2p-1f
shell, where our focus has been to test the method by comparison with
the results of exact shell-model diagonalization. We have carried
out calculations for both even-even and odd-mass nuclei, ranging
from A=48-56.
We find that the method converges rapidly to the exact results for
all nuclei considered. Most importantly, the fraction of the full
space required for a high level of accuracy goes down rapidly with
the size of the full shell-model space, suggesting that the method
may prove useful for heavier nuclei where exact diagonalization is not feasible.
[1] See e.g. J. Dukelsky and S. Pittel, Rep. Prog. Phys. 67 (2004) 513.
[2] B. Thakur, S. Pittel and N. Sandulescu, Phys. Rev. C 78 (2008) 041303.
[3] B. Thakur, Ph.D. thesis, University of Delaware (2010), unpublished.
