Deformed QRPA Code: Final Tests and Applications

1. Deformed QRPA code: Final tests and first applications J. T. and J. Engel Univ. North Carolina • Main accomplishments since last meeting, • flow of calculation, computational aspects • 2. Tests • 3. 172Yb • 4. Summary and plan (already started) Jun. 23, 2010 Lansing

2. Accomplishments since the last meeting: • Speedup of the code • canonical basis • 2. Successful calculation of heavy deformed nucleus • 172Yb • 3. Award of 10M cpu-hours of kraken time, • beginning of systematic study of rare-earth region • 4. Paper submitted: arXiv:1006.0010

3. Primary purpose: To obtain predictions of Skyrme functionals for energies and strengths of excited states throughout the isotopic chart. Calculation of deformed and pairedheavy system is quite challenging. Fully self-consistent deformed QRPA calculations generally limited so far to A~40 or less.

4. Flow of calculation HFB calculation Calculation of matrix elements of Hamiltonian Diagonalization of Hamiltonian matrix Strength functions

5. High-PerformanceComputing Task: Typically we need to compute about 1010 matrix Elements (each consisting of a set of 2D integrals) in each Kπ and nucleus (using about 105 core-hours at desired level of accuracy for heavy nuclei). Info/Issues: Code scales well in simple tests up to 10,000 cores. ADLB might help with larger numbers of cores Working with Teragrid Advanced Support to speed up Vanderbilt HFB code. .

6. Tests in Mg, separation of spurious states Particle-number transition strength Kπ=0+ Angular-momentum transition strength Kπ=1+ SkP, volume pairing

7. Separation of translational spurious state IS E1 transition strength to Kπ=0– states A correction operator is known which removes translational spurious components from the matrix elements SLy4

8. Comparison of J-scheme and current codes: IS E1 strength SLy4

9. 172Yb Questions: • Is our code accurate enough in such a heavy system? • How well do we predict low-energy surface vibrations? • Pygmy resonance? Size of calculation: Box size = 20 fm 4648 proton qp. wave functions 5348 neuron qp. wave functions Number of two-qp pairs ~ 77,000 Size of Hamiltonian matrix: 154,000 x 154,000.

10. Energy-weighted sum rule and strength function Electric quadrupole transition, Kπ=2+ Curves : QRPA value Flat line : analytical value

11. Gamma-vibration Exp. ← http://www.nndc.bnl.gov

12. Gamma-vibration Distribution of for the lowest 2+ states of spherical nuclei J.T. et al., P.R.C 78, 044311 (2008)

13. “Beta-vibration”

14. Isovectorelectric quadrupole strength function “Total” is observable strength.

15. Electric dipole transition, Kπ=1– Corrected strengths are excellent in terms of EWSR No IV peak around separation energy ~6 MeV

16. A. Voinov et al., P.R.C 63, 044313 (2001) “Pygmy resonance” observed in gamma- ray strength function. pygmy resonance

17. Summary of work so far We have a complete and fully tested marix-form Skyrme QRPA code for deformed nuclei. Applied to Kπ = 0+, 1+, 2+, 0−, and 1− in 172Yb, • Accuracy: Kπ=2+ : good Kп=1+ ; still need to eliminate residual spurious strength Others : acceptable as measured by sum rule • Low-energy surface vibrational states: With SLy4, deviation from experiment is similar to typical deviation in spherical • Pygmy resonance ? Not found in the dipole mode

18. Now: 2+ Systematics With 10M cpu-hours of Teragrid time, we are evaluating performance of SkM* and a new optimized UNEDF functional for beta- and gamma- vibrational states in rare-earth region. At least second 2+ energy measured β > 0.3,

19. Deliverables • 2+systematics: First results obtained. Complete over next few months, • Charge-changing QRPA for beta decay: Underway. Tom Shafer (graduate student) working this summer to convert code. • Fold QRPA into ORNL Optimization: Discussions underway • Start 2nd RPA: Gambacurta et al do this almost exactly, find huge differences with ordinary RPA. Thinking about how to proceed…