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Deformed QRPA code: Final tests and first applications

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. 172 Yb 4. Summary and plan (already started). Jun. 23, 2010 Lansing.

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Deformed QRPA code: Final tests and first applications

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  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…

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