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

Accomplishments since the last meeting: 1. Speedup of the code canonical basis 2. Successful calculation of heavy deformed nucleus 172 Yb 3. Award of 10M cpu-hours of kraken time, beginning of systematic study of rare-earth region 4. Paper submitted: arXiv:

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

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

High-Performance Computing Task: Typically we need to compute about matrix Elements (each consisting of a set of 2D integrals) in each K π and nucleus (using about 10 5 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..

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

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

Comparison of J-scheme and current codes: IS E1 strength SLy4 J-scheme, J π =1 – M-scheme, K π =0 – E (MeV)S(IS E1) (fm 6 )E (MeV)S(IS E1) (fm 6 ) x10 – x10 – x10 – x10 –2

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, Yb

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

Gamma-vibration Exp.Cal. E (MeV) B(E2)↑ (e 2 b 2 ) – Exp. ←

Gamma-vibration Exp.Cal. E (MeV) B(E2)↑ (e 2 b 2 ) – Distribution of for the lowest 2 + states of spherical nuclei J.T. et al., P.R.C 78, (2008)

“ Beta-vibration ” Exp.Cal. E (MeV) B(E2)↑ (e 2 b 2 )

Isovector electric quadrupole strength function “Total” is observable strength.

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

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

We have a complete and fully tested marix-form Skyrme QRPA code for deformed nuclei. Summary of work so far Applied to K π = 0 +, 1 +, 2 +, 0 −, and 1 − in 172 Yb, Accuracy: K π =2 + : good K п =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

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. β > 0.3, At least second 2 + energy measured

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 2 nd RPA: Gambacurta et al do this almost exactly, find huge differences with ordinary RPA. Thinking about how to proceed…