# Presentation: 087950

##  Spectroscopy of Odd-Mass Nuclei in Energy Density Functional TheoryImpact of Terascale Computing

** ****Spectroscopy of Odd-Mass Nuclei in Energy Density Functional Theory****Impact of Terascale Computing**

**N. Schunck**
***University of Tennessee, 401 Nielsen Physics , Knoxville, TN-37996, USA***
***Oak Ridge National Laboratory, Bldg. 6025, MS6373, P.O. Box 2008, Oak Ridge, TN-37831, USA***
- In collaboration with:*** J. Dobaczewski, W. Nazarewicz, N. Nikolov and M. Stoitsov***

## Energy density is real, scalar, time-even, iso-scalar but constituting fields are not (necessarily) and therefore need be computed...
Time-even part (depends on time-even fields)

Time-odd part (depends on time-odd fields)

Scalar, vector and tensor terms depend on scalar, vector or tensor fields
Iso-scalar (t = 0), iso-vector (t = 1)
Coefficients C are uniquely related to coefficients (t, x) of Skyrme force
Spirit of the EDF: cutting off correspondence C  (t, x)

**Time-even** part (depends on time-even fields)
**Time-odd **part (depends on time-odd fields)
- Scalar, vector and tensor terms depend on scalar, vector or tensor fields
- Iso-scalar (t = 0), iso-vector (t = 1)
- Coefficients C are **uniquely** related to coefficients (t, x) of Skyrme force
- Spirit of the EDF: cutting off correspondence C  (t, x)

**Nuclear Energy Density Functional**

## Pairing correlations

- Pairing functional ***a priori***** as rich**** **as mean-field functional
- Replace  density matrix by  pairing tensor
- (iso)-scalar, (iso-)vector, tensor terms
- Form considered here: surface-volume pairing
- Cut-off, regularization procedure
- Example:
- 1 element  1 isotopes  1 deformation  24 interactions   45 pairing strengths = **1080** **different calculations**
- Time of calculation: ~ 5 hours on Jaguar
- (Some form of) projection like Lipkin-Nogami prescription on the number of particles required
- Breaking down of pairing correlations
- Fluctuations of particle number

## Determination of V0

- Neutron Pairing Gap in 120Sn in Skyrme HFB Calculations

## EDF Solver on Jaguar

- Modern super-computers allow large-scale calculations
- Symmetry-restricted codes: one mass table in a **couple of hours**
- Symmetry-unrestricted codes: one mass table in a **couple of days**
- MPI-HFODD: all-symmetry-breaking, parallel, public-domain DFT solver
- HFODD core plus parallel interface with master/slave architecture
- About 1.2 Gflops/core on Jaguar
- 2 GB memory/core required for standard calculations (~ 1000x1000 matrices)
- Time of calculation/computing node:  12 hours/node
- Example for odd nuclei:
- 7 elements  14 isotopes  1 deformation  1 interaction   20 nucleonic configurations = **1960** **different calculations**
- Time of calculation: ~ 10 hours on Jaguar
- Can very easily use up all resources !

## Normalized Q.P. Spectrum (1)

**Normalized Q.P. Spectrum (1)**

- SLy4

- Experiment

- SLy4 + Time Odd Fields (Gauge Invariance)

## Normalized Q.P. Spectrum (2)

- What can affect the spectra ?
- Interaction
- Effective mass: 0.7  m*  1.0
- Terms neglected/included (Ex. **Tensor**)
- Pairing: functional, fit

***Almost impossible to do without large-scale parallel architectures***

## Conclusions

- Nuclear Energy Density Functional Theory provides a **consistent framework** to describe nuclear structure
- Current DFT solver allow:
- Breaking all symmetries (geometrical)
- Fast and scalable calculations
**Quality hierarchy** of EDF description of nuclear structure:
- “Standard” force (terms neglected, strong bias in the fit)
- Tensor terms
- All time-odd terms
- Particle-number projected pairing
- (Some) many-body correlations
- Large-scale massively parallel facilities allow to do **undreamt-of** computations and reach to an Universal Energy Density Functional

-  Include all terms