DFT with Continuum Junchen Pei (Peking U) With Collaborators: US : W. Nazarewicz, G. Fann, Yue Shi, R.Harrison, S. Thornton Europe: M. Kortelainen, P. Schuck China: F.R.Xu, Yi Zhu, Y.N.Zhang, Na Fei, X.Y. Xiong ……

2 Contents HFB Developments Weakly-bound nuclei: continuum and excitations Compound nuclei: decays Skyrme DFT extension Summary

3 HFB developments HFB naturally couples continuum, which is important for weakly bound nuclei. HFB solving methods: HO basis expansion: not efficient for weakly bound nuclei Complex energy: Green function, Gamow HFB, not easy for deformed case Coordinate-space: accurate for weakly bound deformed nuclei Pei et al. PRC, 2011 Coordinate space HFB equation: Large coordinate space is essential for weakly bound nuclei: continuum discretization, broad resonances and halo extension For very large deformations and shape-complex large systems: fission and cold atomic systems Breaking symmetry is expensive: 3D is much more expensive than 2D

4 HFB developments 2D: B-splines, parallel E. Teran, V.E. Oberacker, and A.S. Umar, PRC 2003 HFB-AX: J.P., M. Stoitsov, G.Fann, W.Nazarewicz, N.Schuck, F.R.Xu, PRC D: Multi-wavelets, complicated parallel MADNESS-HFB: J.P., G.Fann, R.Harrison, W.Nazarewicz, Yue Shi, S. Thornton, PRC 2014 The differences between B-splines and Multi-wavelets: A single basis vs. truncated multi-basis (much more efficient and accurate)

5 HFB developments = V n-1 ⊕ W n-1 Multi-wavelets Wavelets See also George Fann’s talk Potential applications: weakly bound nuclei, fissioning, ultracold atomic gases, neutron star crusts… Novel mathematics and complicated supercomputing

6 HFB developments HFB too expensive? TF approximation for high energy states J.P., A.Kruppa,W.Nazarewicz, PRC 2011

7 HFB developments 2 nd TF approximation for superconducting systems Here, we consider effective mass and spin-orbit with Green function method. (Na Fei, Y.N.Zhang and P. Schuck)

8 HFB developments 2 nd TF approximation for inhomogeneous superfluid systems Useful for large systems for which computing is limited Will be implemented in MADNESS-HFB J.P., Na Fei, Y.N. Zhang, P.Schuck, in prepare

9 Weakly Bound Nuclei Non-resonant and resonant continuum: box stabilization Y.N.Zhang, J.P. ， F.R.Xu, PRC 2013 J.P.,Y.N.Zhang, F.R.Xu, PRC 2013(R) Particle and Pairing deformed halos

10 Weakly Bound Nuclei Continuum Pairing Deformation Collective Excitation Halo Low lying pygmy resonance (collective or non-collective?, P.-G. Reinhard, Nazarewicz, PRC, 2013 ) The role of continuum to collective modes (not so clear) Self-consistent deformed continuum QRPA is desirable (too costly) The self-consistent approach for dynamics

11 Weakly Bound Nuclei Collective excitation with FAM-QRPA+deformed coordinate-space HFB Fully self-consistent deformed continuum FAM-QRPA Conventional QRPA matrix form FAM-QRPA iteratively solving method Need to calculate (A klmn, B klmn ), Too expensive! Combined parallel calculations in Tianhe-1A for different excitation frequency : MPI distributed parallel for each point in a node: OpenMP multi-thread parallel (12 threads) P. Avogadro and T. Nakatsukasa, PRC(2011) M. Stoitsov, M. Kortelainen, T. Nakatsukasa, C. Losa, and W. Nazarewicz, PRC(R) (2011) N. Hinohara, M. Kortelainen, and W. Nazarewicz, PRC(2013)

Dipole modes have been extensively studied Soft monopole modes due to halos (incompressibility) Clustering indication: Yang ZH, Ye YL, et al. PRL, Pairing halo vibration Not so collective Contrary to earlier expectations! Emergent soft monopole modes J.P., M.Kortelainen, Y.N.Zhang, F.R.Xu, PRC 2014(R) Will be implemented in MADNESS-HFB for multiple excitations

13 Compound nuclei Nuclei lose quantum effects at high temperature: Finite-Temperature HFB In contrast to Bohr statistical model that needs inputs of level density Finite-Temperature coordinate-space HFB neutron emission rates Bohr-Wheeler Statistical model continuum Yi Zhu, J. P, PRC 90, (2014). (Yi Zhu)

14 Compound nuclei Microscopic descriptions of neutron emission rates

15 Compound nuclei Microscopic descriptions of fission rates Temperature dependent Mass inertia parameter J.Damgaard. et al., Physics and Chemistry of fission, IAEA-SM-122/62.

16 FIG.2 FT-HF+BCS mass inertia parameters with cranking approximation T(MeV) Lifetime9.45ms3.0*10 4 s Preliminary result Microscopic descriptions of fission rates of compound nuclei (Yi Zhu) Results are much larger than statistical model Sensitive to pairing, barrier, approaches of mass parameters Non-adiabatic fission is desirable.

17 Skyrme DFT Extension Nuclear theory ignored that nucleon has a radius, so we induce 3-body force, renormalization, and etc…. T. D. Lee and C. N. Yang, Phys. Rev. 105, 1119 (1957). C. DeDominicis and P. C. Martin Phys. Rev. 105, 1417,(1957) Density functional:

18 Skyrme DFT Extension Skyrme is a very low-momentum interaction, and 3- body force is need for saturation So we are interested to study the next-order density dependence: 1/6+1/3=1/2 density-dependent 2-body

19 Skyrme DFT Extension Density dependency in Skyrme interactions (Xueyu Xiong)

20 Skyrme DFT Extension Density dependency in Skyrme interactions Overall improvement compared to SLy4: radii and energies 1/2 term is about 20~30% compared to the 1/6 term, and larger in light nuclei Maybe we can collaborate with UNEDF in this direction

21 Summary Coordinate-space HFB has advantages for weakly bound systems: structures and dynamics New Developments of HFB: 3D MADNESS-HFB, generalized 2 nd Thomas- Fermi, continuum QRPA…(these to be implement in MADNESS) Some initiatives: weakly bound nuclei, compound nuclei, Skyrme forces… Perspectives: We have had fruitful collaborations, and still have strong overlaps and great possibilities for on-going collaborations with US.

22 Thanks !