The coordinate-space HFB approach for describing weakly-bound deformed nuclei 张一怒 指导老师： 裴俊琛 许甫荣 北京大学 October 17 th, 第十五届全国核物理大会 暨第十届会员代表大会 中国 上海 2013 年 10 月

北京大学 October 17 th, 上海 核物理大会 Motivation: Physics of drip-line nuclei J. Erler et al., Nature, 486, 509(2012) Great opportunities and challenges to study unstable nuclei with new facilities!

北京大学 October 17 th, 上海 核物理大会 Motivation: Exotic structures in weakly-bound nuclei Exotic nuclear structures appear as a threshold effect: halo/clustering Pairing anti-halo versus continuum coupling effect 2-n halos still have puzzles due to 3-body and continuum effects Misu, Nazarewicz, NPA, 1997 Zhou SG et al, PRC(R)2010 F. Nunes, NPA, 2005 Egg-like Halo recently predicted Pei, Zhang, Xu, PRC(R)2013 Various core-halo deformation decoupling situations

北京大学 October 17 th, 上海 核物理大会 Model: Hartree-Fock-Bogoliubov approach HFB equation in coordinate-space is written as: HFB equation is the theoretical tool of choice for describing medium-mass and heavier nuclei

北京大学 October 17 th, 上海 核物理大会 Model: Hartree-Fock-Bogoliubov approach Coordinate-space HFB has advantages for describing weakly-bound systems and large deformations: HFB includes generalized quasi-particle correlations; while BCS is a special quasiparticle transformation only on conjugate states. HFB is superior to BCS for describing weakly-bound systems where continuum becomes essential. Bound states, continuum and embedded resonances are treated on an equal footing Very accurate for describing weakly-bound nuclei with diffused density distributions; nuclear fission processes. Deformed coordinate-space HFB approach: Breaking geometric symmetry is very expensive: parallel calculations 2D axial symmetric HFB based on B-spline, finite-difference method J. C. Pei, M. V. Stoitsov, G. I. Fann, W. Nazarewicz, N. Schunck, and F. R. Xu, PRC, 2008 J. C. Pei, A.T. Kruppa, W. Nazarewicz, PRC, 2011

北京大学 October 17 th, 上海 核物理大会 Coordinate-space v.s. Basis calculations Different surface asymptotics; Quasiparticle energy spectrum Basis HFB has problems in describing surface asymptotics and broad resonances Y.N. Zhang, J.C. Pei, F.R. Xu, arXiv: , PRC Accepted, 2013

北京大学 October 17 th, 上海 核物理大会 Exotic “egg” like halo structure of 38 Ne: SLy4 force + density dependent delta pairing 38Ne, (a) neutron density; (b) n pairing density About 2 neutrons in the halo = 0.24, =0.48 Mainly contributed by near-threshold continuum New exotic “egg”-like halo structure obtained; accurate approach is essential J. C. Pei., Y.N. Zhang, F.R. Xu, PRC (R) 87, (2013)

北京大学 October 17 th, 上海 核物理大会 Near-Threshold Continuum Different box calculations to distinguish resonances and continuum states Near threshold non-resonant continuum is responsible for halo and surface deformations No halo in 40 Mg since no near-threshold continuum contributions (N=28) J. C. Pei., Y.N. Zhang, F.R. Xu, PRC (R) 87, (2013)

北京大学 October 17 th, 上海 核物理大会 Large coordinate-space calculations Conventionally, HFB solvers were benchmarked by total binding energy, this is not sufficient for detailed properties of weakly-bound nuclei. Subtle interplay among surface deformations, surface diffuseness, and continuum needs precise HFB solutions. Large coordinate-space resulted in a vast number of continuum states and provides good resolutions for resonances and continuum (proportional L 3 ) Small box may not be sufficient for describing pairing properties. M. Grasso, N. Sandulescu, Nguyen Van Giai, R. Liotta, PRC, H. Oba and M. Matsuo, PRC, (2009) Small box may be not good for broad quasiparticle resonances. (CDCC has been suffering, I. Thompson’s talk in TORUS, 2011)

北京大学 October 17 th, 上海 核物理大会 Density and pairing density at surfaces Huge deformed halos in pairing density, need large coordinate space HFB Y.N. Zhang, J.C. Pei, F.R. Xu, arXiv: , PRC Accepted, 2013

北京大学 October 17 th, 上海 核物理大会 Quasiparticle spectrum near threshold Describing broad resonances and non- resonant continuum Problems in pairing properties Y.N. Zhang, J.C. Pei, F.R. Xu, arXiv: , PRC Accepted, 2013

北京大学 October 17 th, 上海 核物理大会 Box size dependence of energies Total energy is not sensitive to box size, However, pairing, deformation, stability… Y.N. Zhang, J.C. Pei, F.R. Xu, arXiv: , PRC Accepted, 2013

北京大学 October 17 th, 上海 核物理大会 Peninsula of stability Enhance stability due to deformations and continuum effects Fermi surfaces: HFBTHO(30 shells): 68keV HFBAX: -35keV There could be other possible islands or peninsulas of stability by accurate HFB solutions Y.N. Zhang, J.C. Pei, F.R. Xu, arXiv: , PRC Accepted, 2013 Nd

北京大学 October 17 th, 上海 核物理大会 Summary  Coordinate-space HFB has a very good opportunity to explore new exotic structures and continuum effects, with the development of supercomputing facilities.  The precisely treatment of the surface deformations, continuum effects and large spatial extensions, which are essential mechanisms of the exotic structures in weakly-bound deformed nuclei.  New exotic “egg”-like deformed halo structure of spherical core plus deformed halo is predicted.  Large box HFB calculations are necessary to describe the asymptotic behaviors of deformed halos and pairing density distributions, broad quasiparticle resonances and non-resonant continuum. 谢谢 ！ Collaborators: 裴俊琛 许甫荣