FRONTIERS IN HADRON AND NUCLEAR PHYSICS 2015 FHNP’15 January 9-11, 2015,中国科学院大学雁栖湖校区 Personal views and remarks on nuclear theory Jie MENG（孟 杰） School of Physics，Peking University 北京大学物理学院

Goal of nuclear physics

Existence Limit of nucleus stable nuclei ~300 nuclei unstable nuclei observed so far ~2700 nuclei drip-lines (limit of existence)（theoretical predictions) ~8000 nuclei magic numbers proton-rich nuclei proton drip-line neutron-rich nuclei neutron drip-line neutron number (N) proton number (Z) Question 3 How were the elements from iron to uranium made ? 2018/11/19 ~ 2200 nuclear masses were measured

Century of struggling

Birth of nuclear physics 十九和二十世纪之交，Becquerel和Curie夫妇等发现了放射性 Rutherford实验确定了在原子中心存在致密的原子核 In particular, since the 1st PRL on halo phenomena, we have achieved success on 1) giant halo; 2) pion and exchange term on halos; 3) deformations and halos, etc. In this figures, T prepare two taking away messages: 1) giant halos exist in NFT, CDFT, RHFB, GF Skyrme HFB; 2) Beautiful systematic and abnormality coexist! 这些成就开启了核科学领域的探索历程，促进了核能和核技术的开发与利用，对人类产生了巨大的影响。

Milestone toward the nuclear model Chadwick发现中子，确定了原子核由质子和中子构成 In particular, since the 1st PRL on halo phenomena, we have achieved success on 1) giant halo; 2) pion and exchange term on halos; 3) deformations and halos, etc. In this figures, T prepare two taking away messages: 1) giant halos exist in NFT, CDFT, RHFB, GF Skyrme HFB; 2) Beautiful systematic and abnormality coexist! Yukawa提出了核子间强相互作用的介子交换理论

Independent particle shell model & collective model Mayer和Jensen等人建立了原子核独立粒子运动模型 In particular, since the 1st PRL on halo phenomena, we have achieved success on 1) giant halo; 2) pion and exchange term on halos; 3) deformations and halos, etc. In this figures, T prepare two taking away messages: 1) giant halos exist in NFT, CDFT, RHFB, GF Skyrme HFB; 2) Beautiful systematic and abnormality coexist! Bohr和Mottelson建立了原子核集体运动模型

进入20世纪50年代，原子核物理研究进入了一个更加艰难的探索阶段。 虽然独立粒子模型从唯象的平均势场出发，可以给出原子核内部单个核 子运动的描述，但是不能定性给出原子核整体性质的描述。 与之相比，集体运动模型可以给出原子核集体振动和转动统一的唯象描 述，对单个核子的运动却无能为力。

Strutinsky Shell correction calculation Compromise between Shell model and collective model Great success for FRDM WS4 … V.M. Strutinsky, Shell effects in nuclear masses and deformation energies, Nuclear Physics A 95 (1967) 420 Times Cited: 1,664 “Shells” in deformed nuclei, Nuclear Physics A 122 (1968) 1 Times Cited: 1,040

如何从强相互作用出发，给出原子核中单个核子运动和 原子核集体运动的统一微观自洽描述，是原子核物理学 家亟需回答的问题。

New ideas around 1950s Bethe-Goldstone-Brueckner (1957): the effective interaction G within the nucleus is very weak Dürr-Teller (1956): relativistic single particle model: Fujita Miyazawa (1957): three-body force: Hans Bethe Jeffrey Goldstone Keith Brueckner Hans-Peter Dürr Edward Teller 20:57

New ideas around 1950s Skyrme (1958): model with zero range: two-body, three-body, tensor Arima & Horie (1954): first configuration mixing calculations BCS (1957). Bogoliubov (1958) 1960年代，在于敏先生指导下，张宗烨先生提出原子核相干结构及相干对涨落模型理论，成功地解释了16O附近原子核低激发态的主要特性。 20:57

Possible standard model: Density functional

theorem of Hohenberg und Kohn: Hohenberg-Kohn theorem (1964): theorem of Hohenberg und Kohn: Hohenberg Kohn 14

The numbers of papers (in kilopapers) corresponding to the search of a topic “DFT” in Web of Knowledge (grey) for different and the most popular density functional potentials: B3LYP citations (blue), and PBE citations (green, on top of blue). K. Burke Perspective on density functional theory J. Chem. Phys., 136 (2012) 150901 [1-9]

Density functional theory in nuclei: In nuclei DFT has been introduced by effective Hamiltonians: by Vautherin and Brink (1972) using the Skyrme model as a vehicle Based on the philosophy of Bethe, Goldstone, and Brueckner one has a density dependent interaction in the nuclear interior G(ρ) At present, the ansatz for E(ρ) is phenomenological: Skyrme: non-relativistic, zero range Gogny: non-relativistic, finite range (Gaussian) CDFT: Covariant density functional theory: • Spin-orbit automatically included • New saturation mechanism (scalar different from vector density) • Proper treatment of time-odd components (nuclear magnetism) • Pseudospin symmetry • Connection to QCD: (large scalar and vector fields: ~ ±400 MeV) • Lorentz covariance restricts the number of phenomen. parameters… 20:57

Electromagnetic force: The photon 协变密度泛函理论是基于强相互作用的有效场论 和密度泛函理论发展起来的相对论量子多体理论 Strong force: Meson-exchange of the nuclear force (Jp T)=(0+0) s w r (Jp T)=(1-0) (Jp T)=(1-1) Sigma-meson: attractive scalar field Omega-meson: Short-range repulsive Rho-meson: Isovector field Electromagnetic force: The photon

Covariant density functional Progress in Physics. 31(2011)199-336. Covariant density functional σωρ σωρπ ρ π σ ω σωρπ Meng, Peng, Zhang, Zhao, Frontiers of Physics 8:1 Pages: 55-79 2013 Liang, Meng, Zhou, Hidden pseudospin and spin symmetries and their origins in atomic nuclei 1411.6774 [nucl-th] Meng, Toki, Zhou, Zhang, Long, Geng, Prog. Part. Nucl. Phys. 57 (2006) 470

  Hidden pseudospin and spin symmetries and their origins in atomic nuclei Authors: Haozhao Liang, Jie Meng, Shan-Gui Zhou (accepted on Dec 25, 2014 for publication in Physics Reports / 242 pages, 58 figures, 10 tables) http://xxx.yukawa.kyoto-u.ac.jp/abs/1411.6774 Reviewer #1  “After a long introduction, which in itself presents already an excellent overview of the field, they start in the first part with a careful discussion…” , “This review is rather long. However, to my opinion, this is well justified, because the field is large and because this is an excellent review, covering an enormous number of publications of many different authors and groups, not just collecting a few publications of the own group by cut and paste, as it is done nowadays so often. This review will definitely be of great value in the future” Reviewer #2 “The present paper gives a comprehensive review of those recent developments, including applications to systems as diverse as hyperon and anti-nucleon spectra, resonant and deformed states etc. I spent many an hour preparing this report but it was worth it since I learned something in the process”

Relativistic description of nuclear matrix elements in neutrinoless double-β  decay Phys. Rev. C 90, 054309 – Published 10 November 2014 L. S. Song, J. M. Yao, P. Ring, and J. Meng

相比于传统的原子核理论，协变密度泛函理论所基于的介子交换图 像更微观、更基本： 由于相对论协变性，自然包含核力中的自旋-轨道相互作用； 给出核物质新的饱和机制； 借助对称性自发破缺引入各种关联效应； 既可给出原子核内单个核子的运动，而且通过恢复对称性和考虑量 子涨落，可实现对原子核转动、振动、同位旋激发等集体模式的自洽描 述；

未来核物理理论 目前所采用的核子有效相互作用，虽然基于介子交换理论并且具有相对 论协变性，但并不是从强相互作用的基本理论－量子色动力学导出的。 协变密度泛函、相对论多体理论的成功表明，从有效的核子-核子相互 作用出发，实现原子核基态和激发态性质的统一自洽描述是可行的。 未来工作包括：从基本的量子色动力学出发，恰当地得到原子核介质环 境中的核子-核子相互作用，进而与协变密度泛函、相对论多体理论结合， 构建原子核物理的标准模型，实现对原子核的第一性原理（ab initio）计算 。