Physics of Exotic Nuclear Structure and Relativistic Density Functional Theory

Jie MENG  （孟 杰）

School of Physics，Peking University（北京大学物理学院）

Yukawa Institute for Theoretical Physics, Kyoto University(京都大学基礎物理学研究所)

Editorial Board: Science Bulletin (科学通报) SCIENTIA SINICA Physica, Mechanica & Astronomica(中国科学) Frontiers of Physics Chinese Physics Letters Progress in Physics (物理学进展)Chinese Physics C (before 2016)Nuclear Physics Review (核物理评论)WuLi (物理 in Chinese)

Managing Editor: International Journal of Modern Physics E

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

Facilities for Rare Isotope Beams

兰州HIRFL-CSR1997-2008年投资：2.93亿元

北京BRIF-II2014年

韩国 KoRIA 2012年开始建设投资：5.5亿美元

美国MSU-FRIB2008年开始建设

投资：5.5亿美元法国SPIRAL-II2006年开始建设

德国GSI-FAIR2007年开始建设投资：12亿欧元

日本RIKEN-RIBF2006年第一期完工

投资：550亿日元

惠州 HIAF2015年12月立项投资：15亿元

Existence Limit of nucleus

6 2017/12/25

82

8

20

28

50

8

2028

50

82

126

proton-rich nuclei

proton drip-line

neutron drip-line

neutron number (N)

neutron-rich nuclei

proton number (Z)

stable nuclei ~300 nucleiunstable nuclei observed ~2700 nucleidrip-lines （predictions) ~8000 nucleimagic numbers

~ 2200 nuclear masses were measured

New isotopes

New phenomena

New magic number

New collective mode

New radioactivity

Origin of element

Fundamental physics

Nuclear models

… … …

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

Nuclear Existence

Drip-lines in variant models

Figure: 10532 bound nuclei from Z=8 to Z=130 predicted by RCHB theory with PC-PK1. For 2227 nuclei with data, binding energy differences between data andcalculated results are shown in different color. The nucleon drip-lines predicted TMA,HFB-21, WS3, FRDM , UNEDF and without pairing correlation are plotted forcomparison.

The number of bound nuclides with between 2 and 120 protons is around 7,000 2 8 J U N E 2 0 1 2 | V O L 4 8 6 | N AT U R E | 5 0 9

See also: Afanasjev, Agbemava, Ray, Ring, PLB726(2013)680

arXiv:1704.08906

8 ⩽ Z ⩽ 120,9035 nuclei predicted to be bound

Possible isotopes made by FRIB

From Xue-Wei Xia

arXiv:1704.08906

Atomic Data and Nuclear Data Tables

T Baumann et al 2007 Nature 449 1022

Nuclear chart showing the most neutron-rich isotopes from C to Cl

Dripline(201712)

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

From Xin-Hui Wu

Halos, giant halos and deformed halos

Meng and Ring, Phys. Rev. Lett. 77(1996) 3963

Meng and Ring, Phys. Rev. Lett. 80(1998) 460

Zhou, Meng, Ring, Zhao , Phys.Rev.C82 (2010) 011301

Meng, Toki, Zhou, Zhang, Long &Geng, Prog. Part. Nucl. Phys. 57(2006) 470

Meng and Zhou, J. Phys. G: 42(2015) 093101

Shell structure, low density，continuum ， bound state,spatial distribution, pairingcorrelation, coupling betweenbound state and continuum…

I. Tanihata, et al Phys. Rev. Lett. 55, 2676 (1985)

Nuclear Shape

By Bing-Nan Lu

Phys. Rev. Lett. 116, 032501 (2016)Phys. Rev. C 89, 011301(R) (2014)

Simple Nuclear Structure in cadmium @CERN

The simplicity of the linear increase isrevealed to be due to the pairing correlationwhich smears out the abrupt changesinduced by the single-particle shellstructure, and thus leads to a smooth shapeevolution

Multidimentionally constrained CDFT

Figure: Potential energy curve of 240Pu

• MDC-CDFT: all with even included• Triaxial & octupole shapes both crucial

around the outer barrier

1. Lu, Zhao, Zhou, PRC 85, 011301 (2012)2. Zhao, Lu, Zhao, Zhou, PRC 86, 057304 (2012)3. Lu, Zhao, Zhao, Zhou, PRC 89, 014323 (2014)4. Zhao, Lu, Vretenar, Zhao, Zhou, arXiv:1404.5466 (2014) Figure: 3D PES of 240Pu

courtesy of B.N. LUAbusara, Afanasjev, and Ring, PRC 85, 024314 (2012)

Nuclear Clustering

Evgeny Epelbaum et al, Phys. Rev. Lett. 106 (2011) 192501; Evgeny Epelbaum et al, Phys. Rev. Lett. 109 (2012) 252501

Hoyle State

An ab-initio calculation: Lattice EFT

Novel Clustering in exotic nuclei

Stabilization of a linear chain cluster

Zhao, Meng, Itagaki, Phys. Rev. Lett. 115, 022501(2015)

Neutron level

Spin-Isospin Effects

Novel Clustering in exotic nuclei

More experiments requires FRIB …

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

Evolution of the shell structure

From Dobaczewski

New Magic number 16

A. Ozawa, T. Kobayashi, T. Suzuki, K. Yoshida, and I. TanihataPhys. Rev. Lett. 84, 5493 (2000)

Evolution of the shell structure

The frontier: Calcium isotopes

New shell closures at N = 32 & 34?

The large and unexpected increase ofthe size of the neutron-rich calciumisotopes beyond N > 28 challenges thedoubly magic nature of 52Ca and opensnew intriguing questions on theevolution of nuclear sizes away fromstability.

R. F. Garcia Ruiz, et al

A Gade and B M Sherrill

Calcium isotopes in FRIB

FRIB provides access to key

neutron-rich Ca isotopes with

intensities sufficient to measure

crucial observables (masses, half-

lives, decay properties, excitations ).

It will be the only facility with 60Ca

yields above 0.01/s. FRIB will reach64Ca.

In-Beam γ -Ray Spectroscopy of 34,36,38Mg

P. Doornenbal, et al,Phys. Rev. Lett. 111（2013）212502

E(2) and E(4) energies for silicon (opentriangles) and magnesium (filled triangles)isotopes between N=20 and N=28. Thelower panel show the respective R(4/2)ratios

SM: Phys. Rev. C 60, 054315 (1999).3DAMP+GCM：Phys. Rev. C 83, 014308 (2011).

The emergence of a large area ofdeformation extending from N=20 toN=28 shell quenching.

Shell Quenching in Mg Isotopes

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

Novel excitation modes in atomic nucleus

A. Bohr &  B. MottelsonInterpretation 

vibration Rotation

Frauendorf & Meng, NPA 617 (1997)  131

Prediction 

Chiral Rotation

Meng, Peng, Zhang, Zhou, PRC73 (2006) 037303 

Prediction

Exploration of MχD in 78BrSpontaneous chiral and reflection symmetry breaking

H. Iwasaki, et al, Phys. Rev. Lett. 112, 142502 (2014) @ GRETINA

Doppler-shift lifetime measurement: the large collectivity for the 4 → 2 transitionrelative to that for 2 → 0 transition suggests a prolate character of the excitedstates， i.e., the onset of the oblate-prolate shape transition at low spin in 72Kr， presenting an extreme example of the shape transition in atomic nuclei.

Evolution of the Collectivity : Shape Transition

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

New Radioactivity

Proton emitter

Olsen et al., Phys. Rev. Lett. 110, 222501 (2013)Lim et al., Phys. Rev. C93, 014314 (2016)

Non-relativistic DFT Relativistic DFT

Landscape of Two-Proton Radioactivity

Proton radioactivity in relativistic continuum Hartree-Bogoliubov theory

Long Range Plan 2015

New Radioactivity

Neutron emitter

The experiments of two-neutron radioactivity in 26O and 28O willprovide crucial data for refining nuclear models at the limits ofnuclear existence.

Opportunity with Facilities for Rare Isotope Beams

Exotic nucleus: nucleus @ extreme N/Z New isotopes：Limit of existence New phenomena：halo, shape, cluster…… New magic number New collective mode New radioactivity: proton, neutron, cluster…… Origin of element … … …

New opportunities in nuclear Physics

Nuclear astrophysics

Quantity EffectSn neutron separation energy pathT1/2 -decay half-lives abundance pattern

timescalePn -delayed n-emission

branchingsfinal abundance pattern smooth r-abundance

G Nuclear Partition function abundance pattern (weakly)

fission (branchingsand products)

endpointabundance pattern?degree of fission cycling

NA<v> neutron capture rates final abundance pattern during freezeout ?

conditions for waiting point approximation

Isomeric states… Branch of the r-process pathfinal abundance patterntimescale

Nuclear physics input in the r-process

Relativistic Density Functional Theory

for nuclear structure and nuclear astrophysics

J. Meng (Editor)International Review of Nuclear Physics - Vol. 10 Relativistic Density Functional for Nuclear StructureWorld Scientific （2016）

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Brief History

Covariant Density Functional Theory

Numerical details

Nuclear ground state properties

Nuclear excited state properties

Interface with astrophysics and standard model

Summary & Perspectives

Relativistic Density Functional Theory

37

Milestone toward the nuclear model

The discovery of neutron by Chadwickwhich verified the composition of nucleus asprotons and neutrons

The meson-exchange theory for theinteraction between nucleons by Yukawa

During the hundred years’ struggling, in the development of nuclear physics itself, there emerged a lot of significant milestones, including

H. Euler, Z. Physik 105, 553 (1937)Heisenberg's student who calculated the nuclear matter in 2nd order perturbation theory

Isospin and Z1/3-dependence of the nuclear charge radiiEur. Phys. J. A 13, 285–289 (2002).

31A 31A

Nuclear Bulk property

two-nucleon separation energy

∆S2p

much smaller after 8, 20, 28, 50, 82, 126

∆S2n

Nuclear Shell Model

原子核的许多性质呈现出随中子数或质子数而周期变化的现象

ARn + A-4Po TSudden rise at N = 126

Neutron capture cross section

Very small at N = 28, 50, 82, 126

Abrupt change in nuclear radius at N = 20, 28, 50, 82, 126

R = R(Z;N)-R(Z;N-2) 的实验值与液滴模型计算值之比

RRavg

RRavg

Nuclear Shell Model

Only smallest magic numbers are reproduced. Why ?

Spin-orbit term is necessary

Mayer and Jensen et al., 1949

srrV

rVV sso .)(1

M. G. Mayer, Phys. Rev. 75(1949)1969; 78(1950).O. Haxel, J. H. D. Jensen, and H. E. Suess, Phys. Rev. 75(1949)1766;Z. Phys. 128(1950)295;

Nuclear Shell Model

Thanks are due to Enrico Fermi for theremark, "Is there any indication of spin-orbitcoupling?" which was the origin of this paper.

Nuclear Shell Model

Nuclear Shell Model

Strong spin-orbit interaction

Great for:magic numbersground state propertiessome low lying excited states

Lead to deformed Nilsson model

S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No.16(1955).S. G. Nilssion, et al., Nucl. Phys. A131(1969) 1.

Shell model & Collective model

Totally fails for nuclear bulk properties

J. H. D. Jensen

M. G. Mayer E. P. Wigner

Nobel Prize in Physics 1963

Although the independent particleshell model could describe the single-particle motion in a nucleus with aphenomenological mean potential, itcannot provide even a qualitativedescription for the nuclear bulkproperties.

On the contrary, a unifiedphenomenological description ofnuclear vibration and rotation can beachieved by the collectiveHamiltonian whereas it is helpless inunderstanding the motion of a singlenucleon.

A. N. Bohr B. R. Mottelson J. Rainwater

Nobel Prize in Physics 1975

Shell model & Collective model

The independent particle shell model of nucleus by Mayer and Jensen etal., and the collective Hamiltonian for nuclear rotation and vibration byBohr and Mottelson, etc. However, since 1950s, nuclear physics steppedinto a more challenging stage.

0

10

20

30

40

50

60

Ene

rgy

[MeV

]

0

10

20

30

40

50

60

48.56MeV48.51MeV

Strutinsky Shell correction calculation

Compromise between Shell model and collective model

Great success for FRDMWS4 …

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

Weizsäcker-Skyrme (WS) formula “Isospin for S-O & E_sym + mirror nuclei”

inspired by the Skyrme energy-density functional and a macroscopic-

microscopic mass formula, with an rms deviation of 336 keV with respect to

the 2149 measured masses in 2003 Atomic Mass Evaluation.N. Wang, M. Liu and X. Z. Wu, Phys. Rev. C 81, 044322 (2010).

N. Wang, Z. Y. Liang, M. Liu and X. Z. Wu, Phys. Rev. C 82, 044304 (2010).M. Liu, N. Wang, Y. G. Deng, and X. Z. Wu, Phys. Rev. C 84, 014333 (2011).

Taking into account the surface diffuseness effect, the rms deviation with

2353 known masses falls to 298 keV.N. Wang, M. Liu, X. Z. Wu and J. Meng, Phys. Lett. B 734, 215 (2014).

Finite-Range Droplet Model (FRDM) P. Möller, J.R. Nix, W.D. Myers, W.J. Swiatecki, At. Data Nucl. Data Tables 59, 185 (1995). Times Cited: 2,385 Error of the mass model is 0.669 MeV

How to achieve microscopically and self-consistently a unified

description of the single-nucleon and collective motions of nucleus

based on the strong interaction theory is a crucial question to be

answered by nuclear scientists.

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The self-consistent mean-field approach to nuclear structure isanalogous to Kohn-Sham Density Functional Theory.

Density functional theory (DFT) , with the name comes from the use of functionals of the particle density, is aquantum mechanical theory used in physics and chemistry to investigate the structure (mainly the ground state) of many‐particle systems.

ji iiijii

i

rUVrUm

H )()(2

ˆ 22

Mean field potential Residual interaction

EVm

Hji

iji

i2

2

2ˆ

Many-body problems

10:03

• 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

Great ideas around 1950s Great ideas around 1950s