东南大学：对称能与非核子自由度及其它（专题PPT，物理系：蒋维洲）

对称能与非核子自由度及其它 蒋维洲 东南大学物理系 合作者:Bao-AnLi,陈列文、任中洲 学生:张广华、张东睿、杨荣瑶、向 仟飞 May 9, 2013@ USTC

May 9, 2013 @ USTC 对称能与非核子自由度及其它 蒋维洲 东南大学物理系 合作者：Bao-An Li，陈列文、任中洲 学生：张广华、张东睿、杨荣瑶、向 仟飞

Outline Introduction to quantum many-body approaches and the unsettled Renormalization, vacuum, dark energy? Real puzzle of symmetry energy or mal-definition Symmetry energy and quarks hyperons In neutron stars. effect of dark matter? Concluding remarks May 9, 2013@ USTC

May 9, 2013 @ USTC ➢ Introduction to quantum many-body approaches and the unsettled ➢ Renormalization, vacuum, dark energy? ➢ Real puzzle of symmetry energy or mal-definition? ➢ Symmetry energy and quarks & hyperons ➢ In neutron stars, effect of dark matter? ➢ Concluding remarks Outline

从宇宙大爆炸到黑洞形成 What Powered the Big Bang? Waves can Escape from 0-10-100s 宽= p Proton 质子 neutron After 1 Billion years 中子 中子墨R-1km)

May 9, 2013 @ USTC 从宇宙大爆炸到黑洞形成 10-10--100 s Proton neutron After 1 Billion years 中子星 质子 中子 黑洞 (R~10km)

核结构——量子多体问题 宏观模型、宏观-微观模型 准粒子、费米独立气体模型 Hartree Approximation Hartree-Fock(反对称化) Brueckner-Hartree-Fock (since 1960s Relativistic models( since 1970s Dirac旋量(大分量、小分量),自旋,膺 自旋对称性,极化散射 May 9, 2013@ USTC

May 9, 2013 @ USTC 核结构——量子多体问题 • 宏观模型、宏观-微观模型 • 准粒子、费米独立气体模型 • Hartree Approximation • Hartree-Fock (反对称化） • Brueckner-Hartree-Fock（since1960’s) • Relativistic models (since 1970’s) Dirac旋量（大分量、小分量），自旋，膺 自旋对称性，极化散射

Field-theoretic Hamiltonian approach H()=[d3xSm.091(x1) LLL is Lagrangian at 1=o0 OL 0(n/O) Omitting the retardation effect, the Hamiltonia n is H=d' xv(xirV+ M)v(x) +2∑dd((m7w0 1=o丌 May 9, 2013@ USTC

May 9, 2013 @ USTC Field-theoretic Hamiltonian approach     = = +     = −  +      =         −   =            i i i i i i i d x d x x x x x x x i M x t L L t x t H t d x ( ) ( ) (1,2) ( ) ( ) 2 1 H d ( )( γ ) ( ) Omitting the retardation effect, the Hamiltonia n is ( / ) , L is Lagrangian, ( , ) ( ) 3 3 3 3

Basedon the plane wave expansion, it can be written in the momentum space H=T+-7 2u(p, a,(Y p+M)u(p2, a2 )bpla1bp2a2 P1a1,P2,42,t y=∑∑(p1+q947(P1-9,4)(12)-2 P1p2, q a1, a2, t1 (p2,a2)(p12a1)bb PItg, ai P1q, 2 P2, 42 P1s a1 May 9, 2013@ USTC

May 9, 2013 @ USTC 1 2 2 1 1 , , , 1 2 *2 2 , , , , , 1 1 2 2 1 1 2 2 , , , , 1 1 1 2 2 2 1 1 , 1 1 2 1 2 2 1 2 1 1 1 2 2 ( , ) ( , ) q 1 ( , ) ( , ) (1,2) ( , )(γ p ) ( , ) 2 1 H T momentum space Basedon the plane waveexpansion, it can be written in the p q a p a p a i i p p q a a a a p a p a p a p a u p a u p a b b b b m V u p q a u p q a T u p a M u p a b b with V p q a + −  +   + +   + = +  −   =  + = +      

Hartree-Fock approximation Energy density(without retardation n effect) E==+= +=62Q2Onx+∑中 P1+q, ai Pi,a Hartree Fock approximat ion: taking i=0& omitting all intermedia te states Pb P><pIb. b P1+q, a, lo =asO aSn,nO+ Fock term hartree term May 9, 2013@ USTC

May 9, 2013 @ USTC Hartree-Fock approximation Fock term Hartree term | | | | ˆ Hartree Fock approximat ion : taking i 0 & omitting all intermedia te states | | | | ˆ Using the projection operator | | 1, it becomes | | | | | ( ) | | | ˆ Perform operator commutatio ns in potential energy : 2 1 | | Energy density (without retardatio n effect) : 2 1 1 2 2 1 2 2 1 1 2 1 1 2 2 1 2 2 2 2 1 , 1 1 2 1 1 2 2 1 2 2 2 2 1 , 1 1 1 1 , 1 1 2 1 1 2 2 1 2 2 2 2 1 1 , 1 2 2 2 1 1 2 2 2 1 , 1 2 2 2 2 1 , , , ,0 0 1 , , , 0 , , 0 0 , 0 1 , , , 0 , , , i 0 1 , , 0 0 , , , 1 0 , , 0 1 0 , , , , , 0 1 0 , , , 0 0 = + = +   = +     =   = +       = = −   +   = −  −   =  =  =  +     +   + +   + −  + +   + −  + +  + −  +  + +  + −  + −  + +  +  +  +  +    a a a a p p q a a a a a a a a p p q p q a p a p a i a a a a p p q p q a p a i i p a i i p a p a a a p p q p q a p a p a p q a p p q a a p a p a p q a p a p a O b b b b O b b b b b b b b b b b b b b O b b b b H T V p q a p q a p q a p q a p q a                                      q

Relativistic Hartree-Fock Relativistic Hartree-Fock-Brueckner G°(k) G°(k) Σ(k) G Σ G(k) (a) k G(gq) E团:~ G G G(q)+ t B ANW Mwn+wOw = ↑B (P′q) G(pa+q) P2 △ May9,2013@

May 9, 2013 @ USTC Relativistic Hartree-Fock | Relativistic Hartree-Fock-Brueckner

No quantum effect Radiation correction requires the quantization of coulomb field In strong fields the renormalization required Relativistic Hartree Approximation: vacuum polarization of mesons(Chin, AP108, 301(1977).) dg =-2Ja2n)x{2n(-D12)+D1+u1-D12)+D1吗 +[n(1-4I)+4m+n1 4)1-(D)1- No ring energy calculation done in Relativistic Hartree-Fock-Brueckner framework! Two-body correlation is not enough to depict pairing correlation: BCS, Bogoliubov, May 9, 2013@ USTC

May 9, 2013 @ USTC No quantum effect • Radiation correction requires the quantization of Coulomb field • In strong fields, the renormalization required • Relativistic Hartree Approximation: vacuum polarization of mesons (Chin, AP108, 301 (1977).) No ring energy calculation done in Relativistic Hartree-Fock-Brueckner framework! Two-body correlation is not enough to depict pairing correlation: BCS, Bogoliubov,…

k dkE*+△c 2r)3 p=C2p2+2C2n22-7c2(M +3∑如2 △S 0.4 2=p,n where Co=ma/go, and A& is the finite vacuum correction36, 37 0.2 M* +M3∑、 25 0 △S= M/* M M∑ R OL dm )0 ∑C=(v)a 0⊥an108×31p0+ dp dp 2! a Jiang Li, Modern Physics Letters A o23.N0.4943y98 3O USTC

May 9, 2013 @ USTC Jiang & Li, Modern Physics Letters A Vol. 23, No. 40 (2008) 3393