Spin-Orbit Interactions in Nuclei and Hypernuclei

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Ab-Initio Nuclear Structure Bad Honnef July 29, 2008 Spin-Orbit Interactions in Nuclei and Hypernuclei Wolfram Weise Phenomenology Aspects of Chiral Dynamics and Spin-Orbit Forces Nuclei vs.

1 Ab-Initio Nuclear Structure Bad Honnef July 29, 2008 Spin-Orbit Interactions in Nuclei and Hypernuclei Wolfram Weise Phenomenology Aspects of Chiral Dynamics and Spin-Orbit Forces Nuclei vs. -Hypernuclei: understanding the Spin-Orbit Puzzle References: N. Kaiser and W. W., Nucl. Phys. A804 (2008) 60 P. Finelli, N. Kaiser, D. Vretenar and W. W., Phys. Lett. B658 (2007) 90 N. Kaiser and W. W., Phys. Rev. C71 (2005) S. Fritsch, N. Kaiser and W. W., Nucl. Phys. A750 (2005) 259 N. Kaiser, Phys. Rev. C70 (2004) N. Kaiser, S. Fritsch and W. W., Nucl. Phys. A724 (2003) 47

2 1. Nuclear and Hypernuclear Spin-Orbit Forces: Phenomenology

$Nuclear Shell Model Phenomenology :I? { 5hr,r oo0 4h r.t eve n { 3 h o l a A d I - J U - \, ' - J ' 1 :. l /. _ / l X i _ - 2 4 - < X -? 1 5 / " - ' r a ) - '.-,1 r.$

3 Nuclear Shell Model Phenomenology :I? { 5hr,r oo0 4h r.t eve n { 3 h o l a A d I - J U - \, ' - J ' 1 :. l /. _ / l X i _ < X -? 1 5 / " - ' r a ) - '.-,1 r..1 s7, (16)- [184 ]-184 /-3d3/2 - (/+)- - Ls s 1., :--..- i.? \- I -2s-\---1d3/z zn( D a. - 'ld -<-'* e v e n t - 2s1/2-1d 5/z t n u J o 0 d / -. -? d 9 /. - i ' t ' l I - \ - l s t 7 2-1g -(. - 1 a 7 / t a t - -1p-.::_,3'!; 0-1 s s 1 / z 1i13/z -ft )-U26)-126 ( 2 t - ( 8 ) - \ \- 1gsy2- (10)-t ( 2 )- t40l ( 6 ) - [ 3 8 ] ( 4 ) - ( 8 ) - [ 2 8 ] ( 4 \ t ( 2 ) - t ( 6 ) - [ 1 4 ] M. Goeppert-Mayer, J.H.D. Jensen (1955) I 2 r - f R '- l R ( 4 ) - [ 6 ] r ^ 1 L L I Spin-Orbit Interaction H LS = U LS r L = i r f(r) = ρ(r) ρ 0 = df(r) dr L s s = 1 2 σ ( 1 + exp r R ) 1 a U LS 30 MeV fm 2 unusually large: one order of magnitude larger than expectation from Thomas term based on single particle potential and opposite sign

4 Skyrme Phenomenology Energy Density of slightly inhomogeneous nuclear matter Spin-Orbit part of energy density functional E LS [ρ] = F LS (ρ) ρ Ψ α( r) i σ Ψ α ( r) α F F LS (ρ 0 ) 90 MeV fm 5 Relation between shell model phenomenology and Skyrme parametrization F LS (ρ) = 2ρ U LS (ρ)

5 Phenomenology (part I): Strong Scalar-Vector Mean Fields Short-distance contribution to spin-orbit interaction F sr LS = G S + G V 4M N Equivalent descriptions: = 1 4M N ( g 2 σ m 2 σ ) + g2 ω m 2 ω sigma-plus-omega boson exchange models á la Walecka contact terms in NN Effective Field Theory Result: strong scalar-vector mean fields from QCD Sum Rules Σ S = G S ρ S Σ V = G V ρ empirical Σ S Σ V σ N 4(m u + m d ) ( ρs ρ ) 1 (Cohen, Furnstahl; PRL 67 (1991) 961) F LS (ρ 0 ) 90 MeV fm 5 G S σ N M N m 2 f 2 10 fm 2 understood at Hartree level in terms of short-distance NN dynamics 1

6 Phenomenology (part II): Fujita-Miyazawa Mechanism ( J. Fujita, H. Miyazawa; Prog. Theor. Phys. 17 (1957) 360 ) large spin-isospin polarizabilty strong 3-body ga 2 interaction β = N N f 2 (M M N ) 5 fm3 N Pionic Van der Waals - type intermediate range central potential N N 9 g2 A V c (r) = 32 2 f 2 β e 2m r r 6 P(m r) N. Kaiser, S. Fritsch, W. W. Nucl. Phys. A750 (2005) 259 Large contribution to spin-orbit interaction F ( ) LS (50 70) MeV fm5 How can there be a coexistence between short-distance and Fujita-Miyazawa two-pion exchange mechanisms?

7 Spin-Orbit Coupling in -Hypernuclei Central Potential Spin-Orbit Potential U () U(N) 0 U () LS 1 20 U(N) LS E (p 1/2 ) E (p 3/2 ) = (152 ± 54 ± 36) kev unusually small: more than 20 times smaller than the p 1/2 p 3/2 spin-orbit splitting of about 5 MeV for nucleons in nuclei... cannot be understood in terms of short-distance dynamics scalarvector mean fields 1 2

8 2. Chiral Dynamics and Spin-Orbit Interactions

9 CHIRAL DYNAMICS and the NUCLEAR MANY-BODY PROBLEM Relevant small scales: p F 2 m M M N << 4 f 1 GeV PIONS (and DELTA isobars) as explicit degrees of freedom IN-MEDIUM CHIRAL PERTURBATION THEORY pion exchange in presence of filled Fermi sea in medium N, N N N N 2nd order TENSOR force + nucleon s SPIN-ISOSPIN polarizability short-distance dynamics: contact interactions N N

10 CHIRAL DYNAMICS and the NUCLEAR MANY-BODY PROBLEM (contd.) Compute energy density E(p F ) using in-medium chiral perturbation theory (3-loop order) N. Kaiser, S. Fritsch, W.W. ( ) result: realistic nuclear matter equation of state spin-dependent nucleon self-energy in (slightly) inhomogeneous nuclear matter 2nd order tensor force produces spin-orbit term Σ LS ( p, q) = U LS (p F ) i s ( q p)

11 Iterated ONE-PION EXCHANGE - Kaiser s WRONG SIGN Spin-Orbit Interaction - N. Kaiser PRC70 (2004) N. Kaiser, W. W. NPA804 (2008) 60 F () LS (ρ) = m M N 64 ( ga f ) 4 [ 1 m 2 + 4p 2 F 3 ( )] 8p 2 ln 1 + 4p2 F F m 2 exch. Hartree term: 100 Sly, S III, MSk 87 MeV fm 5 at ρ = ρ 0 cancels short-distance spin-orbit contribution F LS F so [MeV fm 5 ] empirical (Skyrme phenomenology) wrong sign spin-orbit from 2nd order tensor force ! [fm -3 ]

12 TWO-PION EXCHANGE Spin-Orbit Interaction: (1230) and 3-Body Terms S. Fritsch, N. Kaiser, W. W. NPA750 (2005) 259 F ( ) LS (ρ) = g 4 A 8 2 f 4 (M M N ) [ m 2 p F + p 3 F m 2 + 4p 2 F ( )] m2 ln 1 + 4p2 F 4p F m 2 exch. F ( ) LS Delta F () LS Miyazawa cancellation

13 Intermediate Summary: Balance of Spin-Orbit Terms Three major contributions to nuclear spin-orbit interactions: Short-distance component (strong scalar and vector fields) survives Wrong-sign spin-orbit term generated by 2nd order pion exchange tensor force cancellation Three-body term induced by two-pion exchange with intermediate Delta(1230) (á la Fujita-Miyazawa) Learn more about underlying mechanisms by comparison with hypernuclear spin-orbit forces (different balance of terms)

14 3. Chiral SU(3) Dynamics and Spin-Orbit Interaction in - Hypernuclei

15 HYPERON SELF-ENERGY short-distance (contact) terms Σ Σ small: ( e.g. scalar-vector mean fields ) ( K exchange Fock term ) large: 1 2 two-pion exchange mechanisms medium insertion medium insertions 2nd order tensor force produces spin-orbit term () () Σ LS ( p, q) = U LS (p F ) i s ( q p) K N. Kaiser, W. W. PRC71 (2005)

16 Spin-Orbit Coupling in -Hypernuclei cancellation between short-distance (contact) and two-pion exchange terms 4 0 U () LS!4 U "ls (k f ) [MeVfm 2 ]!8!12!16 K!20!24 Σ +... wrong sign... + C ls =2/3= 2/3 C ls =1/2= 1/ ρ![fm!3 3 ] ] Σ shortdistance medium insertions U () LS = C ( M M N N. Kaiser, W. W. PRC71 (2005) N ) 2 U (N) LS for short-distance terms NO three-body terms á la Miyazawa: no hyperon Fermi sea

of nuclei and hypernuclei example: 16 O ε (p 1/2 ) ε (p 3/2 ) [MeV] P.

17 Finite Systems translate in-medium chiral dynamics add surface terms (calculable) density functional very satisfactory results for systematics of nuclei and hypernuclei example: 16 O ε (p 1/2 ) ε (p 3/2 ) [MeV] P. Finelli, N. Kaiser, D. Vretenar, W. W. PLB658 (2007) 90 shortdistance 2nd order tensor C

18 SUMMARY towards resolution of Hypernuclear vs. Nuclear Spin-Orbit puzzles based on in-medium Chiral Effective Field Theory short-distance Hartree QCD sum rules NN contact terms scalar-vector MF in-medium ChPT (2nd order tensor) wrong sign spin-orbit (Kaiser) in-medium ChPT (3-body) Fujita- Miyazawa mechanism Comparisons between nuclei and hypernuclei useful in studying the role of 3-body interaction mechanisms

INTERFACE of QCD and NUCLEAR PHYSICS

INTERFACE of QCD and NUCLEAR PHYSICS Confinement8 Mainz 5 September 28 ITERFACE of QCD and UCLEAR PHYSICS Wolfram Weise Low-Energy QCD and CHIRAL SYMMETRY uclear Forces in the context of CHIRAL EFFECTIVE FIELD THEORY uclear Matter Energy