Proton-skins in momentum and neutron-skins in coordinate in heavy nuclei: What we can learn from their correlations. Bao-An Li

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1 Proton-skins in momentum and neutron-skins in coordinate in heavy nuclei: What we can learn from their correlations Bao-An Li Collaborators: Baojun Cai, Texas A&M University-Commerce, USA Lie-Wen Chen, Shanghai Jiao Tong University, China Suorted by

2 Outline of my talk in Phase Sace (R,K)? Exeriments ρ J (r) R Constrained nucleon distribution in r n n n n Wave function in R or K n Isovector Strong Interaction n K Exeriments Extended + Thomas-Fermi Aroximation Constrained nucleon distribution in k

3 Protons are moving faster than neutrons in neutron-skins The average local momentum is defined via

4 N-skins as a testing ground of the isovector art of strong interactions P. Pawłowski and A. Szczurek SHF calculations Relative n/ ratio R. Michaels et al.

5 Sizes of n-skin in 208 Pb extracted from various exeriments M.B. Tsang et al, PRC86, (2012) ρ Coherent ion hotoroduction C. M. Tarbert et al. (Crystal Ball at MAMI and A2 Collaboration) EPJA 50, 20 (2014)

6 What are Short Range Correlations (SRC) in nuclei? (Eli Piasetzky) 2N-SRC SRC ~R N LRC ~R A ~1 fm 1.f k F ~ 250 MeV/c High momentum tail: MeV/c 1.5 K F - 3 K F In momentum sace: ρ o = 0.16 GeV/fm 3 1.7f 1.7f 1.8 fm Nucleons K 1 K 1 > K F, A air with large relative momentum between the nucleons and small CM momentum. K 2 K 2 > K F

7 Tensor force induced (1) high-momentum tail in nucleon momentum distribu8on and (2) isosin deendence of SRC Theory of Nuclear matter H.A. Bethe Ann. Rev. Nucl. Part. Sci., 21, (1971) Fermi Shere

8 JLab. CLAS A(e,e') Result K. Sh. Egiyan et al. PRC 68, (2003) K. Sh. Egiyan et al. PRL. 96, (2006) 2 2 Q >1.4GeV scaling e q e / i a 2N (A/d) 3 He 2.08± He 3.47±0.02 Be 4.03±0.04 C 4.95±0.05 Cu 5.48±0.05 Au 5.43±0.06 P 2 N (A) = a 2 N (A / d) P 2 N (D) P 2N ( ) 20-30% 2 Q x B = 2mω More r(a,d) data: SLAC D. Day et al. PRL 59,427(1987) JLab. Hall C N. Fomin et al. PRL 108:092502, 2012.

9 Trile coincidence measurement of the isosin deendence of SRC A(e,e ) A(e,e ) A(e,e N) A(, N) n C target R. Subedi et al., Science 320, 1476 (2008)). O. Hen et al., Science 346, 614 (2014)

10 Average kinetic energies of neutrons and rotons in nuclei (1) Light nuclei: Predictions of the Variational Many-Body theory with AV18+UX interaction (2) Heavy nuclei: Neutron-roton dominance model with arameters fixed by SRC data O. Hen et al. (Jlab CLAS), Science 346, 614 (2014) (1) Where are these energetic rotons located? (2) How is the -skin in momentum related to the n-skin in coordinate?

11 Isosin deendence of deletion (oulation) of Fermi sea (high momentum tail) A. Rios, A. Polls and W. Dickhoff, PRC89, (2014), A self-consistent Greens Function aroach Below the Fermi surfaces Above the Fermi surfaces Proton fraction

12 Isosin deendence of the average occuation of the Fermi sea at saturation density within BHF Kh.S.A. Hassaneen, H. Müther, Phys. Rev. C70 (2004)

13 The Jlab finding is consistent with earlier findings from the sectroscoic factors of direction reactions and +nucleus scattering The minority comonent is more correlated near the Fermi surface! Examle I: roton occuation from + 40 Ca, + 48 Ca, and + 60 Ca (rediction) Disersive otical model analysis PRL 97, (2006)

14 Phenomenological nucleon momentum distribution n(k) including SRC effects guided by microscoic theories and exerimental findings The n(k) is not directly measurable, but some of its features are observable O. Hen, B.A. Li, W.J. Guo, L.B. Weinstein, and E. Piasetzky, PRC 91, (2015). B.J. Cai and B.A. Li, PRC92, (R) (2015); PRC93, (2016). Isosin-deendent deletion of Fermi sea Isosin-deendent high momentum tail All arameters are fixed by (1) Jlab data: HMT in SNM=25%, 1.5% in PNM, (2) Contact C for SNM from deuteron wavefunction (3) Contact C in PNM from microscoic theories All arameters are assumed to have a linear deendence on isosin asymmetry as indicated by SCGF and BHF calculations

15 The high-momentum tail in deuteron scales as 1/K 4 O. Hen, L. B. Weinstein, E. Piasetzky, G. A. Miller, M. M. Sargsian and Y. Sagi, PRC92, (2015). VMB calculations VMB calculations Ultracold 6 Li and 40 K Ultracold 6 Li and 40 K =k/k F K =K/K F Stewart et al. PRL 104, (2010) Kuhnle et al. PRL 105, (2010)

16 EOS and contact C of ure neutron matter B.J. Cai and B.A. Li, PRC92, (R) (2015). density The contact C of PNM is derived from its EOS using the adiabatic swee theorem n(k)=c/k 4 S. Tan, Annals of Physics 323 (2008)

17 Correlation between measurements in R and K saces Same interaction! different reresentations of the same wave functions in R or K sace Fundamental rinciles guiding hysical intuitions: (1) Liouville Theorem: dρ(r,k,t)/dt=0! <r>"<k> constant (2) Uncertainty Princile! δr"δk h Examle: neutron momentum distribution in the halo nucleus 11 Li Recoil momentum distribution of 9 Li in 11 Li+ 12 C! 9 Li+2n+x reactions 2n randomly selected from (1) A small Fermi shere (2) A large Fermi shere Mixed 2-Fermi sheres

18 The Extended Thomas-Fermi Aroximation (ETF) M. Brack et al, Phys. Re. 123, 275 (1985) Using the semi-classical ħ exansion of the Block-density matrix develoed by Wigner (1932) and Kirkwood (1933) The kinetic energy density in nuclei: (1) The original Thomas-Fermi Aroximation for nuclear matter: (2) The Weizsacker term (1935): (sensitive to surface roerties-a robe of n-skin!) (3) The ħ 4 term: Lalacian term

19 Extended + Thomas-Fermi Aroximation (ETF + ) considering the isosin-deendent SRC and effectively ħ 4 and higher order terms What to we add and modify? Mimic effects of ħ 4 and higher terms H.Krivine and J. Treiner, PLB 88, 212 (1979) X. Cami and S. Stringari, NPA 337, 313 (1980) M. Barranco, M. Pi and X. Vinas, PLB124, 131 (1983) Isosin-deendent SRC constrained by data Φ J =1 for shar Fermi sheres, it is larger than 1 with SRC-induced high momentum tails

20 Connection with neutron-skin via the Extened Thomas-Fermi Aroximation Both the half-radius C and surface diffuseness a contribute to the size of neutron-skin EPJA 50 (2014) 27

21 et al. (1) Need to go beyond inferring the n-skin from its correlation with an observable shown in models (2) Better infer directly the neutron density rofile from data analyses &understand the nature of n-skin Exerimental evidence of Halo domination in 208 Pb from hotoroduction of π 0

22 Constraining the ETF model arameters a n,c n and η n for 208 Pb (1) For rotons, η is the only arameter as the roton density rofile is known (2) For neutrons, given the size of neutron-skin, average kinetic energy, and the normalization condition, only a correlation among a n, c n and η n is fixed

23 Neutron-skin in coordinate and roton-skin in momentum The average local momentum is defined via

24 Constancy of in a given model For symmetric matter, M. Casas, J.Martorell, E. Moya de Guerra and J. Treiner, NPA473, 429 (1987)

25 Two dimensional but correlated constraints on models using indeendent measurements of n-skin in R and -skin in K

26 Summary Protons are moving faster than neutrons in neutron-skins Extended + Thomas-Fermi Aroximation f J (r,k) Exeriments R Constrained nucleon distribution in r n n n n Wave function in R ok K n Isovector Strong Interaction n? K Exeriments Constrained nucleon distribution in k Microscoic Theories

27 The Migdal (1957)-Luttinger (1960) Theorem: (occuation renormalization function) The effective E-mass Physics Reorts 211, 53 (1992). B.J. Cai and B.A. Li, PLB 757, 79 (2016)

28 Levinger s constant BEC Ultracold 40 K BCS C=0.172±0.007

29 Relative robability of SRC in nucleus A with resect to that in deuteron a 2 (A/d) extraolated to infinite SNM P 2 ( D) = ψ D = ± N. 275± 25 Nucleon removal energy P 2 N (A) = a 2 N (A / d) P 2 N (D) P 2N ( ) 20-30% in symmetric matter E. Piasetzky, O. Hen, L. B. Weinstein Proceedings of lenary talk at CIPANP 2012