1. 低密度原子核体系中的双中子关联现象 孙保元 (Bao Yuan SUN) 兰州大学核科学与技术学院 第十四届全国核结构大会 浙江湖州, 13 April 2012  Introduction  Di-neutron Spatial Correlations in Nuclear Matter  Di-neutron Spatial Correlations in Giant Halo Nuclei  Summary

2. Di-neutron Spatial Correlations  Pairing correlations play a crucial role in the fermion systems. J. Bardeen, L. N. Cooper, J. R. Schrieffer, Phys. Rev. 108 (1957) 1175. A. Bohr, B. R. Mottelson, D. Pines, Phys. Rev. 110 (1958) 936.  In nuclear physics, it is expected that di-neutron correlations in low-density nuclear systems should be significant.  A large scattering length for the 1 S 0 neutron-neutron interaction G.F.d. Téramond, B. Gabioud, Phys. Rev. C 36 (1987) 691.  A large value of the 1 S 0 pairing gap at low densities M. Baldo, J. Cugmon, A. Lejeune, U. Lombardo, Nucl. Phys. A 515 (1990) 409. T. Takatsuka, R. Tamagaki, Prog. Theor. Phys. Suppl. 112 (1993) 27.  Enhancement of cross sections in two-neutron transfer reactions W. von Oertzen, A. Vitturi, Rep. Prog. Phys. 64 (2001) 1247.  Small emission angle between 2n in di-neutron decay A. Spyrou, Z. Kohley, T. Baumann et al., Phys. Rev. Lett. 108 (2012) 102501. (2n emission in 16 Be)  Recently, experimental and theoretical progress on halo structure of weakly bound neutron-rich nuclei and possible BCS–BEC crossover of di-neutron pairs at low densities has stimulated lots of interests in di-neutron spatial correlations. I. Tanihata:1985, G. F. Bertsch:1991, J. Meng:1996,1998,2006, J. Dobaczewski:1996 M. Matsuo, Phys. Rev. C 73 (2006) 044309. B. Y. Sun, H. Toki and J. Meng, Phys. Lett. B 683 (2010) 134. K. Hagino, H. Sagawa, J. Carbonell, P. Schuck, Phys. Rev. Lett. 99 (2007) 022506.

3. Typical Experimental Evidence of Di-neutron Correlations in Nuclei A three-body model including a strong di-neutron correlation can well reproduce a strong low-lying E(1) distribution observed in 11 Li. T. Nakamura et al., PRL 96 (2006) 252502. H. Esbensen et al., PRC 76 (2007) 024302. T. Myo et al., PRC 76 (2007) 024305. The “di-neutron” configuration of 6 He make the dominant contribution to the cross sections of two-neutron transfer reactions. Yu.Ts. Oganessian et al., PRL 82 (1999) 4996.

4. Di-neutron Coherence Length in Nuclei In medium or heavy superfluid nuclei: HFB M. Matsuo:2005, N. Pillet:2007, 2010. Quite unique and exceptional situation: 11 Li and 6 He K. Hagino: JPG 37 (2010) 064040. The small value of coherence length in the surface is essentially determined by the finite size properties of single-particle states in the vicinity of the chemical potential and has very little to do with enhanced pairing correlations in the nuclear surface. spatially compact The minimal value of coherence length in surface is essentially determined by the pairing strength. Cooper pair rms radius, measure of the pairing size: small sized Cooper pairs in the surface K. Hagino et al., Phys. Rev. Lett. 99 (2007) 022506. Comment: N. T. Zinner and A. S. Jensen (2008). Reply: K. Hagino et al. (2008). In light halo nuclei:

5. Motivations and Goals  Study the di-neutron spatial correlations in giant halo nuclei with Relativistic Continuum Hartree–Bogoliubov(RCHB) theory J. Meng et al., Prog. Part. Nucl. Phys. 57 (2006) 470.  Spatial distribution of pairing tensor  Coherence length of neutron Cooper pairs B. Y. Sun, Y. Zhang, J. Meng, in preparation.  Explore the di-neutron correlations in nuclear matter based on microscopic calculation (RMF) with a realistic bare nucleon-nucleon interaction (Bonn-B)  Study BCS-BEC crossover phenomenon at low-density nuclear matter B. Y. Sun, H. Toki and J. Meng, Phys. Lett. B 683, 134 (2010). T. T. Sun, B. Y. Sun, J. Meng, H. Toki, submitted to Phys. Rev. C. Whether further similar cases to 11 Li and 6 He exist in the heavier nuclei on nuclear chart? How does pairing correlations account for the small sized Cooper pairs in the surface? Whether further similar cases to 11 Li and 6 He exist in the heavier nuclei on nuclear chart? How does pairing correlations account for the small sized Cooper pairs in the surface? Prediction for giant halo ： N  82 140 Zr N>40 66 Ca Meng & Ring, PRL80, 460 (1998) Meng et al., PRC65,041302R (2002) Prediction for giant halo ： N  82 140 Zr N>40 66 Ca Meng & Ring, PRL80, 460 (1998) Meng et al., PRC65,041302R (2002)

6. BCS (weak coupling)BEC (strong coupling) crossover The transition takes place continuously: BCS-BEC crossover BCS-BEC Crossover Phenomenon Excitonic semiconductors: D. M. Eagles, Phys. Rev. 186, 456 (1969). Ordinary superconductors: A. J. Leggett, J. Phys. Colloq. 41, 7 (1980). Attractive Fermion gas: P. Nozieres and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985). Color superconductivity: Y. Nishida and H. Abuki, Phys. Rev. D 72, 096004 (2005). Nuclear matter: M. Matsuo: PRC2006; J. Margueron: PRC2007; B. Y. Sun: PLB2010.  Weakly interacting fermions  Correlation in p space  Large coherence length  Bosonic bound state  Correlation in r space  Small coherence length

7. BCS (weak coupling)BEC (strong coupling) crossover The transition takes place continuously: BCS-BEC crossover BCS-BEC Crossover Phenomenon  Weakly interacting fermions  Correlation in p space  Large coherence length  Bosonic bound state  Correlation in r space  Small coherence length Excitonic semiconductors: D. M. Eagles, Phys. Rev. 186, 456 (1969). Ordinary superconductors: A. J. Leggett, J. Phys. Colloq. 41, 7 (1980). Attractive Fermion gas: P. Nozieres and S. Schmitt-Rink, J. Low Temp. Phys. 59, 195 (1985). Color superconductivity: Y. Nishida and H. Abuki, Phys. Rev. D 72, 096004 (2005). Nuclear matter: M. Matsuo: PRC2006; J. Margueron: PRC2007; B. Y. Sun: PLB2010.

8. BCS Approximation and Pairing Gap Equation

9. Cooper Pair Wave Function in Nuclear Matter Cooper pair wave function BCS Crossover As the density decreases, the spatial structure evolves continuously from BCS-type to BEC-type.  BCS-type: oscillating attenuation  BEC-type: compact, no oscillation Proper treatment of the short-range repulsion of nuclear force leads to suppressed amplitude around r = 0 As the density decreases, the spatial structure evolves continuously from BCS-type to BEC-type.  BCS-type: oscillating attenuation  BEC-type: compact, no oscillation Proper treatment of the short-range repulsion of nuclear force leads to suppressed amplitude around r = 0 The relativistic pairing theory  ph: RMF with PK1 W. Long (2004)  pp: Realistic bare NN force Bonn-B The relativistic pairing theory  ph: RMF with PK1 W. Long (2004)  pp: Realistic bare NN force Bonn-B B. Y. Sun, H. Toki and J. Meng, Phys. Lett. B 683, 134 (2010).

10. S=0 Probability Density of Neutron Pairs in Nuclear Matter K. Hagino et al., PRL 99(2007)022506 B. Y. Sun, H. Toki and J. Meng, PLB 683(2010)134 A two-dimensional plot for the probability density r 2 |Ψ pair (r)| 2 of the neutron Cooper pair as a function of the relative distance r between the pair partners and the neutron Fermi momentum k Fn in SNM.

11. BCS-BEC Crossover in Nuclear Matter BCS-BEC crossover region: 0.05 fm -1 < k Fn < 0.7 (0.75) fm -1 for the symmetric (neutron) nuclear matter BCS-BEC crossover region: 0.05 fm -1 < k Fn < 0.7 (0.75) fm -1 for the symmetric (neutron) nuclear matter B. Y. Sun, H. Toki and J. Meng, PLB 683(’10)134 The coherence length in infinite NM strongly depends on the pairing strength and approximate inverse proportionality between the gap and the coherence length could be established. No evidence for the appearance of a true BEC bound state of neutron pairing at any density Coherence Length:

12. Relativistic Continuum Hartree Bogoliubov Theory  Bogoliubov Transformation:  Quasi-particle Wave Function:  Relativistic Hartree-Bogoliubov Equations: effective interaction NLSH  Pairing Force: V 0 = −670 MeV fm 3 J. Meng, H. Toki, S.G. Zhou et al., Prog. Part. Nucl. Phys. 57 (2006) 470.

13. To grasp the full physics of nuclear pairing it is very important to work in a large configuration space, comprising several shells below and above the Fermi surface. Probability Density Distribution of Cooper Pairs: |κ(r, R)| 2 r 2 R 2 Different Parity NLSH R m = 5.20 fm R n = 5.47 fm R p = 4.51 fm Contrasted with infinite matter: Different number of levels in the range of the gap value Coulomb barrier: low-j levels

14. WF: Similarity to BCS-BEC Crossover Phenomenon

15. Effects of the Parity Mixing The parity mixing induced by the pairing force leads to a short range di-neutron space correlations in the surface of the nuclei. The concentration only shows up when even and odd parity states are mixed. Same conclusion in: F. Catara:1984, L. Ferreira:1984, Tischler:1998, N. Pillet:2007. The strong concentration of small sized pairs in the surface of nuclei can be treated as a feature of halo nuclei.

16. Influence of the Strength of Pairing Force V 0 = −670 MeV fm 3 V 0 = −460 MeV fm 3 -0.53 -13.6 Whether concentration of small sized pairs in the surface is due to pairing correlation? Pairing Energy In giant halo nucleus 134 Zr: The small coherence length of Cooper pairs in the surface of nuclei is essentially determined by the pairing strength. In giant halo nucleus 134 Zr: The small coherence length of Cooper pairs in the surface of nuclei is essentially determined by the pairing strength.

17. Evolution in Zr Isotope

18. The di-neutron spatial correlations is studied in both nuclear matter and giant halo nuclei with the relativistic bogoliubov theory. Summary Di-neutron spatial correlations in superfluid nuclei  Similar cases to 11 Li and 6 He exist in the heavier nuclei.  BCS-BEC crossover phenomenon is displayed by WF of Cooper pairs.  Parity mixing in large configuration space leads to a strong concentration of small sized Cooper pairs in the nuclear surface. Low-j level is important!  Pairing correlations have effects on small sized pairs in the surface: 134 Zr.  Evolution of pairing in Zr isotope:possible criterion of BCS-BEC crossover Di-neutron spatial correlations in nuclear matter  A strong concentration of the probability density is revealed for the neutron pairs in the fairly small relative distance.  BCS-BEC crossover region: 0.05 fm -1 < k Fn < 0.7 (0.75) fm -1  The coherence length of Cooper pairs in infinite nuclear matter strongly depends on the intensity of pairing correlations. Thank you for your attention !

19. 北京大学物理学院： 孟杰 教授 孙亭亭 博士 张颖 博士 Collaborators 大阪大学 RCNP ： Hiroshi Toki 教授