1. 6 Oct. 2011 DCEN2011 1 A new framework to investigate dineutron correlation in neutron-rich nuclei Kyoto University, Department of Physics, Fumiharu Kobayashi Yoshiko Kanada-En’yo F.K. and Y. Kanada-En’yo, PTP 126 (2011), 457

2. 6 Oct. 2011 DCEN2011 2 Outline Introduction Framework : The dineutron condensate (DC) wave function Result : Dineutron formation in simplified systems Summary, Outlook

3. 6 Oct. 2011 DCEN2011 3 Introduction

4. 6 Oct. 2011 DCEN2011 4 Dineutron correlation A dineutron is a compact spin-singlet pair of two neutrons. Dineutron correlation is enhanced in the low-density region of the nuclear matter. Some neutron-rich nuclei have low-density structure, such as neutron-halo and -skin. Is the strong dineutron correlation formed in neutron-rich nuclei? Does the dineutron condensate state exist? core n n dineutron

5. 6 Oct. 2011 DCEN2011 5 Dineutron in finite nuclei In finite nuclei, what is the universal properties of the dineutron at the nuclear surface? To answer this question, it is necessary to investigate dineutron correlation in various nuclei systematically. We constructed a new model, the “ dineutron condensate (DC) wave function ” Today’s talk : one-dineutron formation at the nuclear surface is investigated.

6. 6 Oct. 2011 DCEN2011 6 Framework

7. 6 Oct. 2011 DCEN2011 7 Framework (one-dineutron case) With AMD+DC w.f., we describe the nuclear states which includes dineutron correlation. AMD+DC = AMD + DC AMD+DC wave function ( = superposition of AMD w.f. and DC w.f. ) core (AMD) states NOT including a dineutron explicitly states including a dineutron explicitly A A-2

8. 6 Oct. 2011 DCEN2011 8 1-DC wave function spatial part ( Not a dineutron condensate state ) Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron core (AMD) dineutron relative partc.o.m. part size of dineutron spread of dineutron (s-wave) (S-wave) β n dineutron core n bnbn r rGrG A-2

9. 6 Oct. 2011 DCEN2011 9 Result

10. 6 Oct. 2011 DCEN2011 10 2α+2n DC w.f. 2α2α dineutron relative part β bnbn αα d size of dineutron spread of dineutron c.o.m. part describing the system decomposed of a dineutron around the 2  core We have analyzed dineutron energy

11. 6 Oct. 2011 DCEN2011 11 Energy surface (  b n ) The dineutron can extend far from the core keeping a compact size. : dineutron energy When the dineutron is distributed near the nuclear surface, its energy has a “valley and barrier” structure. αα d bnbn β b n : size of dineutron (fm)(MeV) (fm)  : spread of dineutron (1.9, 1.5) d = 2fm b n : size of dineutron E : dineutron energy β = 5 : far from the core β = 3 : near the core (MeV)

12. 6 Oct. 2011 DCEN2011 12 (MeV) b n : size of dineutron (fm) E : dineutron energy Valley and barrier in dineutron energy s-wave neutrons in the core angular correlated two-neutron in the higher wave strong Pauli effectweak Pauli effect Near the nuclear surface, uncorrelated two-neutron has higher energy due to the Pauli principle and a compact dineutron is favorable. uncorrelated two-neutron in the s-wave

13. 6 Oct. 2011 DCEN2011 13 t+2n Energy surface of core+2n systems  +2n2  +2n  : spread of dineutron b n : size of dineutron (fm) (MeV) As the core becomes lighter, the “valley and barrier” structure disappears. It originates in a decrease of the potential from the core. barrier valley The potential from the core is essential to dineutron formation.

14. 6 Oct. 2011 DCEN2011 14 dineutron 2-DC wave function core Distributing two same size dineutrons in the S-wave around the core size of dineutron spread of dineutron same parameters β n dineutron core n bnbn r1r1 r G1 bnbn r2r2 r G2

15. 6 Oct. 2011 DCEN2011 15 Energy surface of  +2n+2n system  +2n+2n  +2n  : spread of dineutron b n : size of dineutron (fm) (MeV) In the two-dineutron case, the compact dineutron is unfavored at the nuclear surface, compared to the one-dineutron case. under the analysis : two-dineutron energy

16. 6 Oct. 2011 DCEN2011 16 Summary

17. 6 Oct. 2011 DCEN2011 17 Summary We have proposed a new approach to investigate dineutron correlation in nuclei, the dineutron condensate (DC) wave function. When two neutrons are distributed near the nuclear surface, their energy structure has a “valley and barrier”, so that they favor a somewhat compact size. The potential from the core might be important for correlation between two valence neutrons. We have applied the AMD+DC method to 10 Be and investigated the dineutron components in 10 Be(0 + 1 ). dineutron formation poster session in YKIS

18. 6 Oct. 2011 DCEN2011 18 Outlook Application of the AMD+DC method to the various neutron-rich nuclei where dineutron correlation is expected to be enhanced, and analysis of the dineutron components in them ( for instance, 6 He, 11 Li and 12,14 Be ). Analysis two-dineutron condensate state in 7 H and 8 He in detail, and investigation of the behavior of two dineutrons.

19. 6 Oct. 2011 DCEN2011 19

20. 6 Oct. 2011 DCEN2011 20 k max -dineutron DC w.f. core (AMD) k max -dineutrons spatial part B n n dineutron core YkYk Assuming that the A-nucleon system is composed of (A-2k max )-nucleon core and one k max -dineutron

21. 6 Oct. 2011 DCEN2011 21 core (AMD)dineutron spatial part B n n dineutron core Y fixiing B = B x = B y = B z 1-DC w.f. Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron

22. 6 Oct. 2011 DCEN2011 22 relative and c.o.m. w.f. of the dineutron n n β core 2b n coordinate transformation Y-integral relative partc.o.m. part size of dineutron spread of dineutron

23. 6 Oct. 2011 DCEN2011 23 2-DC wave function Distributing two same size dineutron in the S-wave around the core Approximately replacing one of the Y-integral to the d-sum dineutron same parameters core (AMD) B n n dineutron Y1Y1 Y2Y2 core

24. 6 Oct. 2011 DCEN2011 24 Hamiltonian : Volkov No.2M=0.60, B=H=0.125 : LS part of G3RS v LS = 1600 MeV

25. 6 Oct. 2011 DCEN2011 25 Energy surface  x ≠  z 

26. 6 Oct. 2011 DCEN2011 26 Energy surface (d=1,2,3,4 fm)

27. 6 Oct. 2011 DCEN2011 27 Dineutron kinetic energy and potential energy

28. 6 Oct. 2011 DCEN2011 28 Core effect to dineutron kinetic energy