Dineutron condensate state in 8 He

1. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron condensate state in 8He Kyoto University, Department of Physics, Fumiharu Kobayashi Yoshiko Kanada-En’yo

2. Introduction • Dineutron correlation, cluster condensation • Part I • Dineutron behavior in dineutron condensation of light nuclei • Part II • Excited state of dineutron condensation in 8He • Summary Coexistence of weak and strong binding in unstable nuclei and its dynamics Outline

3. Coexistence of weak and strong binding in unstable nuclei and its dynamics Introduction

4. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron correlation A dineutron: Acompact spin-singlet pair of two neutrons. Dineutron correlation is enhanced in some situations (e.g. inthe low-density region of the nuclear matter, in the neutron-halo and -skin region of neutron-rich nuclei) . What is the mechanism of the dineutron formation? What is the universal properties of the dineutron correlation? dineutron Cooper pair

5. Coexistence of weak and strong binding in unstable nuclei and its dynamics Cluster condensation 12C(0+2); Hoyle state a Condensation : some as in the lowest s-orbit. Such a state is characterized by clusters weakly interacting each other and expanded largely. The a condensate states are being investigated theoretically and experimentally. 0s a a a a a a “a gas”

6. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron condensation • Some studies suggested that • a dineutron becomes compact in neutron-rich nuclei • and • dineutrons in light neutron-rich nuclei (8He, 7H) may condensate. • Is the dineutron condensation formed? • How do the dineutrons behave in dineutron condensate state? (G. F. Bertsch et al. Ann. Phys. (NY) 209 (1991), M. V. Zhukov et al. Phys. Rep. 231 (1993) K. Haginoet al. PRC 72(2005） … ) (Y. Kanada-En’yo, PRC 76 (2007), N. Itagaki et al. PRC 78 (2008), S. Aoyama et al. PRC 80 (2009))

7. Coexistence of weak and strong binding in unstable nuclei and its dynamics 8He a + four valence neutrons part I higher than 0p3/2 part II In this work, we investigate the behavior of two dineutrons in dineutron condensate states of 8He, 6,10He and 7H using a and dineutron condensate (aDC) w.f.. 2n(*) 6He core 6He + 2n cluster w.f. aDC w.f. (including two dineutrons explicitly) the dineutron condensate state in realistic 8He considering 0p3/2-orbits superposing 6He+2ncluster w.f. and8He DC w.f.. 8He DC w.f. (including dineutron explicitly)

8. Coexistence of weak and strong binding in unstable nuclei and its dynamics Part I • Introduction of a new framework; aDC w.f. • Investigation of the dineutron behavior in a+2dineutron condensate state (8He) • Comparison the dineutron behavior in 8He with those in 6,10He and 7H

9. Coexistence of weak and strong binding in unstable nuclei and its dynamics Condensate wave function As a framework to describe an a condensate state in 4N nuclei, a condensate wave function (THSR wave function) is very useful. Our framework, a and dineutron condensate (aDC) wave function originates from a condensate wave function. A. Tohsaki et al. PRL 87 (2001) a a a

10. Coexistence of weak and strong binding in unstable nuclei and its dynamics a condensate wave function of 12C In an a condensate wave function, a clusters move in the lowest s-orbit around an origin. a a a ~b Ri; centers of the ai b ; size of as B ; spatial expansion of as O { B same for all the as

11. Coexistence of weak and strong binding in unstable nuclei and its dynamics Energy surface on B-b plane A. Tohsaki et al. PRL 87 (2001) b : a size b B B : a expansion An a cluster is rigid. The valley at b~1.4 fm is the indication of the Hoyle state.

12. Coexistence of weak and strong binding in unstable nuclei and its dynamics aDC wave function of 8He One a and two dineutrons move in the s-orbit around an origin. β bn2 Ri; centers of the cluster i bi ; size of the cluster i Bi ; spatial expansion of the cluster i { (ba = 1.4 fm) bn1 O Bn2 Bn1 Ba a different for each cluster but here Bn1 = Bn2, bn1 = bn2

13. Coexistence of weak and strong binding in unstable nuclei and its dynamics Hamiltonian : VolkovNo.2 m=0.59, b=h=0.0 (2n is bound) orm=0.55, b=h=0.125 (2n is unbound) {

14. Coexistence of weak and strong binding in unstable nuclei and its dynamics Energy surface on Bn-bn plane Bn1 = Bn2, bn1 = bn2two dineutrons have same size and expansion m = 0.59 m = 0.55 Competition between kinetic and potential energy Valley bn : dineutron size Pauli principle between the neutrons in the s-orbit (Bn~0) Repulsive area Bn: dineutron expansion There is a valley(bn~1.7 fm) and a repulsive area (Bn~0 fm). Compact dineutrons are favorable.

15. Coexistence of weak and strong binding in unstable nuclei and its dynamics Comparison between6,8,10He (The number of dineutrons is 1,2 and 3.) Bn1 = Bn2=Bn3, bn1 = bn2=bn3 m=0.59 6He (1DC) 8He (2DC) 10He (3DC) bn : dineutron size Bn: dineutron expansion Qualitatively similar, but, as neutrons are added, • compact dineutrons become unfavorable, • the repulsive area grows. The valley becomes clear. = Dineutrons become rigid.

16. Coexistence of weak and strong binding in unstable nuclei and its dynamics Comparison between8He and 7H (7H is described by replacing an a with t.) Bn1 = Bn2, bn1 = bn2, m=0.59 7H (t+2dineutrons) 8He (a+2dineutrons) bn : dineutron size In 7H, the attraction is so weak that the 2n correlation is close to that in free space. Bn: dineutron expansion The valley is unclear. = Dineutrons disperse.

17. Coexistence of weak and strong binding in unstable nuclei and its dynamics Summary of part I We analyzed the dineutron behavior in dineutron condensate states by using a toy model of aDC w.f.. We discussed about the mechanism of the dineutron condensation the systematics of the dineutron behavior in He isotopes the essence for the formation of a dineutroncondensation Qualitatively similar but dineutron size changes Energy valley and repulsive region strong attraction is essential

18. Coexistence of weak and strong binding in unstable nuclei and its dynamics Part II • Introduction of 6He+2n cluster w.f. + 8He DC w.f. • Energy spectra of the 0+1,2 states • Dineutron component in the 0+1,2 states

19. Coexistence of weak and strong binding in unstable nuclei and its dynamics Description of 8He 0p3/2-configurations are important for description of 8He (g.s.). In order to describe these configurations, we superpose two kinds of wave functions, that is 6He + 2n cluster wave functions (for (0p3/2)4) and 8He DC wave functions (for dineutron configurations). F.K.and Y. Kanada-En’yo. PTP 126 (2011)

20. Coexistence of weak and strong binding in unstable nuclei and its dynamics Description of 8He 2n(*) 6He core 6He + 2n cluster w.f. 8He DC w.f. (including one dineutron explicitly)

21. Coexistence of weak and strong binding in unstable nuclei and its dynamics 6He + 2n cluster w.f. 6He cluster is described with an a core plus two balance neutrons in 0p-orbits. The other two neutrons have two kinds of configurations, { R = (dc ,0,0) (dineutron-like) R = (dc,±0.5i,0) (dissociated) 2n dineutron-like dissociated 6He 6He 2n* a a dc dc

22. size of the dineutron spatial expantion of the dineutron Coexistence of weak and strong binding in unstable nuclei and its dynamics DC w.f. (one dineutron case) Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron. relative part c.o.m. part 2bn n r b (s-wave) rG n core (S-wave)

23. Coexistence of weak and strong binding in unstable nuclei and its dynamics Core of 8He DC w.f. As in the 6He + 2n cluster w.f., we describe a + 2n core, and distribute a dineutron around the core. 2n 2n* a same size a

24. Coexistence of weak and strong binding in unstable nuclei and its dynamics Description of 8He 2n 2n* a a a 6He + 2n cluster w.f. 8He DC w.f. II 8He DC w.f. I dc = 1 – 4 fm, dI = 1 – 4 fm, dII = 1 – 8 fm, b = 2 – 8 fm, bn; 5 values

25. Coexistence of weak and strong binding in unstable nuclei and its dynamics Hamiltonian : VolkovNo.2 m=0.59, b=h=0.0 orm=0.55, b=h=0.125 : LS part of G3RSvLS = 2000 MeV

26. Coexistence of weak and strong binding in unstable nuclei and its dynamics Energy spectra 0+2 0+2 a+n+n+n+n a+2n+2n a+n+n+n+n 0+1 0+1 0+1 (2n bound) (2n unbound) We consider the dineutroncomponent in the 0+1,2 states.

27. Coexistence of weak and strong binding in unstable nuclei and its dynamics Two dineutron condensate component In order to see the two dineutron condensate (2DC) component, we calculate the overlap with aDC w.f., Two dineutrons with the same size (bn) and expantion (b) move in the s-orbit. We show the overlap of the 0+1,2 states.

28. Coexistence of weak and strong binding in unstable nuclei and its dynamics Ground state (0+1) (fm) bn : dineutron size b : dineutron expansion (fm) Compact dineutrons are at the nuclear surface, but the tail amplitude is not so large. Four neutrons are strongly bound.

29. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron condensate state (0+2) (fm) bn : dineutron size b : dineutron expansion (fm) Compact dineutrons are expanded largely and freely, which is the feature of a condensate state. This state would be a dineutron condensate state.

30. Coexistence of weak and strong binding in unstable nuclei and its dynamics Summary

31. Coexistence of weak and strong binding in unstable nuclei and its dynamics Summary We investigated the dineutron behavior in dineutron condensate states of 8He and 6,10He, 7H, and the possibility of a dineutron condensate state in 8He. Compact dineutrons are formed and a long tail of dineutrons stretches when the system is bound strongly to some extent. In 8He, we found a candidate for a dineutron condensate state, which contains compact dineutron clusters expanded spatially.

32. Coexistence of weak and strong binding in unstable nuclei and its dynamics Outlook In future, we will invesitgatethe component of 6He + one dineutronin 8He(0+1,2). We will also investigate realistic 6,10He and 7H and make clear whether or not dineutron condensate states exist and the systematics of the dineutron behavior.

33. Coexistence of weak and strong binding in unstable nuclei and its dynamics

34. Coexistence of weak and strong binding in unstable nuclei and its dynamics Comparison between6,8,10He m=0.59 6He (1DC) 8He (2DC) 10He (3DC) bn : dineutron size m=0.55 Bn: dineutron expansion

35. Coexistence of weak and strong binding in unstable nuclei and its dynamics Energy surface on Bn-bn plane Bn1 = Bn2, bn1 = bn2two dineutrons have same size and expansion m = 0.59 m = 0.55 bn : dineutron size Bn: dineutron expansion

36. Coexistence of weak and strong binding in unstable nuclei and its dynamics Center of mass motion In the aDC w.f., the center of mass motion can be separated from the intrinsic motion, when (for all i) mass of the cluster i (a; 4, dineutron; 2) When ba = 1.4 fm (fixed), Bn1 = Bn2 and bn1 = bn2,

37. Coexistence of weak and strong binding in unstable nuclei and its dynamics 1-DC wave function ( Not a dineutron condensate state ) Assuming that the A-nucleon system is composed of (A-2)-nucleon core and one dineutron. B core (Brink) dineutron dineutron n Y core n ~ bn Here assuming that B = Bx = By = Bz.

38. size of the dineutron spatial expantion of the dineutron Coexistence of weak and strong binding in unstable nuclei and its dynamics Transformation to relative and c.o.m. w.f. coordinate transformation Y-integral relative part c.o.m. part 2bn n r (s-wave) b rG n core (S-wave)

39. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron condensate component We calculate the overlap with aDC w.f. to see the dineutron condensate components in 8He. Here we approximate aDC w.f. as follows. replace one of the R-integal by the d-summation

40. Coexistence of weak and strong binding in unstable nuclei and its dynamics Ground state (0+1) m = 0.59 m = 0.55 bn : dineutron size b : dineutron expansion

41. Coexistence of weak and strong binding in unstable nuclei and its dynamics Dineutron condensate state (0+2) m = 0.59 m = 0.55 bn : dineutron size b : dineutron expansion