6 Oct DCEN 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

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

6 Oct DCEN Introduction

6 Oct DCEN 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

6 Oct DCEN 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 Oct DCEN Framework

6 Oct DCEN 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

6 Oct DCEN 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

6 Oct DCEN Result

6 Oct DCEN α+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

6 Oct DCEN 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)

6 Oct DCEN (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

6 Oct DCEN 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.

6 Oct DCEN 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

6 Oct DCEN 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

6 Oct DCEN Summary

6 Oct DCEN 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

6 Oct DCEN 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.

6 Oct DCEN

6 Oct DCEN 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

6 Oct DCEN 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

6 Oct DCEN 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

6 Oct DCEN 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

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

6 Oct DCEN Energy surface  x ≠  z 

6 Oct DCEN Energy surface (d=1,2,3,4 fm)

6 Oct DCEN Dineutron kinetic energy and potential energy

6 Oct DCEN Core effect to dineutron kinetic energy