Aye Aye Min, Khin Swe Myint, J. Esmaili & Yoshinori AKAISHI

1. Theoretical Investigation for Production of Double-L Hypernuclei from Stopped Hyperon on By Aye Aye Min, Khin Swe Myint, J. Esmaili & Yoshinori AKAISHI August 23, 2011 APFB2011

2. Abstract • Investigation of the formation ratio of to for various • absorptions from 2S, 2P and 3D orbitals of atom by • assuming a d-a cluster model for • We have also investigated differential cross section for single-L • hypernuclei, and . • Two kinds of d-a relative wave function namely 1s d-a relative wave • function with phenomenological One Range Gaussian (ORG) potential • and that with Orthogonality Condition Model (OCM ) were used in our • calculations.

3. Emulsion Experiment (K. Nakazawa , Nucl. Phys. A 835 (2010)) p t (T. Fukuda et. al., Phys. Rev. Lett. 87 (2001)) BNL DBLL : LLinteraction energy DBLL = BLL(ALLZ) - 2BL(A-1LZ) Weakly attractive LL Interaction ! • It is worthwhile to measure the masses of double-Lhypernucleifor several nuclear • species to determine L-Linteractionwithout ambiguities.

4. S = 0 sector S = -1 sector S = -2 sector XN ~ 28 MeV LL DN SN ~ 80 MeV LN LL-XN coupling effect in ~ 300 MeV (K.S. Myint, S. Shinmura and Y. Akaishi, Nucl. Phys. A 721 (2003) 21) NN Although coupling effect is not significant in non-strangeness sector, coupling effect plays an important role in strangeness sector.

5. Production of Double-L Hypernuclei • In order to produce and , the reaction is d d P P • Target ( ) P P n n t t a a d-a cluster structure X X

6. X L X D Double-L hypernucleus P L S Single-L hypernucleus and L-hyperon Absorption of X- in atom and Production of hypernuclei L L X Two single-L hypernuclei Elementary process for the reaction H-dibaryon and ordinary nucleus L L H 28.33MeV twoLhyperons and ordinary nucleus L L

7. Table 1. Possible reactions for the stoppedhyperon on

8. Formation from stopped on p p p d d d n n n L L X d t • internal wave function of • sub-systems • relative wave functions Triton(t), deuteron(d) L t L t P proton-triton (p-t) deuteron-alpha (d-a) t wave function for target Transition matrix , Transition matrix in terms of relevant momenta ,

9. Interaction for elementary process • Interaction for elementary process,is described by • separable potential. where L L p • By assumption the interaction is zero range ,

10. Decay width to and deutron We will discuss later! • Decay width ( ) is

11. Formation p p p n n n n n L L X P n a L a L a a 1. GBWF (one range phenomenonlogiacl Gaussian potential) 2. GBWF (OCM model)

12. Construction of relative d-a wave function by usingone range phenomenological Gaussian potential • Gaussian basis radial wave function for d-a cluster is bj= range parameter and cj= the expasion coefficient 2.0 fm • Gaussian one range potential -85.42 • weadjusted the potential strength( -85.42MeV) to give energy eigen value • of 1s state(-1.48 MeV ) andeigen function corresponding to this 1s bound state . • By applying Fourier transform,

13. Construction of relative d-a wave function with OCM • The Gaussian potential between a and x particle (E. Hiyama et.al., arXiv:nucl-th 24 (2002) 0204059.) Where, = relative angular momentum between a and x = the spin of x • For our system, case, x is deuteron and . The potential strengths and range parameters for a-d system

14. The Pauli principle between nucleons belonging to aand x (x = n, p, d, t ) • clusters is taken into account bythe Pauli projection operator or OCM • projection operator • The forbidden states for d-acluster are 0s and 0p states. Monte Carlo integration Method

15. Models of single L-hypernuclei

16. Results and Discussions d-a density distribution of In coordinate space Table 2. Formation ratio of to from stopped hyperon on B.E ( ) = 5.0 MeV K.S. Myint, S. Shinmura and Y. Akaishi, Eur. Phys. J. A 16 (2003) 21.

17. d-a density distribution of (in momentum space) to clarify this argument more profoundly! effect of low and high momenta component of d-a relative motion ??? qda (MeV/c) This wave function ( 0s′ ) is obtainedby reducing the strength of one range Gaussian potential (-19.152MeV)to give the ground state energy, E = -1.48 MeV.

18. Significance of d-a relative momentum contribution formation is enhanced and formation is dropped off significantly! It is important to understand the structure of a target to propose a feasible reaction to populate double-L hypernuclei from hyperon captured at rest.

19. For single-L hypernuclei case, and are at rest! 150 MeV/c 113.82 MeV/c 192.0 234.0

20. Concluding remarks Formation of is more dominant thanthat of for all absorption orbitals; 2S, 2P and 3D states from this reaction (1.1 for ORG and 2.0 for OCM for the major 3D absorption case). Low momentum component of d-a relative wave function favors the formation. Binding energy of can be measured without ambiguities. It may be deduced the significance of L-X coupling effect from this experiment. Thus, we have proposed a feasible reaction which can produce , , and with comparable branching ratios.

21. Thank you for your kind attention!

22. LL-XN coupling effect in X + p + t 28.33 MeV X0+ n + t 23.21 MeV Pauli Suppression effect 8.0 MeV X-+ a L + L + t 0.0 MeV X-+ p+ t Coupling effect enhancement

23. Binding Energy of d-a cluster by changing the strength of l value

24. E =-1.48 MeV -85.42 -85.42 -19.152 -85.42

25. formation formation X X d d d Proton speration ~ 19.81 MeV energy n P P P P n n B.E(d ) =2.224 MeV t t t a a a X n X L L L L

26. Pd=191.80 MeV/c KEd=9 MeV KE(LL5H)= 3.04 MeV Q=12.04 MeV Pn= 232.47 MeV KEn=28 MeV KE(LL6He)= 3.88 MeV Q=31.88 MeV

27. The required data are;

28. formation formation X X d d d Proton speration ~ 19.81 MeV energy n P P P P n n B.E(d ) =2.224 MeV t t t a a a X n X L L L L

29. Abundant of Lithium 7% X X 93% d t P P t t -2.5 MeV -1.48 MeV 6Li 7Li

30. New data from Nagazawa Sensei (BE(LLHe6)) Old data from Nagara_paper (BE(LLHe6))

34. Table 3. Probabilities of momentum components of d-a relative wave unction of

35. Introduction Lhyperon • can stay in the nucleus deeply without obeying Pauli exclusion principle • probes a deep interior of the nucleus and investigates the nuclear • structure L hypernucleus • gives a new dimension to the traditional world of nuclei • provides the rich information on the baryon dynamic involving the • strange particles

36. Possible production of hypernuclei • Strangeness-exchange process etc. • Associated production of strange-hadrons process etc. • Combination of strangeness exchange and associated production • of strangeness process etc.

37. High energy heavy-ion collisions Spectator -projectile fragment L coalescenceof hyperons to projectile fragnent participant Spectator -target fragment theoretical model (Wakai, Bando, Sano) From Professor Dr T. Fukuda’s Presentation

38. High energy heavy-ion collisions • Coalescence of strange particles with a nuclear fragment produced • in projectile nuclear fragmentation • Coalescence of strange particles and nucleons bothproduced • in the participant part • Secondary process by p and K mesons produced in the primary • nuclear collisions • Conversion of X- hypernucleus into single and double-L hypernucleus F L p n S ( at 2.1 GeV/nucleon ) p etc. K X F ( at 3.7 GeV/nucleon ) ( at 14.5 GeV/nucleon ) ( at 2.1 GeV/nucleon )

39. Inorder to produce a hypernucleus, • The hyperon emerging from the reaction must remain in the nucleus. Momentum transfer to the hyperon Formation probability of the hypernucleus • Sticking probability, n ,= principal quantum number and orbital angular momentum for nucleon and hyperon state where, q = momentum transfer to the hyperon = bessel function with the orbital angular momentum transfer ( initial and final states are Harmonic Oscillator wave functions )

40. Direct Process Via X atom K+ Prowse (?), Danysz et al. KEK- E 176, E373 BNL- E906 K+ K- K+ P P KEK-E 176 -E 224 KEK-E 176 -E 224 K- K- K+ K+ K- X- H K- L L BNL-E 885 BNL-E 813 -E 836 -E 885 X- X-or H (?) X KEK-E 176 KEK- E 176 E373 L K+ A L L X- atom p0 K- A KEK-E 224 L KEK- E 176 E 224 BNL- E 885 L L L L L L L L or H L L

42. Possible Candidates of double-L hypernuclei in emulsion experiments H. Takahashi, “PhD Thesis”, Kyoto University (2003)

43. Double hyper event from E-176 experiment KEK-PS E176 LLinteraction energy attractive or repulsive ??? or

44. Double hyper event from E-373 experiment p t DBLL : LLinteraction energy DBLL = BLL(ALLZ)-2BL(A-1LZ) Weakly attractive LL Interaction !

46. Nakazawa Sensei, 2003 Presentation (at J-Lab)

47. Nakazawa Sensei, 2003 Presentation (at J-Lab)

48. KEK-PS E176 or (Possibility of excited state was not considered!)

50. KEK-PS E373