1. Aye Aye Min, Khin Swe Myint, J. Esmaili & Yoshinori AKAISHI August 23, 2011 By Theoretical Investigation for Production of Double-  Hypernuclei from Stopped Hyperon on 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-  cluster model for Two kinds of d-  relative wave function namely 1s d-  relative wave function with phenomenological One Range Gaussian (ORG) potential and that with Orthogonality Condition Model (OCM ) were used in our calculations. We have also investigated differential cross section for single-   hypernuclei, and.

3. (K. Nakazawa, Nucl. Phys. A 835 (2010)) It is worthwhile to measure the masses of double-  hypernuclei for several nuclear species to determine  -  interaction without ambiguities. t p Emulsion Experiment  B  :  interaction energy  B  = B  ( A  Z) - 2B  ( A-1  Z) Weakly attractive  Interaction ! (T. Fukuda et. al., Phys. Rev. Lett. 87 (2001)) BNL

4. S = 0 sector S = -1 sector S = -2 sector NN NN NN NN  NN ~ 300 MeV ~ 80 MeV ~ 28 MeV Although coupling effect is not significant in non-strangeness sector, coupling effect plays an important role in strangeness sector. (K.S. Myint, S. Shinmura and Y. Akaishi, Nucl. Phys. A 721 (2003) 21)  N coupling effect in

5. d-  cluster structure Production of Double-  Hypernuclei In order to produce and, the reaction is Target ( ) P t d P n  P t d  P n  

6. two  hyperons and ordinary nucleus       H-dibaryon and ordinary nucleus S P D       Elementary process for the reaction 28.33MeV Single-  hypernucleus and  -hyperon    Two single-  hypernuclei         Double-  hypernucleus Absorption of  - in atom and Production of hypernuclei

7. No.ReactionsQ-value (MeV) 1 231.88 327.75 49.08 527.93 66.86 76.44 87.17 90.92 101.05 119.21 1224.63 Table 1. Possible reactions for the stopped hyperon on

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

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

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

11.  P n     n Formation p n n n p  p 1. GBWF (one range phenomenonlogiacl Gaussian potential) 2. GBWF (OCM model)    n

12. Construction of relative d-  wave function by using one range phenomenological Gaussian potential Gaussian basis radial wave function for d-  cluster is Gaussian one range potential b j = range parameter and c j = the expasion coefficient we adjusted the potential strength( -85.42MeV) to give energy eigen value of 1s state(-1.48 MeV ) and eigen function corresponding to this 1s bound state. By applying Fourier transform, 2.0 fm -85.42

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

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

15. Models of single  -hypernuclei

16. d-  density distribution of In coordinate space Results and Discussions B.E ( ) = 5.0 MeV Table 2. Formation ratio of to from stopped hyperon on d-  wave function types Atomic absorption (arbitary unit) GBWF (1s) (one range pot.) 2S4.461.183.78 2P0.140.131.08 3D85.6377.131.11 OCM 2S8.181.296.34 2P0.240.122.00 3D153.2976.402.01 K.S. Myint, S. Shinmura and Y. Akaishi, Eur. Phys. J. A 16 (2003) 21.

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

18. Significance of d-  relative momentum contribution Wave function types atomic absorption GBWF( 1s )3D85.6377.13 GBWF( )3D239.366.37 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-  hypernuclei from hyperon captured at rest.

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

20. It may be deduced the significance of  -  coupling effect from this experiment. Formation of is more dominant than that 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). Concluding remarks Binding energy of can be measured without ambiguities. Thus, we have proposed a feasible reaction which can produce,, and with comparable branching ratios. Low momentum component of d-  relative wave function favors the formation.

21. Thank you for your kind attention!

22. 0.0 MeV 23.21 MeV 28.33 MeV  +  + t 8.0 MeV    +     + n  t  + p + t    + p + t Pauli Suppression effect  N coupling effect in Coupling effect enhancement

23. Strength ( ) BE of d-  cluster (MeV) remark 0-33.3 -1.48 Unphysical forbidden state 1-32.32 -1.45 Unphysical forbidden state 10 1 -23.35 -1.45 Unphysical forbidden state 10 2 -1.50 -1.48 Unphysical forbidden state 10 3 -1.48 10 4 -1.48Allowed state 10 5 -1.48Allowed state 10 6 -1.48Allowed state Binding Energy of d-  cluster by changing the strength of value

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

25.  P t d  P n  P t d  P n   Proton speration ~ 19.81 MeV energy B.E(d ) =2.224 MeV n formation t d   n     (  6 He) 2S absorption  (  6 He) 2P absorption  (  6 He) 3D absorption BE(2.224 MeV)1.290.1276.4 BE(3.5MeV)1.320.1378.1

26. P d =191.80 MeV/c KE d =9 MeV KE(   H)= 3.04 MeV Q=12.04 MeV P n = 232.47 MeV KE n =28 MeV KE(   He)= 3.88 MeV Q=31.88 MeV

27. The required data are;

28.  P t d  P n  P t d  P n   Proton speration ~ 19.81 MeV energy B.E(d ) =2.224 MeV n formation t d   n     (  6 He) 2S absorption  (  6 He) 2P absorption  (  6 He) 3D absorption BE(2.224 MeV)1.290.1276.4 BE(3.5MeV)1.320.1378.1

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

30. d-  wave function types Atomic absorption (arbitary unit) GBWF (1s) (one range pot.) 2S4.461.213.69 2P0.140.131.08 3D85.6379.191.08 OCM 2S8.181.326.20 2P0.240.131.85 3D153.2978.271.96 (arbitary unit) 4.461.183.78 0.140.131.08 85.6377.131.11 8.181.296.34 0.240.122.00 153.2976.402.01 Old data from Nagara_paper (BE(LLHe6)) New data from Nagazawa Sensei (BE(LLHe6))

34. Wave function types Probabilities of low momentum component Probabilities of high momentum component GBWF(1s) 0.740.26 OCM 0.710.29 Table 3. Probabilities of momentum components of d-  relative wave unction of

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

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

37. participant Spectator -projectile fragment Spectator -target fragment coalescence of hyperons to projectile fragnent  theoretical model (Wakai, Bando, Sano) High energy heavy-ion collisions 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 both produced in the participant part Secondary process by  and K mesons produced in the primary nuclear collisions p n     K F F Conversion of   hypernucleus into single and double-  hypernucleus ( at 2.1 GeV/nucleon ) ( at 3.7 GeV/nucleon ) ( at 2.1 GeV/nucleon ) ( at 14.5 GeV/nucleon ) etc.

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

40. Direct Process Via  atom KEK-E 176 P H K-K- K+K+    K-K- 00 K+K+    K+K+ K-K- -- K-K- K+K+   - or H (?) K-K- K+K+   KEK-E 176 -E 224 BNL-E 813 -E 836 -E 885 KEK-E 176 -E 224 BNL-E 885 KEK-E 224  - atom  K+K+ K-K- -- A A     or H Prowse (?), Danysz et al. KEK- E 176, E373 BNL- E906 KEK- E 176 E373 KEK- E 176 E 224 BNL- E 885

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

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

44. Double hyper event from E-373 experiment t p  B  :  interaction energy  B  = B  ( A  Z) - 2B  ( A-1  Z) Weakly attractive  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

51. Construction of relative d-  wave function by using one range phenomenological Gaussian potential Gaussian basis radial wave function for d-  cluster is Gaussian one range potential b j = range parameter and c j = the expasion coefficient Hamiltonian operator is we adjusted the potential strength( -85.42MeV) to give energy eigen value of 1s state(-1.48 MeV ) and eigen function corresponding to this 1s bound. By applying Fourier transform, 2.0 fm

52. approximate value of an integral Pick n randomly distributed points x 1, x 2, x 3,…, x n in the interval [ a,b ]. Average value of the function Approximate value of an integral Estimation for the error Monte Carlo Integration Method

53. Binding energy of Atomic absorption 3.59 MeV 2S 1.98 2P 0.62 3D 0.57 5.0 MeV 2S 3.78 2P 1.08 3D 1.12 7.25 MeV 2S 6.37 2P 1.69 3D 2.01 Binding energy of Atomic absorption 3.59 MeV 2S 3.99 2P 1.25 3D 1.19 5.0 MeV 2S 6.34 2P 2.00 3D 2.01 7.25 MeV 2S 9.29 2P 2.83 3D 3.17 GBWF (1s) OCM (1s) Binding energy effect of Ms. Hla Hla win (Ph D thesis, private communication)Binding energy of  6 He ( NAGARA event data ) K.S. Myint et.al., Eur. Phys. J. A 16 (2003) 21

54. Wave function types Probabilities of low momentum component Probabilities of high momentum component GBWF(1s) 0.740.26 OCM(1s) 0.710.29 GBWF(0s’) 0.900.10 Table 2. Probabilities of momentum components of d-  relative wave function of

57. 3Li6 no: of proton 3 no: of neutron 3 P  0s(2-1/2),0p(1-3/2) n  0s(2-1/2),0p(1-3/2) J=J(p)+J(n) =3/2+3/2 =3,2,1,0 ( 2 is impossible)  =(-1)**(l_p+l_n) =(-1)**(1+1) =+ J_  =3+,1+,0+ Iso_spin Transition matrix,

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

62. Our University will be held the International Conference on February, 2011.