Inclusive K + spectra for neutron rich 6 L H production by 6 Li( p - - PowerPoint PPT Presentation

International Symposium on Neutron Star Matter (NSMAT2016), Nov. 21-24, 2016, Tohoku University, Sendai, Japan Inclusive K + spectra for neutron rich 6 L H production by 6 Li( p - ,K + ) reactions T. Harada, Y. Hirabayashi † Osaka Electro-Communication University J-PARC Branch, KEK Theory Center, IPNS, KEK † Information Initiative Center, Hokkaido University 1

Outline 1. Introduction - S - doorways and S - p- L n coupling 2 ． Coupled-channel calculations in the DWIA - 6 Li (p - , K + ) reaction 3. Results and discussion S - - 5 He ・ Study of the S -nucleus potentials 6 ・ Production of the neutron-rich L hypernucleus L H 4. Summary 2

Introduction • 6 L H is one of the most interesting candidates to investigate neutron-rich hypernuclei; B [ 6 L H(0 + g.s. )] = 5.8 MeV caused by the coherent LS coupling. Y. Akaishi, Khin Swe Myint, AIP Conf. Proc. 1011 (2008) 277. • FINUDA collaboration reported a binding energy stop , p + ) L H)= 4.5 ± 1.2 MeV in 6 Li( K − of B ( 6 reactions. M. Agnello, et al., PRL. 108 (2012) 042501. 3

Production of neutron-rich 6 Λ H hypernucleus  Double charge-exchange (DCX) reaction 6 Λ H  Coherent ΛN - ΣN mixing in neutron-rich environment 6 Λ H Status - +  + p + 6 6 K Li H (252MeV/c) L Stop  + p - 6 6 H He (130MeV/c) L Agnello et al., Dalitz, Levi Setti, PRL108(2012)042501 Nuovo Cimento 30(1963)498 FINUDA Exp. L glue effects 0 + 5802.87 MeV SM 4.4 MeV 0 + L N- S N mixing t+n+n+ L 4-body calc. 1.4 MeV 0 + E. Hiyama et al., NPA908(2013)29 SM+ L - S coupling BHF + Coherent L - S coupling Gal, Millener, PLB725(2013)445 Khin Swe Myint, Akaishi, PTP Suppl.146(2002)599 4

Λ H hypernucleus by 6 Li( p - , K + ) reactions Search for the 6 1.2GeV/c@J-PARC E10 No peak of the bound state is observed. E10 H.Sugimura et al., (J-PARC E10 Collaboration) PLB 724 (2014)39. R. Honda, Ph.D. thesis, (2014). R. Honda, talk at Nov. 21 5

Introduction • 6 L H is one of the most interesting candidates to investigate neutron-rich hypernuclei; B [ 6 L H(0 + g.s. )] = 5.8 MeV caused by the coherent LS coupling. Y. Akaishi, Khin Swe Myint, AIP Conf. Proc. 1011 (2008) 277. • FINUDA collaboration reported a binding energy stop , p + ) L H)= 4.5 ± 1.2 MeV in 6 Li( K − of B ( 6 reactions. M. Agnello, et al., PRL. 108 (2012) 042501. • No peak is observed around the 4 L H + 2 n threshold in the 6 Li( p - , K + ) 6 L H reaction at p p- = 1.2 GeV/c by J-PARC E10 collaboration. H. Sugimura, Phys. Lett. B729 (2014) 39. R. Honda, Ph.D. thesis, Tohoku University (2014). 6

( p － , K + ) － Double Charge Exchange (DCX) Reaction Two-step mechanism : p - K + p -  L 0 p K  + 0 - p  L K p K n 0 p L K L p K 0 p p n n p -  p p 0 p n  + 0 K p K n + p  L 0 p K K + One-step mechanism : Hyperon-mixing p - p - + -  S p K p -  + S - p K L Doorway - L S  L p n p S - p p n n p via S - doorways caused by L N- S N coupling 7

Our Purpose • We theoretically demonstrate the inclusive spectra of the 6 Li( p - , K + ) reaction within a distorted-wave impulse approximation, using a coupled ( 5 H- L ) +( 5 He- S - ) model with a spreading potential by the one-step mechanism via S − doorways. (1)To extract valuable information on the Σ -nucleus potential for Σ − - 5 He from the data of the J-PARC E10 experiments. S - regions (2)To study the ΣΛ coupling effects related to the Σ - mixing and the strengths of the Λ - 5 H potential in 6 L H(1 + exc. ). [ not 6 L regions L H(0 + g.s. )] 8

Coupled-channel calculations in the DWIA with the optimal Fermi-averaged t -matrix 6 Li (p - , K + ) reactions 9

Model for final states of the hypernucleus Single-particle shell model wf. p n 5 He 5 H L S - mixing probability S - spreading potential for excited states Hyperon-nucleus potentials zero-range interaction: Woods-Saxon form （ V S , W S ) determined V L = -19 MeV as fitting parameters is assumed Coupling L - S folding potential Shell-model w.f. with (s 3 p 2 ) configuration zero-range interaction: =  - 0 v v ( r r ') LL  LL  - N - N volume integral: 10

Coupled-channels DWIA calculation for one-step mechanism S − doorways Coupled- channel Green’s function K + p - L L p S - p p n n p DWIA+CCGFM Inclusive cross sections T. Harada, NPA672(2000)181 Fermi-averaged amplitudes Decomposition of the inclusive spectrum into components ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ - - - - =   +   + † † † ( ) (0) ( ) ( ) (0) ( ) Im G {Im G } {Im G } G W { } G S L S Y T , L escape S - escape Spreading (nuclear-core breakup ） 11

Angular dependence of the optimal Fermi-av. cross section “ p - p  K + S - reactions” in the nucleus 2 f p - + -  S p K Λ  There exists a strong energy dependence in the amplitudes. 12

Results and discussion

Part I Study of the S -nucleus potentials S - - 5 He p s S - p n 14

Inclusive spectrum in 6 Li( p - , K + ) reaction at 1.2GeV/c R. Honda, Ph.D. thesis, (2014)., update (2016). V S = +30 MeV, W S = - 15 MeV 𝑆 = 1.1𝐵 1/3 𝑏 = 0.6 fm, 2 o -14 o ave. L region S region p -hole 6 Li s -hole 15

Dependence of the calculated spectra for the 6 Li( p - ,K + ) reaction p p- =1.2 GeV/c WS potential W S = - 15 MeV is fixed The shape and magnitude of the spectrum are sensitive to the strengths of ( V S , W S ). V S dependence ( V S , W S ) = ( +30, - 15) MeV c 2 / N = 0.69 with f s ( N =65) The c 2 / N -value distribution in V Σ , W Σ V S = +30 MeV is fixed W S dependence The detector resolution of 2.6 MeV FWHM 16

Part II Production of the neutron-rich L hypernucleus 6 L H p s L p n (S) 17

L H production in the 6 Li( p - ,K + ) reaction Schematic illustration of 6 One-step mechanism p - K + p n p- p  K + S - p 1/2 6 Li(1 + g.s. ) p 3/2 s 1/2 reactions Non-spinflip Δ𝑇 = 0 ….. dominant 5 He(g.s.) 5 He* S - S - p n p n S - doorways p 1/2 p 1/2 p 3/2 p 3/2 s 1/2 s 1/2 S N  L N couplings L p n p 1/2 6 L H (1 + 6 L H (0 + exc. ) g.s. ) p 3/2 s 1/2 5 H(g.s.) forbidden 18

Calculated ΣΛ coupling folding potentials in 6 L H(1 + ) using shell-mode (s 3 p) ⨂𝑀 configurations for the core nucleus. 1 0 = (-400 MeV ・ fm 3 , 320 MeV ・ fm 3 ) ( v , v ) S L S L N , N N , N 5 He(g.s.) 5 He* S - S - p p n n p 1/2 p 1/2 p 3/2 p 3/2 s 1/2 s 1/2 L p n p 1/2 p 3/2 s 1/2 5 H(g.s.) ・ Shell-model with spsd model space ・ Central effective YN interaction (D2’g)  The coupling strengths of 𝑞 𝛵 ↔ 𝑡 𝛭 are so large, as well as 𝑡 𝛵 ↔ 𝑡 𝛭 . 19

Cross section and S - mixing prob in 6 Li( p - , K + ) reaction 6 L H(1 + ) good Case agreement D C B A Case D C B A S - mixing probabilities: Cross sections: = =   = = [ P ( s ) 0.11%, P ( p ) 0.47%] d d 0.37 nb/sr P (tot) 0.58% S- S S- S S- 20

Production cross section of 6 Li( p - ,K + ) reactions 6 L H(1 + ) B L = 4.42 MeV B L = 3.01 MeV P S = 2.91 % P S = 1.49 % B A B L = 2.12 MeV B L = 1.64 MeV P S = 0.59 % P S = 0.14 % C D 21

Dependence of the spectrum on V L in the L - 5 H potential  V L = -19, -24, -28 MeV because the structure of 5 H is 6 L H(1 + ) still uncertain experimentally.  The shallow potential V L = -19 MeV is favored to be compared with the data.  The shape of the spectrum is so sensitive to the structure of the 5 H resonance . 22

Summary 6  The calculated spectrum of the L H by the one-step mechanism via S − doorways can explain the data of the DCX 6 Li( p − , K + ) reaction at 1.20GeV/c . S - p  ( V Σ , W Σ )= (+30 MeV, −15 MeV) K +  S - mixing probability L N- S N 6 p coupling P S ~ 0.6 % for L H(1 + exc. ). = = L n [ P ( s ) 0.11%, P ( p ) 0.47%] S- S S- S  Shallow L potential for 5 H res. ( V L ≃ -19 MeV) is favored. p -  Our phenomenological calculation provides the ability to extract the production mechanism from the data.

Thank you very much for your attention. 24