Electroproduction of p-shell hypernuclei

Transcription

1 Electroproduction of p-shell hypernuclei ASTRA workshop Petr Bydžovský Nuclear Physics Institute, Řež, Czech Republic in collaboration with D.J. Millener (BNL), F. Garibaldi and G.M. Urciuoli (Rome) Outline: Introduction DWIA formalism Results 9 Be, 1 C, and 16 O targets (Hall A and C in JLab) Uncertainty of the DWIA calculations elementary production Summary and outlook P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 1 /

2 Introduction Why do we study electroproduction of hypernuclei? γ-ray and reaction spectroscopy of Λ hypernuclei information on the YN interaction, its spin-dependent part in the reaction spectroscopy we can study higher states, Λ p DWIA calculations with a structure from standard Shell-model we learn on the effective (in medium) YN interaction reaction mechanism in DWIA electroproduction better energy resolution than in the π + and K induced productions; large momentum transfer to the hypernucleus: q > 5 MeV/c; strong spin-flip, the highest-spin states in multiplets dominate; the electro-magnetic part is well known and the one-photon exchange is a good approximation production by virtual photons simplification; if K + detected production on the proton other hypernuclei. suitable kinematics: a very small electron scattering angle very small Q = q and sufficiently big virtual photon flux; kaon is detected along the photon direction very-small-angle elementary production; higher energy is preferable as the momentum transfer is smaller. P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 /

3 Introduction kinematics, cross sections e + A Z e + K + + A 1 Λ (Z 1) laboratory frame: ^ y ^x p' e θ e ^z p e Scattering (Leptonic) Plane γ q Φ θ p p H K Reaction (Hadronic) Plane K K input: E e, E e, θ e, θ Ke, Φ K ɛ, Γ, q = p e p e, Q = q, s, t,... the unpolarized lab cross section d 5 [ σ dσt de e dω = Γ + ɛ dσ L + ɛ dσ TT cos Φ K + ɛ(1+ɛ) dσ ] TL cos Φ K e dω K dω K dω K dω K dω K P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 3 /

4 Introduction previous calculations for E94-17 in Hall A Sotona and Frullani, Prog. Theor. Phys. Suppl. 117 (1994) 151 MeV nb sr GeV 4 1 C(e, e K + ) 1 Λ B M. Iodice,... M. Sotona,... et al, Phys. Rev. Lett. 99, 551 (7) dσ dω e dω K de e de exc 16 O(e, e K + ) 16 Λ N F.Cusanno,... M. Sotona,... et al, Phys. Rev. Lett. 13 (9) 51 1 Excitation Energy (MeV) MeV 5 Cross Section (nb/sr^/gev/mev) dσ nb dω de de sr e dω K e exc GeV Binding Energy (MeV) Binding Energy (MeV) 9 Be(e, e K + ) 9 ΛLi G.M. Urciuoli,... M. Sotona,... et al, Phys. Rev. C 91 (15) 3438 P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 4 /

5 DWIA formalism many-particle matrix element Calculation of dσx dω K (Q, s, t) for A + γ v K + + H in DWIA particle momenta are quite high, q, p K 1 GeV/c many-particle matrix element in lab frame Ψ H Z χ γ χ K J j(p Λ, p K, p i p, q) Ψ A = (π) 3 δ( q p K p H ) T j i=1 χ K kaon distorted wave function eikonal approximation: pk 1 GeV/c; KN interaction is weak the first-order optical potential: proton-neutron averaged KN forward scattering amplitude and target-nucleus density (b HO ) χ γ photon wave function, no Coulomb distortion of e and e J j elementary-production hadronic current in two-component formalism Ψ A and Ψ H nucleus and hypernucleus non relativistic wave functions P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 5 /

6 DWIA formalism assumptions, approximations translational invariance of J j : q + p p i = p K + p Λ but the energy conservation is violated E γ + E p E K + E Λ, off-shell effects are neglected; factorization approximation: p p i p = in the lab frame J j ( q, p Λ ) expressed via six CGNL amplitudes important simplification; no Fermi motion; partial-wave decomposition: χ γ χ K = F LM Y LM F LM includes the kaon distorted wave function in eikonal approximation V opt depends on σtot KN, α = Re f KN ()/Im f KN (), and ρ(b HO ); f KN () is the proton-neutron averaged forward angle amplitude from a separable model (with partial waves l =,1,... 7; E kin GeV); elementary current in spherical form: Ji 1 = Fiλ S σs λ, i, λ = ±1,, Fiλ S are non-flip (S=) and spin-flip (S=1) CGNL-like amplitudes, harmonic oscilator basis: α = n l 1 j P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 6 /

7 DWIA formalism final formula for the amplitude The hypernucleus production amplitude T i = The main ingredients [JJ H ] C J HM H Jm 1 α α J A M A Jm Sλ LM C Jm LMSλ F S iλ R LM n l nl MLSJ l j lj (Ψ H [ b + α a α ] J ΨA ) the elementary production: CGNL-like amplitudes Fiλ S from an isobar model, e.g. Saclay-Lyon the radial integral: R LM n l nl = dr r Rn l F LM R nl includes the kaon distortion via F LM (σ KN tot, α, and b HO ); R nl are HO or Woods-Saxon radial wave functions of the proton and Λ nucleus structure information: reduced OBDME (Ψ H [ b + α a α] J ΨA ) Shell-model calculations by John Millener P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 7 /

8 Results the 9 Be(e, e K + ) 9 ΛLi spectrum dσ/(dω e dω K de e de b ) [nb/(sr GeV MeV)] 1,5 1,5 E e = 3.77, E e = 1.56 GeV, θ e = 6, θ Ke = 6, Φ K = 18 E γ =.1 GeV, Q =.64 GeV, p K = 1.96 GeV, θ lab Kγ = 1.8 kaon distortion: σtot KN = 17.9 mb, α =.88, b HO = fm structure: complete p-shell basis for the core, 1/ 3/ in the second doublet W.-S. w.f.: E p p3/ = 16.89, EΛ s1/ = 8.53, EΛ =.1 MeV p3/ experiment theory sum fit 9 new old DWIA DWIA Λ Li E x crs E x J π crs diff Binding Energy (MeV) radiative-corrected data Phys.Rev.C91(15)3438 fitted FWHM 73 kev was used also for theoretical peaks..59± ± sum=1.4-1% ± %.7.54± % P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 8 /

9 Results the 1 C(e, e K + ) 1 Λ B spectrum kinematics is the same as for the 9 Be target kaon distortion: σtot KN = mb, α =.31, b HO = 1.61 fm the full basis of p-shell states for the core coupled to a Λ or a Σ in an s or p orbit; W.-S. w.f.: E p p3/ = 15.96, Ep p1/ = 1.37, EΛ s1/ = 11.37, EΛ p =.4 MeV old new MeV nb sr GeV dσ de exc de e dω K dω e 4 1 Excitation Energy (MeV) Phys. Rev. Lett. 99, 551 (7) dσ/(dω e dω K de e de exc ) [nb/(sr GeV MeV)] Λ B fit theory Excitation Energy (MeV) preliminary radiative-corrected data FWHM for theoretical peaks is 8 kev P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 9 /

10 Preliminary new E94-17 data for 1 Λ B Theoretical predictions E x FWHM Cross section E x J π crs (MeV) (MeV) (nb/sr /GeV ) (MeV) sum diff. ± ± ±.3 ± %.6 ±.5.64 ± ±.11 ± % 5.94 ±.6.56 ±.1.53 ±.1 ± % 1.94 ± ± ±.6 ± % 1.66 ±.6.6 ± ±.1 ± % P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 1 /

11 Kinematics of the JLab Hall A and C experiments for the Carbon target E i E f θ e θ Ke Φ K E γ θ γe Q ɛ Γ p K GeV GeV deg deg deg GeV deg GeV GeV E94-17 (Hall A) E1-11 (Hall C) E5-115 (Hall C) * L. Tang et al, Phys.Rev.C 9 (14) 343; T.Gogami PhD Thesis, private communication Φ K and ɛ dependence: d 5 [ σ dσt de e dω = Γ + ɛ dσ L + ɛ dσ TT cos Φ K + ɛ(1+ɛ) dσ ] TL cos Φ K e dω K dω K dω K dω K dω K P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 11 /

12 Comparison with E1-11 data on 1 C(e, e K + ) 1 Λ B Experimental data Theoretical predictions Peak B Λ E x Cross section E x J π Cross section sum No. (MeV) (MeV) (nb/sr) (MeV) (nb/sr) diff ± ± ± ± % ± ± % ± ± 7.3-6% ± ± ± ± ± ± ± ± % % L. Tang et al, Phys. Rev. C 9 (14) 343, Table III. P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 1 /

13 Comparison with E5-115 data on 1 C(e, e K + ) 1 Λ B Experimental data Theoretical predictions Peak B Λ E x Cross section E x J π Cross section sum No. (MeV) (MeV) (nb/sr) (MeV) (nb/sr) diff ± ± ± ± % ± ± % ± ± % 5 1. ± ± ± ± ± ± ± ± % % L. Tang et al, Phys. Rev. C 9 (14) 343, Table III. P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 13 /

14 / C S / / B 1 Λ B S =1 E x dσ/dω figure by John Millener P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 14 /

15 Results the 16 O(e, e K + ) 16 Λ N spectrum from E94-17 E e = 3.66, E e = 1.45 GeV, θ e = 6, θ Ke = 6, Φ K = 18 E γ =.1 GeV, Q =.58 GeV, p K = GeV, θ lab Kγ =.1 kaon distortion: σtot KN = mb, α =.3, b HO = fm W.-S. w.f.: E p p3/ = 17.8, Ep p1/ = 11., EΛ s1/ = 13.5, EΛ p1/ =.3, EΛ =.9 MeV p3/ dσ/(dω e dω K de e de b ) [nb/(sr GeV MeV)] Λ N fit theory Binding Energy (MeV) Phys. Rev. Lett. 13 (9) 51 fit and theory with Voight functions experiment theory sum E x crs E x J π crs diff. 1.45± % ± % ± % ± % P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 15 /

16 Uncertainty in the DWIA calculations elementary production the largest systematical uncertainty kaon distortion a more precise kaon wave function nuclear structure model calculations of OBDME single-particle wave functions in the radial integral harmonic oscilator Woods-Saxon wave functions parameters of the W.-S. potential approximations in the calculation effective factorization full folding off-shell effects in J j (energy conservation is violated) P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 16 /

17 Uncertainty in the DWIA calculations from elementary production separated cross sections for p(e, e K + )Λ in lab frame: E lab γ =.1 GeV, Q =.6 GeV, ɛ =.7, θ lab Kγ =, Φ K = 18 ( µb sr ) SLA KMa H b BS1 b σ full σ T σ L σ TT σ TL a without longitudinal couplings for N b a simple extention to electroproduction using Gari Krümpelmann e.-m. form factors for N as in the SLA model σ full =... + ɛ(1+ɛ) σ TL cos Φ K dσ/dω (µb/sr) p(γ,k + )Λ at E γ=.1 GeV p(e,e K + )Λ data: Brown, E94-17,6,5,4,3,,1 Q =.18,.7 GeV CLAS LEPS SAPHIR Brown SLA WJC KM H RPR-1 BS1 E θ c.m. K (deg) isobar models: SLA: T.Mizutani et al, P.R.C58(1998)75; H: P.B. and M.Sotona, N.P.A754(5)43c; BS1: D.Skoupil and P.B., P.R.C93(16)54: RPR-1: P.B. and D.Skoupil, N.P.A914(13)14. P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 17 /

18 Uncertainty in the DWIA calculations from elementary production separated lab cross sections for 1 C(e, e K + ) 1 Λ B : Ee = 3.77, E e = 1.56 GeV, θ e = 6, θ Ke = 6, Φ K = 18 ; E γ =.1 GeV, Q =.64 GeV, θ lab Kγ = 1.8 E x J P model σ f st sl stt stl (MeV) (nb/sr). 1 SLA BS SLA BS SLA BS SLA BS d 5 σ de e dω e dω K = Γ σ f = Γ ( st + sl + stt + stl ) the TL term does not contribute in the Hall C experiments, stl cosφ K and Φ K = 9 P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 18 /

19 Summary new DWIA calculations of the cross sections for electroproduction of 9 ΛLi, 1 Λ B, and 16 Λ N in various kinematics are in a reasonable agreement with experimental data from JLab; the calculations mostly underpredicts (by 1 6 %) the cross sections for 9 ΛLi and 1 Λ B (could be attributed to elementary production), however, they overpredict by 14 3 % the cross sections for 16 Λ N; large uncertainty in the calculations comes from the elementary production. Outlook more detailed analysis with various models for elementary production and with various nuclear structure (e.g., with full basis of 1hω states). P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 19 /

20 Thank you for your attention! P. Bydžovský (NPI Řež) Electroproduction of p-shell hypernuclei ECT* Trento, Oct.3-7,17 /