Study of M1 Quenching in 28Si by a (p,p') Measurement at zero-degrees (0度（p,p’）測定による28SiのＭ１クエンチングに関する研究) 核物理研究センター 松原礼明 Feb. 14 2006 defense Collaborators 阪大RCNP 民井淳、畑中吉治、酒見泰寛、伊藤正俊、新原佳弘、清水陽平、 藤田訓裕、中西康介、爲重雄司、橋本尚信、與曽井優 阪大理 Univ. of Witwatersrand 東大CNS 京大理 藤田佳孝、足立竜也 J. Carter 川畑貴裕、笹本良子 坂口治隆、銭廣十三 iThemba LABs F.D. Smit、藤田浩彦 Gent Univ. L.A. Popescu 九州大学 堂園昌伯 Feb. 14 2006 defense Introduction Gammow-Teller (GT) ΔS=1, ΔTz=1 στ+ στ- (n,p) type, στ+ (p,n) type, στ- σ στ0 M1 (1+) transition ΔS=1, ΔTz=0 σ (T=0) isoscalar στ0 (T=1) isovector Feb. 14 2006 defense GT quenching problem • Less strength is observed than predicted with sum rule. (~60%) GT sum rule : S S 3( N Z ) Two mechanisms were proposed to explain the quenching. ・many-particle-many-hole configurations (np-nh) ・Δ-hole excitations (Δ-h) 60 → 90% of the strength is observed up to Ex = 50 MeV. T. Wakasa et al., PRC55(1997)2909 (p,n) reaction K. Yako et al., PLB615(2005)193 (n,p) reaction Feb. 14 2006 defense How about M1 strengths ? Quenching is observed in M1 strengths in 28Si. N. Anantaraman et al.,PRL52(1984)1409 Almost no quenching is observed in 24,26Mg, 28Si, 32S. G.M. Crawley et al.,PRC39(1989)311 Improvements of the data quality are required. ΔT=0 (IS) ΔT=1 (IV) np-nh possible possible Δ-h impossible possible T=1 T=0 Another aspect of the quenching can be found. Feb. 14 2006 defense Experimental condition • • • • 28Si(p,p’) at 0 deg. Measurement Incident energy Ep = 295 MeV Measured angles (lab) 0 ~18 deg High resolution - dispersion matching technique - under focus mode Experimental Setup (0-deg.) Under focus mode As a beam spot monitor in the vertical direction Transport : Dispersive mode Intensity : 3 ~ 8 nA Target : natSi (2.22 mg/cm2) Feb. 14 2006 defense Background subtraction After calibration Feb. 14 2006 defense A typical spectrum of 28Si(p,p’) at 0-deg. Background events were subtracted reasonably. Feb. 14 2006 defense G.M. Crawley et al, PRC39(1989)311, at Orsay 2000 1500 500 d2σ/dωdE [mb/sr/MeV] Present data Excitation energy [MeV] Feb. 14 2006 defense Flow chart of calculations ・Shell model calculation by the code OXBASH. (USD interaction within sd –shell) . ・Distorted wave Born approximation (DWBA) Trans. density : USD (from shell model calculation) NN interaction. : Franey and Love, PRC31(1985)488. (325 MeV data) Optical potential : K. Lin, M.Sc. thesis., Simon Fraser U. 1986. Experimental result Calculated result Spectra Jπ assignment d ( ) d DWBA d d q 0 Wave func. Unit cross section Shell-model calc. B(σ) ; exp Cumulated Quenching B( )exp B( ) shell mod el B(σ) ; predicted The ambiguity of shell-model calc. is canceled !! Distinction between IS and IV DWBA, T=0 ; IS DWBA, T=1 ; IV Ex = 11.45 MeV ; T=1 ×0.35 dσ/dΩ [mb/sr] dσ/dΩ [mb/sr] Ex = 9.50 MeV ; T=0 ×2.50 ×0.11 Θcm [deg] ×0.77 Θcm [deg] From angular distribution, isospin value is identified. Feb. 14 2006 defense Other states identified as 1+ 1+, T=0 states 1+, T=1 states 13.04 MeV 10.60 MeV 12.24 MeV 15.15 MeV 9.50 MeV 10.73 MeV dσ/dΩ [mb/sr] dσ/dΩ [mb/sr] 13.19 MeV 10.90 MeV 13.23 MeV 15.94 MeV 12.33 MeV 13.32 MeV 15.50 MeV 15.76 MeV 2+ : 9.48 MeV 11.95 MeV 14.03 MeV The flat distribution is in nature of the isoscalar excitation. T=0 : IS T=1 : IV ΘCM [deg] ΘCM [deg] Feb. 14 2006 defense Formula of unit cross section d (q, ) = σσ F(q,ω) B(σ) d q : momentum transfer ω : energy transfer σσ : unit cross section for B(σ) F(q,ω) : kinematical factor B(σ) : spin-flip excitation strength σσ = d (q, /) B(σ) d S.M. DWBA ˆT 0 3.23 0.26[mb/ sr / n2 ] T=0 ; IS [μn2] ← Obtained by calculations. [mb/srμn2] [mb/srμn2] At F(q,ω) = 1 : ˆT 1 1.07 0.06[mb/ sr / n2 ] T=1 ; IV [μn2] Feb. 14 2006 defense Strength fragmentation Feb. 14 2006 defense Total sum of the strengths T=1 ; IV Quenching factor ∑ B(σ) [μn2] ∑ B(σ) [μn2] T=0 ; IS (preliminary) Quenching The present result is consistent with the previous one. B( )exp B( ) shell mod el The uncertainty from shell-model cal. is canceled. Feb. 14 2006 defense Summary • We have realized a 28Si(p,p’) measurement at 0o with high resolution . • The present study has found three new 1+, T=0 states and the flat angular distribution of the isoscalar excitation. • Unit cross section is determined by calculations. • The B(σ) strength is quenched. • The Δ-h mixing seems to have little role in the M1 quenching. Future • Comparison with (e,e’) and (γ,γ’) experiments. • Systematic study in other nuclei. Feb. 14 2006 defense 0+ states dσ/dΩ [mb/sr] 9.72 MeV 0+ 1+ 10.80 MeV 11.14 MeV 12.98 MeV 13.79 MeV Θcm [deg] Feb. 14 2006 defense Kinematical factor F(q,ω) Calculated by using DWBA Ambiguity of wave func. Calculated by using shell-model cal. T=1 ; IV dσ/dΩ / B(σ) [mb/sr/μn2] dσ/dΩ / B(σ) [mb/sr/μn2] T=0 ; IS Θ[deg] Θ[deg]
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