1. Feb. 14 2006 defense Study of M1 Quenching in 28 Si by a (p,p') Measurement at zero-degrees 核物理研究センター 松原礼明 (0 度（ p,p’ ）測定による 28 Si のＭ１クエンチングに関する研究 )

2. Collaborators 阪大理 Univ. of Witwatersrand 東大 CNS 京大理 iThemba LABs Gent Univ. 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 J. Carter 川畑貴裕、笹本良子 坂口治隆、銭廣十三 F.D. Smit 、藤田浩 彦 L.A. Popescu 阪大 RCNP 九州大学 堂園昌伯 Feb. 14 2006 defense 藤田佳孝、足立竜也

3. Introduction Feb. 14 2006 defense Gammow-Teller (GT) ΔS=1, ΔT z =1 (n,p) type, στ + (p,n) type, στ - M1 (1 + ) transition ΔS=1, ΔT z =0 σ (T=0) isoscalar στ 0 (T=1) isovector σστ 0 στ + στ -

4. GT quenching problem Less strength is observed than predicted with sum rule. (~60%) 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 GT sum rule : ・ many-particle-many-hole configurations (np-nh) ・ Δ-hole excitations (Δ-h) Two mechanisms were proposed to explain the quenching.

5. How about M1 strengths ? np-nh Δ-h ΔT=0 (IS)ΔT=1 (IV) possible impossible Another aspect of the quenching can be found. Feb. 14 2006 defense T=0 T=1 N. Anantaraman et al.,PRL52(1984)1409 G.M. Crawley et al.,PRC39(1989)311 Quenching is observed in M1 strengths in 28 Si. Almost no quenching is observed in 24,26 Mg, 28 Si, 32 S. Improvements of the data quality are required.

6. Experimental condition Measurement 28 Si(p,p’) at 0 deg. Incident energy E p = 295 MeV Measured angles (lab) 0 ~18 deg High resolution - dispersion matching technique - under focus mode

7. Experimental Setup (0-deg.) Intensity : 3 ~ 8 nA Target : nat Si (2.22 mg/cm 2 ) Under focus mode As a beam spot monitor in the vertical direction Feb. 14 2006 defense Transport : Dispersive mode

8. Background subtraction After calibration Feb. 14 2006 defense

9. A typical spectrum of 28 Si(p,p’) at 0-deg. Background events were subtracted reasonably. Feb. 14 2006 defense

10. Present data G.M. Crawley et al, PRC39(1989)311, at Orsay 2000 1500 500 Feb. 14 2006 defense d 2 σ/dωdE [mb/sr/MeV] Excitation energy [MeV]

11. Flow chart of calculations Spectra B(σ) ; exp Unit cross section B(σ) ; predicted Experimental result Calculated result 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. ・ Distorted wave Born approximation (DWBA) ・ Shell model calculation by the code OXBASH. ( USD interaction within sd –shell ). J π assignment The ambiguity of shell-model calc. is canceled !! Cumulated Wave func. DWBA Shell-model calc.

12. Distinction between IS and IV From angular distribution, isospin value is identified. Feb. 14 2006 defense ×0.35 ×0.11 Θ cm [deg] ×2.50 ×0.77 Θ cm [deg] Ex = 9.50 MeV ; T=0Ex = 11.45 MeV ; T=1 dσ/dΩ [mb/sr] DWBA, T=1 ; IV DWBA, T=0 ; IS

13. Other states identified as 1 + dσ/dΩ [mb/sr] T=1 : IV T=0 : IS Θ CM [deg] Feb. 14 2006 defense 15.94 MeV 13.23 MeV 13.19 MeV 13.04 MeV10.60 MeV 10.73 MeV11.95 MeV 10.90 MeV 12.24 MeV 12.33 MeV 13.32 MeV 14.03 MeV 15.15 MeV 15.50 MeV15.76 MeV dσ/dΩ [mb/sr] Θ CM [deg] 1 +, T=0 states1 +, T=1 states 9.50 MeV 2 + : 9.48 MeV The flat distribution is in nature of the isoscalar excitation.

14. Formula of unit cross section σ σ : unit cross section for B(σ) B(σ) : spin-flip excitation strength F(q,ω) : kinematical factor q : momentum transfer ω : energy transfer = σ σ F(q,ω) B(σ) T=0 ; IS T=1 ; IV At F(q,ω) = 1 : Feb. 14 2006 defense σ σ = / B(σ) ← Obtained by calculations. [μ n 2 ] [mb/srμ n 2 ] DWBA S.M.

15. Strength fragmentation Feb. 14 2006 defense

16. Total sum of the strengths Feb. 14 2006 defense Quenching factor The uncertainty from shell-model cal. is canceled. The present result is consistent with the previous one. ∑ B(σ) [μ n 2 ] T=0 ; IST=1 ; IV (preliminary) ∑ B(σ) [μ n 2 ]

17. Summary We have realized a 28 Si(p,p’) measurement at 0 o 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

19. 0 + states Feb. 14 2006 defense 9.72 MeV10.80 MeV 11.14 MeV12.98 MeV 13.79 MeV Θ cm [deg] 0+0+ 1+1+ dσ/dΩ [mb/sr]

20. Kinematical factor F(q,ω) Calculated by using DWBA

21. Ambiguity of wave func. Calculated by using shell-model cal. T=0 ; IST=1 ; IV Θ[deg] dσ/dΩ / B(σ) [mb/sr/μ n 2 ]