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0度（p,p’）測定による Siの
Ｍ１クエンチングに関する研究
阪大RCNP 松原礼明
Mar. 30 2006 春学会＠松山
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
Wits Univ., Johannesburg
藤田佳孝、足立竜也
J. Carter
東大CNS
川畑貴裕、笹本良子
京大理
坂口治隆、銭廣十三
iThemba LABs
Gent Univ.
九大理
IFIC-CSIC, Valencia
F.D. Smit、藤田浩彦
L.A. Popescu
堂園昌伯
B. Rubio、 A. Perez
Mar. 30 2006 春学会＠松山
GT quenching problem
• Less strength is observed than predicted with GT 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 was 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
Mar. 30 2006 春学会＠松山
How about M1 strengths ?
Main operator of M1 (1+) :  , 
Common with GT
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
σ ：T=0 (IS)
στ：T=1 (IV)
Another aspect of the quenching can be found.
Mar. 30 2006 春学会＠松山
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
Mar. 30 2006 春学会＠松山
Experimental Setup (0-deg.)
Under focus mode
As a beam spot monitor
in the vertical direction
Transport : Dispersive mode
Intensity : 3 ~ 8 nA
Target : 28Si (2.22 mg/cm2)
Mar. 30 2006 春学会＠松山
Background subtraction
After calibration
Mar. 30 2006 春学会＠松山
A typical spectrum of 28Si(p,p’) at 0-deg.
Background events were subtracted reasonably.
Mar. 30 2006 春学会＠松山
G.M. Crawley et al, PRC39(1989)311, at Orsay
2000
1500
500
d2σ/dωdE [mb/sr/MeV]
Present data
Excitation energy [MeV]
Mar. 30 2006 春学会＠松山
Distinction between IS and IV
・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.
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
T=0 ; IS
×2.50
×0.11
Θcm [deg]
×0.77
Θcm [deg]
From angular distribution, isospin value is identified.
Mar. 30 2006 春学会＠松山
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
T=0 : IS
T=1 : IV
ΘCM [deg]
ΘCM [deg]
Mar. 30 2006 春学会＠松山
Strength fragmentation
Unit cross sections were obtained by the DWBA + OXBASH calculations.
・model space : sd-shell
・interaction : USD (Wildenthal)
Mar. 30 2006 春学会＠松山
Total sum of the strengths
T=1 ; IV
Quenching factor
∑ B(σ) [μn2]
∑ B(σ) [μn2]
T=0 ; IS
Quenching
B( )exp
B( ) shell mod el
The present result is consistent with the previous one.
Mar. 30 2006 春学会＠松山
Summary
• We have realized 28Si(p,p’) measurements at 0o with high resolution.
• The present study has found three 1+, T=0 states and two T=1 states newly.
• Unit cross sections are determined by calculations.
• The B(σ) strength is quenched up to Ex = 16 MeV.
• The Δ-h mixing seems to have little role in the M1 quenching.
Future
• Consistency of the unit cross section by other experiments.
• Decomposition of the contributions from the M1 quenching.
(core-pol., MEC, 2p-2h etc.)
• Study of the isoscalar angular distribution.
Mar. 30 2006 春学会＠松山
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]
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]
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  3.31 0.36[mb/ sr / n2 ]
T=0 ; IS
[μn2]
← Obtained by calculations.
[mb/srμn2]
[mb/srμn2]
At F(q,ω) = 1 :
ˆT 1  1.04  0.06[mb/ sr / n2 ]
T=1 ; IV
[μn2] Mar. 30 2006 春学会＠松山
Decomposition of the 2+ 9.48 MeV state
Counts / 3 keV
1+;T=0, 9.50 MeV
2+, 9.48 MeV
Excitation energy [MeV]
Mar. 30 2006 春学会＠松山
Optical potential of 28Si
Preliminary fit
28Si(p,p )
0
Ep=295 MeV
Input parameter : K. Lin, M.Sc. thesis., Simon Fraser U. 1986.
Analyzing power
Mar. 30 2006 春学会＠松山