Post on 30-Dec-2015
Reaction cross sections of unstable nuclei
Contents• What is reaction cross section (R)?
• R Effective matter density distributions of unstable nuclei
• How to measure R.
RIBLL in IMP, RIPS in RIKEN• Recent results in 14-18C isotopes• Summary
A. Ozawa (University of Tsukuba)
Density distributions (Density distributions ( ) of stable ) of stable nucleinuclei
• R A1/3
• Neutron radii ≈ proton radii even for 48Ca, 208Pb
• Diffuseness is constant. a ~ 0.6 fm
How are unstable nuclei?
No thick neutron skin!r
ProtonNeutron
Text book says……
Same radii for mirror pairs
How to deduce of unstable nuclei• Proton elastic scattering at ~400 MeVTested for stable nuclei R&D for unstable nuclei
• Electron scatteringCharge distribution can be deduced. R&D for unstable nuclei (SCRIT in RIBF etc. ) • Reaction cross section (interaction cross section) with different energiesAlready applied to unstable nuclei
(11Be: M. Fukuda et al., Phys. Lett. B 268 (1991) 339. )
(H. Sakaguchi et al., PRC57(98)1749)
Interaction cross-section (Interaction cross-section (II) and rea) and reaction cross section (ction cross section (RR))
• Definition of interaction cross-section (I);
Cross section for the change of Z and/or N in incident nucleus
• Reaction cross-section (R)
R = I + inela, inela: inelastic cross-section
If inela is small enough, R ≈ I. At relativistic energy (~1 A GeV)
Glauber model Optical Limit approximatioGlauber model Optical Limit approximationn
= 2π 1 - T(r)0
∞r drR
T(r) = exp - q(r,z)-∞
∞ dz
q(z) = dη-∞
∞ 2π T(r,z,b,η) P(r,z,b,η) b db
0
∞
T(r):Transmission function
:effective NN cross-sections
of target of projectile
r2 = r2
0
∞
∫ ρP r( )•4πr2dr
Mean square radii
(Zero range calculations)
P(r) = 2π-3/2 -3 (1-1/A)-3/2 exp(-x2) (1+ (N-2) /3x2)x = (r/)2
Harmonic-oscillator type (p-shell)
NN has an energy dependence.
Energy at RIBF
Energy at GSI
Glauber model
Energy at RIPS/RIBLL
Sensitivity of R to the densities
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8 10
12C+
12C
Transmission function
r (fm)
30 A MeV
300 A MeV
radius(12C+12C)
Assumption for shape of densitiesAssumption for shape of densities
(r) = HO()-type (r < rc)
Y exp(-r)/r2 (r ≥ rc)
rc
Example : Effective Example : Effective of of 1111LiLi
500
1000
1500
2000
2500
3000
100 100010-6
10-5
0.0001
0.001
0.01
0.1
1
0 2 4 6 8 10
Energy (A MeV)
R (m
b)
r (fm)
Den
sity
(nu
cleo
n/fm
3 )
Finite range
Zero range
by energy dependence
by target dependencePLB287(1992)307
C target
Famous two neutron halo nucleus
Deduced is consistent with one deduced by other method.
Principle of measurement Principle of measurement
I = -1/t log(No/Ni)
Target (thickness t)
Ni(AZ) No(AZ)
Transmission method
Carbon
R = I + inela
Particle identification is important!Estimation of inela is also important.
RIBLL in IMP
B -E -TOF/B -E-TOF is possible.
E/A<50 MeV
Z.Sun et al., NIMA503(2003)496
Measurements of R at intermediate energies
14Be14Be
11Li 11Li
8He8He
9Li9Li
0 20 40 60 80
TOF (ns)
2
4
6
8
E (
a.u.
)
2
3
4
5
Z
3.0 3.4 4.23.8
A/Z
Good particle identification!
Results of particle identificationResults of particle identification
Before reaction target After reaction target
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0
1 6 0 0
1 8 0 0
1 0 1 0 0 1 0 0 0
E n e r g y ( A M e V )
1 4B
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0
1 6 0 0
1 8 0 0
1 0 1 0 0 1 0 0 0
E n e r g y ( A M e V )
1 4B e
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0
1 6 0 0
1 8 0 0
1 0 1 0 0 1 0 0 0
E n e r g y ( A M e V )
1 5B
Results in RIBLL
We obtained only interaction cross sections (I)with large error bars……
A.Ozawa et al., NIMB in press
Predictions by phenomenological formulae
I (
mb)
I (
mb)
I (
mb)
Q
Q S
D
S
Q
S
D
QS
F1
F2
F3
Q : Quadrupole MagnetS : Sextupole MagnetD : Dipole MagnetF1~3 : Forcus 1~3
Be production target
Primary beam from RRC
SlitAl wedge degraderPPACPlastic scintillator
SlitPPACSiPlastic scintillatorCarbon target
PPACPlastic scintillatorSiNaI
( )E
( )E
( )E
B
TOF
TOF
Experimental setup in RIPSExperimental setup in RIPS
RIPS in RIKEN
Good transmission!
Large momentum acceptance
p// of fragments
E/A<100 MeV
Q: Quadrupole MagnetD: Dipole MagnetF1~3: Focus 1~3
Results of particle identificationResults of particle identification
After reaction targetCase for 16C
Identification is not so easy…..However, good transmission is achieved after the reaction target.
800
900
1000
1100
1200
1300
1400
1500
11 12 13 14 15 16 17 18 19 20 21
C isotopes (C target)
900AMeV83AMeV
R/
I ( )mb
A
Recent results in C isotopes(in RIPS/FRS)
14C
RIPS data
Pure p1/2Pure s1/2
D.Q.Fang et al., PRC 69 (2004) 034613. 15C
RIPS data
16C
RIPS data
RIPS data
17CC.Wu et al., NPA 739 (2004) 3. T.Zheng et al., NPA709(2002)103.
Pure s1/2
800
1000
1200
1400
1600
1800
2000
2200
2400
10 100 1000
R ( )mb
(Energy A )MeV
10-7
10-6
10-5
0.0001
0.001
0.01
0.1
1
0 5 10 15 20
(fm
-3)
r (fm)
18C (Preliminary)
RIPS data
Summary
• Reaction cross section (R) measurements are powerful tools to investigate matter density distributions ( ) of unstable nuclei.
• R with low energy can be measured at RIBLL and RIPS.
• We deduced for 14-18C. Relatively large tail for 15-18C.
• We will extend the measurements to other heavier nuclei in RIBF in RIKEN and CSR in IMP.
Related topics in this symposium:by Wang-san (23Al) and Wu-san (17C)
List of collaborators
A.Ozawa1, X.Z.Cai2, Z.Q.Chen2, M.Chiba3, D.Q.Fang2, M.Fukuda4, Z.G.Guo5, N.Iwasa6, T.Izumikawa7, R.Kanungo8, R.Koyama7, J.X.Li5, R.S.Mao5, T.Ohnishi3, T.Ohtsubo7, W.Q.Shen2, W.Shinozaki7, T.Suda3, Z.Y.Sun5, T.Suzuki9, M.Takahashi7, I.Tanihata8, W.D.Tian5, J.S.Wang5, M.Wang5, Y.B.Wei2, C.Wu10, G.Q.Xiao5, Z.G.Xiao5, T.Yamaguchi9, Y.Yamaguchi3, A.Yoshida3, W.L.Zhan5, H.Y.Zhang2, T.Zheng10, C.Zhong2
1University of Tsukuba, 2Shanghai Institute of Applied Physics, 3
RIKEN, 4Osaka University, 5Institute of Modern Physics, 6Tohoku University, 7Niigata University, 8TRIUMF, 9Saitama University, 10Peking University
I strongly appreciate Chinese collaborators!