Nuclear radii of unstable nuclei
-neutron/proton skins and halos--- OUTLINE --•Introduction
Situation @ stable nuclei
How to measure radii?
ƒ σR / σI measurements
Transmission method
Experimental setup
•Glauber model analysis
Optical limit approximation
Density distribution
•Deduced radii
Isotope dependence
Isobar dependence
•Skins & Halos
Skins in Na & Ar isotopes
Skins from other nuclei
2-n halo nucleus 17B
Recent results from S-250@FRS
•Summary
Summary and future prospects
16th Dec. 2004 / T. Suzuki
German-Japanese Nuclear Structure and Astrophysics Workshop
Saitama University
SIS-FRS-ESR
EXPERIMENTS
Nuclear r adii of unstable nuclei
-neutron/proton skins and halos-
Nuclear radii of stable nuclei
Text book says……
• R ∝ A1/3
Same radii for mirror pairs
• Neutron radii ≈ proton radii even for
208Pb (126-82=44 excess neutrons!)
Proton
Neut
ρ
No thick neutron skin!
• Diffuseness isr constant. a ~ 0.6 fm
How are unstable nuclei?
16th Dec. 2004 / T. Suzuki
Situation @ stable/unstable nuclei
P. 1
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
- neutron/proton skins and halos -
How to measure radii of
unstable nuclei
• Optical isotope shift
Charge radii can be measured.
Only limited atomic numbers (Na,
Ar, Kr, Sr, Sn, etc…).
• Elastic electron scattering was
so far, impossible.
• Reaction cross-section
(Interaction cross section)
Matter radii can be deduced.
No limitation to atomic number.
16th Dec. 2004 / T. Suzuki
How to measure radii?
P .2
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
- neutron/proton skins and halos -
What is reaction crosssection (σR)?
• Reaction cross-section (σR)
σR = σI + σinela, σinela: inelastic crosssection
• Definition of interaction crosssection (σI);
Cross section for the change of Z
and/or N in incident nucleus
If σinela is small enough, σR ≈ σI.
At relativistic energy (~1 A GeV)
16th Dec. 2004 / T. Suzuki
σR / σI measurements
P .3
Nuclear radii of unstable nuclei
- neutron/proton skins and halos -
SIS-FRS-ESR
EXPERIMENTS
10 4
γ-ray yield (counts/channel)
34 Cl
+C →
34 Cl
1000
9.1 ps
5.2 ps
32 m
1.5 s
T 1/2
461 keV
100
1+
1+
3+
0+
100
100
100
Iπ
34 Cl
665
461
146
0
E x (keV)
σinela
665 keV
40 mb
20 mb
10
10 mb
1
0
0.2
0.4
0.6
0.8
1
Corrected E γ (MeV)
Inelastic scattering
σinela ≤ 20mb
Typical error for σI
16th Dec. 2004 / T. Suzuki
σR / σI measurements
P .4
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
- neutron/proton skins and halos -
σR
radii; a simple
picture
Let’s assume black disk nuclei!
RI(T)
Target
nucleus
RI(P)
Projectile
nucleus
σR = π [RI(T) + RI(P)]2
For quantitative analysis,
Glauber model is necessary.
16th Dec. 2004 / T. Suzuki
σR / σI measurements
P .5
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Principle of measurement
Transmission method
Carbon
Target (thickness t)
Ni(AZ)
No(AZ) σI = -1/t log(No/Ni)
No*(AZ)= No (AZ)-N*(AZ*)
σR = -1/t log(No*/Ni)
16th Dec. 2004 / T. Suzuki σR
/ σI measurements
p.7
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
Experimental setup
Be production
target
TOF/Bρ
TOF/Bρ
∆E
∆E
F4
F3
F1
40
Ar/ 36Ar primary
beam
(~1A GeV)
C reaction
target
previous exp.@FRS
F2
1400
Collimator
TPC
MUSIC/IC
NaI array
ANa+C
σ
Ι
(mb)
Plastic
scintillators
1200
1000
19
23
27
31
A
16th Dec. 2004 / T. Suzuki σR
/ σI measurements
p.8
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Glauber model Optical Limit
approximation
∞
σR= π
2
(Zero range calculations)
1 -T(r)rd
T(r):Transmission function
q(r,z) dz
σ:effective NN corss-sections
0
∞
T(r) = exp-
σ
-∞
ρ of target ρ of projectile
∞
∞
q(z) = dη2π ρT(r,z,b,η)ρP(r,z,b,η)bdb
-∞
0
Harmonic∞
r = ∫ r ρP (r )• 4πr dr
0
2
2
2
Mean square radii
16th Dec. 2004 / T. Suzuki σR
oscillator type
(p-shell)
ρP(r) = 2π-3/2 λ-3 (1-1/A)-3/2 exp(-x2)・
(1+ (N-2) /3x2)；x = (r/λ)2
/ σI measurements
p.9
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Isotope dependence of matter radii
19C
3.4
RMS matter radii (fm)
3.2
3
C-isotopes
R ∝ A3/4
2.8
2.6
2.4
R ∝ A1/3
2.2
2
8 10 12 14 16 18 20 22
A
R ∝ A1/3 in unstable nuclei
16th Dec. 2004 / T. Suzuki
Isotope dependence
p.12
SIS-FRS-ESR
EXPERIMENTS
Nuclear
radii
of unstable
Nuclear
radii
of unstable
nuclei nuclei
skins
and
halos--neutron/proton
neutron/proton skins
a nd
halos-
R.M.S. radius (fm)
A=17 system
3
2.9
2.8
2.7
Phys. Lett . B 334 (1994) 18
17 Ne
17 N
2.6
2.5
2.46
-3/2
-1/2
7
8
7/2
12
13
Nucl . Phys. A 603 (1996) 219
20 O
R.M.S. radius (fm)
A=20 system
3.2 20
3.1 Mg
3
2.9
2.8
2.7
2.67 -28 -19
1/2
3/2 5/2
9
10
11
Tz (isospin )
0
10
1
11
2
12
3
13
414
15T z
(isospin )
Mirror nuclei do not have the same radii
16 th Dec. 2004 / T . Suzuki
Isobar dependence
p. 13
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
Neutron skin in Na-isotopes
•
Definition ;
n-skin = (rms-n) - (rms-p)
p-skin = (rms-p) - (rms-n) Optical isotope-shift
• Relationship
(rms-m)2 = (Z/A) (rms-p)2 + (N/A) (rms-n)2
We can deduce rms-n if we know both rms-m& rms-p.
3.5
Phys. Rev. Lett. 75 (1995)3241.
Neutron
rms radii (fm)
Neutron
skin~
0.4 fm
3
stable
Proton
Calculation by
RMF
2.5
20
22
24
26
28
30
A
32
G. Lalazissis, D. Vretenar, P. Ring Eur. Phys. J. A22 (2004) 37
16th Dec. 2004 / T. Suzuki
neutron skin in Na isotopes
p.15
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
0.6
0.5
Nucl. Phys. A709(2002)60
0.4
Proton skin (fm)
0.3
Ar
Proton skin
Calculation by
RMF(NL3)
0.2
0.1
0
-0.1
-0.2
A
30 32 34 36 38 40 42
Thick skins appear in proton-rich side
too.
16th Dec. 2004 / T. Suzuki
proton skin in Ar isotopes
p.16
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
Correlation between skin and (S
(Sp-Sn)
0.6
Proton s kin (f m)
Ar-isotopes
22
32
0.4
21
0.2
34
33
Na-isotopes
20 36 38 37
35
40
0
39
23
-0.2
RMF(NL3) (Ar)
27
29
25 26
30
28
31
-0.4
-0.6
-20
-10
0
..
10
20
Formation of n/p- skins is
common phenomenon
in unstable nuclei
S p-S n (MeV)
Skin thickness ---> Relative merits of various param. used in
the RMF model.
---> EOS pressure in neutron matters
---> pygmy dipole resonance
S. Yoshida & H. Sagawa PRC61 (2004) 024318
N. Tsoneva, H. Lenske, Ch Stonyanov PLB 586 , (2004) 213
M. Yokoyama , T. Otsuka, N. Fukunishi, NPA599 , (1996) 367
W.D. Myers & W.J. Swiatecki NPA336 , (1980) 267
Droplet model ,Hartree-Fock RPA, RMF, (R)Hartree-Bogolubov, ...
Another example
20Mg,20N
O. Bochkarev et al., Eur. Phys.J. A 1 (1998)
σR mesuremnet -> 0.56 +- 0.29 fm
Neutron-rcih K & Sc N. Aissaouri et al., PRC 60(1999) 03614
40S
F. Marechal et al., PRC 60 (1999) 034615
proton scattering inverse kinematics --->
16th Dec. 2004 / T. Suzuki
skin formation & EOS via matter radius
p.17
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
Hadron probes suffer from the uncertainties in the reaction mechanism
Table.2 summary of current values for the neutron skin
thickness, S, in 208Pb
Probe
S (fm) Error (fm)
reference
+ and ｦﾐ
ｦﾐ
0.0
0.1
Allardyce, et al. NPA
(1973)
Proton (650 MeV)
0.20
0.04
Strarodubsky, et al.
PRC (1994)
Giant dipole resonance
excitation
Nucleon (40-200 MeV)
0.19
0.09
Krasznahorkay, et al.
NPA (1994)
0.17
Karataglidis, et al.
PRC (2002)
Proton (0.5-1.04 GeV)
0.097
0.014
Clark, et al. PRC
(2003)
Anti-protonic atoms
0.15
0.02
Trzci_ska, et al. PRL
(2002)
0.15+-0.02_
(fm) from p
(p,n) reaction on stable 114-124Sn
using Spin Dipole Resonance
A. Karsznahorkay et al. P.R.L. 82(99) 3216
(Liverpool - Surrey-GANIL - Saclay-Caen) ENAM04
N=20~ 28 systematic measurements of σR
by Villari et al. 35Mg, 44S (new halo candidate)
16th Dec. 2004 / T. Suzuki
Another examples
p.18
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
What is known so far on 17B
11Li
14Be
17B
2.8
2n
SG.Audi,O.Bersillon,J.Blachot,A.H.Wapstra,
Nucl.Phys.A624(97)1
~
r
m
(fm)
3.2
12Be 15B
2.4
analogy
0.1
1
~rm
.
.,
Nucl.Phys.A658(99) 313
10
(MeV)
2n
S
14Be
dσ (θ
) Γ~ 50 +-5 MeV/c
dΩ neutron
12
Γ~ 88 +-5 MeV/c
P|| ( Be)
kinematically
complete exp.
σ(-2n) ,
Invariant mass spectra
K.Riisageretal., Nucl.Phys.A540 (92) 365.
M.Zaharetal., Phys.Rev. C48(93)R1484
M.Labicheetal., Phys.Rev. Lett.(00)1111
Neutron halo structure in 14Be
in 17B
?
16th Dec. 2004 / T. Suzuki
proton
in Ar 17
isotopes
2-n haloskin
nucleus
B
p.16
p.19
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
rms matter radii for B isotopes
17B
Nucl. Phys. A658
(1999) 313.
Radius of 17B is much larger
than neighbors!
Necessary condition
Phys. Rev. Lett. 89 (2002)012501.
Narrow width in
Momentum distr.
Sufficient condition
16th Dec. 2004 / T. Suzuki
proton
in Ar 17
isotopes
2-n haloskin
nucleus
B
p.16
p.20
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
SIS-FRS-ESR
EXPERIMENTS
• Characterizing feature;
Large rms radii narrow p//
core
halo
ρ
• Closeness of a threshold
r
Small neutron separation energies
• Dominating cluster structure
Core + neutron(s)
Density distribution
100
mixed
10-1
Phys. Rev. C70
(2004) 05320
[fm-3]
10-3
ρ
10-2
10-4
17
B
10-5
10-6
10-7
0
2
4
6
8
10
12
r [fm]
16th Dec. 2004 / T. Suzuki
proton
in Ar 17
isotopes
2-n haloskin
nucleus
B
p.16
p.21
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Proton Skin in Kr Isotope
S-250 @FRS
27.10-7.11
/Z ：
⊿Z
0.998%(Z=31)
TOF :
σ ∼ 15 [ps]
99.99%> is required for PID!Analysis is in progress
Analysis is in progress
16th Dec. 2004 / T. Suzuki
proton
skin in from
Ar isotopes
recent results
@250@ FRS
p.16
p.22
Nuclear determined
radii
σRat
from
~1
AGeV
4He
(Radius
of(1.47
fm) is subtract
20
15
Z
Proton drip-line
10
Neutron drip-l
5
0.51 1.52fm
0
0
5
10
15
N
20
25
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Future plans...(EOS)……
We want to understand the nuclear matter equation of state
The energy per nucleon near the saturation point:w
⎡
⎤ 2
K0
2
L
w = w0 +
(n − n0 )⎥α
2 (n − n0 ) + ⎢ S0 +
18n0
3n0
⎣
⎦
w0: the saturation energy, n0:the saturation density,
K0: the incompressibility, α:neutron excess,
S0: the density-dependent symmetry energy at n=n0,
L=3n0(dS/dn)n=n0:the symmetry energy density-derivative coefficient
Y=-(K0S0)/(3n0L):the slope of the saturation line near α=0
Recent theoretical
works show that
matter radii
depend
strongly
on L.
Proposed
accuracy
54-72Ni
16th Dec. 2004 / T. Suzuki
isotopes
K. Oyamatsu &
K.Iida
In preparation.
proton
skin
in Ar isotopes
future
plans
p.16
p ..23
SIS-FRS-ESR
EXPERIMENTS
Nuclear radii of unstable nuclei
-neutron/proton skins and halos-
Summary
Stable nuclei
Unstable nuclei
R ∝ A1/3
Same radii
R ∝ A1/3
Large difference
for mirror pairs
for some pairs
No thick skin
Constant diffuseness
Magic number;
2, 8, 20, 28...
thick skin
Existence of halo tail
Existence of
Another magic number
; 16
Nuclear structure for unstable nuclei is quite different from
stable nuclei.
Reaction (interaction) cross-section measurements are a very
powerful tool to study nuclear structure of unstable nuclei.
Future plan in 54-72Ni isotopes
Required accuracy 0.25% in σI
0.01 fm in radius
16th Dec. 2004 / T. Suzuki
proton
skin in Ar isotopes
Summary
p.16
p.24
List of collaborators
H. Geissel, K. Suemmerer, G. Muenzenberg
M. Fukuda, T. Izumikawa, T. Oonishi(Tetsu)*,
T. Ootsubo(Taka1), T. Suda*, A. Ozawa(Aki),
T. Yamaguchi(Taka2), T. Suzuki
GSI-RIKENUni.Osaka - Uni. Niigata - Uni. Tsukuba - Uni. Saitama
Thank you for your
attention!