One- and two-phonon mixed-symmetry states in · High resolution required to resolve all 2+ states...
Transcript of One- and two-phonon mixed-symmetry states in · High resolution required to resolve all 2+ states...
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
94One- and two-phonon mixed-symmetry states in Moin high-resolution electron and proton scattering*
1 2 3 2 4 5 3,4O. Burda , N. Botha , J. Carter , R.W. Fearick , S.V. Förtsch , C. Fransen , H. Fujita ,1 1 1 4 6M. Kuhar , A. Lenhardt , P. von Neumann-Cosel , R. Neveling , N. Pietralla ,
1 1 7 3 4 1V.Yu. Ponomarev , A. Richter , O. Scholten , E. Sideras-Haddad , F.D. Smit and J. Wambach
1 2 Technische Universität Darmstadt - University of Cape Town 3 4 University of the Witwatersrand - iThemba LABS, Somerset West
5 6 Universität zu Köln - SUNY, Stony Brook7 University of Groningen
* Supported by DFG through contracts SFB 634 and Ne 679/2-1
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
Identification of Mixed-Symmetry States:nteracting oson odel - 2I B M
Pairing of nucleons to s-/ d-bosons
F =xma
N|N - |p n
2£ F £
+ NN p n
2
p boson: F = 1/20
n boson: F = -1/20
F-Spin:
® F = F : symmetric statesmax
® mixed-symmetry states (ms) F < F : max
Q-Phonon scheme:
Q Qp nQ = ms )
Q = Q + Qs p n
)N Np n2 N
| 2 ñ µ Q | 0 ñs1 1
| 2 ñ µ Q | 0 ñmsms 1
+ +
+ +
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
90Zr
94Mo
98Ru
Fmax
F -1max
F -2max
5p 4p + 1n 3p + 2n
F-Spin Multiplet
sym. states
ms states
boson number:
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
94The low-energy spectrum of Mo is well studied andcandidates for most one- and two-phonon stateshave been identified
N. Pietralla et al., Phys. Rev. Lett. 83 (1999) 1303N. Pietralla et al., Phys. Rev. Lett. 84 (2000) 3775C. Fransen et al., Phys. Lett. B 508 (2001) 219C. Fransen et al., Phys. Rev. C 67 (2003) 024307
94Why Mo?
isoscalar / isovector decomposition
+Study of 2 states with (e,e´) and (p,p´)
sensitive to one-phonon components of the wave function
purity of two-phonon states
test of fundamental phonon character
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
Experiments
+High resolution required to resolve all 2 states below 4 MeV
Lateral dispersion matching techniques
(e,e´): S-DALINAC, TU Darmstadt
(p,p´): SSC, iThemba LABS
E = 70 MeVe
Q = 93°- 165° DE = 30 keV (FWHM)
E = 200 MeVp
Q = 7°- 26°DE = 35 keV (FWHM)
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
S-DALINAC
High-resolution (e,e´) experiments
5 m0
Experimental HallAccelerator Hall Experimental HallAccelerator Hall
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
LINTOTT Spectrometer and Focal Plane Detector System
New Si microstrip detector system:4 modules, each contains 96 stripswith active width of 500 mm
-4Resolution: DE/E = 4 x 10
Data rates up to 100 kHz
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
Separated-Sector Cyclotron Facility
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
eb amofr m
SSC
2 m
K600 Magnetic Spectrometer and Detector System
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
3C
ou
nts
(x1
0)
Co
un
ts / m
C
iThemba LABS
S-DALINAC
x1
15
30 keVFWHM
94Mo(e,e´) E = 70 MeVe
Q = 141°
0.0
0.1
0.2
x1
100
35 keVFWHM
94Mo(p,p´)
E = 200 MeVp
Q = 9°
21
+
23
+
31
0
1
2
3
Measured Spectra
0 1 2 3 4
Excitation Energy (MeV)
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
1.5 2.0 2.5 3.0 3.5 4.0
0.01
0.0294Mo(e,e´) E = 70 MeVe
Q = 141°
Excitation Energy (MeV)
3C
ou
nts
(x1
0)
Co
un
ts / m
C
0.1
0.294Mo(p,p´) E = 200 MeVp
Q = 9°
2+
22
+ 25
+24
+
iThemba LABS
S-DALINAC
Measured Spectra
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
Quasi-Particle Phonon Model
coupling up to 3 phonons
Theoretical Calculation
Shell Model88Sr core / Surface Delta Interaction
Cross Sections
DWBA / Love-Franey effectivenucleon-target interaction for (p,p´)
IBM-2
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
One-Phonon Symmetric State
21
+
-1q (fm )
-1q (fm )
(ds
/dW
) / (d
s/d
W) M
ott
ds
/dW
(m
b/s
r)
94Mo(e,e´) 94Mo(p,p´)
M
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
One-Phonon MS State
-1q (fm )
-1q (fm )
(ds
/dW
) / (d
s/d
W) M
ott
ds
/dW
(m
b/s
r)
94Mo(e,e´) 94Mo(p,p´)23
+
M
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
pure two-phonon state
22
+
Two-Phonon Symmetric State
-1q (fm ) -1
q (fm )
(ds
/dW
) / (d
s/d
W) M
ott
ds
/dW
(m
b/s
r)
94Mo(e,e´) 94Mo(p,p´)
two-step contributions?
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
25
+
Two-Phonon MS State
-1q (fm )
-1q (fm )
(ds
/dW
) / (d
s/d
W) M
ott
ds
/dW
(m
b/s
r)
94Mo(e,e´) 94Mo(p,p´)
7-10% one-phonon admixture two-step contributions?
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
U (r)fi =bLR0
Ö2L+1
d
drU(r), L £ 2
bL
2
= ( (dsdW
exp
L( (dsdW
DWBA
L
Coupled-Channel Analysis
Collective model
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
pure two-phonon symmetricstate confirmed
Coupled-Channel Analysis:One and Two-Phonon Symmetric States
-1q (fm )0.3 0.6 0.9 1.2 1.5
ds
/dW
(m
b/s
r)-2
10
-110
-110
010
11094Mo(p,p´)
21
+
22
+
01
21
22
+
+
+
b = 1.23
b = 0.0
Experiment
CHUCK3
CHUCK3
sym
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
94Mo(p,p´)
23
+
25
+
-1q (fm )0.3 0.6 0.9 1.2 1.5
ds
/dW
(m
b/s
r)
-210
-110
-210
-110
010
one-phonon admixtures totwo-phonon ms state confirmed
01
21
22
+
+
+23
25
+
+
b = 0.35
b = 0.2
Coupled-Channel Analysis:One and Two-Phonon MS States
Experiment
CHUCK3
CHUCK3
sym
ms
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
+ 94Study of one- and two-phonon 2 states in Mo with
high-resolution (e,e´) and (p,p´) experiments
Combined analysis with microscopic models reveals:
about 25% admixtures in the two-phononms wave function (mostly 3-phonon)
quantitatively consistent results after inclusion oftwo-step processes in (p,p´)
Summary
symmetric and ms character of one-phonon states
two-phonon symmetric state extremely pure
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
92The case of Zr: Mixed-symmetry concept seems to failC.Fransen et al., Phys. Rev. C 71 (2005) 054304
Outlook
Experiments:
(p,p´) at iThemba LABS
(e,e´) at S-DALINAC
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
nstitut für Kernphysik
S DALINACTechnische Universität Darmstadt
F = Fmax
(sym. states)F = F -1max
(ms states)
Qms
0 ,...,4ms ms
2ms+
M1
0 ,2 ,42 2 1
+ + +
Q Qs s
Q Qs ms
E2
+
21
+
Qs
01
+ +
Identification of Mixed-Symmetry States:Q-Phonon Scheme
Strong transitions for decay of sym. Q-phonon
E2
Weak transitionsfor decay ofms Q-phonon
E2
Strong transitionsfor decay of ms statesto sym. states
M1