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



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

+ +

+ +



90Zr

94Mo

98Ru

Fmax

F -1max

F -2max

5p 4p + 1n 3p + 2n

F-Spin Multiplet

sym. states

ms states

boson number:



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



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)



S-DALINAC

High-resolution (e,e´) experiments

5 m0

Experimental HallAccelerator Hall Experimental HallAccelerator Hall



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



Separated-Sector Cyclotron Facility



eb amofr m

SSC

2 m

K600 Magnetic Spectrometer and Detector System



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)



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



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



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



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



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?



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?



U (r)fi =bLR0

Ö2L+1

d

drU(r), L £ 2

bL

2

= ( (dsdW

exp

L( (dsdW

DWBA

L

Coupled-Channel Analysis

Collective model



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



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



+ 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



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



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

one- and two-phonon mixed-symmetry states in · high resolution required to resolve all 2+ states...

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