108Sn studied with intermediate-energy Coulomb excitation

Dissertation zur Erlangung des Grades “Doktor der Naturwissenschaften”

am Fachbereich Physikder Johannes Gutenberg-Universität

in Mainz

Leontina Adriana Banu

OutlineOutline

Motivation Why to study Why to study 108108Sn ?Sn ? Why to study it with Coulomb excitation ?Why to study it with Coulomb excitation ?

Experimental method description Most significant features of intermediate-energyMost significant features of intermediate-energy Coulomb excitationCoulomb excitation Experimental set-up

Data analysis

Experimental results Theoretical interpretation

Why to study Why to study 108108Sn ?Sn ?

• magic numbers shell closuresmagic numbers shell closures

Nuclear shell modelNuclear shell model

• 100100Sn (N=Z=50)Sn (N=Z=50) principle test groundprinciple test ground

• insight into the structure of insight into the structure of 100100SnSn by by studying the nuclei in its vicinitystudying the nuclei in its vicinity

• how rigid is the the doubly-magic core how rigid is the the doubly-magic core when valence neutrons are being when valence neutrons are being added ?added ? ((studying A=102-130 Sn isotopesstudying A=102-130 Sn isotopes))

• investigation on quadrupole investigation on quadrupole polarization ofpolarization of the doubly-magic corethe doubly-magic core ((E2 core polarization effectE2 core polarization effect))

• B(E2;0B(E2;0++->2->2++)=|<)=|<ff||||OOE2E2||||ii>|>|22 is the is the mostmost sensitive to E2 collective effectssensitive to E2 collective effects

108108SnSn

5858

112112SnSn

6262

N=ZN=Z

Number of neutrons (N)

Num

ber

of

pro

tons

(Z)

Z = 2,8,20,28,50,82Z = 2,8,20,28,50,82 N = N = 2,8,20,28,50,82,1262,8,20,28,50,82,126

100Sn

Sn(N,Z) = B(N,Z) – B(N-1,Z)N oddZ even

22 88 2020 2828 5050 8282 126126

Neutr

on s

epara

tion e

nerg

y [

MeV

]

Avera

ge e

nerg

y o

f th

e fi

rst

exci

ted s

tate

s in

even

- even n

ucl

ei

Why Coulomb excitation to study Why Coulomb excitation to study 108108Sn ?Sn ?

• B(E2) determination:B(E2) determination:Lifetime measurement B(E2) valueB(E2) value

( ~ 7 ns) isomeric state( ~ 7 ns) isomeric state

B(E2;6B(E2;6++->4->4++) = 3 W.u.) = 3 W.u.

Z. Phys. A352 (1995) 373Z. Phys. A352 (1995) 373

E2E2

00++

22++

44++

66++

108108SnSn

905905

253253

12061206

(HI,xn(HI,xn) reaction) reaction

(< 0.5 ps)(< 0.5 ps)

• Electromagnetic decay of lowest excited 2Electromagnetic decay of lowest excited 2++state:state:

transition probability

τ1

secB(E2)ET(E2) 15γ

lifetime

22++

00++

EE(())

Coulomb excitation B(E2) valueB(E2) value

cross section

((E2) ~ B(E2))

66++

E2E2

2+

0 keV0 keV

1207 keV

Intermediate-energy Coulomb Intermediate-energy Coulomb excitationexcitation

~ ~ 3%3%

E=1.3 MeVD = 70 cm

1 Ge-Cluster 1 Ge-Cluster detectordetector

Composite

Composite

detector

detector

E/E

0 [%

]

Detector opening angle Detector opening angle =3°=3°

lab

[deg]

= 0.57= 0.57

= 0.43= 0.43

= 0.11= 0.11

• Nuclear excitation (±)

• Lorentz boost (+)

• Doppler broadening (-)

• Atomic background

radiation (-)

n

Nuclear excitationNuclear excitation

Coulomb excitationCoulomb excitation

target1.5θmax( in our case ) = 0.43

UNILACSIS

ESR

FRSFRS

GSI accelerator facilityGSI accelerator facility

Experimental set-upExperimental set-up

Primary beam

124Xe @ 700 A•MeV

9Be, 4 g/cm2

• projectile fragmentation (production method)

• in-flight fragment separation

(Bρ-E-Bρ method)

βγBρ

uce

ZA

(~ 150 A•MeV)

Secondary beam @ reaction target:108Sn/112Sn

197Au, 0.4 g/cm2

Beam directionBeam direction

CATE (Si) CATE (CsI)

Fragment identification Fragment identification beforebefore//afterafter targettarget

108108SnSn

Selection with FRSSelection with FRS Selection with CATESelection with CATE

βγBρ

uce

ZA

res

2

EΔEAZ

ΔE

Scattering angle measurementScattering angle measurement

p

MW MW CATE

Si CsITarget

Beam trackingBeam tracking

• Event–by–event Doppler shift correction:Event–by–event Doppler shift correction:

• Impact parameter determination:Impact parameter determination:

γ

20γγ βcosΘ1

β1EE

[rad]Θ1

MeV]}[AT2ucMeV])[A{(TA

MeV])[AT(ucZZ~b[fm]

plab22

labp

lab2

tp

511 keV

40K

~ 50%

rest

in-flight

Analysis of intermediate-energy Coulomb Analysis of intermediate-energy Coulomb excitationexcitation

• Fragment selectionFragment selection beforebefore secondary secondary targettarget

• Fragment selectionFragment selection afterafter secondary secondary targettarget

• Scattering angle selection (1°- 2°)Scattering angle selection (1°- 2°)

• Prompt Prompt time ‘window’ time ‘window’

• Ge-Cluster multiplicity: MGe-Cluster multiplicity: M(E(E > 500 keV) > 500 keV) = 1= 1

Elastic scattering dominates

Nuclear excitation contributiongrazzing = 1.5° ± 0.5°

Experimental resultsExperimental results

B(E2; 0B(E2; 0+ + -> 2-> 2++) = 0.230 (57) e) = 0.230 (57) e22bb22

A. Banu et al.A. Banu et al., submitted to Phys. Rev. C (2005), submitted to Phys. Rev. C (2005)

0.88I

N

N

I)B(E2)B(E2 112

γ

112p

108p

108γ112108

• Measure:Measure:-particle coinc.-particle coinc.

particle singles

II

Np

• Deduce B(E2) for Deduce B(E2) for 108108Sn as follows:Sn as follows:

)(atom/cmNN

/εIσ(E2) 2

tp

γγ

)B(E2)f(bσ(E2) min

exp.exp.

theorytheory

0.240 (14) e0.240 (14) e22bb22 --- previous work

Theoretical interpretationTheoretical interpretation

Neutron numberNeutron number

B(E

2 )

eB

(E2

) e

2 2 bb

22

This workThis work

theory (theory (neutron valenceneutron valence and and 100100SnSn as closed-shell core)as closed-shell core)

••••••••

5810850Sn

Neutron/proton single-particle statesin a nuclear shell-model potential:

theory (theory (neutron valenceneutron valence + proton core excitations+ proton core excitations and and

9090ZrZr as closed-shell core)as closed-shell core)

t=0

t=2t=4

t=4

Proton np-nh core excitations (t=n)&

100Sn core is open

Conclusion and OutlookConclusion and Outlook

• 108108Sn the heaviest Z-nucleus studied with Sn the heaviest Z-nucleus studied with intermediate-energy Coulomb excitationintermediate-energy Coulomb excitation

• B(E2;0B(E2;0++->2->2++) measured for the first time) measured for the first time

• The experimental result is in agreementThe experimental result is in agreement with latest large scale shell model calculationswith latest large scale shell model calculations

• This work brings more insight into the investigation ofThis work brings more insight into the investigation of E2 correlations related to E2 correlations related to 100100Sn core polarizationSn core polarization

• 108108Sn further step towards Sn further step towards 100100SnSn

““Art is I, Science is We.” - Claude BernardArt is I, Science is We.” - Claude Bernard

Thanks to…Thanks to…

J. Gerl (GSI), J. Pochodzalla (Uni. Mainz) - thesis advisorsJ. Gerl (GSI), J. Pochodzalla (Uni. Mainz) - thesis advisors

C. Fahlander (Lund), M. GC. Fahlander (Lund), M. Górska (GSI) - spokespersonsórska (GSI) - spokespersons

H. Grawe, T.R. Saito, H.-J. Wollersheim (GSI) H. Grawe, T.R. Saito, H.-J. Wollersheim (GSI)

M. Horth-JensenM. Horth-Jensen et al. (Oslo Uni.), et al. (Oslo Uni.), F.NowackiF.Nowacki et.al et.al (IRES)(IRES)

and last but not least…and last but not least…

The local RISING team

Seniority scheme in Sn isotopes:Seniority scheme in Sn isotopes:

E(E(jj22J) ~ VJ) ~ V00tan(tan(/2)/2) for T=1, J even for T=1, J even

-residual interaction in a -residual interaction in a jjnn configuration configuration

00++

22++

44++

66++

jjnn00

22

22

22

= 2= 2

= 0= 0

= 0= 0

22++

44++

66++

00++

(V(V1212(() = -V) = -V00((rr11--rr22))))

minmin

ener

gy a

xis

jj

j

j

j

j

j j

JJ

JJJJ

JJ

Data SummaryData Summary

Primary beamPrimary beam

SIS energySIS energy (MeV/nucleon)

Primary beam intensityPrimary beam intensity (s-1)

124124XeXe

700700

6 6 × 10× 1077

124124XeXe

700700

6 6 × 10× 1077

Secondary beamSecondary beam

Sec. beam abundance Sec. beam abundance (%)

Sec. beam rate Sec. beam rate (s-1)

Sec. beam energy @ target Sec. beam energy @ target (MeV/nucleon)

112112SnSn

6060

24002400

147147

108108SnSn

6262

24802480

142142

EE(2(211++->0->0++) ) (keV)

Data collection timeData collection time (h)

12571257

3333

12061206

5858

Single-particle states in shell-model Single-particle states in shell-model potentialpotential

2j+12j+1 nnjjll

Spectrsoscopic notation:Spectrsoscopic notation:

ll -> orbital angular momentum

jj -> total angular momentum

l= 0, 1, 2, 3, 4, 5, 6

s, p, d, f, g, h, is, p, d, f, g, h, i

jj = = ll + s + s

s = 1/2s = 1/2j = l ± ½

2j+1 2j+1 nucleons /orbitalnucleons /orbital

inertinert core

+activeactive valencenucleons

••••••••

5810850Sn

Single-particle states in shell-model Single-particle states in shell-model potentialpotential

2j+12j+1 nnjjll

Spectrsoscopic notation:Spectrsoscopic notation:

ll -> orbital angular momentum

l= 0, 1, 2, 3, 4, 5, 6

s, p, d, f, g, h, is, p, d, f, g, h, i

jj -> total angular momentum

jj = = ll + s + s

s = 1/2s = 1/2j = l ± ½

2j+1 2j+1 nucleons /orbitalnucleons /orbital

B(E2;0B(E2;0++ -> 2 -> 2++) ) ~ f(1-f)~ f(1-f) wherewhere

Generalized seniority scheme:Generalized seniority scheme:

f = (N – 50)/ 32f = (N – 50)/ 32