EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

GOSIA GOSIA as a tool for COULEX as a tool for COULEX

on exotic beamson exotic beamsKatarzyna WrzosekKatarzyna Wrzosek

Heavy Ion Laboratory Heavy Ion Laboratory

Warsaw UniversityWarsaw University

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

LOW - ENERGY COULOMB LOW - ENERGY COULOMB EXCITATION:EXCITATION:

Well-established method to study collective Well-established method to study collective excitations in nuclei.excitations in nuclei.

Purely electromagnetic Purely electromagnetic the only nuclear the only nuclear properties involved are the properties involved are the matrix elementsmatrix elements of the electromagnetic multipole moments.of the electromagnetic multipole moments.

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

Gamma ray spectrometerGamma ray spectrometer EXOGAM – up to 11 segmented Ge clovers (90 and 135)

Particle detectorCD-detector - annular, highly segmented double silicon strip detector (DSSD)covered angles: 23,8-54,5 in the LAB ≡ 24-145 in the C.M. frame

208Pb

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

COULEX Analysis SchemeCOULEX Analysis Scheme

Measured yields

Measured yields

available spectroscopic

data(, BR, )

available spectroscopic

data(, BR, )

Level schemeLevel scheme Experimental setup geometry:

particle and detectors

Experimental setup geometry:

particle and detectors

set of matrix elements

set of matrix elements

shape parameters for

individual states

shape parameters for

individual statesSIGMA

GOSIA

MINIMALIZATION PROCEDURE

MINIMALIZATION PROCEDURE

Errors estimationErrors estimation

Quadrupole rotational invariant

sum rules

Quadrupole rotational invariant

sum rules

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

GOSIAGOSIA GOSIA is a Rochester – Warsaw semiclassical coupled-GOSIA is a Rochester – Warsaw semiclassical coupled-

channel Coulomb excitation least-squares search code.channel Coulomb excitation least-squares search code. Developed in early eighties by Developed in early eighties by

T. Czosnyka,T. Czosnyka, D. Cline, C.Y.Wu D. Cline, C.Y.Wuand continuously upgraded to fulfill requirements of new and continuously upgraded to fulfill requirements of new experiments.experiments.

Used extensively for Coulomb excitation studies of a wide Used extensively for Coulomb excitation studies of a wide range of nuclei.range of nuclei.

Typical use of GOSIA:Typical use of GOSIA:1.1. Fitting of the matrix elements to the experimental data.Fitting of the matrix elements to the experimental data.2.2. Simulation of the experiments:Simulation of the experiments:

to predict which to predict which - ray will be observed - ray will be observedto check to what extent the observation will depend on to check to what extent the observation will depend on individual matrix elements.individual matrix elements.

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

AN EXAMPLE:AN EXAMPLE:COULOMB EXCITATION OF COULOMB EXCITATION OF 74,7674,76Kr @ GANILKr @ GANIL

Coulomb excitation is the only method that can Coulomb excitation is the only method that can directly distinguish between different shapes of the directly distinguish between different shapes of the nucleus nucleus ideally suited to verify the shape coexistence ideally suited to verify the shape coexistence scenario in the Kr isotopes.scenario in the Kr isotopes.

Shape parameters of the two lowest 0Shape parameters of the two lowest 0+ + states in states in 7474Kr Kr and and 7676Kr nuclei were inferred from coulomb Kr nuclei were inferred from coulomb excitation data.excitation data.

The Coulomb excitation analysis were performed The Coulomb excitation analysis were performed using the last squares fitting code GOSIA.using the last squares fitting code GOSIA.

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

EXPERIMENTS EXPERIMENTS (SPIRAL @ GANIL)(SPIRAL @ GANIL)

7474Kr + Kr + 208208Pb Pb (5(5··101055 pps, pps, 4.74.7··A MeV)A MeV)

7474KrKr 7676KrKr7676Kr + Kr + 208208PbPb

((101066 pps, pps, 4.44.4··A MeV)A MeV)

E. Clement E. Clement et al.et al., submitted to , submitted to Phys Rev CPhys Rev C

508 keV 770 keV

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

39.5° - 49.0° 61.4° - 71.8° 71.0° - 87.7° 107.0° - 121.5°

76 Kr

7676KrKr

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

RESULTSRESULTS

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

QUADRUPOLE ROTATIONAL QUADRUPOLE ROTATIONAL

INVARIANTINVARIANT SUM RULES SUM RULES model independent description of the nuclear shapemodel independent description of the nuclear shape

is based on a fact, that scalar products of E2 is based on a fact, that scalar products of E2 operators are operators are rotational invariantsrotational invariants. . Operator products may be expressed using the Operator products may be expressed using the intermediate state expansion formula:intermediate state expansion formula:

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

QUADRUPOLE ROTATIONAL INVARIANTQUADRUPOLE ROTATIONAL INVARIANT SUM RULES SUM RULES

model independent description of the nuclear shapemodel independent description of the nuclear shape

To get information on triaxiality the higher order To get information on triaxiality the higher order invariant is neededinvariant is needed::

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

RESULTSRESULTS The deformation of the 0The deformation of the 0++

11 is very similar in is very similar in 7474Kr and Kr and 7676Kr. Kr.

Triaxiality parameterTriaxiality parameter: : the ground state of the ground state of 7676Kr is Kr is prolateprolate, while the 0, while the 0++

22 state has an state has an triaxialtriaxial shape.shape.

Both, the ground state and the 0Both, the ground state and the 0++22 state of state of 7474Kr are Kr are triaxialtriaxial,, but with but with

different different parameter. parameter.

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

Collaboration of Collaboration of 74,7674,76Kr Project Kr Project CEA Saclay, FranceCEA Saclay, France

E.ClémentE.ClémentA.GörgenA.GörgenW.KortenW.KortenE.BouchezE.BouchezA.ChatillonA.ChatillonA.HürstelA.HürstelY.Le CozY.Le CozA.ObertelliA.ObertelliCh.TheisenCh.TheisenJ.N.WilsonJ.N.Wilson

CEA/DIF, FranceCEA/DIF, FranceJ.-P. DelarocheJ.-P. DelarocheM.GirodM.GirodH.GoutteH.GoutteS.PéruS.Péru

GANIL, Caen, FranceJ.M.CasandjianG. de France

HIL Warsaw, PolandHIL Warsaw, PolandT.CzosnykaT.CzosnykaJ.Iwanicki (OLLJ.Iwanicki (OLL, , Liverpool)Liverpool)P.J.NapiorkowskiP.J.NapiorkowskiM.Zielińska (CEA Saclay)M.Zielińska (CEA Saclay)

Oliver Lodge Lab., Liverpool, UKC.Andreoiu P.A.ButlerR.-D.HerzbergD.G.JenkinsG.D.Jones

Univ. Of Surrey, Guildford, UKW.N.CatfordC.Timis

GSI, Darmstadt, GermanyF.BeckerJ.Gerl

NBI, Copenhagen, DenmarkG.Sleten

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

List of the experiments List of the experiments where GOSIA was recently usedwhere GOSIA was recently used

ISOLDE (MINIBALL), CERNISOLDE (MINIBALL), CERN:: J. Cederkall – J. Cederkall – 108108Sn, Sn, 110110SnSn J. Iwanicki - J. Iwanicki - 8888Kr, Kr, 9292KrKr A. Hurst - A. Hurst - 7070SeSe I. Stefanescu – I. Stefanescu – 6868Cu, Cu, 7070CuCu J. Van de Walle – J. Van de Walle – 7474ZnZn GANIL (EXOGAM), FRANCEGANIL (EXOGAM), FRANCE:: E. Bouchez – E. Bouchez – 7676KrKr E. Clement – E. Clement – 7474KrKr M. Zielińska – M. Zielińska – 4444ArArJYVASKYLA, FINLANDJYVASKYLA, FINLAND F. Becker – F. Becker – 7878KrKrJAEA, TOKAI, JAPANJAEA, TOKAI, JAPAN:: M. Koizumi - M. Koizumi - 6666Zn, Zn, 6868ZnZn T. Hayakawa – T. Hayakawa – 7878SeSe A. Osa - A. Osa - 8484KrKr Y. Toh – Y. Toh – 7070GeGe M. Zielińska – M. Zielińska – 9696MoMoANL (Gammasphere), USAANL (Gammasphere), USA A.Hayes – A.Hayes – 178178HfHf

Next experimentsNext experiments

ISOLDE (MINIBALL), CERNISOLDE (MINIBALL), CERN:: E. Clement – E. Clement – 9696Sr Sr

(Jul 2007)(Jul 2007) P.Butler, P. Van Duppen - P.Butler, P. Van Duppen - 182,184182,184Hg Hg

(Aug 2007)(Aug 2007)

JRA6JRA6INTAGINTAG

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

Warsaw Coulomb Excitation GroupWarsaw Coulomb Excitation Group@ Heavy Ion Laboratory, Warsaw Univ.@ Heavy Ion Laboratory, Warsaw Univ.

Tomasz CzosnykaTomasz Czosnyka Julian SrebrnyJulian Srebrny Jędrzej IwanickiJędrzej Iwanicki Paweł NapiorkowskiPaweł Napiorkowski Magdalena Zielińska (CEA Saclay)Magdalena Zielińska (CEA Saclay) Katarzyna WrzosekKatarzyna Wrzosek Katarzyna Hadyńska (UAM, Poznań)Katarzyna Hadyńska (UAM, Poznań) Daniel Piętak (PW, Warsaw)Daniel Piętak (PW, Warsaw)

EWON Workshop, Prague, 10-12 May 2007 EWON Workshop, Prague, 10-12 May 2007

Thank you Thank you