EWON Workshop, Prague, 10-12 May 2007 GOSIA as a tool for COULEX on exotic beams Katarzyna Wrzosek Heavy Ion Laboratory Warsaw University.

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EWON Workshop, Prague, May 2007 GOSIA as a tool for COULEX on exotic beams Katarzyna Wrzosek Heavy Ion Laboratory Warsaw University

EWON Workshop, Prague, May 2007 LOW - ENERGY COULOMB EXCITATION:  Well-established method to study collective excitations in nuclei.  Purely electromagnetic  the only nuclear properties involved are the matrix elements of the electromagnetic multipole moments.

EWON Workshop, Prague, May Pb

EWON Workshop, Prague, May 2007 COULEX Analysis Scheme Measured  yields available spectroscopic data ( , BR,  ) available spectroscopic data ( , BR,  ) Level scheme Experimental setup geometry: particle and  detectors set of matrix elements shape parameters for individual states SIGMA GOSIA MINIMALIZATION PROCEDURE Errors estimation Quadrupole rotational invariant sum rules

EWON Workshop, Prague, May 2007 GOSIA  GOSIA is a Rochester – Warsaw semiclassical coupled- channel Coulomb excitation least-squares search code.  Developed in early eighties by T. Czosnyka, D. Cline, C.Y.Wu and continuously upgraded to fulfill requirements of new experiments.  Used extensively for Coulomb excitation studies of a wide range of nuclei.  Typical use of GOSIA: 1. Fitting of the matrix elements to the experimental data. 2. Simulation of the experiments: to predict which  - ray will be observed to check to what extent the observation will depend on individual matrix elements.

EWON Workshop, Prague, May 2007 AN EXAMPLE: COULOMB EXCITATION OF 74,76 GANIL  Coulomb excitation is the only method that can directly distinguish between different shapes of the nucleus  ideally suited to verify the shape coexistence scenario in the Kr isotopes.  Shape parameters of the two lowest 0 + states in 74 Kr and 76 Kr nuclei were inferred from coulomb excitation data.  The Coulomb excitation analysis were performed using the last squares fitting code GOSIA.

EWON Workshop, Prague, May 2007 EXPERIMENTS GANIL) 74 Kr Pb (5·10 5 pps, 4.7·A MeV) 74 Kr 76 Kr 76 Kr Pb (10 6 pps, 4.4·A MeV) E. Clement et al., submitted to Phys Rev C 508 keV 770 keV

EWON Workshop, Prague, May ° °61.4° °71.0° °107.0° ° 76 Kr

EWON Workshop, Prague, May 2007 RESULTS

QUADRUPOLE ROTATIONAL INVARIANT SUM RULES model independent description of the nuclear shape is based on a fact, that scalar products of E2 operators are rotational invariants. Operator products may be expressed using the intermediate state expansion formula: is based on a fact, that scalar products of E2 operators are rotational invariants. Operator products may be expressed using the intermediate state expansion formula:

EWON Workshop, Prague, May 2007 QUADRUPOLE ROTATIONAL INVARIANT SUM RULES model independent description of the nuclear shape To get information on triaxiality the higher order invariant is needed: To get information on triaxiality the higher order invariant is needed:

EWON Workshop, Prague, May 2007RESULTS  The deformation of the is very similar in 74 Kr and 76 Kr. Triaxiality parameter:  the ground state of 76 Kr is prolate, while the state has an triaxial shape.  Both, the ground state and the state of 74 Kr are triaxial, but with different  parameter.

EWON Workshop, Prague, May 2007 Collaboration of 74,76 Kr Project CEA Saclay, France E.ClémentA.GörgenW.KortenE.BouchezA.ChatillonA.Hürstel Y.Le Coz A.ObertelliCh.TheisenJ.N.Wilson CEA/DIF, France J.-P. Delaroche M.GirodH.GoutteS.Péru GANIL, Caen, France J.M.Casandjian G. de France HIL Warsaw, Poland T.Czosnyka J.Iwanicki (OLL, Liverpool) P.J.Napiorkowski M.Zielińska (CEA Saclay) Oliver Lodge Lab., Liverpool, UK C.Andreoiu P.A.Butler R.-D.Herzberg D.G.Jenkins G.D.Jones Univ. Of Surrey, Guildford, UK W.N.Catford C.Timis GSI, Darmstadt, Germany F.Becker J.Gerl NBI, Copenhagen, Denmark G.Sleten

EWON Workshop, Prague, May 2007 List of the experiments where GOSIA was recently used ISOLDE (MINIBALL), CERN:  J. Cederkall – 108 Sn, 110 Sn  J. Iwanicki - 88 Kr, 92 Kr  A. Hurst - 70 Se  I. Stefanescu – 68 Cu, 70 Cu  J. Van de Walle – 74 Zn GANIL (EXOGAM), FRANCE:  E. Bouchez – 76 Kr  E. Clement – 74 Kr  M. Zielińska – 44 Ar JYVASKYLA, FINLAND  F. Becker – 78 Kr JAEA, TOKAI, JAPAN:  M. Koizumi - 66 Zn, 68 Zn  T. Hayakawa – 78 Se  A. Osa - 84 Kr  Y. Toh – 70 Ge  M. Zielińska – 96 Mo ANL (Gammasphere), USA  A.Hayes – 178 Hf Next experiments ISOLDE (MINIBALL), CERN:  E. Clement – 96 Sr (Jul 2007)  P.Butler, P. Van Duppen - 182,184 Hg (Aug 2007) JRA6 INTAG

EWON Workshop, Prague, May 2007 Warsaw Coulomb Excitation Heavy Ion Laboratory, Warsaw Univ.  Tomasz Czosnyka  Julian Srebrny  Jędrzej Iwanicki  Paweł Napiorkowski  Magdalena Zielińska (CEA Saclay)  Katarzyna Wrzosek  Katarzyna Hadyńska (UAM, Poznań)  Daniel Piętak (PW, Warsaw)

EWON Workshop, Prague, May 2007 Thank you Thank you