N=28, Shell Closure and Shapes LEA - COLLIGA – Catania : October 2008 L. Gaudefroy CEA/DIF – Bruyères-le-Châtel Courtesy of M. Rejmund

N=28 -1 st magic number originating from SO interaction -Evolution of SO with isospin -Role of  interaction on structure 28 f 7/2 p 3/2 f 5/2 p 1/2 20 d 5/2 d 3/2 s 1/2 Shell Structure Without SO interaction 20 8 sd fp 40 Ca Ar S Si  (s 1/2 & d 3/2 ) Full Empty Proton removal in N/Z Experimental difficulty N=28 S. Péru et al. EPJA 9, 35 (2000) F. Nowacki and A. Poves from ArXiv First evidence for shell erosion :  -decay studies around 44 S => Unexpected deformations requiered to reproduced T 1/2 O. Sorlin et al. PRC 47, 2941 (1993) 28 f 7/2 p 3/2 f 5/2 p 1/2 20 d 5/2 d 3/2 s 1/2 Shell Structure

N=28 Progressive erosion of the gap predicted in both MF and SM frameworks -E(2 + ) = 1577 keV H. Scheit et al. PRL 77, 3967 (1996) -E(2 + ) = 1297 keV T. Glasmacher et al. PLB 395, 163 (1997) - E(2+) = 1330 keV S. Grévy et al. EPJ A 25 (2005) 2 +  0 + : 770 ± 20 keV NEW -E(2 + ) = keV B. Bastin, S. Grévy et al. PRL 99 (2007)

In this talk Ca Ar S Si  (s 1/2 & d 3/2 ) Full Empty Spher. Def. Part I : -Study of the 46 Ar(d,p) reaction. -Reduction of N=28 Gap -Reduction of SO splittings -Density dependence of SO & tensor L. Gaudefroy et al. – PRL 97, (2006) A. Signoracci & B.A. Brown – PRL 99, (2007) L. Gaudefroy et al. – PRL 99, (2007) -Study of the 44 Ar(d,p) reaction. Part II : g-factor measurement in 43 S.

44 Ar(d,p) 45 Ar : Principle  p,E p d d 28 f 7/2 p 3/2 p 1/2 44 Ar 26 f 5/2 (d,p) transfer reaction 45 Ar 27 p Study of the fp single particle states at N=28 MUST 8 modules Si 960 strips X-Y Exotic beam MeV.A SPIRAL/GANIL CD 2 CATS Beam tracking  p, E p SPEG Spectro. 45 Ar 44 Ar pp EpEp

0 5 E (MeV) l from the shape C 2 S from the relative normalisation 44 Ar(d,p) 45 Ar : Results

44 Ar(d,p) 45 Ar : Exp. vs Theorie Interaction sdpf : S. Nummela et al. PRC63 (2001) Code ANTOINE : E. Caurier & F. Nowacki Satisfactory agreement 45 Ar Ca /2 3/ x 7/2 -

47 Ca 27 & 45 Ar 27 : Shell Model 47 Ca /2 3/ Ar /2 3/ /  d 3/2 20 s 1/2 d 5/2 2 + x f 7/2 p 3/2 Increase of correlations already at Z=18

More exotic N=27 isotones E = E SPE + E Mono + E Multi Orbits HF-MF Correl Z E Multi (MeV) Ca Ar S Si S. Péru et al. EPJA 9, 35 (2000) L. Gaudefroy et al. PRC 78, (2007)

g-factor measurement in 43 S -Mass measurement at GANIL: F. Sarazin et al. PRL 84, 5062 (2000) => Low lying isomeric state (7/2 - ) (3/2 - ) 43 S ns p 3/2 p 1/2 s 1/2 28 f 7/2 f 5/2 d 5/2 d 3/  3/2 - 7/2 - g factor of the isomeric state : -Direct detemination of spin/parity. -Test the WF of the state.  = g I

Principle Fragmentation : ~ S/sec B t I(t) H = - µ B H = g.I B t R(t) G - B G + B R(t) = A cos(  t+  )  = -gB

Results g Schmidt = ± gsgs 2ℓ+1 (j=ℓ ±1/2) Schmidt Exp f 7/2 p 3/2 g s =

Experiment vs. Theories -K=1/2 decoupled band. Rotor Part. Particule.+Rotor GS deformed band:  = /2 - (isom.) not in this band Rather spherical f 7/2 p 3/2 f 5/2 p 1/2 d 5/2 d 3/2 s 1/2 20 Valence space Code ANTOINE : Caurier & Nowacki - Strasbourg

Mean Field : -HFB – Gogny D1S -Blocking -GCM + GOA Ground State: -K=1/2 (from p 3/2 ) -  =0.37 -Decoupling parameter & Inertia parameter=> in agreement with PR States from f 7/2 orbit: -Within 400keV -Around  =0 Experiment vs. Theories L. Gaudefroy et al. To be submitted to Phys. Rev. Lett.

Conclusion Part I : 44 Ar(d,p) -Structure of 45 Ar already points toward an increase of correlations. -SM description of N=27 isotones showing the evolution of multipolar energy. -Agreement with mean field description in this mass region. Part II : g-factor of 43m S -Direct evidence of config. inversion f 7/2 -p 3/2 -Successfully interpreted with 3 models -Deformed ground state K=1/2 band -Rather spherical isomeric state

Collaboration France : CEA-Bruyères-le-châtel, IPNO, GANIL, CEA-Saclay, CSNSM, CENBG, IReS, LPSC Bulgaria : Faculty of Physics Germany : Universität Mainz Hungary : INR Israel : Weizmann Institute Japan : Riken USA : FSU Russia : FLNR/JINR

Conclusions Z=20 Z=18 Z=16 Z=14

Perspectives Z=20 Z=18 Z=16 Z=14 Même phénomène dans 41 Si => 42 Si déformé 44 S 42 Si N=28 43 S 45 S 43 Si 41 Si 43 P Hypothèse: Bandes de rotation partout!  Décrire la structure de ces noyaux dans un cadre SM Travail en cours avec T. Faul L. Gaudefroy et al. soumis à PRC

p 3/2 p 1/2 f 5/2 f 7/2 d 3/ Ar s 1/2 Fermi

Polarisation du coeur 28 f 7/2 p 3/2 f 5/2 p 1/2 20 d 5/2 d 3/2 s 1/2 Shell Structure Without SO interaction 20 8 sd fp 40

3/2 - 7/2 - (7/2 - ) 43 S 43 S vs 44 S S E0 S. Grévy et al. EPJ A 25 (2005) -1n Si coexistence de forme dans 44 S : cf. le tableau  |<  f | a(nlj) |    | 2  (0 1 +,3/2) =  (0 2 +,3/2) = 0.5  (0 1 +,7/2) = 2  (0 2 +,7/2) = 0.4 Recouvrements compatibles avec mixing important entre deux états 0 + (Sphér.  Déform.)

Principe de l’expérience Faisceau primaire : A.MeV Cible : Be Système de détection