Structural Evolution in the (N,Z,I) Coordinate Frame for A~100

Paddy Regan*

Dept. of Physics

University of Surrey,UK

E-mail: p.regan@surrey.ac.uk

*partially supported by WNSL-Yale Flint and Science Development Fund

Sr-Mo region ‘famous’ for dramatic collapse in I=2+ energy going from N=58 to N=60

Explanation by Federman & Pittel in terms of quadrupoledeformation ‘driving’ T=0 (pn) interaction.

Particularly noticeable forprotons and neutron orbitalswith large spatial overlaps

(e.g., Spin Orbit Partners such as g9/2 and g7/2 in A~100)

Other aspects ?Correlation betweendeformation & populationof ‘deformation aligned’,low-h11/2 neutronintruder orbitals.

Classic ‘chicken and egg’.Does population of orbital ‘cause’ deformationor is deformation there from the core and thush11/2 orbital lies closerto the Fermi Surface ?

How does this situationevolve with spin ?

Alignment (rotational picture at least) driven by Coriolis interaction on high-j, low- orbitals (ie. ones with large jx on collective rotation axis.

Vcor = -jx.

eg.

h11/2 [550]1/2 ‘intruder’

FS for N~57, 2~0.15->0.2

jx

50

82

[550]1/2-

1h11/2

1g9/2

[541]3/2-

= 101Mo,new data,see later

Alignments and rotational motion in ‘vibrational’ 106Cd (Z=48, N=58),

PHR et al. Nucl. Phys. A586 (1995) p351

Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL allows triples to show band-like structures in 101Ru.

see A.D.Yamamoto et al., Phys. Rev. C66 (2002) 024302

TRS calculations for 101Ru by F.R. Xu (Bejing) for differentparity (and signature) configs.

2

=0.2MeV

=0.4MeV

=0.3MeV

=0.6MeV

A.D.Yamamoto et al. Phys. Rev. C66 (2002) 024302

Crossing and alignments well reproduced by CSM, although AHVs see PHR et al., Phys. Rev. C68 (2003) 044313

PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502

24

24

2 :Rotor

0 : Vibrator

)2(

242

),1(2

:Rotor

,2

:Vibrator

22

22

J

J

J

n

JR

JR

J

JJER

JEJJE

EJ

nE

PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502

PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502

Vibrator-Rotator phase change is a feature of near stable (green) A~100.

‘Rotational alignment’ can be a crossing between quasi-vibrational GSB & deformed rotational sequence.(stiffening of potential by population of high-j, equatorial (h11/2) orbitals).

PHR, Beausang, Zamfir, Casten, Zhang et al., Phys. Rev. Lett. 90 (2003) 152502

Simon et al., Nucl. Inst. Meth. A452, 205 (2000)

BLF

TLF

beam tlftlf

blfblf

Ge

TOF ~5-10 ns.ns-s isomers can de-excite in bestopped by CHICO position detector. Delayeds can still be viewedby GAMMASPHERE.

Rochester Group

-1

cos-1

by calculated then is correctionDoppler The

coscoscoscossinsinsinsin)cos(

where

)cos(r.r

by given is angleray -fragment/ the

k )cos( , j )sin()sin( ,i )cos()sin(

k, and j i, rsunit vectoCartesian For

2

2,1'

2121212112

122121

1,2

1,2

EE

rr

rzryrx

z

x

y

Use ‘isomer gating’ to identify h11/2 bandin N=59, 101Mo.

{180}{429,616,772,891}

total, DICprompts

delayed

delayed coincs with prompt 429, 616, 772 & 891 keV

891

772

429

616

180

See PHR, Yamamoto, Beausang, Zamfir, Casten, Zhang et al., AIP Conf. Proc. 656 (2002) p422

‘Weak Coupling’

E/(I-j) E-GOS extension for odd-A

Suggests 11/2- band is an anharmonic vibratoror -soft rotor?

seems to work ok for +ve parity bandsthough

case. 0 even)-(even for the toreduces which

22

2

24 by, simplified becan This

24

24

2

24

2

2

2

2

2

22

jI

E

jI

jRER

RKIRjI

jjIE

jIRjI

jE

jI

jI

I

I

I

EIR

jGOSE

j

jII

Wheldon suggested extension of E-GOS by ‘renormalising’ the rotational energies at the bandhead.

If the band-head spin of a sequence is given by j then substituting Ij in place of I, one obtains,

seems to work ok, h11/2 bands now look like rotors,

Even-Even yrast sequences and odd-A +ve parity only show rotational behaviour after (h11/2 )2 crossing….

Even simpler to just take E(I->!-2) / I for odd-A e.g., R = [ E(15/2- ->11/2-) / (11/2) ]

Other signatures of (perfect) vibrators and rotors

State lifetimes, i.e., B(E2) values and selection rules (eg. n=1).

Need to measure lifetimesB(E2) values of yraststretched E2 decays in

N=58 isotones (best cases)+ h11/2 bands in N=57isotones.

RDM measurements in 103,4Pd, 105,6Cd due Aug. 2004 at Yale to ‘prove’ vibrator-to-rotor picture.

( Frauendorf’s ‘tidal wave’ picture is similar).

From Dudek et al.,Phys. Rev. Lett.59 (1987) p1405

Single particle spectra (for minimised LDMenergy at spin 60 hbar) shows distinct gaps for 2~0.4 at Z=42, N=58 (100Mo).

Note these arethe homologs of A~80 SD (N=42)and A~130 SD (Z=58)

• SD (2=0.4) minimum predicted in 100Mo to become yrast around spins 25-30 h.

• ‘Doubly-Magic’ SD shell gaps at (Z=42, N=58) = 100Mo.

J. Skalski et al.,Nucl. Phys. A617 (1997) p282

DIC Pb + Mo proposal to Be submitted to upcomingGAMMASPHERE PAC (deadline 26th April!)

P.H. Regan1,2, C. Wheldon1,3, A.D. Yamamoto1,2, S. Ashley1, P. Mumby-Croft1, D. Seaborne1, C.Y. Wu4, A.O. Macchiavelli5,

D. Cline4, J.F. Smith6, R.S. Chakrawarthy6, M. Cromaz5, P. Fallon5, S.J. Freeman6, W. Gelletly1, A. Görgen5, A. Hayes4,

H. Hua4, S.D. Langdown1,2, I.Y. Lee5, C.J. Pearson1, Zs. Podolyák1, R. Teng4, J.J. Valiente-Dobón1,

1University of Surrey, UK2Wright Nuclear Structure Laboratory, Yale University, USA

3HMI, Berlin, Germany4Nuclear Structure Research Laboratory, University of Rochester, USA

5Nuclear Science Division, Lawrence Berkeley National Laboratory, USA6Department of Physics and Astronomy ,The University of Manchester, UK

E-GOS story, PHR, Con Beausang, Victor Zamfir, Rick Casten, Jing-Ye Zhang

Money from…EPSRC (UK) , DOE (USA) , NSF (USA), Yale Flint-Science Development Funds

Acknowledgments

International ConferenceOn NUclear STructure, Astrophysics & Reactions University of Surrey, Guildford, UK5-8 January 2005

http://www.ph.surrey.ac.uk/cnrp/nustar05