From Nuclear Vibrations to Rotations as a Function of Spin Paddy Regan Dept. of Physics, University of Surrey, Guildford, GU2 7XH, UK e-mail: [email protected].

From Nuclear Vibrations to Rotations as a Function of Spin

Paddy Regan

Dept. of Physics, University of Surrey,

Guildford, GU2 7XH, UK

e-mail: [email protected]

Main physics question, how is spin generated in the nucleus ? and related to this

Are nuclei (with Z=40-50) Rotating or Vibrating ?

* Signatures of vibrator-rotor structural evolution. * 102Ru* an excellent ‘E-GOS’ example. * Odd-A cases; N=57 isotones 99Mo, 101Ru*, 103Pd, 105Cd * Future work, lifetime measurements

* = Experiment performed at WNSL-Yale.

Outline

Date: Mon, 16 Sep 1996 23:03:57 +0100

From: Con Beausang [email protected] To: [email protected]

Hi Paddy,

Greetings from the colonies (i know that this came from Liverpool but that’s because the primitive Yanks haven't got mail up on the new system yet .... give them time.

Anyway I hope that we can do things together here. Let me tell you what we have or hope to have setup and running sometime ....Ge detectors: We will have a variety adding up to a total of around 30 detectors. These comprise a mixed bag of detectors some better than others probably and coming from a variety of sources.

Yale: 4-5 25%ish plus 5 70-80%ish plus plus 4 leps and coming from .....Rochester 8 25%ish

On a longer term I have money to build (or start to build) a inner charged particle ball for p and alpha discrimination etc. There are also a variety of devices that one stumbles across including a plunger (perhaps of somewhat dubious character).

The accelerator runs well to all accounts and beam time should be plentiful. Obviously not all the bits for the Ge array exist right now, which perhaps makes it a good time to start collaborations going. At the moment we (I) an trying to figure out a geometry that will suit the variety of detectors we will have in the short term and also the longer term upgradeability.

Anyway drop me a line with your thoughts etc. All the best

Con

Date: Tue, 21 Sep 1999 11:35:52 +0100 (BST)

From: Miss Heather Newman <[email protected]>

To: [email protected]

Subject: M Phys Placements

Dear Dr. Regan,

I was wondering if you happened to have any additional information on the placement that I have applied for at Yale. Perhaps I could arrange to pop by and talk about it with you later on in the week?

Thanks

Heather Newman

Date: Thu, 23 Sep 1999 16:41:06 +0100 (BST)

From: Dr Patrick H Regan <phs1pr@phmaila>

To: [email protected]

Cc: a.clough, [email protected]

Subject: Re: M Phys Placements

Hi Heather,

can you mail Prof. Con Beausang at Yale to `touch base' re. your placement there. I spoke to him today on the phone and he is looking forward to you going there. He is starting the paperwork which needs to be done (you need something called an IAP66 form to get a J-1 visa before they'll let you into the US!)

Anyway mail Con on [email protected] so he knows who you are...

he's a very nice man!

cheers

Paddy

Other Yale-Surrey collaborations

Subject: Visiting Staff

Date: Tue, 15 Oct 2002 10:38:31 +0100

From: [email protected]

To: [email protected]

Dear Prof. Tostevin,

For information, earlier this morning the Visiting Staff Appointments

Committee approved Professor Cornelius Beausang's appointment of

Visiting Reader with effect from 1st September 2002.

A letter will be sent to him in due course.

Beth Herbert

PA to Professor Bernard L Weiss, Head of School

2

V

2

En

n=0

n=1

n=2

n=3

http://npl.kyy.nitech.ac.jp/~arita/vib

What do we mean by vibrating or rotating nuclei ?

Nuclear Rotations and Vibrations

• What are the signatures (in even-even nuclei) ?– (extreme) theoretical limits

2 (4 ) 4(5) 20

( 1), 3.332 (2 ) 2(

(4 ) 2 = 2.00

3)

( 1

6

2 )N

J

EE N

EE J J

E

E

Other signs of extreme rotation….

Coriolis-induced backbending.

e.g., 135,7Pm, C.W.Beausang et al.,

Phys. Rev. C36 (1987) p602

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 ?

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

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

Can subtract off a reference (core) aligned angular momentum to see effect of quasi-particle alignments as a function of frequency.

2( 1)X

x X ref

ref X ref

I I I K

i I I

I I

ix=5h

CSM ref. Bengtsson Frauendorf and May, At. Data. Nuc. Data. Tab. 35 (1986) p15

Alignment (in the rotational picture) 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-

Ru (Z=44) in the centre of the ‘deformed’region for N=56-58

Anharmonic vibrator for the ground state ‘band’ is the usual explanation for 100Ru and neighbours....butmid-shell (Z=40-50) natureis consistent with largest collectivity in the region.

Q.Are these nuclei deformed or vibrational ?

RuMoZr Pd Cd Sn

Experimental Details (Jan. 2002) 96Zr (9Be,3n)102Ru, pace~100mb

96Zr(9Be,4n)101Ru, pace~800mb

Enriched (85%) 670g/cm2 96Zr foil on 5mg/cm2 natPb support.

Ebeam=44 MeV, lmax~25 h

YRASTBALL array at WNSL

6 clover germaniums @ 90o

5 co-axial detectors @ 50o + 126o

3 co-axial detectors @ 160o

see Yamamoto, PHR, Beausang et al.,

Phys. Rev. C66 (2002)024302

PHR, Beausang, Zamfir, Casten et al., Phys. Rev. Lett. 90 (2002) 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

If we parameterize with (E / J) vs. JCan see if rotor or vibrator by inspection

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

E-GOS plot appears to indicate that Vibrator-Rotator phase change is a feature of near stable (green) A~100 nuclei.

BUT….what is the microscopic basis ?

‘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

Q. Are backbends necessarily due to rotational alignment ?

A. NO ! Can be vibrational – rotational structure change!!

Vib.

rotor

E-GOS for other regions ? Z ~90 ?

rotor

vibrator

(h11/2)2 alignment in A~130 region appears tohave analogous behaviourto (h11/2)2 alignment in A~100 region.

Conclusion?

In many cases, ‘rotational alignment’ is actually acrossing between a quasi-vibrational groundstate configuration and a deformed rotational sequencecaused by stiffening of potential by population of high-j, equatorial (h11/2) orbitals

What about for odd-A (odd-neutron) Cases ?

Detailed spectroscopy allowed by investigating gamma-decay sequences from high-spin states. YRASTBALL used to identify band-like structures in N=57, 101Ru.

Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002) 024302

Quasi-particle alignments and kinematic moments of inertia

ix=10 h11/2

band

h11/2

band

N=57, intruder h11/2 bands

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

2

=0.2MeV

=0.4MeV

=0.3MeV

=0.6MeV

Yamamoto, PHR, Beausang et al., Phys. Rev. C66 (2002) 024302

PROBLEM: Fusion-evaporation reactions can’t study high-spin states (and thus vibrational-rotational transitions, alignments etc.) in stable and neutron-rich systems such as next N=57 isotone, 99Mo.

SOLUTION: Use multi-nucleon transfer (DIC) reactions.

Z

N

Ebeam ~15-20% above Coulomb barrier

beam

target

(i) (ii) (iii)

-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

max

3

1blfmax

3

1tlf

max

3/13/1

0

221

max

1

1

7

2

1

1

7

2

fragments. twoebetween th mom. ang. relative the

and , intosplit is limit, mode rolling In the

25.12

cosec1.4

where, approach,closest of distance by thegiven is

max. issection -cross DIC the whereangle The

. and 219.0

is mom. ang. peripheral max. y theclassicall-Semi

l

AA

ll

AA

l

lll

fmAAE

eZZd

d

grazing

AA

AAVERl

B

T

T

B

blftlf

TBgraz

k

TB

TBCMCM

100Mo + 136Xe @ 750 MeVGAMMASPHERE + CHICO

TLFs

BLFs

elastics

PHR et al., Phys. Rev. C68 (2003) 044313

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

50

82

[550]1/2-

1h11/2

1g9/2

[541]3/2-

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

Carl Wheldon (HMI-Berlin) has 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) ]

Summary and Future Look• 101,102Ru (and neighbours) look like -soft, anharmonic vib. nuclei at low-

spins (eg. E(4+)/E(2+)~2.3)..... BUT also have apparent rotational-like behaviour eg. band-crossing,

alignments etc. • Paradoxically, Coriolis (rotational) effects are largest in nuclei which have

SMALL deformations (ie. require large energies/frequencies to rotate). ‘Vibrational’ A=100 may be the best tests of nuclear Coriolis effects.

• Vibrational – Rotational ‘phase’ change around spin 10? Smooth evolution with crossing of anharmonic vibrational states and rotation-aligned configurations.

• ‘E-GOS’ Plot of E/J vs. J gives model independent information on vibrational-rotational crossing.

• Lifetime (RDM) measurements needed for further work.

many thanks to......• Arata Yamamoto, Scott Langdown (Surrey/Yale students).• 101-102Ru Expt. Con Beausang (+ other Yalies, Des, Gulhan,

Mark, Jo… )• 100Mo+136Xe CHICO, Rochester (Chin-Yen Wu, Doug Cline

et al.,), Manc. (John Smith et al,) + LBNL (Augusto Macchiavelli, Paul Fallon et al.,)

• Vibrator-Rotator (E-GOS) plots, Con B., Rick Casten, Victor Zamfir, Jing-Ye Zhang et al.,

• Odd-A, Carl Wheldon (ex-Surrey now at HMI-Berlin)• TRS calcs, Furong Xu (Peking University).

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

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

GOOD LUCK CON & CINDY! The south (Munster) has risen again!