Picosecond Lifetime Measurements in ‘Vibrational’ Cadmium and Palladium Isotopes

Paddy ReganDepartment of Physics, University of Surrey

Guildford, GU2 7XH, UK

p.regan@surrey.ac.uk

Survey of Even-Even Cadmium Isotopes

A. Aprahamian et al., Phys. Lett. B 140, 22 (1984)

Nomically ‘vibrational’ nuclei agree very well with CSM, (rotational) description.

ix = 10 h= (h11/2)2

Odd-A Cadmium Isotopes: Vibrators or

Rotors ?• Odd-A Cd A = 105 – 123, all have a ‘rotational’ bands built upon the 11/2

- state

• For 105-109Cd, from the B(E2: 15/2- → 11/2

- ) value

rotational structure associated with rotational alignment coupling (RAC)†

• B(E2: 15/2- → 11/2

- ) for 107Cd suggests coupling

of unpaired neutron to vibrational core (PVC)‡† D.C. Stromswold et al, Phys. Rev. C 17 (1978) 143 F.M. Stephens, R.M. Diamond, S.G. Nilsson, Phys Lett B 44 (1973) 429

‡ O. Häusser et al, Phys Lett B52 (1974) 329 G. Alaga, V. Paar, V. Lopac, Phys Lett B43 (1973) 459 G. Dracoulis, R. Chapman et al., Part. Nucl. 4 (1972) 42

Crossing and alignments well reproduced by CSM, but 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

ix=10h

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

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-

see PHR, G.D. Dracoulis et al., J. Phys. G19 (1993) L157

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

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

PHR, C. Wheldon et al., Acta Phys. Pol. B36 (2005) 1313

B(E2) Signatures of Collectivity– For a perfectly harmonic oscillator:

– For axially deformed rotor (Bohr and Mottelson) :

– For U(5) of the IBA (valence limited case, see Casten and Warner, Rev. Mod. Phys. 60 (1988) 389 ; Kern et al., Nuc. Phys. A593 (1995) 21 .)

220

2 2016

5:2 KJKJQeJJEB ifif

NJJEB if :2

02:2 :2 EBNJJEB if

02:222

4

12:2 EB

N

INIIIEB

B(E2: I -> 1-2) Theoretical Limits

0

50

100

150

200

250

0 5 10 15 20 25

Spin,

B(E

2: J → J

-2), W

.u.

Vibrator: 02:2 :2 EBNJJEB if

220

2 2016

5:2 KJKJQeJJEB ifif

Rotor:

U(5) limit (for 106Cd):

02:222

4

12:2 EB

N

INIIIEB

Rotor

U(5) limit (for 106Cd)

Vibrator

Recoil (Doppler) Distance Method

θ

Es

E0

cos10 c

vEES

12C @ 60MeV98Mo

98Mo(12C, xn)110-xCd98Mo(12C, αxn)106-xPd

)()(10223.1

12

5522

sMeVEbeEB

SPEEDY and NYPD

SPEEDY γ-ray array, 4 clovers each at 41.5° and 138.5°.

New Yale Plunger Device:Thin target + 197Au stopper. Piezoelectric motor to control target-stopper distance.Capacitance measured to giveaccurate distance value.

R. Krucken et al.,J. Res. Nat. Inst. St.Tech. 105 (2000) 53.

RDM and DSAM Expts. at WNSL, August 2004

• Experiment to determine the various B(E2) values of 103,4Pd and 106,7Cd

• Fusion-evaporation reaction used to produce the nuclei of interest

98Mo(12C,3n)107Cd + ,p2n)107Ag98Mo(12C,4n)106Cd + ,p3n)106Ag98Mo(12C,α2n)104Pd98Mo(12C,α3n)103Pd

RDM and DSAM Expt. at WNSL, August 2004

• RDM, 98Mo target, ~900 μg/cm2 , v/c~0.7-.8% (~2 m/ps)

• DSAM, 98Mo target.~500 g/cm2 on 9 mg/cm2 197Au.

• Distances 11, 14, 18, 23, 28, 41, 56, 127, 330, 2008 m.. (tof) ~ 22, 28, 36,46, 56, 82, 102, 154, 660, 4000 ps)

• 2 coincident γ-ray events within a time window of ~ 50ns

• (a ‘ b) matrices sorted for each plunger distance

Differential Decay Curve Method (DDCM)

• Lifetime deduced from following equation: where

• For an intra-band direct feeding transition, the above equation reduces to

dx

xdQv

xQII

bxQ

xij

hhi

ij

hiijij

.

ijij

ijij SU

UQ

Gate

Ihi = Uhi + Shidt

dS

UUx

ij

hiij )(

Iij = Uij + SijG. Bohm, A. Dewald et al., NIM A329 (1993) 248S. Harrissopulos, Nucl. Phys. A683 (2001) 157

Differential Decay Curve Method

dtdSU

xC

C)(

C

B

A

)()(10223.1

12

5522

sMeVEbeEB

Direct Gating (on SB) from above

Nomenclature: U denotes “Unshifted” Transition

S denotes “Shifted” Transition

G. Bohm, A. Dewald et al., NIM A329 (1993) 248

Differential Decay Curve Method

• Inaccurate lifetimes may be obtained, for 2+ or 4+ gated due to “de-orientation’’.

C

B

A

BB

B

USdt

dU

x

)(

Direct Gating (on UC) from below

60 MeV beam energy

104Pd: N=58W. Andrejtscheff et al, Nucl. Phys. A448 (1986), 301

J.A. Grau et al, Phys. Rev. C14 (1974), 2297

Lifetime Plots for 2+ → 0+ in 104Pd

Average τ = 14.7(1.0)psB(E2:2-0) = 36(2) W.u.

forward backward

S. Raman et al., At.Data Nucl.Data Tab. 36 1 (1987) (2+, 104Pd) = 14.3(9)ps, 

RDM DDCM Lifetime Analysis in 107Cd

dt

dS

Ux

ij

ij)( 19/2

-

15/2

-

11/2

-

798keV

515keV

D.C. Stromswold et al, Phys. Rev. C17 (1978) 143

K. Andgren, S.F.Ashley, PHR, E. McCutchan et al., in press J. Phys. G (2005)

cf. (15/2-) = 23.5(1.5)ps O. Häusser et al, Phys Lett B52 (1974) 329

DDCM Lifetime Analysis in 107Cd

515 keV 798 keV

= 28.2(1.0)W.u. = 24.5(4.3) W.u.

Unevaluted report for 956 keV decay of Vishnevsky et al., ,Sov. Jour. Nucl. Phys. 54, 191 (1991) gives =1.15(43)ns -> B(E2:23/2- ->19/2-) = 30(11)Wu.

~0.36(6)ps

very preliminary !!not to be quoted

= 99.6 (16.5) W.u. !!

DSAM data can give information on higher lying (<1ps) lifetimes in 107Cd.

B(E2) ratio plot for 11/2- band in

107Cd

0.87

0

1

2

3

4

5

5.5 7.5 9.5 11.5 13.5 15.5 17.5

Spin,

Vibrational

Axial symmetricperfect rotor

U(5) limit for 106Cd

B(E2: 15/2 -> 11/2) = 0.085e2b2 = 28.2(1.0) Wu B(E2: 19/2 -> 15/2) = 0.074e2b2 = 24.5(4.3) WuB(E2: 23/2 -> 19/2) ~ 0.280e2b2 = 100(17) Wu

106Cd Challenges: Isomers

• τ = 90ns, four quasi-particle isomer at 4660 keV (12+)

• Various, ns isomers, associated with two quasi-particle configurations which feed low-lying states

W. Andrejtscheff et al, Nucl. Phys. A437 (1985), 167

106Cd Challenges: Doublets

P.H. Regan et al, Nucl. Phys. A586 (1995), 351

106Cd: High Spin States

602 keV12+ ->10+

= 13(1) ps -> B(E2:12->10)= 27(2) Wu

‘nti-magnetic rotation in 106Cd, A. Simons, R. Wadsworth et al., PRL 91 (2003)

B(E2:2+ –>0+) = 27 Wu

B(E2:4+->2+) = 44 Wu

B(E2:12+–>10+) = 27(2) Wu

B(E2:18+->16+) = 50(4) Wu

B(E2:20+->18+) = 47(6) Wu

B(E2:22+->20+) = 27(2) Wu

B(E2:24+->22+) = 20(2) Wu

Conclusions

• RDM (+DSAM) for B(E2)s in 106,7Cd, 103,4Pd

• B(E2) values for the 19/2- and 15/2

- states in 107Cd suggests rotational behaviour.

• Future work, B(E2)s for 106,107Cd & 103,104Pd

• (n,n’) work to get lower lying lifetimes in (stable) 106Cd, see talk by A. Linnemann

Acknowledgements

University of Surrey:P.H. ReganS.F. AshleyN.J. Thomas

University of Paisley:K.L. KeyesA. Papenberg

CCLRC Daresbury:D.D. Warner

Yale University:E.A. McCutchanN.V. ZamfirR.F. CastenD.A. MeyerC. PlettnerJ. VinsonV. WernerE. Williams

SUNY, Stony Brook:N. PietrallaG. Rainowski

Clark UniversityG. Gürdal

Royal Institute of Technology, Stockholm:K. Andgren

Istanbul University:L. AmonR.B. CakirliM.N. Erduran

Uni. de São Pãulo:R.V. Ribas

This work is supported by EPSRC (UK), U.S. Dept. Of Energy, under Grant No.DE-FG02-91ER-40609 and by the Yale University Flint and Science Development Fund