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The Decline and Fall of β-Vibrations

Newton: by William Blake (1757-1827)

Newton: by Godfrey Kneller

1689

John Sharpey-SchaferUniversity of the Western Cape

South Africa

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Bohr & Mottelson Vol II

Page 363 !!

Ben on hisBike 2008

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So, WHAT are the 02+ states ??

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Two Neutron Transfer to 154Gd (N=90)

N.B. Log10 scale

Shahabuddin et al; NP A340 (1980) 109

Kπ =

2+ B

andh

ead

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01+

02+ 03

+

04+

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J V Maher et al.PRL 25 (1970) 302

238U(p,t)236U17 MeVθ = 30º

02+

02+ NOT a β-vibration

NOR a pairing vibration

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Configuration Dependentor Quadrupole Pairing

R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). Suggested that Δpp ≈ Δoo >> Δop

for Actinide Nuclei where 02+ states were observed in (p,t) that were not

pairing- or β-vibrations.Suppose there are n prolate and n oblate degenerate levels at the Fermi Surface;

Assume that each pairing matrix element is the same for the same type -a

BUT the prolate-oblate matrix elements are very weak –εa

Then if the prolate n*n matrix is A, the oblate matrix is also A

The matrix for the total system is;

A εA

εA A

Then there are (2n-2) states with ZERO energy and 2 states with energies

E1,2 = -(1 ± ε) na (2n-2)

02+

01+6/11/2014

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Configuration Dependentor Quadrupole Pairing

R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971). Suggested that Δpp ≈ Δoo >> Δop

for Actinide Nuclei where 02+ states were observed in (p,t) that were not

pairing- or β-vibrations.

W. I. van Rij and S. H. Kahana, Phys. Rev. Lett. 28, 50 (1972).

S. K. Abdulvagabova, S. P. Ivanova and N. I. Pyatov, Phys. Lett. 38B, 251 (1972).

D. R. Bès, R. A. Broglia and B. Nilsson, Phys. Lett. 40B, 338 (1972).

took up the suggestion

I. Ragnarsson and R. A. Broglia, Nucl. Phys. A263, 315 (1976).

coined the term “pairing isomers” for these 0+ states

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Single-Particle

Quadrupole Moments

in a deformed W-S

potential

A=155

A=239

N=90[505]11/2-

Abdulvagabova, Ivanova & Pyatov

Phys. Lett. 28B (1972) 215

Low Density of Oblate s-p States Below theFermi Surface

qν

qν

εν

εν

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What is the │02+ > Configuration ?

۞ (t,p) & (p,t) │02+ > is 2pn- 2hn

this gives Jπ but nothing on the orbit.

۞ Single particle transfer would give ln but does not populate │02

+ >.

In { │02+ > + neutron }, look to see

which orbit does NOT couple to │02+ >.

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[505]11/2-

681 keV│02

+ >

Kπ=15/2-

=2γ+ + [505]11/2-

15564Gd91

High-K states

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

Spin I

Excit

atio

n En

ergy

(ke

V)

[521]3/2-

[400]1/2+

[651]3/2+

[642]5/2+

[505]11/2-

[505]+G-

J155G(+)

Missing 11/2-

JFS-S et al. EPJ A47 (2011) 6

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Tshifhwa Madibaen familie

[505]11/2- is BLOCKED from coupling to the core 02

+

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1000

1200

1400

800

600

400

200

0

Ex

(keV)

[521]3/2-

[651]3/2+ [505]11/2-

│02+ >

BLOCKED

155Gd91

Seen by Schmidt et al;

J. Phys. G12(1986)411

in (n,γ) (d,p) & (d,t)

[642]5/2+[402]5/2+

[532]3/2-

[400]1/2+

681 keV

K=3/2-

K=3/2+ {K=11/2-}

Kγ=2

K=1/2-

=2-Ω

K=1/2+

=2-Ω K=15/2-

=2+Ω

996 keV

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[660]1/2+

“Prolate”

[505]11/2-

“Oblate”

Configuration Dependent or QuadrupolePairing; Assume Δpp≈ Δoo>> Δop

82 Neutrons

Prolate Deformation =>

R. E. Griffin, A. D. Jackson and A. B. Volkov, Phys. Lett. 36B, 281 (1971).

W. I. van Rij and S. H. Kahana, Phys. Rev. Lett. 28, 50 (1972).

S. K. Abdulvagabova, S. P. Ivanova and N. I. Pyatov, Phys. Lett. 38B, 251 (1972).

D. R. Bès, R. A. Broglia and B. Nilsson, Phys. Lett. 40B, 338 (1972).

I. Ragnarsson and R. A. Broglia, Nucl. Phys. A263, 315 (1976).

First Excited 02+ states in even-even nuclei are NOT β-vibrations.

In N=88,90 nuclei they are “PAIRING ISOMERS”

Flying Fish[505]11/2-

orbital

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162Yb92 gsb

163Yb93 gsb

[521]3/2-

Jerry Garrett et al, Phys. Lett. B 118, 297 (1982)

Full Unblocked Pairing

Pairing Reduced by Odd Neutron (Blocking)

155Dy89

[505]11/2-

[505]11/2-

even-even

even-odd

The Extruded [505]11/2- orbital does

NOT partake in the Monopole neutron

Pairing

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Jerry Garrett

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0

200

400

600

800

1000

1200

1400

1600

1800

84 86 88 90 92 94 96 98 100

Neutron Number N

Ex

cit

ati

on

En

erg

y (

ke

V) Nd 0+(2)

Sm 0+(2)

Gd 0+(2)

Dy 0+(2)

Er 0+(2)

Sm[505]

Gd[505]

Dy[505]

Er[505]

Systematics of Energies of 02+ and [505]11/2- states

for Z = 60-68 and N = 86-98

02+

[505]11/2-

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0

200

400

600

800

1000

1200

1400

86 88 90 92 94 96 98 100

Neutron Number N

Ga

mm

a P

ho

no

n E

ne

rgy

(k

eV

)

Nd

Sm

Gd

Dy

Er

Yb

Egnd state = ½ ħωβ + ħωγ

Ex (0,0,2,2) = ħωγ + ħ2/I K = 2 Gamma Vibration Band Head Energy

ħωγ

keV

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150Sm(12C,4n)158Er 65 MeV

Tshepo Dinoko, PhD Thesis, UWC

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Tshepo DinokoN=90

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0 2 4 6 8 10 12 140

500

1000

1500

2000

2500

3000

N=92 gsb & SV bands Z=60→70

gsb Ybgsb Ergsb Dygsb Gdgsb Smgsb Nd0^2+ Yb0^2+ Er0^2+ Dy0^2+ Gd0^2+ Sm0^2+ Nd

Spin

Ex

keV

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0 2 4 6 8 10 12 140

500

1000

1500

2000

2500

3000

3500

4000

N=88 gsb & SV bands Z=60→70

gsb Ybgsb Ergsb Dygsb Gdgsb Smgsb Nd0^2+ Er0^2+ Dy0^2+ Gd0^2+ Sm0^2+ Nd

Spin

Ex

keV

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THE PROBLEM for (3He,n) Two Proton Stripping:1. How to get good resolution ΔEn ≈ 2 keV2. How to separate the 1 in 1000 (3He,n) direct reaction events from the flood of (3He,xn) fusion-evaporation events ??

THE SOLUTION:1. Use HPGe detectors having ΔEγ ≈ 2 keV2. (i) Note that Q (3He,n) ≈ + 7 MeV En ≈ 32 MeV Fast while Q (3He,xn) ≈ - 17 MeV En < 6 MeV Slow (ii) To 0+ states, the (3He,n) cross-section peaks at 0°

while for (3He,xn) all neutrons are emitted isotropicallyie. the direct reaction L=0 neutrons to 0n

+ states are focused at 0°While the evaporation neutrons are emitted in all directions.

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We have 2 neutron transfer data to 02+ levels

We would like 2 proton transfer data to compare

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AFRODITE9 HPGe Cloversin BGO shields

target

beam stop

12 Neutron detectorsEach 10x10x60 cm

~2.0m

Pb γ-ray shielding wall

25 MeV3He beam

Schematic set-up for (3He,n) experiments

AFRODITE = AFRican Omnipurpose Detector for Innovative Technologies and Experiments

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Fast Neutronsfrom (3He,n)

Statistical Neutronsfrom (3He,xn)

γ-rays from target γ-rays from beam stop

5927Co32(3He,n)61

29Cu32

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Papka et al., Eur. Phys. J. A50, 158 (2014)

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148Nd(3He,n)150Sm

150Sm

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Paul Papka

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Summary:

Why are 02+ states not β-Vibrations ?

1. There are no 2 phonon states [Kulp et al., PR C77, 061301 (2011)]

2. Strongly populated in 2n transfer, Weakly in 2p transfer; {a truly collective state would not have uneven properties}

3. There are Congruent states to 01+ built on 02

+

Why are the 02+ states in N=88,90 [505]11/2- Pairing Isomers ?

1. The coupling of the [505]11/2- odd neutron to 02+ is BLOCKED

2. The back-bending frequency ħωc is NOT reduced by blocking and is therefore not involved in the monopole pairing3. The Explanation of Griffiths, Jackson and Volkov is more than adequate

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Many thanks to all my collaborators:

Rob Bark, iThemba LABSSuzan Bvumbi, University of JohannesburgTshepo Dinoko, University of Western Cape

Pete Jones, iThemba LABSAmel Korichi, CSNSM Orsay

Kati Juhász, University of DebrecenElena Lawrie, iThemba LABSKobus Lawrie, iThemba LABS

Kevin Li, University of StellenboschTshifhwa Madiba, University of Western CapeSiyabonga Majola, University of Cape Town

Ani Minkova, University of SofiaSimon Mullins, iThemba LABS

Barna Nyakó, ATOMKI DebrecenPaul Papka, University of Stellenbosch

David Roux, University of Western CapeMaciej Stankiewicz, University of Cape TownPreston Vymers, University of Johannesburg

Mathis Wiedeking, iThemba LABSAnd many others