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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
6/11/2014
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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
6/11/2014
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
6/11/2014
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.
6/11/2014
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
6/11/2014
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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
6/11/2014
Papka et al., Eur. Phys. J. A50, 158 (2014)
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148Nd(3He,n)150Sm
150Sm
6/11/2014
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