university of zululand siyabonga majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ jurogam...
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![Page 1: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/1.jpg)
Low lying collective phenomena in N ~ 90 nuclei
University of Zululand
Siyabonga Majola
UniZulu 2019
![Page 2: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/2.jpg)
Background and motivation- Bohr Approach
),( VTTH rotvib
22
02
222
2
2
2
2
2
2
1)(
2
1
2))1((
2
111
2 '
CCK
KIIBB
Hz
β γ
V(β) V(γ)
Song et al
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Background and motivation - Early success of the Bohr Approach
Early success of the Bohr
in the Rare earth Region
First excited 0+ state
First excited 2+ state K=2+
K=0+
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Background and motivation - 0+ bands do not ALL have the
characteristics predicted for β-bands
Beautiful!!!
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V(β)
β
Ground
Ground
Shape Coexistence
Shape Coexistence
Pure
Mixing
V(β)
β
Background and motivation - Shape Coexistence
Song et al
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Further confusion caused by pairing in the N=90, A ≈ 160
- quadrupole pairing
Give rise to 0+ ground states in even-even
'
,'0
VUG
Background and motivation - Pairing
Monopole term
![Page 7: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/7.jpg)
Further confusion caused by pairing in the N=90, A ≈ 160
- quadrupole pairing
Give rise to 0+ ground states in even-even
' '
'',' )()( '
2220
VUqqGVUG
Background and motivation - Pairing
Quadrupole termMonopole term
![Page 8: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/8.jpg)
Background and motivation
)'(2
).(2' ''
)'(2
)(22
qqVUqqGq
Background and motivation
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• Three modes of excitation, which could lead to
a formation of a first-excited Kπ = 0+ bands.
• Are the first excited zero plus states β, shape co-existence or Quadrupole pairing bands (Second vacuum bands)??
Background and motivation
![Page 10: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/10.jpg)
• To get a deeper insight, this study looks at the spectroscopy of 156Dy and 157Dy. The main objective is to observe the coupling of the h11/2[505]11/2-
neutron orbital in 157Dy, to the first-excited Kπ = 0+ and Kπ = 2+ rotational bands of 156Dy.
Ener
gy
0 0+
0+
2+
156Dy
Ene
rgy
0
157Dy = 156Dy + n
0+ ± 11/2-
0+ ± 11/2-
Background and motivation - Quadrupole pairing Hypothesis test
n → [505]11/2-
ɣ 2+ ± 11/2-ɣ
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• if the first-excited Kπ = 0+ state band is comprised of essentially an h11/2 pair of
neutrons as called for by the quadrupole pairing hypothesis, then the band
formed by the coupling of the h11/2 neutron orbital to the first-excited Kπ = 0+ state
will be absent or Pauli-blocked in 157Dy, thus providing a yes or no test of the
hypothesis.
Ener
gy
0 0+
0+
2+
156Dy
Ene
rgy
157Dy = 156Dy + n
0+ ± 11/2-
0+ ± 11/2-
Hypothesis test
n → [505]11/2-
(h11/2)2
ɣ
Blocked
2+ ± 11/2-ɣ
(h11/2)2
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Experimental Details
• 155Gd (α,2n)157Dy ; 25 MeV ~(2-3 days)
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Experimental Details
• 155Gd (α,2n)157Dy ; 25 MeV ~(2-3 days)
Siya Majola
Department of Physics
University of Jyväskylä, Finland
JUROGAM II ARRAY Collaborators
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Previous in-beam worksHayakawa et al, Eur, Phys. J. A 15, 299-302 (2002)
[521]3/2-[651]3/2- [505]11/2-
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11 New Bands
Results & Discussion- New additions in 157Dy
[521]3/2- [651]3/2-
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Results: New additions in 157Dy
[651]3/2-[523]3/2-
[402]3/2+
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Results: New additions in 157Dy
[505]11/2-
K = 15/2-
New BandsJ. Sharpey-Schafer et al, Eur Phys G
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Results: New additions in 157Dy
J. Sharpey-Schafer et al, Eur Phys G
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Conclusion
• First γ-bands in the odd-even Dy isotope has been observed
• The Tracking of [505]11/2 by its own γ-bands demonstrates the nature of
γ-bands
• No sign of β-band
Ene
rgy
157Dy = 156Dy + n
0+ ± 11/2-
0+ ± 11/2-
n → [505]11/2-
OBSERVED
2+ ± 11/2-ɣ
(h11/2)2
NOT
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End of part 1
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Systematics of β and γ bands in even-
even N ≈ 90 nuclei
Part 2
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Background and motivation-Studied by iThemba LABS
This study ranges from Sm to Yb isotopes, with neutron numbers from N = 88- 92
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15 experiments performed to study 12 nuclei
Nucleus
(N)
Reaction(s) Beam
energy
(MeV)
Target
thickness
Statistics
events
Spectrometer(s
)
150Sm
(88)
136Xe(18O,4n),
148Nd(α,2n)
75,
25
∼ 5 mg/cm2
5 mg/cm2
0.5 × 109 γγ
2 × 1010 γγγ
Afrodite,
Jurogam II
152Gd
(88)
152Sm (α,4n) 45 5mg/cm2 0.5 × 109 γγ Afrodite
154Dy
(88)
155Gd(α,4n) 37.5 3.2 mg/cm2 0.4 × 109 γγ Afrodite
156Er
(88)
147Sm(12C,3n) 65 6 mg/cm2 1.4 × 109 γγ Afrodite
158Yb
(88)
144Sm(18O,4n) 78 3 mg/cm2 2.0 × 109 γγ Afrodite
154Gd
(90)
152Sm(α,2n) 25 4 mg/cm2 0.5 × 109 γγ Afrodite
156Dy
(90)155Gd(α,3n),
148Nd(12C,4n)
25,
65
0.98 mg/cm2
1.53 mg/cm21.4x109 γγ,
2.0 × 109 γγγ
Jurogam II,
Gammasphere
158Er
(90)
150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite
160Yb
(90)
147Sm(16O,3n) 73 4 mg/cm2 2.0 × 109 γγ Afrodite
158Dy
(92)
156Gd(α,2n),155Gd(α,n)
27,
25
11 mg/cm2,
0.98 mg/cm2
1.1 × 109 γγ,
1.4x109 γγ
Afrodite,
Jurogam II
160Er
(92)
152Sm(12C,4n) 64 5 mg/cm2 2.7 × 109 γγ Afrodite
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148Nd(12C,4n)156Dy, Gammasphere
Siyabonga Majola, Darryl Hartley, Lee Riedinger
S. Majola, D. Hartley, L. Riedinger, et al PRC 91 034330 (2015)
D. Hartley, L. Riedinger, S. Majola, et al PRC 95 014321 (2017)
g
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152Sm(a,2n)154Gd
g
g
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147Sm(16O,3n)160Yb, AFRODITE
g
Rob Bark
S. Majola et al Phys. Rev. C (2019)
R. A. Bark, J. F. Sharpey-Schafer, et al., Phys. Rev. Lett. 104,
022501 (2010).
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156Gd(a,2n) 158Dy, AFRODITE
S. Majola, et al., PRC, to be published
Maciek Stankiewicz
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Also:
156Er JM Rees et al, PRC83, 044314(11)
ES Paul et al, PRC79 044324(09)160Er K Dushing et al. PRC73 014317(06)
J Ollier et al, PRC, 064322 (09)158Dy T Hayakwaw PRC 68, 067303(03)
152Sm P Garrett et al PRL 103, 062501(09)
Beta & Gamma Bands identified to ~12h for the first time
in many cases
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Relativistic Mean Field “Density Functionals” Coupled
to the:
Bohr Hamiltonian
Zhipan Li Zhi Shi
Jie Meng Bangyan Song
Chunyan Song
Jiangjing Yao
Shuangquan Zhang
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Important point:
All parameters fixed. Nothing fitted to
positive-parity bands
Up Next:
Calculated quantities compared with
observables
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The determination of a comprehensive set of level
energies and branching ratios between bands
allows their electromagnetic properties to be
compared to nuclear models. To come to an
understanding of the properties of these bands,
the data obtained in this work are explained using
a relativistic mean-field combined with the Bohr
Hamiltonian.
Beta & Gamma Bands identified to ~12h for the first time
in many cases
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Calculated Energies
(lines)
compared to experiment
(points)
ground band
band
band
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Theory
Exp.
g
158Yb
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Theory
Exp.
g
- predicts different moments of inertia for
and bands
Impressive!!!
156Er
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Theory
Exp.
g
- Predicts the order very well
- Predicts signature splitting very well
- Ground parallel to bands
154Dy
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Theory
Exp.
g
- Predicts the order very well
- Predicts signature splitting very well
- Ground parallel to bands
152Gd
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Theory
Exp.
g- N= 88 covered extremely well by the theory
150Sm
Not so good!
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Theory
Exp.
g
Beautiful!!!
- predicts different moments of inertia for
and bands
- Predicts the order very well
- Ground parallel to bands
160Yb
![Page 40: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/40.jpg)
Theory
Exp.
g
- Same story here
Great!!!
158Er
![Page 41: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/41.jpg)
Theory
Exp.
g
- predicts similar moments of inertia for
and bands
- Predicts the order very well
- Again! ground parallel to bands
Great!!!
156Dy
![Page 42: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/42.jpg)
Theory
Exp.
g
Great!!!
154Gd
![Page 43: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/43.jpg)
Theory
Exp.
g
Good!!!
- N= 90 covered extremely well by the theory
152Sm
![Page 44: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/44.jpg)
Bandhead energies: 02+ states
- Most N = 92 underestimated
![Page 45: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/45.jpg)
Bandhead energies: 22+ states
- Trends are generally good
![Page 46: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/46.jpg)
Branching Ratios -band
Ground
-band I
(I – 2)(I – 2)g
N=88 N=90
![Page 47: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/47.jpg)
Branching Ratios -band
Ground
-band I
(I – 2)Ig
N=88 N=90
![Page 48: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/48.jpg)
160Yb160Yb
Branching Ratios -band
Ground
-band I
(I – 2)(I – 2)g
N=88 N=90
![Page 49: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/49.jpg)
Branching Ratios -band
-band I
(I – 2)
(I – 2)g
N=88 N=90
![Page 50: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/50.jpg)
Branching Ratios -band
-band I
(I-2)
Ig
N=88 N=90
![Page 51: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/51.jpg)
Staggering N=88 N=90
![Page 52: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/52.jpg)
Staggering N=88 N=90
![Page 53: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/53.jpg)
Second minima in Er, Yb isotopes (N=88)
N= 88
![Page 54: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/54.jpg)
Second minima in Er, Yb isotopes (N=90)
N= 902 ~ 0.45 and ~ 10 in
Er, Yb isotopes
Are |02+> states, Triaxially
super deformed bands??
![Page 55: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/55.jpg)
In order to produce a complete and
definitive microscopic picture of the so-
called β and γ bands, we have carried
out an extensive systematic study of
even-even nuclei in the 160 mass
region.
Conclusion
![Page 56: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/56.jpg)
Based on this data:
“From Sm to Dy, the |02+> ” are well
described as “-bands”
Maybe not “harmonic vibrations” but are
essentially well described as solutions
of the Bohr Hamiltonian with a realistic
potential
Conclusion
![Page 57: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/57.jpg)
Second minima for Er and Yb isotopes is located at
~2 ~ 0.45 and ~ 10.
This may imply that the 02+ bands in Er and Yb
isotopes are Triaxially super deformed bands
Conclusion
![Page 58: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/58.jpg)
Energy staggering and PES plots show
that the almost all the N=88 isotones
from Sm to Yb are soft.
Conclusion
![Page 59: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/59.jpg)
NtshangaseR. Bark
L. Mdletshe
A. Sithole
Bucher
T. Dinoko
E. Lawrie
J. Sharpey-Schafer
J. Lawrie
G. Zimba
+
AFRODITE CREW
JYVASKYLA
GAMMASPHERE…
iThemba LABS
University of Zululand
University of the Western Cape
University of Cape Town
Stellenbosch University
University of Johannesburg
Zhipan Li
Zhi Shi
Jie Meng
Bangyan Song
Chunyan Song
Jiangjing Yao
Shuangquan Zhang
……
University of South West China
Peking University
Beihang University
EXPERIMENTALISTS
RELATIVISTIC MEAN FIELDERS
& COLLECTIVE MODELLERS:
![Page 60: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/60.jpg)
Moment of Inertia: Inglis-Belyaev formula
Mass Parameters calculated in Cranking approximation
Improved by using Thouless-Valatin moments-of-inertiaZ.P. Li. et al PRC 86, 034334 (2012)
![Page 61: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/61.jpg)
Re-cast Bohr Hamiltonian
Need to determine I’s, B’sT. Niksic et al PRC 79, 034303 (2009)
Z.P. Li et al., PRC 79, 054301 (2009)
![Page 62: University of Zululand Siyabonga Majola€¦ · 1.53 mg/cm2 1.4x109 γγ, 2.0 × 109 γγγ Jurogam II, Gammasphere 158Er (90) 150Sm(12C,4n) 65 1 mg/cm2 4.2 × 108 γγ Afrodite 160Yb](https://reader034.vdocuments.net/reader034/viewer/2022052016/602e46faf40361788c11b736/html5/thumbnails/62.jpg)
Vcoll from Relativistic
Mean Field
Parameters of PC-F1 functional
And pairing strengths adjusted to
ground observables of spherical
nuclei (binding energies, pairing
gaps, charge radii etc)
T. Niksic et al PRC 79, 034303 (2009)
Z.P. Li et al., PRC 79, 054301 (2009)