![Page 1: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/1.jpg)
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
configuration 1 configuration 2
Nuclear Shell Model
![Page 2: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/2.jpg)
3/2-
1/2-
5/2-
3/2-
0
2.12
4.44
5.02
MeV
115B6
1s1/2
1p3/2
1p1/2
1s1/2
1p3/2
1p1/2
0+
1s1/2
1p3/2
1p1/2
2+
Nuclear Shell Model
![Page 3: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/3.jpg)
With a spherical potential:
1s1/2 [2]
1p3/2 [4]
1p1/2 [2]
The g.s. of 11Be : Ip = 1/2-
In reality…..
1/2-
1/2+
0.32 MeV
11Be1s1/2
1p3/2
1p1/2
2s1/2
?
“parity inversion”
What happens if 11Be is deformed?
Level scheme of 114Be7
very artificial
![Page 4: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/4.jpg)
β
Nuclear Deformation
Deformed energy surface for a given nucleus
LDM only always spherical ground state
![Page 5: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/5.jpg)
B = BLDM + Bsh
![Page 6: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/6.jpg)
![Page 7: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/7.jpg)
β
Nuclear Deformation
Deformed energy surface for a given nucleus
LDM only always spherical ground state
Shell correction may lead to a deformed g.s.
* Spontaneous Symmetry Breaking
![Page 8: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/8.jpg)
0+2+
4+
6+
8+
00.082
0.267
0.544
0.903
(MeV)
154Sm
Excitation spectra of 154Sm
cf. Rotational energy of a rigid body
(Classical mechanics)
154Sm is deformed
Nuclear Deformation
![Page 9: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/9.jpg)
Evidences for nuclear deformation
existence of rotational band
0+2+
4+
6+
8+
00.093
0.309
0.641
1.084
(MeV)
180Hf
![Page 10: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/10.jpg)
The energy of the first 2+ state in even-even nuclei
deformed nuclei
K.S. Krane, “Introductory Nuclear Physics”
![Page 11: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/11.jpg)
Spontaneous symmetry breaking
The vacuum state does not have (i.e, the vacuum state violates)
the symmetry which the Hamiltonian has.
(A Nambu-Goldstone mode (zero-energy mode) appears
in order to restore the symmetry.)
![Page 12: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/12.jpg)
偶偶核における E(4+)/E(2+)
deformed nuclei:
E(4+)/E(2+) ~ 3.3
spherical nuclei:
E(4+)/E(2+) ~ 2
K.S. Krane, “Introductory Nuclear Physics”
deformed nucleiE(4+)/E(2+)
![Page 13: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/13.jpg)
Nuclear deformation
Energy change due to nuclear deformation:
deformation in nuclei
deformation in a potential which nucleons feel
deformation dependent shell correction energy
![Page 14: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/14.jpg)
(note) radius of ellipsoid (axial symm.):
Woods-Saxon potential
R0 R(q)
Deformed Woods-Saxon potential
z
q
if the density is deformed, so is the mean-field potential
One-particle motion in a deformed potential
![Page 15: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/15.jpg)
Deformed Woods-Saxon potential
One-particle motion in a deformed potential
breaking of rotational symmetry
angular momentum: is not a good quantum number
(non-conservation)
Let us discuss the effect of Y20 term using the first order
perturbation theory
![Page 16: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/16.jpg)
(note) the first order perturbation theory
Suppose we know all the eigen-values and eigen-functions of H0 :
The eigen-values and the eigen-functions are modified by H1 as:
![Page 17: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/17.jpg)
Deformed Woods-Saxon potential
One-particle motion in a deformed potential
the effect of Y20 term the first order perturbation theory
Eigen-functions for b2=0 (spherical pot.) :eigen-values: Enl (no dependence on K)
The energy change:
positive quantity
![Page 18: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/18.jpg)
Deformed Woods-Saxon potential
One-particle motion in a deformed potential
the effect of Y20 term the first order perturbation theory
β20
E different energy changes for K
( non-degenerate)
For b2 > 0, the energy is lower
for smaller K
Opposite when b2 < 0
K and –K : degenerate
The energy change:
![Page 19: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/19.jpg)
Geometrical interpretation
•K: projection of angular momentum onto z-axis
•nucleon motion: in a plane perpendicular to the ang. mom. vector
•for prolate deformation, a motion with small K is along the longer axis
•therefore, the energy is lowered
•a motion with large K is along the shorter axis, and loses the energy
![Page 20: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/20.jpg)
z
r = Y20
(K=0)
r = Y21
(K=1)
r = Y22
(K=2)
![Page 21: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/21.jpg)
One-particle motion in a deformed potential
Next, a change in wf:
• l does not conserve, and the wf includes several l components
• For axial symmetry (Y20), K does not change (K’ = K),
therefore K is a good quantum number
• Y20 does not change parity. The parity is thus also conserved.
the effect of Y20 term the first order perturbation theory
Eigen-functions for b2=0 (spherical pot.) :
mixing of states which are connected by
![Page 22: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/22.jpg)
Nilsson diagram
![Page 23: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/23.jpg)
With a spherical potential:
1s1/2 [2]
1p3/2 [4]
1p1/2 [2]
The g.s. of 11Be : Ip = 1/2-
In reality…..
1/2-
1/2+
0.32 MeV
11Be1s1/2
1p3/2
1p1/2
2s1/2
?
“parity inversion”
What happens if 11Be is deformed?
Level scheme of 114Be7
very artificial
![Page 24: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/24.jpg)
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
1s1/2
1p3/2
1p1/2
1d5/2
2s1/2
1d3/2
???
Very unnatural.
The 2s1/2 state is more naturally explained
if one considers a deformation of 11Be.
![Page 25: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/25.jpg)
114Be7
1/2-
1/2+
0.32 MeV
11Be
assume some deformation,
and put 2 nucleons in each
level from the bottom
(degeneracy of +K and –K)
Look for the level which is
occupied by the valence
nucleon (the 7th level for 11Be)
Identify the value of Kp for
that level with the spin and
parity of the whole nucleus.
cf. particle-rotor modeldeformation parameter
![Page 26: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/26.jpg)
114Be7
1/2-
1/2+
0.32 MeV
11Be
assume some deformation,
and put 2 nucleons in each
level from the bottom
Look for the level which is
occupied by the valence
nucleon (the 7th level for 11Be)
Identify the value of Kp for
that level with the spin and
parity of the whole nucleus.
![Page 27: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/27.jpg)
Can the level scheme of 94Be5 be explained in a similar way?
cf. 10B(e,e’K+)10LBe (= 9Be+L)
0 3/2-
1.68 1/2+
2.43 5/2-
1/2-2.78
(MeV)
9Be
The 5/2- state at 2.43 MeV:
rotational state with the same
configuration as the g.s. state
(not considered here)
![Page 28: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/28.jpg)
cf. 10B(e,e’K+)10LBe (= 9Be+L)
0 3/2-
1.68 1/2+
2.43 5/2-
1/2-2.78
(MeV)
9Be
a an
9Be
Can the level scheme of 94Be5 be explained in a similar way?
![Page 29: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/29.jpg)
Nobel prize in physics (2008)
“for the discovery of the mechanism of spontaneous
broken symmetry in subatomic physics”
Prof. Y. Nambu
“for the discovery of the origin of the broken symmetry which predicts
the existence of at least three families of quarks in nature”
Kobayashi and Maskawa
![Page 30: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/30.jpg)
Spontaneous symmetry breaking
The vacuum state does not have (i.e, the vacuum state violates)
the symmetry which the Hamiltonian has.
(A Nambu-Goldstone mode (zero-energy mode) appears
in order to restore the symmetry.)
![Page 31: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/31.jpg)
0+2+
4+
6+
8+
00.082
0.267
0.544
0.903
(MeV)
154Sm
Excitation spectra of 154Sm What is 0+ state (Quantum Mechanics)?
0+: no preference of direction (spherical)
Mixing of all orientations with an
equal probability
c.f. HF + Angular Momentum Projection
Nuclear Deformation
![Page 32: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/32.jpg)
Quiz
•Connect the dots.
•The number of lines is not limited.
•Two lines can cross.
•Connect the dots so that one can go from one dot to all the other dots.
There are a few dots.
How do you connect the lines if you want to make the total length of
lines the shortest?
e.g.) Equilateral triangle Connect symmetrically
![Page 33: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/33.jpg)
Quiz
•Connect the dots.
•The number of lines is not limited.
•Two lines can cross.
•Connect the dots so that one can go from one dot to all the other dots.
There are a few dots.
How do you connect the lines if you want to make the total length of
lines the shortest?
(question) how about the case for a square?
![Page 34: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/34.jpg)
(answer)
60 deg. 60 deg.
60deg. 60deg.
Length
cf.
Length
Ref. Takeshi Koike,
“Genshikaku Kenkyu” Vol. 52 No. 2, p. 14
![Page 35: Nuclear Shell Model 1d 1phagino/lectures/nuclth15/...Nuclear Shell Model 3/2-1/2-5/2-3/2-0 2.12 4.44 5.02 MeV 11 5 B 6 1s 1/2 1p 3/2 1p 1/2 1s 1/2 1p 3/2 1p 1/2 0+ 1s 1/2 1p 3/2 1p](https://reader033.vdocuments.site/reader033/viewer/2022050103/5f4235ff2fa4c43f0779e563/html5/thumbnails/35.jpg)
invariant with
rotation by 90 deg.
rotation by 90 deg.
Courtesy: Takeshi Koike
a good example of spontaneous symm. breaking