abinio symmetry’adapted++ no’core+shell+model+results++ … · 2016. 9. 19. ·...
TRANSCRIPT
Ab ini&o symmetry-‐adapted no-‐core shell model results
for light and medium-‐mass nuclei
1Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA USA 70803 2Nuclear Physics Ins&tute, 250 68 Řež, Czech Republic
Robert B. Baker1, T. Dytrych1,2, K.D. Launey1, J.P. Draayer1
MoJvaJon
Ab ini&o symmetry-‐adapted no-‐core shell model (SA-‐NCSM)
T. Dytrych, et al., Phys. Rev. LeO. 111 (2013) 252501
(0 μ) oblate
(λ 0) prolate
(0 0) sphere
CollecJve basis based on deformaJon:
MoJvaJon
Ab ini&o symmetry-‐adapted no-‐core shell model (SA-‐NCSM)
T. Dytrych, et al., Phys. Rev. LeO. 111 (2013) 252501
Largest deformaJon + symplecJc excitaJons Lowest spin
(0 μ) oblate
(λ 0) prolate
(0 0) sphere
CollecJve basis based on deformaJon:
MoJvaJon
SymplecJc symmetry arises naturally from first principles.
Ab ini&o symmetry-‐adapted no-‐core shell model (SA-‐NCSM)
T. Dytrych, et al., Phys. Rev. LeO. 111 (2013) 252501 J.P. Draayer, et al., Prog. Part. Nucl. Phys. 89 (2016) 101
Largest deformaJon + symplecJc excitaJons Lowest spin
(0 μ) oblate
(λ 0) prolate
(0 0) sphere
CollecJve basis based on deformaJon:
SA-‐NCSM: 16O, 20Ne, and 42Ti
0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.005
0.005
0.005
0.005
0.01
0.01
0.01
0.01
0.02
0.02
0.05
0.1
0.11
0.12
0.130.14
0.15
0.16
0.18
0.190.2
-4 -2 0 2 4-4
-2
0
2
4
rxy
z
SA-‐NCSM: 16O, 20Ne, and 42Ti
16O 0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.005
0.005
0.005
0.005
0.01
0.01
0.01
0.01
0.02
0.02
0.05
0.1
0.11
0.12
0.130.14
0.15
0.16
0.18
0.190.2
-4 -2 0 2 4-4
-2
0
2
4
rxy
z
SA-‐NCSM: 16O, 20Ne, and 42Ti
Nmax
16O 42Ti
0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.005
0.005
0.005
0.005
0.01
0.01
0.01
0.01
0.02
0.02
0.05
0.1
0.11
0.12
0.130.14
0.15
0.16
0.18
0.190.2
-4 -2 0 2 4-4
-2
0
2
4
rxy
z
SA-‐NCSM: 16O, 20Ne, and 42Ti
0 2 4 6 8 10 12
3 0p-0hall 0p-0hdominant 0p-0h+2p-2hNCSM
Sp(3,R)
NCSM
(b)
Nmax
16O
100
102
104
106
108
1010
1012
0 2 4 6 8 10 12Dim
ensio
n of
mod
el sp
ace
NCSM
Sp(3,R)
(a)
Nmax
12C
Nmax Nmax
NCSM
Symplectic J = 0, 2, 4
NCSM
Symplectic J = 0
Mod
el s
pace
dim
ensi
on
T. Dytrych, et al., Phys. Rev. LeO. 98 (2007) 162503
A few symplecJc irreps capture a major porJon of the physics; for ab ini&o studies, several hundred symplecJc irreps may be needed.
131 irreps
3 irreps 89 irreps
1 irrep
11 12 13 14 15 16 17 18!0
10
20
30
40
50
60
70
80
90
100
11 12 13 14 15 16 17 18
Prob
abili
ty d
istrib
utio
n (%
)
h ̄—— (MeV)
(a)
12C
6h4h2h0h
12 13 14 15 16h ̄—— (MeV)
(b)
16O
(c)
12C, 0gs +
ħΩ (MeV) ħΩ (MeV) ħΩ (MeV)
Symplectic irreps starting at 0p-0h + 2p-2h 3 symplectic irreps starting at 0p-0h
16O, 0gs + 12C, 0gs
+
6 ħΩ 4 ħΩ 2 ħΩ 0 ħΩ
All!
Symplectic!
11 12 13 14 15 16 17 18!0
10
20
30
40
50
60
70
80
90
100
11 12 13 14 15 16 17 18
Prob
abili
ty d
istrib
utio
n (%
)
h ̄—— (MeV)
(a)
12C
6h4h2h0h
12 13 14 15 16h ̄—— (MeV)
(b)
16O
(c)
12C, 0gs +
ħΩ (MeV) ħΩ (MeV) ħΩ (MeV)
Symplectic irreps starting at 0p-0h + 2p-2h 3 symplectic irreps starting at 0p-0h
16O, 0gs + 12C, 0gs
+
6 ħΩ 4 ħΩ 2 ħΩ 0 ħΩ
All!
Symplectic!Sp Sp
12C 16O
ab ini&o wave funcJons
Nmax
16O 42Ti
0.001
0.001
0.001
0.001
0.002
0.002
0.002
0.002
0.005
0.005
0.005
0.005
0.01
0.01
0.01
0.01
0.02
0.02
0.05
0.1
0.11
0.12
0.130.14
0.15
0.16
0.18
0.190.2
-4 -2 0 2 4-4
-2
0
2
4
rxy
z