Abinio symmetry’adapted++ no’core+shell+model+results++ … · 2016. 9. 19. ·...

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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

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