Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Precision Calculation of ElectromagneticObservables for Light Nuclei
Laura Mertes, Thomas Huther, Robert Roth
1 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Outline
1 Motivation
2 Ab initio calculationsSimilarity Renormalization Group (SRG)No-Core Shell Model (NCSM)
3 Electromagnetic Observables
4 ResultsElectromagnetic Observables of DeuteronM1 Observables of 6LiE2 Observables of 12CM1 Observables of Light Nuclei
5 Summary and Outlook
1 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Motivation
precision calculation of electromagnetic observables
→ provide information about structure of nuclei
→ accessible in experiments
→ examples: electromagnetic moments, transition strengths
ab initio calculations from first principles
→ consistent treatment of electromagnetic observables
→ neglected contributions
2 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Motivation
precision calculation of electromagnetic observables
→ provide information about structure of nuclei
→ accessible in experiments
→ examples: electromagnetic moments, transition strengths
ab initio calculations from first principles
→ consistent treatment of electromagnetic observables
→ neglected contributions
2 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Motivation
precision calculation of electromagnetic observables
→ provide information about structure of nuclei
→ accessible in experiments
→ examples: electromagnetic moments, transition strengths
ab initio calculations from first principles
→ consistent treatment of electromagnetic observables
→ neglected contributions
2 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Motivation
precision calculation of electromagnetic observables
→ provide information about structure of nuclei
→ accessible in experiments
→ examples: electromagnetic moments, transition strengths
ab initio calculations from first principles
→ consistent treatment of electromagnetic observables
→ neglected contributions
2 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Ab initio nuclear-structure calculations
Chiral Effective Field Theory (χEFT)
→ construct consistent interaction and electromagneticoperator
Similarity Renormalization Group (SRG)
→ accelerate convergence
Importance-Truncated No-Core Shell Model (IT-NCSM)
→ solve many-body Schrodinger equation
3 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Ab initio nuclear-structure calculations
Chiral Effective Field Theory (χEFT)
→ construct consistent interaction and electromagneticoperator
Similarity Renormalization Group (SRG)
→ accelerate convergence
Importance-Truncated No-Core Shell Model (IT-NCSM)
→ solve many-body Schrodinger equation
3 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Ab initio nuclear-structure calculations
Chiral Effective Field Theory (χEFT)
→ construct consistent interaction and electromagneticoperator
Similarity Renormalization Group (SRG)
→ accelerate convergence
Importance-Truncated No-Core Shell Model (IT-NCSM)
→ solve many-body Schrodinger equation
3 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
Similarity Renormalization Group (SRG)
initial Hamiltonian induces short-range correlations
idea: prediagonalization of H
→ decoupling of high- and low-energy physics
→ accelerate convergence
Continuous unitary transformation and flow equation
Hα = U†αH0Uα ⇒ d
dαHα = [ηα,Hα]
with initial conditions Hα=0 = H
Uα=0 = 1
antihermitian generator ηα = m2N [Trel,Hα]
4 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
Similarity Renormalization Group (SRG)
initial Hamiltonian induces short-range correlations
idea: prediagonalization of H
→ decoupling of high- and low-energy physics
→ accelerate convergence
Continuous unitary transformation and flow equation
Hα = U†αH0Uα ⇒ d
dαHα = [ηα,Hα]
with initial conditions Hα=0 = H
Uα=0 = 1
antihermitian generator ηα = m2N [Trel,Hα]
4 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
Similarity Renormalization Group (SRG)
initial Hamiltonian induces short-range correlations
idea: prediagonalization of H
→ decoupling of high- and low-energy physics
→ accelerate convergence
Continuous unitary transformation and flow equation
Hα = U†αH0Uα ⇒ d
dαHα = [ηα,Hα]
with initial conditions Hα=0 = H
Uα=0 = 1
antihermitian generator ηα = m2N [Trel,Hα]
4 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
Similarity Renormalization Group (SRG)
initial Hamiltonian induces short-range correlations
idea: prediagonalization of H
→ decoupling of high- and low-energy physics
→ accelerate convergence
Continuous unitary transformation and flow equation
Hα = U†αH0Uα ⇒ d
dαHα = [ηα,Hα]
with initial conditions Hα=0 = H
Uα=0 = 1
antihermitian generator ηα = m2N [Trel,Hα]
4 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
Similarity Renormalization Group (SRG)
initial Hamiltonian induces short-range correlations
idea: prediagonalization of H
→ decoupling of high- and low-energy physics
→ accelerate convergence
Continuous unitary transformation and flow equation
Hα = U†αH0Uα ⇒ d
dαHα = [ηα,Hα]
with initial conditions Hα=0 = H
Uα=0 = 1
antihermitian generator ηα = m2N [Trel,Hα]
4 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉= 〈ψ|UαU†αOUαU†α |ψ〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉 = 〈ψ|UαU†αOUαU†α |ψ〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉 = 〈ψ|Uα︸ ︷︷ ︸〈ψα|
U†αOUα U†α |ψ〉︸ ︷︷ ︸|ψα〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉 = 〈ψ|Uα︸ ︷︷ ︸〈ψα|
U†αOUα︸ ︷︷ ︸|O(α)
α 〉
U†α |ψ〉︸ ︷︷ ︸|ψα〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉 = 〈ψ|Uα︸ ︷︷ ︸〈ψα|
U†αOUα︸ ︷︷ ︸|O(α)
α 〉
U†α |ψ〉︸ ︷︷ ︸|ψα〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Similarity Renormalization Group (SRG)
SRG for arbitrary operators
evolved eigenstates of Hamiltonian |ψα〉 = U†α |ψ〉
expectation value of operator with eigenstates |ψ〉
〈ψ|O |ψ〉 = 〈ψ|Uα︸ ︷︷ ︸〈ψα|
U†αOUα︸ ︷︷ ︸|O(α)
α 〉
U†α |ψ〉︸ ︷︷ ︸|ψα〉
Differential equation
d
dαUα = −Uαηα
so far: bare operator with evolved eigenstates
5 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
No-Core Shell Model (NCSM)
solve time-independent many-body Schrodinger equation
H |ψ〉 = Em |ψ〉
model space is spanned by Slaterdeterminants of single-particle HOstates |Φν〉
truncation via unperturbedexcitation energy Nmax~Ω
convergence with increasing Nmax
as result obtain energies and
eigenstates |ψ(m)〉 =∑
ν C(m)ν |Φν〉
limited by model space size
[S. Schulz, modified]
6 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
Importance Truncated No-Core Shell Model (IT-NCSM)
starting point: approximation of target state
|ψ(m)ref 〉 =
∑νεMref
C(m)ref,ν |Φν〉
importance measure from 1st order perturbation theory
κ(m)ν = − 〈Φν |H|ψ(m)
ref 〉εν−εref
IT-model space is spanned by basis states |Φν〉 with|κν | ≥ κmin
κmin is importance threshold
solve EV problem in new model space
7 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
Importance Truncated No-Core Shell Model (IT-NCSM)
starting point: approximation of target state
|ψ(m)ref 〉 =
∑νεMref
C(m)ref,ν |Φν〉
importance measure from 1st order perturbation theory
κ(m)ν = − 〈Φν |H|ψ(m)
ref 〉εν−εref
IT-model space is spanned by basis states |Φν〉 with|κν | ≥ κmin
κmin is importance threshold
solve EV problem in new model space
7 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
Importance Truncated No-Core Shell Model (IT-NCSM)
starting point: approximation of target state
|ψ(m)ref 〉 =
∑νεMref
C(m)ref,ν |Φν〉
importance measure from 1st order perturbation theory
κ(m)ν = − 〈Φν |H|ψ(m)
ref 〉εν−εref
IT-model space is spanned by basis states |Φν〉 with|κν | ≥ κmin
κmin is importance threshold
solve EV problem in new model space
7 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
Importance Truncated No-Core Shell Model (IT-NCSM)
starting point: approximation of target state
|ψ(m)ref 〉 =
∑νεMref
C(m)ref,ν |Φν〉
importance measure from 1st order perturbation theory
κ(m)ν = − 〈Φν |H|ψ(m)
ref 〉εν−εref
IT-model space is spanned by basis states |Φν〉 with|κν | ≥ κmin
κmin is importance threshold
solve EV problem in new model space
7 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
No-Core Shell Model (NCSM)
Importance Truncated No-Core Shell Model (IT-NCSM)
starting point: approximation of target state
|ψ(m)ref 〉 =
∑νεMref
C(m)ref,ν |Φν〉
importance measure from 1st order perturbation theory
κ(m)ν = − 〈Φν |H|ψ(m)
ref 〉εν−εref
IT-model space is spanned by basis states |Φν〉 with|κν | ≥ κmin
κmin is importance threshold
solve EV problem in new model space
7 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Magnetic Dipole Moment
interaction between external field and nucleus
caused by orbital motion of protons and spins of nucleons
Magnetic dipole operator
M10 =
√3
4πµN
A∑i=1
[gpsz(i) + lz(i)Πp(i) + gnsz(i)Πn(i)]
magnetic moments are defined as expectation values of M10
Magnetic dipole moment
µ =
√4π
3〈J,MJ = J|M10|J,MJ = J〉
8 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Magnetic Dipole Moment
interaction between external field and nucleus
caused by orbital motion of protons and spins of nucleons
Magnetic dipole operator
M10 =
√3
4πµN
A∑i=1
[gpsz(i) + lz(i)Πp(i) + gnsz(i)Πn(i)]
magnetic moments are defined as expectation values of M10
Magnetic dipole moment
µ =
√4π
3〈J,MJ = J|M10|J,MJ = J〉
8 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Magnetic Dipole Moment
interaction between external field and nucleus
caused by orbital motion of protons and spins of nucleons
Magnetic dipole operator
M10 =
√3
4πµN
A∑i=1
[gpsz(i) + lz(i)Πp(i) + gnsz(i)Πn(i)]
magnetic moments are defined as expectation values of M10
Magnetic dipole moment
µ =
√4π
3〈J,MJ = J|M10|J,MJ = J〉
8 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Magnetic Dipole Moment
interaction between external field and nucleus
caused by orbital motion of protons and spins of nucleons
Magnetic dipole operator
M10 =
√3
4πµN
A∑i=1
[gpsz(i) + lz(i)Πp(i) + gnsz(i)Πn(i)]
magnetic moments are defined as expectation values of M10
Magnetic dipole moment
µ =
√4π
3〈J,MJ = J|M10|J,MJ = J〉
8 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Electromagnetic Observables of Deuteron
Electromagnetic Observables of Deuteron
Magnetic dipole moment
0 0.02 0.04 0.06 0.08 0.10.82
0.84
0.86
0.88
0.9
2H
SRG evolved M1 operator
bare M1 operator
α[fm4]
µgs(M1)[µ
N]
Electric quadrupole moment
0 0.02 0.04 0.06 0.08 0.10.26
0.27
0.28
0.29
2H
SRG evolved E2 operator
bare E2 operator
α[fm4]
Qgs(E2)[efm
2]
expectation value of bare operators is α dependent
consistent SRG changes moments by a few percent
9 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Electromagnetic Observables of Deuteron
Electromagnetic Observables of Deuteron
Magnetic dipole moment
0 0.02 0.04 0.06 0.08 0.10.82
0.84
0.86
0.88
0.9
2H
SRG evolved M1 operator
bare M1 operator
α[fm4]
µgs(M1)[µ
N]
Electric quadrupole moment
0 0.02 0.04 0.06 0.08 0.10.26
0.27
0.28
0.29
2H
SRG evolved E2 operator
bare E2 operator
α[fm4]
Qgs(E2)[efm
2]
expectation value of bare operators is α dependent
consistent SRG changes moments by a few percent
9 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of 6Li
M1 Observables of 6Li
bare M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
SRG evolved M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
10
12
contributions to µ by using consistent SRG transformation
small contributions to transition strength
10 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of 6Li
M1 Observables of 6Li
bare M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
SRG evolved M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
10
12
contributions to µ by using consistent SRG transformation
small contributions to transition strength
10 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of 6Li
M1 Observables of 6Li
bare M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
SRG evolved M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
10
12
contributions to µ by using consistent SRG transformation
small contributions to transition strength
10 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of 6Li
M1 Observables of 6Li
bare M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
SRG evolved M1 operators
experiment
6Li
μ(1+) [μN]
B(M
1,0+->
1+)[μ
N2]
0.81 0.82 0.83 0.84 0.85 0.8614.5
15
15.5
16
16.5
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
10
12
contribution of chiral currents: [S. Pastore et al., Phys.Rev.C87, 035503(2013)]
→ to magnetic-dipole moment: weak→ to transition strength: not negligible
11 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
E2 Observables of 12C
E2 Observables of 12C
bare E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
SRG evolved E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
description of strong correlation by rotor model
contributions from consistent SRG are small
12 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
E2 Observables of 12C
E2 Observables of 12C
bare E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
SRG evolved E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
description of strong correlation by rotor model
contributions from consistent SRG are small
12 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
E2 Observables of 12C
E2 Observables of 12C
bare E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
SRG evolved E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
description of strong correlation by rotor model
contributions from consistent SRG are small
12 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
E2 Observables of 12C
E2 Observables of 12C
bare E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
SRG evolved E2 operators
experiment
12C
Q(2+) [efm2]
B(E
2,2+->
0+)[e
2fm
4]
3 4 5 6 7 8 94
5
6
7
8
9
IT-NCSMhω 16 MeVα 0.08fm4
(open) NN+3Nind
(filled) NN+3Nfull
EM+500EGM(450/500)(600/500)(550/600)(450/700)(600/700)
Nmax
2
4
6
8
description of strong correlation by rotor model
contributions from consistent SRG are small
12 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
Magnetic Dipole Moments of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
contribution by performing a consistent SRG depends onnucleus
13 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
Magnetic Dipole Moments of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
contribution by performing a consistent SRG depends onnucleus
13 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
Magnetic Dipole Moments of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
contribution by performing a consistent SRG depends onnucleus
13 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
Magnetic Dipole Moments of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
contribution by performing a consistent SRG depends onnucleus
14 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
M1 Transition Strengths of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
small contributions through consistent SRG
15 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
M1 Transition Strengths of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
small contributions through consistent SRG
15 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
M1 Transition Strengths of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
small contributions through consistent SRG
15 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
M1 Observables of Light Nuclei
M1 Transition Strengths of Light Nuclei
IT-NCSMNN+3Nfull
EM+500
~ω 16 MeV(open) 0.04 fm4
(filled) 0.08 fm4
bare
SRG evolved
experiment
underestimation of M1 transition strengths
16 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Summary and Outlook
contribution of consistent SRG evolution depends on
→ nuclei
→ observable
for 6Li: consistent SRG evolution of M1-operator
→ adds contributions to magnetic moment
→ has small effect on transition strength
Outlook
next step to improve consistency → include two-body currentsfrom chiral EFT
Mlm ∝∫ (
~r × ~j (~r))~∇r lYlm(θ, φ) d3r
17 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Summary and Outlook
contribution of consistent SRG evolution depends on
→ nuclei
→ observable
for 6Li: consistent SRG evolution of M1-operator
→ adds contributions to magnetic moment
→ has small effect on transition strength
Outlook
next step to improve consistency → include two-body currentsfrom chiral EFT
Mlm ∝∫ (
~r × ~j (~r))~∇r lYlm(θ, φ) d3r
17 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Summary and Outlook
contribution of consistent SRG evolution depends on
→ nuclei
→ observable
for 6Li: consistent SRG evolution of M1-operator
→ adds contributions to magnetic moment
→ has small effect on transition strength
Outlook
next step to improve consistency → include two-body currentsfrom chiral EFT
Mlm ∝∫ (
~r × ~j (~r))~∇r lYlm(θ, φ) d3r
17 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Summary and Outlook
contribution of consistent SRG evolution depends on
→ nuclei
→ observable
for 6Li: consistent SRG evolution of M1-operator
→ adds contributions to magnetic moment
→ has small effect on transition strength
Outlook
next step to improve consistency → include two-body currentsfrom chiral EFT
Mlm ∝∫ (
~r × ~j (~r))~∇r lYlm(θ, φ) d3r
17 / 18
Motivation Ab initio calculations Electromagnetic Observables Results Summary and Outlook
Epilog
Thanks to my group
S. Alexa, E. Gebrerufael, T. Huther, R. Roth,S. Schulz, H. Spielvogel, C. Stumpf, A. Tichai,K. Vobig, R. WirthInstitut fur Kernphysik, TU Darmstadt
Thank you for your attention!
Verwendete Schriften
Schriftzug oben:Frutiger light regularKerning 0 % Geviert
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JURECA LOEWE-CSC LICHTENBERG
COMPUTING TIME
18 / 18
