Ab Initio Predictions of Light Nuclei · 2018. 11. 9. · of Light Nuclei Anna McCoy TRIUMF Theory...

2017-10-18 Dis

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Ab Initio Predictions of Light Nuclei

Anna McCoy TRIUMF Theory Department

Ab initio nuclear theory

!2

M. A. Caprio, University of Notre Dame

Goals of ab initio nuclear structureFirst-principles understanding of nature Nuclei from QCDWhat is the origin of simple patterns in complex nuclei?

B. Schwarzschild, Physics Today 63(8), 16 (2010).

Solving the nuclear many-body problem

!3

▪Also called no-core shell model (NCSM)

Nuclear many-body problem

Solve many-body Schrodinger equation

AX

i

� ~2

2mir2i +

12

AX

i,j=1

V(|ri� rj|) = E

Expanding wavefunctions in a basis

=1X

k=1

ak�k

Reduces to matrix eigenproblem0BBBBBBBBBB@

H11 H12 . . .H21 H22 . . ....

...

1CCCCCCCCCCA

0BBBBBBBBBB@

a1a2...

1CCCCCCCCCCA= E

0BBBBBBBBBB@

a1a2...

1CCCCCCCCCCA

No-core shell model (NCSM)

!3

Harmonic oscillator basis

– Basis states are configurations, i.e., distributions of particlesover harmonic oscillator shells (nlj substates)

– States organized by total number of oscillator quanta abovelowest Pauli allowed number Nex.

– Basis must by truncated, typically by restricting number ofoscillator quanta to Nex Nmax

N = 2n+ `

Nex = 0

Nex = 2

How large must Nmax be?

Harmonic oscillator basis

!4

Convergence challenges

!5

2H

3He4 He

6 Li

8 Be

12 C

16 O

20 Ne24 Mg

100

102

104

106

108

1010

1012

Dimension

0 2 4 6 8 10 12 14 16 18 20Nmax

�

�

��

��

�� +

-��

-��

-��

-��

-��

-��

�(��

)

�� ℏω (��)

Results for calculations in a finite space depend upon:

• Many-body truncation Nmax • Parameter associated with harmonic oscillator length ℏω

�

�

��

�� +

��

��

��

��

��

� �(��

)

�� ℏω (��)

Goal

+ γ

2He (α, γ) 6Li

Obtain accurate predictions using finite computational resources

Symplectic no-core configuration interaction (SpNCCI)

No-core shell model with continuum (NCSMC)

!6

63Li3-2 From ENSDF

63Li3-2

Adopted Levels, Gammas 2002Ti10,1988Aj01 (continued)

6Li Levels (continued)

E(level) Jπ T1/2 XREF Comments

24890 55 4− 5.32 MeV 11 B %IT=?; %n=?; %3H=?T=1

26590 65 2− 8.68 MeV 13 B %IT=?; %n=?; %3H=?; %α=?T=1

31.×103? (3+) B %3H=?; %α=?Γ: broad.

γ(6Li)

Ei(level) Jπi

Eγ E f Jπf

Mult. Comments

2186 3+ 2186 0.0 1+ E2 Γγ=4.40×10−4 eV 34; B(E2)(W.u.)=16.5 13

3562.88 0+ 3561.75 0.0 1+ M1 Γγ=8.19 eV 17; B(M1)(W.u.)=8.62 18

4312 2+ 4310 0.0 1+ E2 Γγ=5.4×10−3 eV 28; B(E2)(W.u.)=6.8 35

5366 2+ 5363 0.0 1+ M1 Γγ=0.27 eV 5; B(M1)(W.u.)=8.3×10−2 15

1+ 0.0 stable

3+ 2186 24 keV 2

0+ 3562.88 8.2 eV 2

2+ 4312 1.30 MeV 10

2+ 5366 541 keV 20536

3M

143

10E

235

61.7

5M

121

86E

2

Level Scheme

Adopted Levels, Gammas 2002Ti10,1988Aj01

63Li3

2

d+4He threshold

Excitation energy State width

Taking advantage of approximate symmetries

!7

Sp(3,R):

• Describes collective modes • Giant quadrupole and monopole resonances • Nuclear rotations

• Connects different nuclear shapes (shape coexistence) • Conserved by the kinetic energy J. Phys. G: Nucl. Part. Phys. 35 (2008) 123101 Topical Review

Figure 2. A traditional (βγ ) plot, where β (β ! 0) is the radius vector and γ (0 " γ " π/3)is the azimuthal angle, demonstrates the relationship between the collective model shape variables(βγ ) and the SU(3) irrep labels (λµ).

a prolate shape, irreps with λ = 0 correspond to an oblate geometry, and irreps with λ = µdescribe a maximally asymmetric shape. A spherical nucleus is described by the (00) irrep.

In short, the SU(3) classification of many-body states allows for a geometrical analysisof the eigenstates of a nuclear system via relations (54) and (55) and hence gives insight intophenomena associated with nuclear deformation.

5. Symplectic shell model

The symplectic model [10–12] is a microscopic algebraic model of nuclear collective motionthat includes monopole and quadrupole collective vibrations as well as vorticity degrees offreedom for a description of rotational dynamics in a continuous range from irrotational torigid rotor flows. It can be regarded as both a microscopic realization of the successfulphenomenological Bohr–Mottelson–Frankfurt collective model and a multi-h̄% extension ofthe Elliott SU(3) model.

While the NCSM divides the many-nucleon Hilbert space into ‘horizontal’ layers ofNh̄% subspaces, the symplectic model divides it into ‘vertical’ slices of Sp(3, R) irreduciblerepresentations, which is schematically illustrated in figure 4. The symplectic model thusallows one to restrict a model space to vertical slices that admit the most important modes ofnuclear collective dynamics.

The symplectic model is based on the 21-dimensional algebra sp(3, R) and has a veryrich group structure (see figure 3). In particular, there are two important subgroup chainsthat unveil the physical content of the symplectic model: the shell model subgroup chainassociated with the Elliott SU(3) group and the collective model chain related to the generalcollective motion GCM(3) group. The intersection of these chains is the group of rotationsSO(3).

15

T. Dytrych

M. A. Caprio

Nex

Nex

T+VH=V+T

H≈T

D. R. Rowe, A. E. McCoy and M. A. Caprio, invited comment, Phys. Scripta, 91 0330003 (2016).

Symplectic no-core configuration interaction (SpNCCI)

!8

• Construct nuclear Hamiltonian in an Sp(3,R) basis.

• Basis states are linear combinations of original harmonic oscillator states with Sp(3,R) symmetry.

Truncation by Sp(3,R) symmetry

!9

Nex=0 Nex=2Nex=4 Nex=6

6Li 11+Sp(3,R)

10-3

10-2

10-1

100

Probability

Sp(3,R)xSU(2) irrep σS

Allow higher Nmax states that are necessary for describing, e.g., charge radius and B(E2), to be included.

A. E. McCoy, M. A. Caprio and T. Dytrych, Ann. Acad. Rom. Sci. Ser. Chem. Phys. Sci. 3, 17 (2018).

Bound states vs. resonances

!10

Free particle has continuum of energies

T =p2

2m

Particle in potential has discrete, resonant, and continuous energies

E =ℏ2π2n2

2mL2

Bound particle has discrete energies

110To find the Scattering matrix – Coupled channels

3. Solve equation with respect to the scattering matrix U

4. You can demonstrate that the solution is given by:

§ Scattering phase shifts are extracted from the scattering matrix elements

Rc ′c

k ′c a

µ ′c v ′c′I ′c (k ′c a)δci −U ′c i ′O ′c (k ′c a)[ ]

′c

∑ =1

µcvc

Ic(k

ca)δ

ci−U

ciOc(k

ca)[ ]

U = Z−1Z*, Zc ′c = k ′c a( )

−1Oc(k

ca)δ

c ′c − k ′c a Rc ′c ′O ′c (k ′c a)

U = exp(2iδ)

€

δ

Need to include dynamics properties “include continuum effects”

NCSMC

123NCSMC phenomenology

EλNCSM energies treated as adjustable parameters

Cluster excitation energies set to experimental values

Lawrence Livermore National Laboratory 9 LLNL#PRES#650082

… to be simultaneously determined by solving the coupled NCSMC equations

HNCSM h

h HRGM

!

"

####

$

%

&&&&

c

γ

!

"

###

$

%

&&&= E

1NCSM g

g NRGM

!

"

####

$

%

&&&&

c

γ

!

"

###

$

%

&&&

A ′ν

∧

H Aν

∧

€

r'

€

r A !ν∧

Aν∧

€

r'

€

r

H Aν∧

€

rA( ) Aν∧

€

rA( )Eλ

NCSM δλ !λ δλ !λ

Ψ (A) = cλλ

∑ ,λ + dr γ v (r )∫ Âν

ν

∑ ,νA− a( )

a( )

rHΨ(A) = EΨ(A)

89

Coupled NCSMC equations

Lawrence Livermore National Laboratory 9 LLNL#PRES#650082

… to be simultaneously determined by solving the coupled NCSMC equations

HNCSM h

h HRGM

!

"

####

$

%

&&&&

c

γ

!

"

###

$

%

&&&= E

1NCSM g

g NRGM

!

"

####

$

%

&&&&

c

γ

!

"

###

$

%

&&&

A ′ν

∧

H Aν

∧

€

r'

€

r A !ν∧

Aν∧

€

r'

€

r

H Aν∧

€

rA( ) Aν∧

€

rA( )Eλ

NCSM δλ !λ δλ !λ

Ψ (A) = cλλ

∑ ,λ + dr γ v (r )∫ Âν

ν

∑ ,νA− a( )

a( )

rHΨ(A) = EΨ(A)

Expand basis to include relative motion of composite clusters

Recast as a cluster dynamics problem

Solutions for bound-state energies and scattering matrix (phase shifts)

!11

Energies and widths of resonances

128Unified description of 6Li structure and d+4He dynamics

§ Continuum and three-nucleon force effects in d+4He and 6Li

3

-135

-90

-45

0

45

90

135

180

δ[deg]

0 2 4 6

Ekin [MeV]

expt.NN+3NNN+3N-indNN-only3S1

3D1

d-4He

D23

P 03

3D3

FIG. 3. (Color online) S-, 3P0- and D-wave d-4He phase shiftscomputed with the NN-only, NN+3N-ind and NN+3NHamiltonians (lines) compared to those extracted from R-matrix analyses of data [27, 28] (symbols). More details inthe text.

convergence for the HO expansions at Nmax = 11. Weadopt the HO frequency of 20 MeV around which the 6Lig.s. energy calculated within the square-integrable basisof the NCSM becomes nearly insensitive to !Ω [13].

We start by discussing the influence of 3N forces –those induced by the SRG transformation of the NN po-tential (NN+3N -ind) as well as those initially present inthe chiral Hamiltonian (NN+3N). In Fig. 3 we compareour computed d-4He S-, 3P0- and D-wave phase shiftswith those of the R-matrix analyses of Refs. [27, 28]. Theresults based on the two-body part of the evolved NNforce (NN -only) resemble those obtained with a softerpotential [14]. Once the SRG unitary equivalence is re-stored via the induced 3N force, the resonance centroidsare systematically shifted to higher energies. By con-trast, the agreement with data is much improved in theNN+3N case and, in particular, the splitting betweenthe 3D3 and 3D2 partial waves is comparable to the mea-sured one.

In Fig. 4, the resonance centroids and widths ex-tracted [36] from the phase shifts of Fig. 3 (shown onthe right) are compared with experiment as well as withmore traditional approximated energy levels (shown onthe left) obtained within the NCSM by treating the 6Liexcited states as bound states. In terms of excitation en-ergies relative to the g.s., in both calculations (i.e., withor without continuum effects) the chiral 3N force affectsmainly the splitting between the 3+ and 2+ states, and toa lesser extent the position of the first excited state. Sen-sitivity to the chiral 3N force is also seen in the widthsof the NCSMC resonances, which tend to become nar-rower (in closer agreement with experiment) when thisforce is present in the initial Hamiltonian. Overall, theclosest agreement with the observed spectrum is obtained

-2

0

2

4

6

Ekin [M

eV]

Γ = 1.3

NN+3N

2+

3+

1+

1+

Γ = 0.024

Γ = 1.5

0.7117

2.8377

4.17

-1.4743g.s.

NN+3N-indExpt.

1.05Γ = 0.07

2.90Γ = 1.18

4.27Γ = 3.42

-1.49g.s.

2.10

Γ = 1.51

4.22

Γ = 3.68

Γ = 0.53

3.13

g.s.-0.76

NN+3NNN+3N-ind

4.99(22)

3.24(9)

0.99(9)

-1.58(4)g.s.-0.94

1.52

4.12

0.19

5.74

3.14

g.s.

NCSM (extrapolated)

NCSMC

FIG. 4. (Color online) Ground-state energy and low-lying 6Lipositive-parity T = 0 resonance parameters extracted [36]from the phase shifts of Fig. 3 (NCSMC) compared to theevaluated centroids and widths (indicated by Γ) of Ref. [1](Expt.). Also shown on the left-hand-side are the best(Nmax = 12) and extrapolated [37] NCSM energy levels. Thezero energy is set to the respective computed (experimental)d+4He breakup thresholds.

with the NN+3N Hamiltonian working within the NC-SMC, i.e. by including the continuum degrees of freedom.Compared to the best (Nmax = 12) NCSM values, allresonances are shifted to lower energies commensuratelywith their distance from the d+4He breakup threshold.For the 3+, which is a narrow resonance, the effect isnot sufficient to correct for the slight overestimation inexcitation energy already observed in the NCSM calcula-tion. This and the ensuing underestimation of the split-ting between the 2+ and 3+ states point to remainingdeficiencies in the adopted 3N force model, particularly

TABLE I. Absolute 6Li g.s. energy, S- (C0) and D-wave (C2)asymptotic normalization constants and their ratio using theNN + 3N Hamiltonian compared to experiment. Indicatedin parenthesis is the Nmax value of the respective calculation.The error estimates quoted in the extrapolated (∞) NCSMresults include uncertainties due to the SRG evolution of theHamiltonian and !Ω dependence [13].

Ground-State Eg.s. C0 C2 C2/C0

Properties [MeV] [fm−1/2] [fm−1/2]

NCSM (10) -30.84 − − −

NCSM (12) -31.52 − − −

NCSM (∞) [37] -32.2(3) − − −

NCSMC (10) -32.01 2.695 -0.074 -0.027

Expt.[1, 39, 40] -31.99 2.91(9) -0.077(18) -0.025(6)(10)

Expt. [38, 41] − 2.93(15) − 0.0003(9)

6Li vs. (4He+d)+6Li calculation

4He+d

d+4He Scattering Phase Shifts

-135

-90

-45

0

45

90

135

180

�[deg]

0 2 4 6

Ekin [MeV]

expt.N N+3NN N+3N - ind

3 S1

3D1

d- 4He

D23

P 03

3D3

Unified Description of 6 Li Structure and Deuterium-4He Dynamicswith Chiral Two- and Three-Nucleon Forces

Guillaume Hupin,1,* Sofia Quaglioni,1,† and Petr Navrátil2,‡1Lawrence Livermore National Laboratory, P.O. Box 808, L-414, Livermore, California 94551, USA

2TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia V6T 2A3, Canada(Received 12 December 2014; published 29 May 2015)

We provide a unified ab initio description of the 6Li ground state and elastic scattering of deuterium (d)on 4He (α) using two- and three-nucleon forces from chiral effective field theory. We analyze the influenceof the three-nucleon force and reveal the role of continuum degrees of freedom in shaping the low-lyingspectrum of 6Li. The calculation reproduces the empirical binding energy of 6Li, yielding an asymptoticD- to S-state ratio of the 6Li wave function in the dþ α configuration of −0.027, in agreement with adetermination from 6Li-4He elastic scattering, but overestimates the excitation energy of the 3þ state by350 keV. The bulk of the computed differential cross section is in good agreement with data. These resultsendorse the application of the present approach to the evaluation of the 2Hðα; γÞ6Li radiative capture,responsible for the big-bang nucleosynthesis of 6Li.

DOI: 10.1103/PhysRevLett.114.212502 PACS numbers: 21.60.De, 24.10.Cn, 25.45.-z, 27.20.+n

Introduction.—Lithium-6 (6Li) is a weakly bound stablenucleus that breaks into an 4He (or α particle) and adeuteron (d) at the excitation energy of 1.4743 MeV [1]. Acomplete unified treatment of the bound and continuumproperties of this system is desirable to further our under-standing of the fundamental interactions among nucleons,but also to inform the evaluation of low-energy crosssections relevant to applications. Notable examples arethe 2Hðα; γÞ6Li radiative capture (responsible for the big-bang nucleosynthesis of 6Li [2–6]) and the 2Hðα; dÞ4Hecross section used in the characterization of deuteronconcentrations in thin films [7–9]. Contrary to the lighternuclei, the structure of the 6Li ground state (g.s.)—namely,the amount of the D-state component in its dþ αconfiguration—is still uncertain [1]. Well known exper-imentally, the low-lying resonances of 6Li have been shownto present significant sensitivity to three-nucleon (3N)interactions in ab initio calculations that treated them asbound states [10–13]. However, this approximation is welljustified only for the narrow 3þ first excited state, and noinformation about the widths was provided. At the sametime, the only ab initio study of d-4He scattering [14] wasbased on a nucleon-nucleon (NN) Hamiltonian and did nottake into account the swelling of the α particle due to theinteraction with the deuteron.As demonstrated in a study of the unbound 7He nucleus,

the ab initio no-core shell model with continuum(NCSMC) [15] is an efficient many-body approach tonuclear bound and scattering states alike. Initially devel-oped to compute nucleon-nucleus collisions starting froma two-body Hamiltonian, this technique was later extendedto include 3N forces and successfully applied to makepredictions of elastic scattering and recoil of protons off

4He [16] and to study continuum and 3N-force effectson the energy levels of 9Be [17]. Recently, we havedeveloped the NCSMC formalism to describe more chal-lenging deuterium-nucleus collisions and we present in thisLetter a study of the 6Li ground state and d-4He elasticscattering using NN þ 3N forces from chiral effective fieldtheory [18,19].Approach.—We cast the microscopic ansatz for the

6Li wave function in the form of a generalized clusterexpansion,

jΨJπTi ¼X

λ

cλj6Li λJπTiþXZ

ν

drr2γνðrÞr

AνjΦJπT

νr i; ð1Þ

where J, π, and T are, respectively, total angularmomentum, parity, and isospin, j6Li λJπTi representsquare-integrable energy eigenstates of the 6Lisystem, and

jΦJπTνr i ¼ ½ðj4He λαJπαα Tαij2H λdJ

πdd TdiÞðsTÞYlðr̂α;dÞ&ðJ

πTÞ

×δðr − rα;dÞ

rrα;dð2Þ

are continuous basis states built from a 4He and a 2Hnuclei whose centers of mass are separated by the relativecoordinate ~rα;d, and that are moving in a 2sþ1lJ partialwave of relative motion. The translationally invariantcompound, target, and projectile states (with energy labelsλ, λα, and λd, respectively) are all obtained by means of theno-core shell model (NCSM) [20,21] using a basis ofmany-body harmonic oscillator (HO) wave functions withfrequency ℏΩ and up to Nmax HO quanta above the lowest

PRL 114, 212502 (2015) P HY S I CA L R EV I EW LE T T ER Sweek ending29 MAY 2015

0031-9007=15=114(21)=212502(5) 212502-1 © 2015 American Physical Society


6Li Resonances

!12



3

-135

-90

-45

0

45

90

135

180

δ[deg]

0 2 4 6

Ekin [MeV]


3D1

d-4He

D23

P 03

3D3





-2

0

2

4

6

Ekin [M

eV]

Γ = 1.3

NN+3N

2+

3+

1+

1+

Γ = 0.024

Γ = 1.5

0.7117

2.8377

4.17

-1.4743g.s.

NN+3N-indExpt.

1.05Γ = 0.07

2.90Γ = 1.18

4.27Γ = 3.42

-1.49g.s.

2.10

Γ = 1.51

4.22

Γ = 3.68

Γ = 0.53

3.13

g.s.-0.76

NN+3NNN+3N-ind

4.99(22)

3.24(9)

0.99(9)

-1.58(4)g.s.-0.94

1.52

4.12

0.19

5.74

3.14

g.s.

NCSM (extrapolated)

NCSMC






NCSM (10) -30.84 − − −

NCSM (12) -31.52 − − −

NCSM (∞) [37] -32.2(3) − − −

NCSMC (10) -32.01 2.695 -0.074 -0.027

Expt.[1, 39, 40] -31.99 2.91(9) -0.077(18) -0.025(6)(10)

Expt. [38, 41] − 2.93(15) − 0.0003(9)


4He+d











jΨJπTi ¼X

λ

cλj6Li λJπTiþXZ

ν

drr2γνðrÞr

AνjΦJπT

νr i; ð1Þ




πTÞ

×δðr − rα;dÞ

rrα;dð2Þ






3

-135

-90

-45

0

45

90

135

180

δ[deg]

0 2 4 6

Ekin [MeV]


3D1

d-4He

D23

P 03

3D3





-2

0

2

4

6

Ekin [M

eV]

Γ = 1.3

NN+3N

2+

3+

1+

1+

Γ = 0.024

Γ = 1.5

0.7117

2.8377

4.17

-1.4743g.s.

NN+3N-indExpt.

1.05Γ = 0.07

2.90Γ = 1.18

4.27Γ = 3.42

-1.49g.s.

2.10

Γ = 1.51

4.22

Γ = 3.68

Γ = 0.53

3.13

g.s.-0.76

NN+3NNN+3N-ind

4.99(22)

3.24(9)

0.99(9)

-1.58(4)g.s.-0.94

1.52

4.12

0.19

5.74

3.14

g.s.

NCSM (extrapolated)

NCSMC






NCSM (10) -30.84 − − −

NCSM (12) -31.52 − − −

NCSM (∞) [37] -32.2(3) − − −

NCSMC (10) -32.01 2.695 -0.074 -0.027

Expt.[1, 39, 40] -31.99 2.91(9) -0.077(18) -0.025(6)(10)

Expt. [38, 41] − 2.93(15) − 0.0003(9)


4He+d











jΨJπTi ¼X

λ

cλj6Li λJπTiþXZ

ν

drr2γνðrÞr

AνjΦJπT

νr i; ð1Þ




πTÞ

×δðr − rα;dÞ

rrα;dð2Þ






3

-135

-90

-45

0

45

90

135

180

δ[deg]

0 2 4 6

Ekin [MeV]


3D1

d-4He

D23

P 03

3D3





-2

0

2

4

6

Ekin [M

eV]

Γ = 1.3

NN+3N

2+

3+

1+

1+

Γ = 0.024

Γ = 1.5

0.7117

2.8377

4.17

-1.4743g.s.

NN+3N-indExpt.

1.05Γ = 0.07

2.90Γ = 1.18

4.27Γ = 3.42

-1.49g.s.

2.10

Γ = 1.51

4.22

Γ = 3.68

Γ = 0.53

3.13

g.s.-0.76

NN+3NNN+3N-ind

4.99(22)

3.24(9)

0.99(9)

-1.58(4)g.s.-0.94

1.52

4.12

0.19

5.74

3.14

g.s.

NCSM (extrapolated)

NCSMC






NCSM (10) -30.84 − − −

NCSM (12) -31.52 − − −

NCSM (∞) [37] -32.2(3) − − −

NCSMC (10) -32.01 2.695 -0.074 -0.027

Expt.[1, 39, 40] -31.99 2.91(9) -0.077(18) -0.025(6)(10)

Expt. [38, 41] − 2.93(15) − 0.0003(9)


4He+d











jΨJπTi ¼X

λ

cλj6Li λJπTiþXZ

ν

drr2γνðrÞr

AνjΦJπT

νr i; ð1Þ




πTÞ

×δðr − rα;dÞ

rrα;dð2Þ




NCSM



3

-135

-90

-45

0

45

90

135

180

δ[deg]

0 2 4 6

Ekin [MeV]


3D1

d-4He

D23

P 03

3D3





-2

0

2

4

6

Ekin [M

eV]

Γ = 1.3

NN+3N

2+

3+

1+

1+

Γ = 0.024

Γ = 1.5

0.7117

2.8377

4.17

-1.4743g.s.

NN+3N-indExpt.

1.05Γ = 0.07

2.90Γ = 1.18

4.27Γ = 3.42

-1.49g.s.

2.10

Γ = 1.51

4.22

Γ = 3.68

Γ = 0.53

3.13

g.s.-0.76

NN+3NNN+3N-ind

4.99(22)

3.24(9)

0.99(9)

-1.58(4)g.s.-0.94

1.52

4.12

0.19

5.74

3.14

g.s.

NCSM (extrapolated)

NCSMC






NCSM (10) -30.84 − − −

NCSM (12) -31.52 − − −

NCSM (∞) [37] -32.2(3) − − −

NCSMC (10) -32.01 2.695 -0.074 -0.027

Expt.[1, 39, 40] -31.99 2.91(9) -0.077(18) -0.025(6)(10)

Expt. [38, 41] − 2.93(15) − 0.0003(9)


4He+d











jΨJπTi ¼X

λ

cλj6Li λJπTiþXZ

ν

drr2γνðrÞr

AνjΦJπT

νr i; ð1Þ




πTÞ

×δðr − rα;dÞ

rrα;dð2Þ




Expt. NCSMCExtrapol.

6Li vs. (4He+d)+6Li

See M. Vorabbi poster for theoretical predictions for 7Be and 7Li

Precision measurements at ISAC of resonances and phaseshifts:• Complete: 4He+3He• Approved: 6He+p,

7Be+p, 11C+p

Summary

!13

Solving the nuclear many-body problem ab initio is very computationally demanding.

NCSM is computationally limited by the large dimensions of the Hamiltonian matrix needed to obtain accurate predictions.

▪ Use of approximate symmetries of the nucleus to reduce dimension (SpNCCI).

NCSM cannot accurately describe resonances or continuum states.

▪ Expand the basis to include dynamics — 4He+d (NCSMC).

Both NCSMC and SpNCCI seek to describe long range behavior of the wavefunctions

▪ NCSMC: 4He +d ▪ SpNCCI: Collective motion

Incorporate both collective excitations and continuum dynamics of clusters by combining NCSMC and SpNCCI

Collaboration: SpNCCI

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Mark Caprio University of Notre Dame

Tomas Dytrych Academy of Sciences of the Czech Republic Louisiana State University

Chao Yang Applied math and computational sciences, Lawrence Berkeley National Lab

Acknowledgements David Rowe, University of Toronto Pieter Maris, Iowa State University Petr Navratil, TRIUMF Calvin Johnson, San Diego State University Patrick Fasano, University of Notre Dame Robert Power, University College Cork (REU)

Collaboration: NCSMC

!15

Petr Navrátil TRIUMF

Sofia Quaglioni Lawrence Livermore National Lab

Guillaume Hupin Institut de Physique Nucléaire IN2P3/CNRS Université Paris-Saclay

Acknowledgements Peter Gysbers, TRIUMF Matteo Vorabbi, TRIUMF Michael Gennari, TRIUMF Michael Powers, TRIUMF Jérémy Dohet-Eraly, Université Libre de Bruxelles Robert Roth, Institut für Kernphysik — Theoriezentrum, TU Darmstadt

https://www.researchgate.net/institution/Universite_Libre_de_Bruxelles

Thank you  Merci

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Thank you  Merci

Ab Initio Predictions of Light Nuclei · 2018. 11. 9. · of Light Nuclei Anna McCoy TRIUMF Theory...

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