NeutrinosandFundamentalSymmetries

Scatterting in the NCSM:tetraneutron application

James P. Vary, Iowa State UniversityProgress in Ab Initio Techniques in Nuclear Physics

TRIUMF, Vancouver, Canada, February 28-March 3, 2017

FRIB: Opening New Frontiers in Nuclear Science

2

Achieving this goal involves developing predictive theoretical models that allow us to understand the emergent phenomena associated with small-scale many-body quantum systems of finite size. The detailed quantum properties of nuclei depend on the intricate interplay of strong, weak, and electromagnetic interactions of nucleons and ultimately their quark and gluon constituents. A predictive theoretical description of nuclear properties requires an accurate solution of the nuclear many-body quantum problem — a formidable challenge that, even with the advent of super-computers, requires simplifying model assumptions with unknown model parameters that must be constrained by experimental observations.

Fundamental to Understanding

The importance of rare isotopes to the field of low-energy nuclear science has been demonstrated by the dramatic advancement in our understanding of nuclear matter over the past twenty years. We now recognize, for example, that long-standing tenets such as magic numbers are useful approximations for stable and near stable nuclei, but they may offer little to no predictive power for rare isotopes. Recent experiments with rare isotopes have shown other deficiencies and led to new insights for model extensions, such as multi-nucleon interactions, coupling to the continuum, and the role of the tensor force in nuclei. Our current understanding has benefited from technological improvements in experimental equipment and accelerators that have expanded the range of available isotopes and allow experiments to be performed with only a few atoms. Concurrent improvements in theoretical approaches and computational science have led to a more detailed understanding and pointed us in the direction for future advances.

We are now positioned to take advantage of these developments, but are still lacking access to beams of the most critical rare isotopes. To advance our understanding further low-energy nuclear science needs timely completion of a new, more powerful experimental facility: the Facility for Rare Isotope Beams (FRIB). With FRIB, the field will have a clear path to achieve its overall scientific goals and answer the overarching questions stated above. Furthermore, FRIB will make possible the measurement of a majority of key nuclear reactions to produce a quantitative understanding of the nuclear properties and processes leading to the chemical history of the universe. FRIB will enable the U.S. nuclear science community to lead in this fast-evolving field.

Figure 1: FRIB will yield answers to fundamental questions by exploration of the nuclear landscape and help unravel the history of the universe from the first seconds of the Big Bang to the present.

Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015

Emergence of rotational bands

in light nuclei from No-Core CI calculationsPieter Maris

pmaris@iastate.edu

Iowa State University

SciDAC project – NUCLEI

lead PI: Joe Carlson (LANL)

http://computingnuclei.org

PetaApps award

lead PI: Jerry Draayer (LSU)

INCITE award – Computational Nuclear Structure

lead PI: James P Vary (ISU)

NERSC

Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015, TRIUMF, Vancouver – p. 1/50

No-Core Configuration Interaction calculations

Barrett, Navrátil, Vary, Ab initio no-core shell model, PPNP69, 131 (2013)

Given a Hamiltonian operator

H =!

i<j

(pi − pj)2

2mA+!

i<j

Vij +!

i<j<k

Vijk + . . .

solve the eigenvalue problem for wavefunction of A nucleons

HΨ(r1, . . . , rA) = λΨ(r1, . . . , rA)

Expand wavefunction in basis states |Ψ⟩ ="

ai|Φi⟩

Diagonalize Hamiltonian matrix Hij = ⟨Φj |H|Φi⟩

No-Core CI: all A nucleons are treated the same

Complete basis −→ exact result

In practice

truncate basis

study behavior of observables as function of truncation

Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015, TRIUMF, Vancouver – p. 2/50

Expand eigenstates in basis states

No Core Full Configuration (NCFC) – All A nucleons treated equally

In practice, for bound states:

How does one use the no-core results for unbound states to extract scattering information?

That is, we want to employ results within a finite and real harmonic oscillator (HO) basis to evaluate the scattering phase shifts. From the scattering phase shifts one then extracts resonance energies and widths.

Two examples here: (1) neutron – alpha scattering (2)  tetraneutron

Other no-core approaches: NCSMC, NCSM/RGM Gamow Shell Model Level density (Lifshits, Rubtsova, . . .) Complex Scaling of the HO basis ACCC (Lazauskas & Carbonell, . . . )

Phenomeological NN interaction: JISP16

JISP16 tuned up to 16O

Constructed to reproduce np scattering data

Finite rank seperable potential in H.O. representation

Nonlocal NN -only potential

Use Phase-Equivalent Transformations (PET) to tune off-shellinteraction to

binding energy of 3H and 4He

low-lying states of 6Li (JISP6, precursor to JISP16)

binding energy of 16O

Physics Letters B 644 (2007) 33–37

www.elsevier.com/locate/physletb

Realistic nuclear Hamiltonian: Ab exitu approach

A.M. Shirokov a,b,∗, J.P. Vary b,c,d, A.I. Mazur e, T.A. Weber b

a Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russiab Department of Physics and Astronomy, Iowa State University, Ames, IA 50011-3160, USA

c Lawrence Livermore National Laboratory, L-414, 7000 East Avenue, Livermore, CA 94551, USAd Stanford Linear Accelerator Center, MS81, 2575 Sand Hill Road, Menlo Park, CA 94025, USA

e Pacific National University, Tikhookeanskaya 136, Khabarovsk 680035, Russia

Received 6 March 2006; received in revised form 11 September 2006; accepted 30 October 2006

Available online 27 November 2006

Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015, TRIUMF, Vancouver – p. 6/50

Energies of narrow A=6 to A=9 states with JISP16

Maris, Vary, IJMPE22, 1330016 (2013)

6 7 8 9A

-55

-50

-45

-40

-35

-30G

roun

d sta

te e

nerg

y (M

eV)

6Li

6He

7Li

8Be

8Li8He

9Be

9Li

rotationalband

JISP16expt

2+

0+

4+

Excitation spectrum narrow states in good agreement with data

Progress in Ab Initio Techniques in Nuclear Physics, Feb. 2015, TRIUMF, Vancouver – p. 11/50

Compare theory and experiment for 33 states Maris, Vary, IJMPE22, 1330016 (2013) Many of these states are cluster-states

Eig

enen

ergy

(MeV

)

Daejeon16NNInterac8on

ChiralN3LO(EntemandMachleidt)SRG(Hjorth-Jensen&Hagen,)PETs+abexitufits(Daejeon)

λ =1.5 fm−1

Shirokov,Shin,Kim,Sosonkina,Maris,Vary,Phys.LeUs.B761,87(2016)

2 4 6 8 10 12 14 16A

-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

(Eex

p − E

th)/E

exp

14C

4He

3H8He

6He 6Li 7Li 8Be10B

11B

12B

12C

13C

15N

14N16O

3He

14hΩ

9Be10Be

20hΩ 18hΩ

16hΩ

14hΩ 12hΩ 10hΩ

8hΩ

Upperbound − JISP16Extrap. B − JISP16Extrap. B − Daejeon16Upperbound − Daejeon16

inte

gran

d

kà λ Λ

max

Lattice Gauge Theory:λ = L−1 = inverse of linear dimensionΛ = a−1 = inverse of lattice spacing

Simple example of IR and UV regulators

=> What are the IR and UV regulators of an HO basis?

Synopsis of the SS-HORSE method: accounts for the continuum limit in an infinite HO basis

λ≤Λ≥

Guidelines for application of the SS-HORSE method: 1. Select HO basis regulators: all IR scales in H except Trel

all UV scales in H except Trel 2. Since Trel has analytic IR and UV asymptotics, scattering domain (continuum physics) is accessible – e.g. scattering phase shifts: ²  J-matrix for scattering ²  SS-HORSE method developed for evaluating phase shifts

λ≈ !ΩNmax

Λ≈ !Ω Nmax

General idea of the HORSE formalism

This is an exactly solvable algebraic problem!

Arises as a natural extension of NCSM where both potential and kinetic energies are truncated

T + V

Infinite set of algebraic equations:

Tnn 'l +Vnn '

l −δ nn 'E( )n '=0

N

∑ an 'l E( )= 0. n≤N−1

Matching condition at n = N

TNn 'l +VNn '

l −δ Nn 'E( )n '=0

N

∑ an 'l E( ) + TN , N+1l aN+1, l E( )= 0. n≤N−1

T

Then for n≥N +1

Tnn 'l −δ nn 'E( )

n '=0

∞

∑ an 'l E( )= 0, which produces:

Tn, n−1l an−1, l (E)+ Tnn

l −E( )anl E( )+Tn, n+1l an+1, l (E) = 0.

λ≈ λNN & Λ≈ ΛNN

“think outside the box”=>

NCSM with:

Single-State HORSE (SS-HORSE)

Eλ are eigenstates of the NCSM (for given ħΩ and Nmax) that are extended to scattering states, from which the phase shift is derived. A.M. Shirokov, A.I. Mazur, I.A. Mazur and J.P. Vary, Phys. Rev. C 94, 064320 (2016); arXiv:1608.05885

Hnn 'I

n'= 0

N

∑ n' λ = Eλ n λ , n ≤ N

H−E( )nn '−1≡−Gnn ' =

n λ ' λ ' n 'Eλ '−Eλ '=0

N

∑

tanδ (E) =−SNl (E)−GNNTN , N+1

l SN+1, l (E)CNl (E)−GNNTN , N+1

l CN+1, l (E)Suppose E = Eλ '

tanδ (Eλ ) =SN+1, l (Eλ )CN+1, l (Eλ )

= (−1)l q2l+1Γ(−l+ 12)

L(N−l )/2l+1

2 (q2 )Φ(−N

2− l2− 1

2 ,−l+ 12;q2 )

where L(N−l )/2l+1

2 are associated Laguerre polynomials, Φ are confluent hyper-

geometric functions and q= 2Eλ

!Ω

Example of the neutron-alpha phase shift evaluations Solve the NCSM on mesh of Nmax and -values for 4He and 5He. Use set of NCSM eigenvalues satisfying IR and UV constraints for: Compare with experimental phase shifts channel-by-channel Extract resonance parameters by fitting the phase shifts to effective range expansion that includes possible resonance contributions Results (consistency check) should provide a single curve of with:

s= !Ω

Nmax +ℓ+72= λsc

2

λsc as defined in S. A. Coon, M. I. Avetian, M. K. G. Kruse, U. van Kolck, P. Maris, and J. P. Vary, Phys. Rev. C86, 054002 (2012); arXiv: 1205.3230

!Ω

tanδ (Eλ ) =SN+1, l (Eλ )CN+1, l (Eλ )

where Eλ = Eλ ( 5 He, Nmax, !Ω)−E0 ( 4 He, Nmax, !Ω)

Eλ (s)

A.M. Shirokov, A.I. Mazur, I.A. Mazur and J.P. Vary, Phys. Rev. C 94, 064320 (2016); arXiv:1608.05885

Single State – Harmonic Oscillator Representation of Scattering Equations “SS-HORSE”

Application to the Tetraneutron

Motivations v  Better knowledge of nn interaction v  High precision access to T=3/2 nnn interacton v  Stepping stone to putative 6n, 8n, . . . systems

http://physics.aps.org/articles/v9/14

Tetraneutron, JISP16

Nmax =10-12 resonance params: Er = 844 keV, Γ = 1.378 MeV, Efalse = -55 keV.

0 5 10 15 20 25 30E [MeV]

0

30

60

90

120δ

[deg

rees

] Nmax= 10 12 14 16 18Nmax= 10 - 18Nmax= 10 - 12

4n, gsRes. + False poles

Nmax =10-18 resonance params: Er = 844 keV, Γ = 1.377 MeV, Efalse = -55 keV.

vs

Tetraneutron, Daejeon16

Options: Resonance parameters: Er = 185 keV, Γ = 818 keV, with large background phase

0 5 10 15 20 25 30 35 40E [MeV]

0

30

60

90

120δ

[deg

rees

] Nmax= 6 8 10 12 14 16 18SS HORSE

4n, gsDaejeon16Select1: Res

Resonance parameters: Er = 0.794 MeV, Γ = 1.619 MeV, Efalse = -53.6 keV.

vs

Preliminary

J

J

0

0.5

1

1.5

2

2.5

3

3.5

4

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

Wid

th (M

eV)

Er (MeV)

Experiment: Kisamori, et al., PRL 116, 052501 (2016)

JISP16 Shirokov, et al., PRL 117, 182502 (2016)

Daejeon16Preliminary

Tetraneutron resonance

Systematic error: Light shadedStatistical error: Pattern area

Experimental upper bound on width

Search for 6He dissociating to 3-body final states: Tetraneutron observed as peaks in a missing mass analysis

Target

6He

Pin

P1

P2

P4n

Conservation of invariant 4-momentum with complete kinematics (“exclusive” expt)

Yield

x x x x x x

x x x x x x x x x

x

P4n2 →16mn

2 P4n2 ≥16mn

2

Pin +Ptarget = P1 +P2 +P4n +Ptarget'

Schematic result

Ecm > 30 MeV

F.Wamers et al., PRL112(2014)132502.C(17Ne,16,15Ne)

13O+p+p

K.Kisamori et al., PRL116(2016)052501.4He(8He,8Be)4n

Discovery Potential! Super Light Nuclei

Conclusions and Outlook Much work yet to be done on multi-neutron systems Structure of 3n, 4n, 5n, . . . Direct production with rare isotope beams Transfer reactions Production during fission => Better knowledge of nn, 3n and 4n interactions => Properties of neutron-rich nuclei => Properties of neutron stars => Extend the theory to charged particle scattering . . .

Thank you for your attention

I welcome your questions