ab initio no-core shell model/ resonating group method › conferences › elba › 2014_talks ›...

Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada

Propriété d’un consortium d’universités canadiennes, géré en co-entreprise à partir d’une contribution administrée par le Conseil national de recherches Canada

Canada’s national laboratory for particle and nuclear physics

Laboratoire national canadien pour la recherche en physique nucléaire

et en physique des particules

Accelerating Science for Canada

Un accélérateur de la démarche scientifique canadienne

Carolina Romero-Redondo

Petr Navrátil, Sofia Quaglioni and Guillaume Hupin

Ab initio no-core shell model/resonating group method

C. Romero Redondo, Elba XIII Workshop. June 25th, 2014

Introduction: NCSM/RGM

Binary clusters

Three-body cluster states

6He: 4He+n+n

NCSMC

Summary and outlook

Outline


Introduction

* Assumes nucleons as the effective degrees of freedom

* Uses realistic interactions

The goal is to achieve a predictive theory for light nuclear systems to study:

- Exotic nuclei

- Reactions important in nuclear astrophysics

- Reactions important for energy production projects

Ab initio in nuclear physicsnucleus


NCSM

No-core shell model (NCSM)Is an ab initio method capable of studying light bound nuclei from an accurate Hamiltonian.

Traditionally, has not been able to deal with continuum states.

Resonances

ReactionsHalo nuclei wf


NCSM/RGM


Traditionally, has not been able to deal with continuum states.

Resonating group method (RGM)Microscopic cluster approach.

Permits studying the scattering of clusters

Non-realistic Hamiltonian



Is not able to deal with continuum states and therefore is not applicable to

reactions.

Resonating group method (RGM)Microscopic cluster approach.

Permits studying the scattering of clusters

Non-realistic Hamiltonian

NCSM/RGM

Combines NCSM and RGM to obtain anab initio formalism which uses an accurate

nuclear Hamiltonian and is capable of studying both structure and scattering

problems in light nuclear systems

NCSM/RGM


NCSM/RGM


NCSM/RGM-2B

S. Quaglioni and P. Navrátil- PRL 101, 092501 (2008)- PRC 79, 044606 (2009)


n-4He


NCSM/RGM-2B


R-matrix


R-matrix

R matrix:


R-matrix

R matrix:

Scattering Matrix


A-nucleon system

S. Quaglioni and P. Navratil

- PRL 101, 092501 (2008)- PRC 79, 044606 (2009)

NCSM/RGM

Formalism presented for the first time. Nucleon-nucleous scattering: n+4He, n+3Hen+10Be, p+3He and p+4He

Applications

Radiative Capture: 7Be(p,γ)8B S-factor -PLB 704 (2011) 379 In collaboration with R. Roth

-PRC 83, 044609 (2011) Deuteron projectile: scattering (d+4He), 6Li states-PRL 108, 042503 (2012) Fusion reactions: 3He(d,p)4He and 3H(d,n)4He


NCSM/RGM-3B

C. Romero-Redondo

S. Quaglioni, P. Navrátil, G. Hupin

Extension to three-body cluster


NCSM/RGM-3B

Why?



NCSM/RGM-3B


Bound and resonant states:2n Halo nuclei


NCSM/RGM-3B


9Li

n

n4He n

n



NCSM/RGM-3B


9Li

n

n4He n

n

3-body continuum states:Transfer reactions



NCSM/RGM-3B


+3H 3H 4He n

n

n

n

9Li

n

n4He n

n

3-body continuum states:Transfer reactions



NCSM/RGM-3B

Basis

36


NCSM/RGM-3B

Basis


NCSM/RGM-3B

NCSM wave functions

Basis


NCSM/RGM-3B

Schrödinger equation

Norm kernelHamiltonian Kernel


NCSM/RGM-3B


Norm kernelHamiltonian Kernel Relative motion wavefunction


Orthogonalization

NCSM/RGM-3B



NCSM/RGM-3B

Hyperspherical coordinates:



NCSM/RGM-3B



NCSM/RGM-3B

After changing to hyperspherical coordinates and integrating in α,α':



After changing to hyperspherical coordinates and integrating in α,α':

Coupled-channel microscopic R-matrix method on a Lagrange mesh

NCSM/RGM-3B


R-matrix

External region: known asymptotic behaviour (ρ > a)

Internal region: expansion on a basis (ρ < a)

* Bound state:

* Continuum state:


4He+n+n

4He n

n6He: 2 neutron halo (4He-n-n)

42


4He+n+n

4He n

n6He: 2 neutron halo (4He-n-n)

Input:

- Accurate soft NN potential(SRG-evolved chiral N3LO with λ=1.5fm-1)

- NSCM 4He wave function

- Fully antisymmetric channel states


Norm Kernel


Hamiltonian Kernel


HO model space Eg.s. (4He) [MeV](NCSM)

Eg.s. (6He) [MeV](NCSM)

Eg.s. (6He) [MeV](NCSM/RGM)

Nmax = 8 -28.173 -28.952 -28.616Nmax = 10 -28.215 -29.452 -28.696Nmax = 12 -28.224 -29.658 -28.697

4He+n+n

6He ground state, NCSMNCSM/RGM results- n+n+4He, Nmax= 11, ħΩ = 14 MeV

- SRG-NN chiral with λ=1.5 fm-1

Comparison with NCSM:

- ~ 1MeV difference in Egs due to excitations

of the 4He core only included in the NCSM

calculation.

-Contrary to NCSM, NCSM/RGM n+n+4He

w.f. Has the appropriate asymptotic behaviour


4He+n+n

6He ground state wave function


4He+n+n

6He ground state wave functionProbability distribution


4He+n+n


Small

Small


4He+n+n



4He+n+n


Di-neutron

Cigar


4He+n+n continuum

Continuum

Calculation of phase shifts for different channels and study the stability of the results


4He+n+n continuumDependence in Nmax


Dependence in Kmax

4He+n+n continuum


4He+n+n continuum

SpectrumComparison with experiment


In progress

No-core shell model with continuum (NCSMC) for three-cluster basis


NCSMC


+

For a 3-cluster system like 6He:

NCSMC


Improvements in 6He calculationin order to obtain a complete ab initio calculation

Introduce 4He core excitations by coupling the 4He-n-n basis to 6He NCSM eigenstates (NCSMC)

Run calculations with 3N force

4He+n+n


Transfer reactions, i.e, 3H(3H,2n)4He

Derive and calculate couplings between two and three body clusters

Other systems: 5H, 11Li, 12Be

Outlook

Approach is very useful for studying different types of nuclear systems

Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada

Propriété d’un consortium d’universités canadiennes, géré en co-entreprise à partir d’une contribution administrée par le Conseil national de recherches Canada

Canada’s national laboratory for particle and nuclear physics

Laboratoire national canadien pour la recherche en physique nucléaire

et en physique des particules

Thank you!

TRIUMF: Alberta | British Columbia | Calgary Carleton | Guelph | Manitoba | McMaster Montréal | Northern British Columbia | Queen’s Regina | Saint Mary’s | Simon Fraser | Toronto Victoria | Winnipeg | York


7He: 6He+n


R-matrix

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ab initio no-core shell model/ resonating group method › conferences › elba › 2014_talks ›...

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