Aim

Ab initio calculations in three-cluster systems:Bound state and resonances of 6He

Carolina Romero-Redondo, TRIUMF; Petr Navratil, TRIUMF ; Sofia Quaglioni, LLNL; Guillaume Hupin, LLNL

Continuum states for n+n+4He

Introduction

The ab initio no-core shell model/resonating-group method (NCSM/RGM) [1,2] is a technique that is able to treat both, structure and reaction problems in light nuclear systems. This approach combines a microscopic cluster technique with the use of realistic interactions and an ab initio description of the nucleon clusters and has been shown to work effectively in different systems [1-4].

NCSM/RGM for a three- body cluster system

Conclusions and outlookWe presented an extension of the NCSM/RGM which includes three-body dynamics. This new feature permits us to study a new range of systems that present three-body configurations. In particular, we presented results for both bound and continuum states of the 6He nucleus studied within a 4He+n+n basis. The obtained g.s. wave function features an appropriate asymptotic behavior. Low-lying resonances in 2+ and 1+ channels are found while none are present for 0+ and 1- channels. These results are consistent with recent measurements [5].

In the future we plan to include 3N forces and core excitations through the no-core shell model with continuum. Future projects include the study of 5H (3H+n+n), 11Li (9Li+n+n) and the derivation of couplings between two and three body clusters in order to be able to study transfer reactions.

Norm Kernel

It is well known that 6He is a two-neutron halo nucleus. This implies that there are two neutrons with low separation energy that are unusually distant from the rest of the nucleons (an α-particle), presenting a three-cluster configuration. We calculate bound and continuum states of the system using a realistic nucleon-nucleon potential derived from chiral effective field theory.

There are many nuclear systems that have a three-body cluster configuration and, therefore, their description is better achieved when this configuration is taken into account in the calculations. The extension of the NCSM/RGM formalism to the treatment of three-body clusters will permit studying these types of systems. The method is well suited for the description of bound and resonant states in nuclei with three-body configuration, e.g., two-neutron halo nuclei such as 6He and 11Li or 12Be. Furthermore, it will make possible to describe three-body scattering states and, therefore, study nuclear reactions with three nuclear fragments in the final state, e.g., transfer reactions such as 3H(3H,2n)4He or 3He(3He,2p)4He.

References[1] S. Quaglioni and P. Navrátil, PRL 101, 092501 (2008)

[2] S. Quaglioni and P. Navrátil, PRC 79, 044606 (2009)

+3H 3H 4He n

n

9Li

n

n11Li

The wave function of the system will be expanded over three-cluster channel states This basis contains the internal no-core shell model wave function of each of the three clusters in the system. The expansion can be written as:

where is the intercluster antisymmetrizer operator and are the relative motion wave functions, which can be determined by solving the Schrödinger equation:

We can orthogonalize eq. (1) and introduce hyperspherical coordinates ( , ) in order to obtain an equation in the hyperradius. This will be solved using the coupled-channel R-matrix method on a Lagrange mesh:

4He n

n

Reaction and structure problems that can be studied with the NCSM/RGM with three-body cluster states

[3] P. Navrátil and S. Quaglioni, PRC 83, 044609 (2011)

[4] P. Navrátil and S. Quaglioni, PRL 108, 042503 (2012)

NCSM wave functions

Di-neutron

Cigar

Norm kernelHamiltonian Kernel

Results for 6He within a n+n+4He basis

Ground state: 0+

Ab initio approaches in nuclear physics describe nuclear systems considering their nucleons as the fundamental components. Their aim is to be able to predict the properties of such systems starting from the fundamental inter-nucleon interactions.

Support

The use of three-cluster dynamics is essential for describing 6He states in the continuum. We present, for the first time, results that include these dynamics from an ab initio approach. Using continuum asymptotic conditions, we solve the set of equations (2) in order to obtain the low-energy phase shifts for the Jπ=0+, 1-, 1+ and 2+ channels.

(2)

(1)

6He spectrum recently measure at GANIL [5].

[5] X. Mougeot et al, Phys. Lett. B 718, 441 (2012)

Diagonal elements of the exchange part of some of the norm kernel partial waves,which give a measure of the influence of the Pauli exclusion principle.

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

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

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

Nmax

= 12 -28.22 -29.75 -28.72The NCSM/RGM wave function (w.f.) presents the appropriate asymptotic behavior (contrary to the NCSM). In the figure, the probability distribution of the main component of the w.f. is shown, featuring the two characteristic peaks. However, the 6He g.s. is underbound due to the lack of the excitations of the core. The inclusion of these excitations will be achieved in a future work through the NCSMC.

Probability distribution of the main component of 6He g.s.

We introduce a fully antisymmetrized treatment of three-cluster dynamics within the NCSM/RGM which will permit us to study a wide range of systems that present three-body configurations. Results for 6He are shown.

Resonances

Resonance

Two low-lying resonances are found for the 2+ channel and one for the 1+ channel, while no low-lying resonances are present for 1- and 0+ channels.These results are consistent with the spectrum recently measured at GANIL [5].