Borromean Halo Nuclei: Continuum Structures and Reactions

J.S. Vaagen, Ø. Jensen ,Department of Physics and Technology, University of BergenB.V. Danilin, Russian Research Center ”The Kurchatov Institute”

S.N. Ershov, Joint Institute for Nuclear Research, DubnaG. Hagen, Physics Division, Oak Ridge National Laboratory / Department of Physics and Astronomy, University of Tennessee

SummaryHalo nuclei exhibit a new type of structure foundin extremely neutron-rich light nuclei, at the limitsof nuclear existence. Of particular interest areBorromean nuclei, where none of the binarysubstructures can bind, demonstrating features ofuniversality. Nuclear physics has in recent yearstaken further steps to explore the nature of thehalo continuum, this being in fact the major partof the spectrum since halo nuclei support onlyone or a few bound states.

Since 3 → 3 scattering is prohibitively difficultto perform, the halo continuum has so far beenexcited in binary collisions, proceeding via theexotic ground state which to various degrees putsits imprint on the result. We discuss via exampleshow to disentangle continuum structures,comparing with recent correlation data, and thechallenges of linking reaction theory and modernstructure calculations.

Fig. 1. The cigar and dineutron configurations in the6He ground state.

Fig. 2. Spatial correlations for the 2+ partial componentof an APW (left) and the 2+(1) 6He resonancecalculated at resonant energy in T coordinate system.Very similar correlations are found in the translationinvariant ’shell model’ Y coordinate system.

Fig. 3. Spatial correlations for the energy peak positionof the 0+ soft monopole mode (upper row) and aftersubtraction of the APW density (lower row) in T and Ysystems.

Fig. 4. Energy correlation plot for 2+ states in cluster Tbasis: left - NoFSI, right - with FSI (2+(1) resonance).

Fig. 5. Comparison of the theoretical 6He excitationspectrum (thick solid line) for 6He + 208Pb breakup at240 MeV/nucleon with experimental GSI data. The thinsolid, dashed and dotted lines show the dipole 1−,quadrupole 2+, and monopole 0+ contributions.Threshold is at 1 MeV.

Fig. 7. In an open quantum system (left) excitations tothe continuum and the corresponding correlationsshould be treated correctly. For some nuclei, asdepicted, the Fermi level is above the single particlethreshold. In contrast, the particles in a closed quantumsystem (right) are trapped in a deep well.

Fig. 8. The binding energies for the Helium chain .Thenuclei are underbound, but the odd/even mass patternis recognizable, and the lifetimes agree semi-quantitatively.

Many-Body ab initio Approaches

Fig. 6. Energy ((a) and (b)) and angular ((c) and (d))fragment correlations (solid line) in the 6He + 208Pbbreakup at 240 MeV/nucleon for continuum energyregion 1 < Eκ < 3 MeV. (a) and (c) are shown in Jacobiconfiguration T, (b) and (d) in configuration Y. Thedashed, dotted and dash-dotted lines show the dipole1−, monopole 0+, and quadrupole 2+ contributions,respectively.

Borromean Physics- Dreams and realizationThe basic halo dynamics can be characterized asa coexistence of two subsystems: one whichconsists of core nucleons and the other of haloneutrons moving relative the core center of mass.With good accuracy the Borromean halo wavefunction Ψ can be written as a product of twofunctions:

Ψ(r1, . . . , rA) = ϕϕϕϕ · ψ(x, y) The function ϕϕϕϕ describes the internal structure ofthe core while ψ(x, y) describes the relativemotion of halo neutrons around the core CM inJacobi coordinates. The wave function ψ(x, y) issolution of the Schrödinger three-body equation:

( T+V − E)ψ(x, y) = 0, V = V1 + V2 + V12This is solved within the method of hypersphericalharmonics.

See International School of Physics ”Enrico Fermi”, Course CLXIX (2008)

TUNING the NUCLEAR PARADIGM to NEW DISCOVERIES From Halo Discoveries to Physics of MBOQS (Many Body Open Quantum Systems) This contribution is dedicated to my friend and colleague, halo-pioneer Misha Zhukov (Chalmers, Kurchatov,RNBT), who officially retires from Chalmers this summer. 2010 - 25 years for the discovery of nuclear halos at Berkeley by the Tanihata group, and the subsequent (1987) first binary halo-model suggestion by Hansen and Jonson. Halo physics, as an essential part of nuclear dripline physics, has become a significant part of European nuclear physics activity, at universities and large facilities such as CERN-ISOLDE, GANIL and GSI, listed according to increasing beam energy, from a few to hundreds MeV/nucleon. 2010 - 20 years for the take-off for serious theory work in the new field, delayed by a few years before it captured the attention of the nuclear theory community, and still for a while the exclusive playground for some pioneers who envisioned the potential paradigmatic importance of the new discoveries. The Russian-Nordic-British Theory collaboration RNBT (coordinated by Bergen) was formed to create a concerted theory effort, and became a key player, with international outreach to young scientists via Halo Study Weekends. RNBT coined the name Borromean nuclei for the most exotic 3-body like halo nuclei, 6He and 11Li with two halo neutrons being the cardinal examples. RNBT’s 1993 Physics Reports 231(1993)151- became a standard reference in a rapidly growing field, badly in need of relevant theoretical literature. Thus, a bridge was also created to similar predicted phenomena, such as Efimov states, in bosonic systems, increasing the general interest in the growing field. MBOQS. Today there is a new cross disciplinary physics community, MBOQS, dealing with Many Body Open Quantum Systems, spanning from nano- to femtometers, and interested in universality features and generic exotic quantum phenomena. In February this year the community had its second ECT* Workshop; “MBOQS – From Atomic Nuclei to Quantum Dots”, organized by JSV and Wolfgang Schleich. The physics at the nuclear driplines and beyond is the physics of transient phenomena where reactions and structure merge in exotic resonant phenomena and continuum structures. Thus it has parallels in the study of the quark gluon plasma. It includes the extremes of nuclear existence, thus tunes the nuclear paradigm to encompass non-mean-field physics, such as halos. Dripline physics is a fertile playground for MBOQS physics. Driven by experiment. Exploration of these frontiers has been driven by experiment. But theory has added fundamentally new insight, by underpinning and stimulating the experimental work, and also by embedding the field in generic exploration of universality properties of few- and many-body quantum systems. The RNBT has, upon invitation, recently contributed a paper Halo formation and breakup: Lessons and open Questions to a special issue of Journal of Physics G. Few-body cluster constituent modelling of halo nuclei and their reactions has turned out to be very successful and taught us surprising new aspects of structural nuclear self-organization. It has however not fully answered why and how exotic structures such as halos, arise from exclusively nucleon degrees of freedom and their interplay.

Ab initio computational physics. A large part of the young theory community call themselves computational physicists. With back-up in the largest computers around, they have higher ambitions than their predecessors could entertain, aiming at consistent calculations for large areas of the nuclear chart, thus also addressing the self-organization issue. Ab initio structure physics has made considerable progress, and Europeans (including Oslo/Bergen) working in Europe or abroad have played key roles. Øyvind Jensen will, in the next talk, provide some insight in one of the most promising approaches, that of Coupled-Cluster expansions. He will also address the issue of the contact with experiment via the old workhorse, nucleon-transfer reactions. He is the main author of the first comprehensive paper in its kind, accepted by Phys.Rev.C for publication later this year. This brings me to some closing remarks. Dripline -Tailored Reaction Theory The last 25 years have seen a growth from harvesting outstanding new physics using rather crude reaction tools and simple, not always quantum mechanically justifiable structure models, to presents days steadily more sophisticated structure theories. The same development has not happened to reaction, often considered merely a tool for unravelling the beauty of nature. Dripline physics has changed this, structure and reactions being now intertwined in hitherto unknown exotic continuum structures. It is a European and NuPECC challenge, to now give priority to reaction theory, also to underpin the upcoming new experimental installations. New ideas imply new people, trained at both universities and facilities. The field also needs phenomenologists who can communicate between theory and experiment, and joint training of theorists and experimentalists, such as earlier provided at the “Halo Study Weekends”. Now we could provide joint training at accelerator centres, such as CERN/GSI/GANIL , as suggested recently under the name EUTIPEN . 25 years ago I co-authored the Physics Reports 125(1985) 253- “One- and two-particle Overlap Functions” with Bang, Gareev and Pinkston, all regrettably gone in the last few years. This PR summed up work in our international community to properly compute relationships between states in neighbouring nuclei, useful for nucleon transfer reactions, and going beyond simple mean-field recipes for occupation of shell-model type orbitals. This PR, written by four reaction theorists, has again turned out to be useful, which of course should make me happy. I would however been happier if a new wave of reaction theory relegates our old work to where it should belong, the historical archives.