NUCLEAR CLUSTERS AND NUCLEAR MOLECULES IN LIGHT NUCLEI

1. NUCLEAR CLUSTERS AND NUCLEAR MOLECULES IN LIGHT NUCLEI Neven Soić Ruđer Bošković Institute Zagreb, Croatia

2. Research programme: cluster structure of light nuclei and reactions between light deformed nuclei • 8,9,10Be, 10,11,12B, 11,12,13,14C, 16,17,18O, 20,22Ne • Accelerator facilities: RBI Zagreb, LNS Catania, Vivitron Strasbourg, ANU Canberra, UCL Louvain-la-Neuve, GANIL Caen • Short introduction to clustering phenomena in light nuclei and nuclear molecules • The first experimental results on clustering in 10Be: Zagreb experiment • Further studies of 10Be at LNS Catania, CRC UCL Louvain-la-Neuve and Ganil • Experimental evidence for the first molecular structure in 10Be: experiments at Louvain-le-Neuve • Current and future research: 12Be, 10B, 10C, 14C, 16C

3. Introduction - Light nuclei • Light nuclei: 3 < A < 20 • Unique quantum laboratories: number of particles between a few (exact description) and many (statistical approach) • Experimental results in last 2 decades: a number of new and interesting quantum phenomena with no analogues in other areas of physics neutron halo proton halo neutron skin neutron drip line

4. Strange bindings of three-body system that have no bound two-body subsystems: Borromean nuclei: • 6He: α+2n, binding energy 0.97 MeV • 9Be: 2α+n, binding energy 1.57 MeV • 8He: 6He+2n, binding energy 2.14 MeV • 14Be: 12Be+2n, binding energy 1.12 MeV • “Super-Borromean” nucleus 10C: four-body system with no bound three- and two-body subsystems • 10C: 2α+2p, binding energy 3.73 MeV • Spatially extended and deformed nuclei • Closely related to those phenomena are recently established nuclear molecules • Ordinary nuclei: strength and short range of strong force: majority of ground states and low-lying excited states are spherical

5. Deformations are pronounced in light nuclei – ground and excited states - clusterization increase binding energy • Basic subunit: α-particle (4He) – very stable and strongly bound nucleus – doubly magic (1st excited state at 20.21 MeV) • Strong repulsive force(Pauli principle) between nucleons in 2 α-particles holds deformed structure 6Li 7Li 7Be 8Be 16O 12C

6. Ikeda diagram for nα nuclei Cluster structures appear mainly at excitation energies close to the thresholds for nucleus decomposition into clusters – these excitations are labeled in Ikeda diagram

7. Nuclear molecules • Structures formed by two or more strongly bound clusters (e.g. α-particles) surrounded with valence neutrons 9Be • Additional neutrons don’t destroy cluster structure, they actually enhance it • This idea was introduced already in 30’s, discussed by Seya in early 80’s, in the mid 90’s reintroduced by von Oertzen (Z. Phys. A 354 (1996) 37) • Valence neutrons are transferred between two cores – exchange force between the cores – stronger bindings • Exchange force: quantum effect knownin atomic physics –covalent bindings of atomic molecules • Analogy: cores – atoms, valence neutrons - electrons

8. Potential between the cores is very similar to the van der Waals potential: repulsive at small distance, attractive at larger distances Molecular local potential between two α-particles (8Be) • Large transfer probability of valence particles between the cores • Molecular structure may appear only if the core system is intrinsically very deformed • Essential difference between atomic and nuclear molecules: neutron mass comparable to the core mass, valence neutrons identical to the core neutrons (Pauli principle)

9. Weakly bound single-particle orbitals of valence particles (neutrons in p-orbital around α-particle) • Molecular wave functions in two-centre system for 2 p levels (harmonic oscillator with (nx, ny, nz) = (1, 0, 0) i (0, 0, 1) ), cores on z-axis vertical to projection plane σ orbital: s.p. w.f. parallel with z axis π orbital: s.p. w.f. vertical to z axis

10. 9Be i 10Be nuclei (valence neutrons in p3/2 orbit around α–particle) are crucial for understanding of nuclear molecular phenomena 3-D view of p=1 molecular orbit for m=1 (π orbit) and m=0 (σ orbit) • Experimental signatures of cluster (molecular) structure: selective (strong) population of levels in (cluster) transfer reactions large reduced widths for specific cluster structure rotational bands of states corresponding to very deformed structure

11. core+valence neutrons structures appear at excitations close to the thresholds for cluster decays • Expanded Ikeda diagram (von Oertzen diagram): neutron-rich nuclei with valence neutrons in covalent molecular orbitals around 4He and 16O • Recently large interest for studies of neutron-rich and exotic weakly bound nuclei – exotic cluster structure • review article by W. von Oertzen, M. Freer, Y. Kanada-En’yo, Physics Reports 432 (2006) 43

12. Experimental studies of 10Be nucleus 1988 2004

13. RBI accelerator facility

14. CRC Louvain-la-Neuve radioactive ion beam facility

15. Our first experiment (1994) on 10Be cluster structure • Measurement of the 7Li+7Li → α+α+6He (Q= 7.37 MeV) reaction at the RBI EN tandem Van de Graaff accelerator, beam energy 8 MeV • Idea of the experiment: use of the well developed cluster structure of 7Li to excite possible deformed structure in 10Be • Only 8Be contribute to the excitation spectra

16. Q=7.37 MeV Relative energy spectra for various pairs of reaction products Q-value spectra (reaction total energy) for 7Li(7Li,αα)6He and 7Li(7Li,α6He)4He reactions

17. Results interpreted in terms of extremely deformed structure rotational band: 0+ at 6.18 MeV, 2+ at 7.54 MeV, (4+) at 10.2 MeV New excited state at 10.2 MeV which decays exclusively by α-particle emission

18. Further experiments: 7Li+7Li → α+α+6He E0=30 MeV at tandem Van de Graaf accelerator of Laboratori Nazionali del Sud, Catania 9Be+7Li → α+6Li+6He E0=52 MeV at tandem Van de Graaf accelerator of Laboratori Nazionali del Sud, Catania 7Li+7Li → α+α+6He E0=8 MeV at RBI tandem Van de Graaf Fizika B 10 235 (2001)

19. Inclusive 10Be excitation energy spectra for two measured reactions 10Be excitation spectra for coincidence events for three measured reactions

20. Idea for following experiments: use of radioactive 6He ion beam to pickup α-particle and excite 10Be states with deformed structure • 6He β-decays with half-life of 800 ms • structure: compact α-core with two weakly bound valence neutrons • Measurements of the 6He+6Li → 6He+α+d and 6He+7Li → 6He+α+t reactions in two experiments in 1998. and 1999. at Louvain-la-Neuve • Beam energies: 17 and 18 MeV, beam intensity: 3 x 106 p/s • Particle identification: time of flight, reaction kinematics

21. Be+d coincidence events for 6Li(6He,d)10Be reaction Experimental angular distributions for 6Li(6He,10Be)2H reaction Theory: disturbed wave Born approximation (FRDWBA) Large cross-section for α-particle transfer for doublet of states at 7.5 MeV → well developed α+6He structure

22. results confirmed in measurements at higher beam energy • α-spectroscopic factor for 7.5 MeV doublet 3-5 times larger than s. f. for the ground and first excited state • one of the doublet states hascluster structure, more likely it is 7.54 MeV state 10Be excitation energy spectrum for 6He+6Li →α+6He+d (triple coincidence)

23. Measurements of the 7Li(7Li,α6He)4He reaction Eb=58 MeV at tandem Van de Graaf accelerator ANU Canberra Results indicate Jπ=3- for 10.15 MeV state, for state at 11.8 MeV possible are 4+,6+ Experimental correlation function

24. Experiment with radioactive 10Be ion beam at GANIL Measurements of 12C(10Be,α6He)12C reaction beam energy 302 MeV

25. In this experiment we used neutron detector DEMON – array of 81 modules with liquid scintillator NE213 Reactions 12C(10Be,αα) i 12C(10Be,ααn) Two neutrons removal from 10Be mainly excite 8Be 2+ state Two (or more) steps complex process, excitation of various 9Be states, core excitation

26. 10Be excitation energy spectra: peaks at 7.54 (130 keV above threshold) and 10.15 MeV

27. Angular correlation analysis for 10.15 MeV state Angular correlations between decay products may provide information on spin and parity of decaying state (if both products are Jπ= 0+) Ex=10.15 MeV, Jπ=4+

28. Results: state at 10.15 MeV has spin • and parity Jπ=4+ (with assumption of • the reaction mechanism), confirmed • its well developed cluster structure • α+6He ; for 7.54 MeV state (Jπ=2+) • confirmed its well developed • α+6He structure • These results confirm our previous speculation of very deformed structure for 10Be excited states and rotational band 0+ (6.18 MeV), 2+ (7.54 MeV), 4+ (10.15 MeV) • Band rotational parameter: ℏ/2I = 200 keV  2.5 times larger than for 8Be ground state band ! • Two neutrons move along symmetry axis between two separated α-particles → σ-orbitals

29. Final evidence and confirmation of results

30. Experiment: 6He beam and 4He gas target • Louvain-la-Neuve RIB facility • Resonant elastic scattering: provides direct determination of spin and parity, excitation energy, total and partial width Results for 10.15 MeV state can be described only with 4+ (coincidence events)

31. Γα= 0.10 – 0.13 MeV ; Γα /Γ = 0.35 – 0.46 • Extremely large value for spectroscopic factor for α-cluster • These results are final confirmation of our previous claims Singles data compared with non-resonant elastic scattering

34. Results of antisymmetrized molecular dynamics (AMD) calculations for structure of 10Be nucleus, Y. Kanada-En’yo, H. Horiuchi, A. Dote, Phys. Rev. C 60 064304 (1999) Results of molecular orbital model calculations for 0+ levels in 10Be, N. Itagaki, S. Okabe, Phys. Rev. C 61 044306 (2000)

35. Conclusion and outlook • Importance of results: experimentally confirmed extremely deformed structure in 10Be – the first nuclear molecule • Two neutrons move along symmetry axis between two separate α-particles → σ-orbitals • Studies of light nuclei still and again provide unexpected new results • Further studies: 10Be complete spectroscopy, isospin analog states in 10B i 10C (very exotic nucleus) • Neutron-rich beryllium nuclei: 12Be (2α + 4 neutrons) • Thee-centre nuclear molecules: neutron-rich carbon nuclei:13C,14C, 16C • 16C: three α chain state stabilized by valence neutrons

36. Collaborators • RBI:M. Milin, Đ. Miljanić, M. Zadro, S. Blagus, M. Bogovac, S. Fazinić, D. Rendić, T. Tadić • Laboratori Nazionali del Sud INFN Catania & Universita di Catania, Italija: M. Lattuada, C. Spitaleri, M. Aliotta, S. Cherubini, A. Di Pietro, P. Figuera, A. Musumarra, R. G. Pizzone, S. Romano, A. Tumino, E. Costanzo, M. G. Pellegriti • University of Edinburgh, Ujedinjeno Kraljevstvo: A. C. Shotter, T. Davinson, A. N. Ostrowski • University of Birmingham, Ujedinjeno Kraljevstvo: M. Freer, N. M. Clarke, N. Curtis, N. I. Ashwood, S. Ahmed, V. A. Ziman, C. J. Metelko, D. Price • University of Surrey, Guildford, Ujedinjeno Kraljevstvo: W. N. Catford, S. Pain, D. Mahboub, C. Harlin • Laboratoire de Physique Corpusculaire ISMRA & Universite de Caen, Francuska: N. A. Orr, L. Achouri, F. M. Marques, J. C. Angelique, J. C. Lecouey, G. Normand, C. Timis, B. Laurent • Universite Libre de Bruxelles, Belgija: F. Hanappe, T. Materna, V. Bouchat • Universite Catholique de Louvain, Louvain-la-Neuve, Belgija: C. Angulo, E. Casarejos, P. Demaret • Katholieke Universiteit Leuven, Belgija: R. Raabe