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

Research programme: cluster structure of light nuclei and reactions between light deformed nuclei 8,9,10 Be, 10,11,12 B, 11,12,13,14 C, 16,17,18 O, 20,22 Ne 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 10 Be: Zagreb experiment Further studies of 10 Be at LNS Catania, CRC UCL Louvain-la-Neuve and Ganil Experimental evidence for the first molecular structure in 10 Be: experiments at Louvain-le-Neuve Current and future research: 12 Be, 10 B, 10 C, 14 C, 16 C

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 proton halo neutron halo neutron skin neutron drip line

Strange bindings of three-body system that have no bound two-body subsystems: Borromean nuclei: – 6 He: α+2n, binding energy 0.97 MeV – 9 Be: 2α+n, binding energy 1.57 MeV – 8 He: 6 He+2n, binding energy 2.14 MeV – 14 Be: 12 Be+2n, binding energy 1.12 MeV “Super-Borromean” nucleus 10 C: four-body system with no bound three- and two-body subsystems – 10 C: 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

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

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

Nuclear molecules Structures formed by two or more strongly bound clusters (e.g. α-particles) surrounded with valence neutrons 9 Be 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 known in atomic physics – covalent bindings of atomic molecules Analogy: cores – atoms, valence neutrons - electrons

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 ( 8 Be) 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)

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 π orbital: s.p. w.f. vertical to z axis σ orbital: s.p. w.f. parallel with z axis

9 Be i 10 Be nuclei (valence neutrons in p 3/2 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

Expanded Ikeda diagram (von Oertzen diagram): neutron-rich nuclei with valence neutrons in covalent molecular orbitals around 4 He and 16 O core + valence neutrons structures appear at excitations close to the thresholds for cluster decays 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

Experimental studies of 10 Be nucleus

RBI accelerator facility

CRC Louvain-la-Neuve radioactive ion beam facility

Our first experiment (1994) on 10 Be cluster structure Measurement of the 7 Li+ 7 Li → α+α+ 6 He (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 7 Li to excite possible deformed structure in 10 Be Only 8 Be contribute to the excitation spectra

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

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

Further experiments: 7 Li+ 7 Li → α+α+ 6 He E 0 =30 MeV at tandem Van de Graaf accelerator of Laboratori Nazionali del Sud, Catania 9 Be+ 7 Li → α+ 6 Li+ 6 He E 0 =52 MeV at tandem Van de Graaf accelerator of Laboratori Nazionali del Sud, Catania 7 Li+ 7 Li → α+α+ 6 He E 0 =8 MeV at RBI tandem Van de Graaf Fizika B (2001)

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

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

Experimental angular distributions for 6 Li( 6 He, 10 Be) 2 H 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+ 6 He structure Be+d coincidence events for 6 Li( 6 He,d) 10 Be reaction

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 has cluster structure, more likely it is 7.54 MeV state 10 Be excitation energy spectrum for 6 He+ 6 Li →α+ 6 He+d (triple coincidence)

Measurements of the 7 Li( 7 Li,α 6 He) 4 He reaction E b =58 MeV at tandem Van de Graaf accelerator ANU Canberra Results indicate J π =3 - for MeV state, for state at 11.8 MeV possible are 4 +,6 + Experimental correlation function

Experiment with radioactive 10 Be ion beam at GANIL Measurements of 12 C( 10 Be,α 6 He) 12 C reaction beam energy 302 MeV

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

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

Angular correlation analysis for MeV state E x =10.15 MeV, J π =4 + Angular correlations between decay products may provide information on spin and parity of decaying state (if both products are J π = 0 + )

These results confirm our previous speculation of very deformed structure for 10 Be 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 8 Be ground state band ! Two neutrons move along symmetry axis between two separated α- particles → σ-orbitals Results: state at MeV has spin and parity J π =4 + (with assumption of the reaction mechanism), confirmed its well developed cluster structure α+ 6 He ; for 7.54 MeV state (J π =2 +) confirmed its well developed α+ 6 He structure

Final evidence and confirmation of results

Experiment: 6 He beam and 4 He 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 MeV state can be described only with 4 + (coincidence events)

Γ α = 0.10 – 0.13 MeV ; Γ α /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

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

Conclusion and outlook Importance of results: experimentally confirmed extremely deformed structure in 10 Be – 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: 10 Be complete spectroscopy, isospin analog states in 10 B i 10 C (very exotic nucleus) Neutron-rich beryllium nuclei: 12 Be (2α + 4 neutrons) Thee-centre nuclear molecules: neutron-rich carbon nuclei: 13 C, 14 C, 16 C 16 C: three α chain state stabilized by valence neutrons

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