1. Leonid Grigorenko Flerov Laboratory of Nuclear Reactions, JINR, Dubna, Russia Advances and prospects in the theoretical studies of few-body decays 25th International Nuclear Physics Conference, June 2-7, 2013, Florence, Italy  Flerov Laboratory – world leader in superheavy nuclei research.  ACCULINNA fragment separator – light exotic nuclei research.  New ACCULINNA-2 fragment separator to be commissioned in 2014.  Theoretical group interested in few-body physics in the dripline nuclei: I.A. Egorova, S.N. Ershov, Yu.L. Parfenova, P.G. Sharov, M.V. Zhukov

2. Irreducible few-body dynamics  Many nuclear models are based on utilization of the single-particle basis  For certain situations (certain observables) single-particle basis is far from being adequate  Basis states based on collective coordinates. E.g. in hyperspherical harmonics method:  Borromean halo nuclei: none of the subsystems are bound.  Borromean rings logo:

3. Energy conditions and few-body phenomena Borromean 2n halo systems “Soft excitations” Three-body virtual states 2p radioactivity Democratic decays True three-body decay True 5n-body decay (4n radioactivity)

4. Few-body dynamics at the driplines Exotic phenomena in vicinity of driplines: Haloes (green) True 2p/2n decays (red) 4p/4n emitters (blue) NOT INVESTIGATED (gray) Exotic phenomena in vicinity of driplines: Haloes (green) True 2p/2n decays (red) 4p/4n emitters (blue) NOT INVESTIGATED (gray) Modern RIB research: move towards and beyond the driplines Few-body dynamics at the driplines as consequence of corresponding clusterization NOT SO EXOTIC: More or less every second isotope in vicinity of the driplines has features connected to few-body dynamics See also about heavy 2p candidates: Olsen et al., PRL 110, 222501 (2013) See also about heavy 2p candidates: Olsen et al., PRL 110, 222501 (2013)

5. Three-body decay in cluster model  Decays: Schrodinger equation with complex energy  “Natural” definition of width  Adopted to radioactive decay studies Typical precision: stable solution for     L.V. Grigorenko, Phys. of Part. and Nucl. 40 (2009) 674 M. Pfutzner, L.V. Grigorenko, M. Karny, and K. Riisager, Rev. Mod. Phys. 84 (2012) 567 [arXiv:1111.0482]. L.V. Grigorenko, Phys. of Part. and Nucl. 40 (2009) 674 M. Pfutzner, L.V. Grigorenko, M. Karny, and K. Riisager, Rev. Mod. Phys. 84 (2012) 567 [arXiv:1111.0482]. L.V. Grigorenko, R.C. Johnson, I.G. Mukha, I.J. Thompson, M.V. Zhukov, PRL 85 (2000) 22.  Three-body Hyperspherical Harmonic method  Approximate boundary conditions of the three- body Coulomb problem  Classical extrapolation to improve momentum distributions  Reactions: Inhomogeneous Schrodinger equation with real energy  Source function formulation is straightforward for several types of direct reactions. E.g. for knockout reactions ( 6 Be populated with 7 Be beam):  Very precise results could be obtained for reactions with well defined “clean” mechanism.

6. Three-body correlations in decays and reactions  2-body vs. 3-body continuum  Decays: 2-dimensional “internal” 3- body correlations  Reactions: there is a selected direction. 5-dimensional correlations: “internal” + “external”  For direct reactions the selected direction is momentum transfer vector Which kind of useful information (if any) can be obtained from three-body correlations? M.S.Golovkov et al., PRL 93 (2004) 262501. M.S.Golovkov et al., PRC 72 (2005) 064612. L.V. Grigorenko et al., PRC 82 (2010) 014615. A.S.Fomichev et al., PLB 708 (2012) 6. S.I. Sidorchuk et al., PRL 108 (2012) 202502 I.A. Egorova et al., PRL 109 (2012) 202502 M.S.Golovkov et al., PRL 93 (2004) 262501. M.S.Golovkov et al., PRC 72 (2005) 064612. L.V. Grigorenko et al., PRC 82 (2010) 014615. A.S.Fomichev et al., PLB 708 (2012) 6. S.I. Sidorchuk et al., PRL 108 (2012) 202502 I.A. Egorova et al., PRL 109 (2012) 202502 Observables in reactions: Nuclear structure + Reaction mechanism + Final state interaction Observables in reactions: Nuclear structure + Reaction mechanism + Final state interaction Experimental bias: Acceptance + Resolution + Physical backgrounds Experimental bias: Acceptance + Resolution + Physical backgrounds Problem of comparison with experiment for correlation data MC codes based on density matrix formalism:

7. 2p decay of 45 Fe. General systematics of 2p lifetimes Complete momentum correlations provided Miernik et al., PRL 99 (2007) 192501 L.Grigorenko et al., PLB 677 (2009) 30 L.Grigorenko et al., PRC 82 (2010) 014615 Pfützner et al., EPJA 14 (2002) 279 Giovinazzo et al., 89 (2002) 102501 Dossat et al., PRC 72 (2005) 054315 Miernik et al., PRL 99 (2007) 192501 45 Fe: the first found and the best studied

8. Excitation spectra for democratic decays of 6 Be states  Simple model for neutron knockout: sudden removal of neutron  Schematic 7 Be WF with free parameters  Spin content of the source A way to define second 0 + and second 2 + We know how to “control” 6 Be spectrum Continuum spin composition for theoretical spectrum fitted to experiment I.A. Egorova et al., PRL 109 (2012) 202502. L.V. Grigorenko et al., PRC 86 (2012) 061602(R). Excited states are “sitting” on the “tails” of lower excitations. Broad states are overlapping

9. Correlations in democratic decays of 6 Be states Note: the higher decay energy – the more developed is low-energy p-p correlation (“diproton”) Note: when two-body states enters the decay window the intensity at expected peak position is suppressed Sequential decay patterns appears only for E T > 2E r +  However, even at higher energies the correlations are not reduced to sequential mechanism I.A. Egorova et al., PRL 109 (2012) 202502.

10. IsoVector Soft Dipole Mode in 6 Be  Large cross section above 2 + and no resonance   L = 1 identification – some kind of dipole response  No particle stable g.s. – can not be built on spatially extended g.s. WF  Built on the spatially extended 6 Li g.s. A.S.Fomichev et al., PLB 708 (2012) 6. Experimentally observed and theoretically discussed: IVSDM as a specific form of SDM

11. Democratic 2n decays. 10 He puzzle. Recently studied light true 2n emitters:  10 He: Golovkov et al., PLB 672, 22 (2009), Johansson et al., NPA 842, 15 (2010), Sidorchuk et al., PRL 108, 202502 (2012), Z. Kohley et al., PRL 109, 232501 (2012).  13 Li: Aksyutina et al., PLB 666, 430 (2008), Z. Kohley et al., PRC 87, 011304(R) (2013).  16 Be: Spyrou et al., PRL 108, 102501 (2012).  26 O: Lunderberg et al., PRL 108, 142503 (2012), Caesar et al., arXiv:1209.0156, Z. Kohley et al., PRL 110, 152501 (2013). 10 He spectrum from transfer reaction 10 He spectrum for knockout from 11 Li Fourier transform of 11 Li source function (no 10 He FSI) 10 He data vs. calculations 10 He populated from 11 Li is a pileup of states with different J  Sidorchuk et al.: 8 He(t,p) 10 He reaction 10 He spectrum populated in knockout from halo states is dominated by the initial state contribution

12. Two- (and more)-neutron radioactivity search prospects  Two-proton radioactivity is the long awaited and the most recently found mode of the radioactive decay. Can neutron radioactivity exist?  Estimates: one-neutron radioactivity is highly unlikely.  There are additional effective few-body “centrifugal” barriers making few-body emission relatively slower.  Long-living Two-neutron decay and moreover four-neutron decay states are reasonably probable. L.V. Grigorenko, I.G. Mukha, C. Scheidenberger, and M.V. Zhukov, Phys. Rev. C 84 (2011) 021303(R)

13. On possibility of 2n radioactivity in 26 O Importance of fine three-body effects Extreme low-energy decay of 26 O should be inferred 2p radioactivity: Core recoil – negligible Paring - factor 200-500 2n radioactivity: Core recoil – factor 5-10 Paring - factor 2000-10000 T 1/2 = 4.5 ps: 2n radioactivity discovered? T 1/2 = 4.5 ps: 2n radioactivity discovered?

14. Conclusions  Few-body dynamics is widespread beyond the driplines and in the excitation spectra of the systems close to driplines.  The major phenomena:  True 2p (2n) decays, including radioactive decays  Democratic 2p (2n) decays  Soft excitations (various soft dipole excitations are most widespread)  True 4n decays (4n radioactivity)  Significant advances in understanding of 2p radioactivity and 2p “democratic” decays (including the particle correlations) within the last decade. Both theory and experiment.  List of challenges for theory and experiment:  To fill the gaps in the information about dripline 2p decays from 19 Mg to 45 Fe and from 54 Zn to 100 Sn.  Understanding of “democratic” 2n decays.  Search for 2n radioactivity. May be it is already found in 26 O?  Search for 4n radioactivity – possible novel type of radioactive decay.