Double β-decay Process mediated by the weak interaction occurring in even-even nuclei where the single  -decay is energetically forbidden The role of the pairing force 1

Double β-decay but one should know Nuclear Matrix Element (NME) Great new physics inside Single and double charge exchange 2

2) 0 double β-decay Neutrino has mass Neutrino is Majorana particle Violates the leptonic number conservation Experimentally not observed Beyond the standard model 1)2 double β-decay 1)Does not distinguish between Dirac and Majorana 2)Experimentally observed in several nuclei since 1987 and anti- can be distinguished and anti- are the same β β-decay 3

From NOON2004 summary by A. Yu. Smirnov νeνe νeνe 5meV 50meV Next generation experiments are aiming to explore 50meV region 4

Seesaw mechanism Dirac mass will be the same order as the others. (0.1~10 GeV) Right handed Majorana mass will be at GUT scale GeV Beyond the standard model 5

but requires Nuclear Matrix Element (NME)! Calculations: QRPA, Large scale shell model, IBM ….. Measurements: Network cross sections including Double Charge Exchange, Single charge exchange, transfer reactions and so on (see [ S.J. Freeman and J.P. Schiffer JPG 39 (2012) ] for review). New physics for the next decades 6

Figure 2: The neutrinoless double-beta decay; "state-of-the-art" NMEs: QRPA [30] (red bars) and [21, 22] (diamonds), ISM [31] (squares), IBM [25] (circles), and GCM [26] (triangles). From A. Giuliani and A. Poves Adv. in High En. Phys (2012) State of the art NME calculations 7

( 20 Ne, 20 O) and ββ decay ( 20 Ne, 20 F) ( 20 Ne, 18 O) ( 20 Ne, 22 Ne) 76 Se 78 Se 76 Ge 74 Ge 76 As 77 Se 75 As 77 As 75 Ge ( 18 O, 18 Ne) ( 18 O, 18 F) ( 18 O, 20 Ne) ( 18 O, 16 O) Double charge exchange reactions

Pion DCE (π +, π - ) or (π -, π + ) Heavy Ion DCE Direct mechanism: isospin-flip processes Sequential mechanism: two-proton plus two-neutron transfer or vice-versa Zero spin cannot excite Gamow-Teller (GT) K.K. Seth et al., Phys.Rev.Lett. 41 (1978) 1589 D.R.Bes, O. Dragun, E.E. Maqueda, Nucl. Phys. A 405 (1983) 313. Double charge exchange reactions

1 Sequential nucleon transfer mechanism 4 th order:  Brink’s Kinematical matching conditions D.M.Brink, et al., Phys. Lett. B 40 (1972) 37 2 Meson exchange mechanism 2 nd order:  Momentum transfer correction of the GT unit cross- section (valid for small momentum transferred q): T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125 Meson component of DCE cross- section as the product of the two charge-exchange ones. Heavy-ion DCE

( 18 O, 18 Ne) DCE reactions in Catania 40 Ca( 18 O, 18 Ne) MeV  18 O and 18 Ne belong to the same multiplet in S and T  Very low polarizability of core 16 O  Sequential transfer processes very mismatched  Target T = 0 only T = 2 states of the residual 0° < θ lab < 10° Q = -5.9 MeV Scattering angle (deg) dσ/dω (µb/sr) direct DCE sequential transfer 11

Experimental Set-up  18 O 7+ beam from Cyclotron at 270 MeV (10 pnA)  40 Ca solid target of 300 μg/cm 2  Ejectiles detected by the MAGNEX spectrometer  Angular setting 18 O + 40 Ca 18 F + 40 K 18 Ne + 40 Ar 20 Ne + 38 Ar 16 O + 42 Ca Measured Not measured 12

Particle Identification A. Cunsolo, et al., NIMA484 (2002) 56 A. Cunsolo, et al., NIMA481 (2002) 48 F. Cappuzzello et al., NIMA621 (2010) 419 F. Cappuzzello, et al. NIMA638 (2011) 74 A identificationZ identification E resid (ch) F Ne Na X foc (m) E resid (ch) 18 Ne 19 Ne 20 Ne 21 Ne 22 Ne 13

40 Ca( 18 O, 18 Ne) MeV FWHM ~ 0.5 MeV 14 The 40 Ar 0 + ground state is well separated from the first excited state 2 + at 1.46 MeV

40 Ca g.s. (0 + )( 18 O, 18 Ne) 40 Ar g.s. ( MeV 15 preliminary

counts 40 Ca( 18 O, 20 Ne) MeV 0°< θ lab <10° g.s. l = 0 g.s. * l = 2 Preliminary 16 O( 18 O, 20 Ne) 14 C 12 C( 18 O, 20 Ne) 10 Be E* (MeV) Suppression of l = 0 in the transfer l = 4 l = 6 l = 8 Preliminary spectrum of 38 Ar