NUclear Matrix Element for Neutrinos LNS NUclear Matrix Element for Neutrinos Determining the Nuclear Matrix Elements for 0 double β-decay by Heavy-Ion Double Charge Exchange Reactions Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud Catania C. Agodi, F. Cappuzzello, M. Bondì, L. Calabretta, F. Cappuzzello, D. Carbone, M. Cavallaro, M. Colonna, A. Cunsolo, G. Cuttone, A. Foti, P. Finocchiaro, V. Greco, L. Pandola, D. Rifuggiato, S. Tudisco INFN - Laboratori Nazionali del Sud, Catania, Italy; INFN - Sezione di Catania, Catania, Italy; Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy; C.Agodi – Roma, CSN3 31- Marzo 2014

Historical background LNS Historical background Neutrinos play a fundamental role in various areas of modern physics from nuclear and particle physics to cosmology. 1986: first discovery of 2 decay predicted by Maria Goeppert Mayer in 1935 (today found in 12 nuclei) 1998: discovery of neutrino oscillations and the non-zero mass of neutrinos, predicted by Pontecorvo in 1957 2013: discovery of Higgs boson and start of the era of research beyond the standard model Described for the first time by Maria Goeppert-Mayer (1935), based on the Fermi theory The Higgs mechanism cannot explain the mass of neutrinos C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS Double beta decay Observable when the (much faster) single-beta decay is forbidden by energy conservation (e.g. in even-even nuclei) Role of the pairing force: The displacement of the even–even and odd-odd mass parabolas due to the pairing energy is responsible for the existence of double beta decay candidates C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS The  decay 2 double β-decay Respect the conservation low. Does not distinguish between Dirac and Majorana Experimentally observed in several nuclei  and anti- can be distinguished  and anti- are the same 82Se, 100Mo, 48Ca,76Ge, … 0 double β-decay Neutrino has mass Neutrino is Majorana particle Violates the leptonic number conservation Experimentally not observed Forbidden in the standard model C. Agodi Roma - CSN3 31- Marzo 2014

The role of nuclear physics LNS The role of nuclear physics In the 0νββ double beta decay the decay rate can be expressed as a product of independent factors, that also depends on a function containing physics beyond the standard model throught the masses and the mixing coefficients of the neutrinos species : A lot of new physics inside ! Thus, if the M0νββ nuclear matrix elements were known with sufficient precision, the neutrino mass could be established from 0νββ decay rate measurements. C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 Search for 0 decay: a worldwide race Experiment Isotope Lab Status GERDA 76Ge LNGS Phase I completed Migration to Phase II CUORE0 /CUORE 130Te Data taking / Construction Majorana Demonstrator SURF Construction SNO+ SNOLAB R&D / Construction SuperNEMO demonstrator 82Se (or others) LSM Candles 48Ca Kamioka COBRA 116Cd R&D Lucifer 82Se DCBA many [Japan] AMoRe 100Mo [Korea] MOON C. Agodi Roma - CSN3 31- Marzo 2014

The unconfermed claim on 76Ge LNS The unconfermed claim on 76Ge Claim from the re-analysis of the Heidelberg-Moscow data Klapdor-Kleingrothaus et al. NIM A 522 (2004) PLB 586 (2004) Unconfirmed (and controversial) claim Dominates the field since 2004 Difficult to scrutinize by experiments not using 76Ge because of NME uncertainties A later publication by the same group (Mod. Phys. Lett. A 21, 1547 (2006)) reports T1/20ν = 2.23 x1025 yr after PSD analysis. Inconsistencies have been pointed out (missing efficiency factors!) in the conversion counts  T1/2 Klapdor-Kleingrothaus et al., NIM A 522 (2004), PLB 586 (2004): 71.7 kg yr Bgd 0.17 / (kg yr keV) 28.75 ± 6.87 events (bgd:~60) Claim: 4.2 evidence for 0ββ reported T1/20ν = 1.19 x1025 yr C. Agodi Roma - CSN3 31- Marzo 2014

State of art of NME calculations LNS State of art of NME calculations The calculation of mee from T1/2 requires the knowledge of the nuclear matrix element A. Giuliani and A. Poves, Adv. in High Energy Phys., 857016 (2012) Complex theoretical calculations, and not so many groups working on it worldwide Different approaches (flavours of QRPA, Shell Model, etc.) can differ by a factor of 2 Data suitable for the benchmark of the calculations not readily available the agreement of calculation does not imply correctness! C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS What’s next ? C. Agodi Roma - CSN3 31- Marzo 2014 !

LNS The idea Determining the Nuclear Matrix Elements for Neutrinoless Double Beta Decays by Heavy-Ion Double Charge Exchange Reactions HI Double charge exchange reactions are characterized by the transfer of leaving the mass number unchanged C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS Heavy-Ion DCE and 0νββ decay The initial and final nuclear states involved in DCE reaction and ββ decay are the same and the operators connecting them have the same spin-isospin mathematical structure. Both have the property to carry a relevant amount of linear momentum (of the order of 100 MeV/c). Even if the two processes are mediated by different interactions, the involved nuclear matrix elements are connected. A similar link is firmly established between single β decay strengths and single charge exchange reaction cross sections, such as (n,p) or (p,n) . These quantities are found proportional, at a level of few percent, under specific dynamical conditions. C. Agodi Roma - CSN3 31- Marzo 2014

Double charge exchange reactions LNS Double charge exchange reactions Heavy Ion DCE Direct mechanism: isospin-flip processes Sequential mechanism: two-proton plus two-neutron transfer or vice-versa Heavy ion-DCE: estimation of both contributions Sequential mechanism: Brink’s Kinematical matching conditions D.M.Brink, et al., Phys. Lett. B 40 (1972) 37 Direct mechanism: Momentum transfer correction of the GT unit cross- section : T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125 Direct DCE cross-section as the product of the two charge-exchange ones C. Agodi Roma - CSN3 31- Marzo 2014

Past experimental attempts LNS Past experimental attempts 40Ca(14C,14O)40Ar @ 51 MeV 10° < θlab < 30° Q = -4.8 MeV Few experimental attempts: not conclusive because of the very poor yields in the measured energy spectra and the lack of angular distributions, due to the very low cross-sections involved. not easy to measure, in the same experimental conditions, the different competitive reaction channels (limit due to the prohibitive small cross-sections). D.M.Drake, et al., Phys. Rev. Lett. 45 (1980) 1765 C.H.Dasso, et al., Phys. Rev. C 34 (1986) 743 C. Agodi Roma - CSN3 31- Marzo 2014

The experimental tool @ LNS: MAGNEX Measured Resolution: Energy E/E  1/1000 Angle Δθ  0.3° Mass Δm/m  1/160 Optical characteristics Actual values Maximum magnetic rigidity (Tm) 1.8 Solid angle (msr) 50 Momentum acceptance (cm/%) -14%, +10% Momentum dispersion 3.68 First order momentum resolution 5400 F. Cappuzzello et al., MAGNEX: an innovative large acceptance spectrometer for nuclear reaction studies, in Magnets: Types, Uses and Safety (Nova Publisher Inc., NY, 2011) pp. 1–63.

Phase1 : the experimental feasibility LNS Phase1 : the experimental feasibility PILOT experiment 40Ca(18O,18Ne)40Ar with the competing processes: 40Ca(18O,18F)40K single charge exchange 40Ca(18O,20Ne)40Ar two-proton transfer 40Ca(18O,16O)42Ca two-neutron transfer. 21Ne 22Ne 20Ne 19Ne 18Ne ECPcorr (Ch) Xfoc (m) Eresid (Ch) F Ne Na C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS Experimental set-up 18O7+ beam from Cyclotron at 270 MeV (10 pnA) 40Ca solid target of 300 μg/cm2 Ejectiles detected by the MAGNEX spectrometer Angular setting 18O + 40Ca 18F + 40K 18Ne + 40Ar 20Ne + 38Ar 16O + 42Ca Measured Not measured C. Agodi Roma - CSN3 31- Marzo 2014

40Cag.s.(0+)(18O,18Ne)40Arg.s. (0+)@ 270 MeV LNS 40Cag.s.(0+)(18O,18Ne)40Arg.s. (0+)@ 270 MeV Very preliminary lab (deg) Counts/0.25 Scattering angle (deg) dσ/dω (µb/sr) sequential transfer direct DCE preliminary suitable information on the DCE reaction mechanism can be extracted ! C. Agodi Roma - CSN3 31- Marzo 2014

…experimental limits LNS Determination of nuclear matrix elements seems to be at our reach… BUT : About one order of magnitude more yield would have been necessary for the reaction studied, especially at backward angles in order to extract more quantitative information on the background generated by competing multi-nucleon transfer reactions; In some cases gas target will be necessary, e.g. 136Xe or 130Xe, which are normally much thinner than solid state ones, with a consequent reduction of the collected yield; In some cases the energy resolution we can provide (about half MeV) is not enough to separate the ground state form the excited states in the final nucleus. In these cases the coincident detection of -rays from the de-excitation of the populated states is necessary, but at the price of the collected yield. An upgraded set-up, able to work with two orders of magnitude more current than the present, is thus necessary! This goal can be achieved by a substantial change in the technologies used in the beam extraction and in the detection of the ejectiles C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS Phase2: Two “hot” cases To optimize the experimental conditions to open a new and challenging research field, we propose an experimental Phase2 using, as probe, two targets of interest as candidate nuclei for the 0νββ decay: C. Agodi Roma - CSN3 31- Marzo 2014

The experimental campaign LNS The experimental campaign To perform the experimental campaign that we propose it is necessary a PHASE3: Facility Upgrade CS upgrade to give high beam intensity a new focal plane detector, suitable to resist to high rates 3. a modular gamma detector system for coincidences measurements PHASE4 : Experimental campaign A series of experimental campaigns at high beam intensities and long experimental runs in order to reach in each experiment integrated charge of hundreds of mC up to C, for the experiments in coincidences, spanning all the variety of 0νββ decay candidate isotopes, like: 48Ca,82Se,96Zr,100Mo,110Pd,124Sn,128Te,130Te,136Xe,148Nd,150Nd,154Sm,160Gd,198Pt C. Agodi Roma - CSN3 31- Marzo 2014

C. Agodi Roma - CSN3 31- Marzo 2014 LNS Summary An innovative technique to access the nuclear matrix elements entering in the expression of the life time of the 0νββ decay by relevant cross sections of double charge exchange reactions is proposed. The basic point is the coincidence of the initial and final state wave-functions in the two classes of processes and the similarity of the transition operators. First pioneering experimental results obtained at the INFN-LNS with MAGNEX for the 40Ca(18O,18Ne)40Ar reaction at 270 MeV, give encouraging indication on the capability of the proposed technique to access relevant quantitative information. A main limitation on the beam current delivered by the accelerator and the maximum rate accepted by the MAGNEX focal plane detector must be sensibly overcome with the upgrade of the LNS facilities. rigorous determination of the absolute cross sections values for all the system of interest, to the challenging determination of the 0νββ decay nuclear matrix elements An amazing time for new and challenging nuclear research field in the era of the physics beyond the Standard Model! C. Agodi Roma - CSN3 31- Marzo 2014

Beyond the standard model C. Agodi Roma - CSN3 31- Marzo 2014 LNS 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 1015 GeV C. Agodi Roma - CSN3 31- Marzo 2014

The role of the involved nuclei LNS The role of the involved nuclei The nucleon transfer reaction cross sections can be deduced from simple dynamic considerations, according to semi-classical arguments, when the incident energy is above the Coulomb barrier. Assuming a mechanism where a cluster is transferred: the cross section tends to maximize within a Q-window, which depends on the reaction Qgg, on the target, on the projectile radii and on the incident energy. Brink’s matching conditions D.M. Brink, Phys. Lett. B 40 (1972) 37-40 The survival of a preformed pair in a transfer process is favoured when the initial and final orbitals are the same