1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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., (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

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

10. 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

11. 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

12. 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

13. Past experimental attempts
LNS
Past experimental attempts
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

14. 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.

15. Phase1 : the experimental feasibility
LNS
Phase1 : the experimental feasibility
PILOT experiment Ca(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

16. 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

17. 40Cag.s.(0+)(18O,18Ne)40Arg.s. (0+)@ 270 MeV
LNS
40Cag.s.(0+)(18O,18Ne)40Arg.s. 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

18. …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

19. 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

20. 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

21. 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

23. 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

24. 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