1. NUMEN
Determining the Nuclear Matrix Elements of Neutrinoless Double Beta Decays by Heavy-Ion Double Charge Exchange Reactions
Proponenti: F. CAPPUZZELLO1,2, C. AGODI1, D.L. BONANNO3, D.G. BONGIOVANNI3, V. BRANCHINA1,3, L. CALABRETTA1, A. CALANNA1, D. CARBONE1, M. CAVALLARO1, M. COLONNA1, A. CUNSOLO1, G. CUTTONE1, A. FOTI1,3, P. FINOCCHIARO1, V. GRECO1,2, G. LANZALONE1,4, F. LONGHITANO3, D. LO PRESTI2,3, A. MUOIO1,5, L. PANDOLA1, D. RIFUGGIATO1, S. TUDISCO1
1 INFN – LABORATORI NAZIONALI DEL SUD, CATANIA, ITALY
2 DIPARTIMENTO DI FISICA E ASTRONOMIA, UNIV. DI CATANIA, CATANIA, ITALY
3 INFN – SEZIONE DI CATANIA, CATANIA, ITALY
4 UNIV. DEGLI STUDI DI ENNA "KORE", ENNA, ITALY
5 UNIV. DEGLI STUDI DI MESSINA, MESSINA, ITALY
Collaborazioni attivate
INFN LNF
INSTITUTO DE FISICA DA UNIVERSIDADE DE SAO PAULO, BRAZIL
INST. DE FISICA DA UNIV. FEDERAL FLUMINENSE, NITEROI, BRAZIL
CICANUM, UNIVERSIDAD DE COSTA RICA, SAN JOSE, COSTA RICA
DEP. OF PHYSICS AND HINP, THE UNIV. OF IOANNINA, IOANNINA, GREECE
INSTITUT FÜR THEORETISCHE PHYSIK, GIESSEN UNIVERSITY, GERMANY
DÉPARTEMENT DE PHYSIQUE, UNIVERSITÉ HASSAN II – CASABLANCA, MOROCCO
CERN
BROKHAVEN NATIONAL LABORATORY
INSTITUTE OF MODERN PHYSICS, CHINESE ACADEMY OF SCIENCES, LANZHOU, CHINA
RCNP, OSAKA UNIVERSITY, OSAKA, JAPAN
Spokespersons: F. Cappuzzello and C. Agodi
LNS
CSNIII, 31 Marzo 2015

2. Great new physics inside
Double β-decay
Within standard model
Beyond standard model
Great new physics inside
but one should know Nuclear Matrix Element

3. 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

4. but requires Nuclear Matrix Element (NME)!
New physics for the next decades
but requires Nuclear Matrix Element (NME)!
Calculations (still sizeable uncertainties): QRPA, Large scale shell model, IBM …..
Measurements (still not conclusive for 0):
(+, -)
single charge exchange (3He,t), (d,2He)
electron capture
transfer reactions …
A new experimental tool: heavy-ion Double Charge-Exchange (DCE)
E. Caurier, et al., PRL 100 (2008)
N. L. Vaquero, et al., PRL 111 (2013)
J. Barea, PRC 87 (2013)
T. R. Rodriguez, PLB 719 (2013) 174
F.Simkovic, PRC 77 (2008)
N. Auerbach, Ann. Of Phys. 192 (1989) 77
S.J. Freeman and J.P. Schiffer JPG 39 (2012)
D.Frekers, Prog. Part. Nucl. Phys. 64 (2010) 281
J.P. Schiffer, et al., PRL 100 (2008)

5. More about NME For L = 0 decays Gamow-Teller like Fermi like
Warning: Normally the coupling constants gA and gV are kept out form the matrix element and we talk of reduced matrix elements

6. State of the art NME calculations
Courtesy of Prof. F.Iachello

7. A new esperimental tool: DCE

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

9. Double charge exchange reactions Abandoned for  physics
Pion DCE
(π+, π-) or (π-, π+)
Zero spin
Very different mechanism for Gamow-Teller (GT)
K.K. Seth et al., Phys.Rev.Lett. 41 (1978) 1589
Direct mechanism: isospin-flip processes
Heavy Ion DCE
Very low cross sections
Sequential mechanism: two-proton plus two-neutron transfer or vice-versa
D.R.Bes, O. Dragun, E.E. Maqueda, Nucl. Phys. A 405 (1983) 313.

10. Heavy-ion DCE Sequential nucleon transfer mechanism 4th order:
Brink’s Kinematical matching conditions 1
D.M.Brink, et al., Phys. Lett. B 40 (1972) 37
Meson exchange mechanism 2nd order: 2

11. 0 vs HI-DCE
Initial and final states: Parent/daughter states of the 0ββ are the same as those of the target/residual nuclei in the DCE;
Spin-Isospin mathematical structure of the transition operator: Fermi, Gamow-Teller and rank-2 tensor together with higher L components are present in both cases;
Large momentum transfer: A linear momentum transfer as high as 100 MeV/c or so is characteristic of both processes;
Non-locality: both processes are characterized by two vertices localized in two valence nucleons. In the ground to ground state transitions in particular a pair of protons/neutrons is converted in a pair of neutrons/protons so the non-locality is affected by basic pairing correlation length;
In-medium processes: both processes happen in the same nuclear medium, thus quenching phenomena are expected to be similar;
Relevant off-shell propagation in the intermediate channel: both processes proceed via the same intermediate nuclei off-energy-shell even up to 100 MeV.

12. About the reaction mechanism

13. Connection between -decay and Single Charge Exchange
Y. Fujita Prog. Part. Nuc. Phys. 66 (2011) F. Osterfeld Rev. Mod. Phys. 64 (1992) 491
H. Ejiri Phys. Rep. 338 (2000) T.N. Taddeucci Nucl. Phys. A 469 (1997) 125
(3He,t): In general for B(GT)>0.05
𝐵(𝐺𝑇) [(3He,t);𝑞=0] 𝐵(𝐺𝑇) [β−decay] =1±0.05
Similar results for the (d,2He)
g.s.
Tz=1/2
Tz=-1/2
(3He,t)
b decay
1.01
2.21
2.74
2.98
0.98
2.17
2.65
2.88 5+ 3+ 7+
2Jπ
2713Al14
2714Si13
Strong interaction
Weak interaction

14. For heavier projectiles
(7Li,7Be)
𝐵(𝐺𝑇) [(7Li,7Be);𝑞=0] 𝐵(𝐺𝑇) [β−decay] =1±0.2
S. Nakayama PRC 60 (1999)
Confirmed by us on different nuclei: 11Be, 12B, 15C, 19O
Microscopic and unified theory of reaction and structure is mandatory for quantitative analyses
Best results for transitions among isospin multiplets in the projectiles as (7Ligs(3/2-),7Begs(3/2-))
(18Ogs(0+),18Fgs(1+)) should be better than (7Li,7Be) even if not really explored to now
See also
F.Cappuzzello et al. Phys.Lett B 516 (2001) 21-26
F.Cappuzzello et al. EuroPhys.Lett 65 (2004)
S.E.A.Orrigo, et al. Phys.Lett. B 633 (2006)
C.Nociforo et al. Eur.Phys.J. A 27 (2006)
M.Cavallaro Nuovo Cimento C 34 (2011) 1

15. Single CEX 116Sn(18O,18F)116In at 25 MeV/u
Single CEX 40Ca(18O,18F)40K
at 15 MeV/u
3.5° < θlab < 4.5°
Preliminary analysis!
x-section (2MeV < Ex < 3MeV)
≈ 0.5 mb/sr
x-section (within 1 MeV)
≈ 0.17 mb/sr
Extracted upper limit for B(GT) < 0.8
B(GT) from (d,2He) = 0.4
S.Rakers, et al., PRC 71 (2005)
Extracted B(GT) = 0.087
B(GT) from (3He,t) = 0.083
Y. Fujita

16. NME 2 - decay NME 0 - decay q-transfer like ordinary β-decay
(q ~ 0.01 fm-1 ~ 2 MeV/c)
only allowed decays possible
(L=0)
neutrino enters as virtual particle,
q~0.5fm-1 (~ 100 MeV/c)
degree of forbiddeness weakened
L=0,1,2……
Single state dominance
Closure approximation

17. Methodology for NME 2 - decay
Assumption: all the signs are positive in the coherent sum of the amplitudes!
(3He,t)
(β– type)
(d, 2He)
(β+ type)

18. Methodology for NME 0 - decay
DCE
Suhonen

19. Factorization of the charge exchange cross-section. . .
-decay transition strengths
(reduced matrix elements)
for single CEX:
𝑑𝜎 𝑑Ω 𝑞,𝜔 = 𝜎 𝛼 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝑞,𝜔 𝐵 𝑇 (𝛼) 𝐵 𝑃 (𝛼)
For small q
𝜎 𝐸 𝑝 ,𝐴 =𝐾( 𝐸 𝑝 ,0) 𝐽 𝑆𝑇 2 𝑁 𝑆𝑇 𝐷
unit cross-section
𝐹 𝑞,𝜔 = 𝐾( 𝐸 𝑝 ,𝜔) 𝐾( 𝐸 𝑝 ,0) 𝑒 − 1 3 𝑞 2 𝑟 2 𝑒 𝑝 𝜔 − 𝑎 0
generalization to DCE:
𝑑𝜎 𝑑Ω 𝐷𝐶𝐸 𝑞,𝜔 = 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔 𝐵 𝑇 𝐷𝐶𝐸 𝛼 𝐵 𝑃 𝐷𝐶𝐸 𝛼
For small q
𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 =𝐾( 𝐸 𝑝 ,0) 𝐽 ′ 𝑆𝑇 2 𝑁 𝑆𝑇 𝐷
𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔 = 𝐾( 𝐸 𝑝 ,𝜔) 𝐾( 𝐸 𝑝 ,0) 𝑒 − 𝑞 𝑟 𝑒 − ( 𝑞 − 𝑞 1 ) 2 𝑟 𝑒 𝑝 𝜔 − 𝑎 0

20. The unit cross section Single charge-exchange Double charge-exchange
𝜎 𝐸 𝑝 ,𝐴 =𝐾( 𝐸 𝑝 ,0) 𝐽 𝑆𝑇 2 𝑁 𝑆𝑇 𝐷
𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 =𝐾( 𝐸 𝑝 ,0) 𝐽 ′ 𝑆𝑇 2 𝑁 𝑆𝑇 𝐷
J’ST Volume integral of the VSTGVST potential, where 𝐺= 𝑛 |𝑛 𝑛| 𝐸 𝑛 −( 𝐸 𝑖+ 𝐸 𝑓 )/2 is the intermediate channel propagator (including off-shell)
JST Volume integral of the VST potential
𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 is the Holy Graal
If known it would allow to determine the NME from DCE cross section measurement, whatever is the strenght fragmentation

21. The volume integrals Volume integrals are larger at smaller energies
They enter to the fourth power in the unit cross section!
GT-F competion at low energy

22. INFN-LNS

23. The Superconducting Cyclotron (CS) at LNS

24. MAGNEX Achieved resolution Energy E/E  1/1000 Angle Δθ  0.2°
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.
F.Cappuzzello et al., Nature Comm (2015)
Achieved resolution
Energy E/E  1/1000
Angle Δθ  0.2°
Mass Δm/m  1/160
Optical characteristics
Measured values
Maximum magnetic rigidity
1.8 T m
Solid angle
50 msr
Momentum acceptance
-14.3%, +10.3%
Momentum dispersion for k= (cm/%)
3.68
Quadrupole
Dipole
Focal Plane
Detector
Scattering
Chamber

25. (18O,18Ne) DCE reactions at LNS
270 MeV
0° < θlab < 10° Q = -5.9 MeV
18O and 18Ne belong to the same multiplet in S and T
Very low polarizability of core 16O
Sequential transfer processes very mismatched Qopt  50 MeV
Target T = only T = 2 states of the residual

26. Experimental Set-up
18O7+ beam from Cyclotron at 270 MeV (10 pnA, 3300 C in 10 days)
40Ca solid target 300 μg/cm2
Ejectiles detected by the MAGNEX spectrometer
Unique angular setting: -2° < lab< 10° corresponding to a momentum transfer range from 0.17 fm-1 to about 2.2 fm-1
Measured
18O + 40Ca
18F + 40K
18Ne + 40Ar
20Ne + 38Ar
16O + 42Ca
Not measured

27. Particle Identification
Z identification
A identification
22Ne
21Ne
20Ne Na
19Ne
18Ne Ne F
Xfoc(m)
Eresid (ch)
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
Eresid (ch)

28. The role of the transfer reactions
270 MeV
Suppression of the 40Ca(18O,16O)42C channel
0°< θlab<10°
Very weak
40Ca
42Ca
counts
38Ar
40Ar
d/d(L=0; =0)  10 b/sr
Lmax = 8
Lmax = 6
g.s.* L = 2
Suppression of L = 0 in the pair transfer
Lmax = 4
g.s. L = 0
Suppression of L > 0 in the double pair transfer
E* (MeV)

29. Single charge exchange
Many overlapping states
2- is the strongest low lying transition
0+, 1+, 4- also present
1+ and 0+ cross section compatible with known values of B(GT) and B(F)
40Ca
40K
40Ar

30. 270 MeV
40Ca
42Ca
38Ar
40Ar
The 40Ar 0+ ground state is well separated from the first excited state 2+ at 1.46 MeV
FWHM ~ 0.5 MeV

31. preliminary 40Cag.s.(0+)(18O,18Ne)40Arg.s. (0+) @ 270 MeV
𝑑𝜎 𝑑Ω 𝐷𝐶𝐸 𝑞,𝜔 = 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔 𝐵 𝑇 𝐷𝐶𝐸 𝛼 𝐵 𝑃 𝐷𝐶𝐸 𝛼
𝑑𝜎 𝑑Ω 𝐷𝐶𝐸 𝑞,𝜔 = 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔
𝐵 𝑇 𝐷𝐶𝐸 𝐺𝑇 𝐵 𝑃 𝐷𝐶𝐸 𝐺𝑇  0.20
to be compared with 0.11
preliminary

32. Preliminary matrix elements
Pure GT
Pure F
A measurement at another energy is important to consolidate this NME
Pauli blocking about 0.14
Pauli blocking corrected result 1.9
to speculate on 48Ca

33. The NUMEN goals

34. The unit cross section (an ambitious task)
Studying if the 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 is a smooth (and thus controllable) function of Ep and A is the most ambitious goal of our project
This requires that a systematic set of appropriate data is built, facing the relative experimental challenges connected with the low cross sections and resolution requests
Goal N.1 for NUMEN

35. Measured DCE cross section and theory
The degree of complexity of DCE cross sections and 0 is comparable
The measured DCE cross sections provide a powerful tool for theory in order to give very stringent constraints in the NME estimation
The DCE processes can be artificially generated in the lab! (Few labs. as the LNS)
A new generation of DCE constrained 0 NME theoretical calculations can emerge
Promoting this kind of evolution is a main purpose of our project
Goal N.2 for NUMEN

36. DCE cross sections and sensitivity of 0 experiments
Providing relative NME information on hot cases of 0 is strongly required by the community in order to compare the sensitivity of different half-life experiments
This could impact in future development of the field
Goal N.3 for NUMEN

37. Conclusions and Outlooks
Exciting new fundamental physics is emerging beyond the standard model
Basic role of nuclear physics in the game
Many facilities for 0 half life, but not for the NME
Pioneering experiments at RCNP (Osaka) and LNS (Catania) are showing that the (18O,18Ne) cross section can be suitably measured
First results for the (18O,18Ne) are encouraging, showing that quantitative information on 0 NME are at our reach

38. LNS can realistically compete
The role of LNS
What we put on the table
We have MAGNEX, perhaps the most suitable instrument for these studies
We have a long tradition in heavy-ion physics, experimental and theoretical
We have a solid experience in accelerator physics
What we need to upgrade
We need to carefully explore other targets and reactions as (20Ne,20O) or (12C,12Be)
We need to have a factor more beam current from the accelerator
LNS can realistically compete

39. 40Ca(18O,18Ne)40Ar Projectile Target B(GT) = 3.27 B(GT) = 1.09 18O 18F
Super-allowed transition
GT strength not fragmented
Y. Fujita, private communication
40Ar
40Ca
40K 4- 1+
2.73
g.s. 0+
B(GT)=0.069(6)
B(GT)=0.023
B(GT)total < 0.15
Target
GT strength not much fragmented

40. About 40Ca ground state Pauli blocked
1f5/2
1f7/2
1d3/2
2s1/2
1d5/2
1p1/2
1p3/2
1s1/2 n p n p n p
|40Cag.s.>=0.88|[1d3/21d3/2]0+> |[1f7/21f7/2]0+>+0.06 |[1f5/21f5/2]0+>
Pauli blocked

41. Double Charge Exchange on 40Ca ground state
1f5/2
1f5/2
1f7/2
1f7/2
1d3/2
1d3/2
2s1/2
2s1/2
1d5/2
1d5/2
1p1/2
1p1/2
1p3/2
1p3/2
1s1/2
1s1/2 n p n p n p
40Cag.s.
40Kg.s.
40Arg.s.

42. 40Ca response to charge exchange
BGT=0.069(6)
About half of the total GT strenght goes to the 2.73 MeV state of 40K
Courtesy of Prof. Y. Fujita

43. Survey of heavy-ion DCE

44. Collaborazioni internazionali
INFN - Laboratori Nazionali del Sud, Catania, Italy; INFN –
Sezione di Catania, Catania, Italy;
Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy;
INFN – Laboratori Nazionali di Frascati
What next? ………………………
Instituto de Fisica Nuclear, Universidade de Sao Paulo, Brasil
Instituto de Fisica, Universidade Federal Fluminense, Niteroi, Rio de Janeiro, Brazil
Department of Physics and HINP, The University of Ioannina, Ioannina, Greece
Institute of Modern Physics, Chinese Academy of Sciences, 509 Nanchang Road, Lanzhou, China
LRSA, Department of Physics, Faculty of Science Ben M'Sik, University Hassan II Mohammedia-Casablanca, Morocco
What next? ………………………….

45. Past experimental attempts
124 MeV
51 MeV
10° < θlab < 30° Q = -4.8 MeV
θlab = 8° Q = MeV
J. Cerny, et al., Proc. 3° Int. Conf. on Nuclei Far from Stability, Cargese, 1976
D.M.Drake, et al., Phys. Rev. Lett. 45 (1980) 1765
C.H.Dasso, et al., Phys. Rev. C 34 (1986) 743

46. Past experimental attempts
24Mg(18O,18Ne)24Ne at 1.37GeV
J.Blomgren, et al., Phys. Lett. B 362 (1995) 34

47. Double charge exchange reactions at RCNP (Japan)
80 AMeV
Grand Raiden spectrometer
Beam energy 80AMev
Beam intensity 25 pnA
Limitation: Energy resolution 1.2 MeV
Interest for 48Ca (CANDLES)
T. Uesaka et al., Prog. of Theor. Phys. 196 (2012) 150
H.Matsubara et al. Few Body Syst DOI /s

48. Preliminary FPD cost estimation
Gas tracker
Detector cost estimate: GEM foils (~ 5 kCHF), Readout PCB (~ 15 kCHF), Mechanics (~ 30 – 40 k€ -??)
Gas system (MKS like): ~ 20 k€
HV system (CAEN): ~ 10 k€
Readout system, possible solution (tbc) with APV25 + SRS (from RD51): ~ 150 k€
Global cost (order of magnitude): ~ 250 k€
Silicon detector wall
Silicon detectors (for 108 ions/cm2): ~ 130 k€
Silicon mechanics: ~ 35 k€
Silicon electronics: ~ 60 k€
Power supply: ~ 80 k€
Global cost (order of magnitude): ~ 300 k€

49. - - + Induction Pads GASSIPLEX Proportional Wires (750 V)
SINGOLA PAD
Induction Pads
Proportional Wires
Frisch Grid
Silicon detectors
STRIP - +
Induction Pads
GASSIPLEX PC
cathode
Proportional Wires (750 V)
DC1
DC2
DC3
DC4
Frisch grid (0 V) -
Drift electrons

50. The reconstruction problem
The image at the focus is meaningful if it can give us information about the object in its position!
To see means to reconstruct
Inversion of the transport matrix
Geometrical Parameters measured at the FPD
Physical Parameters at the target
The optical aberrations make this reconstruction difficult
F. Cappuzzello, et al., NIM A 638, (2011) 74

51. MAGNEX: a ray-reconstruction spectrometer
Possible definition: spectrometer reconstructing a net image by an optically aberrated one
Practically
One needs
High order inversion algorithms (10th order for MAGNEX)
Specialized Focal Plane Detectors (FPD) to measure positions and angles at the focus
Detailed knowledge of the magnetic field maps
inversion
Long learning step

52. The 40Ca(18O,18Ne)40Ar case: To be compared to:
Assuming pure GT
The 40Ca(18O,18Ne)40Ar case:
𝑑𝜎 𝑑Ω 𝐷𝐶𝐸 𝑞,𝜔 = 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔 𝐵 𝑇 𝐷𝐶𝐸 𝛼 𝐵 𝑃 𝐷𝐶𝐸 𝛼
87 μb/sr
0.72
0.17
To be compared to:
B2[GT;18Ogs(0+) 18Fgs(1+)] * B2[GT;40Cags(0+) 40K0-6MeV(1+)] =
= 3.56
Y. Fujita private communication
0.098
D.J.Mercer et al. Phys. Rev. C 49 (1994) 3104

53. The 40Ca(18O,18Ne)40Ar case: To be compared to:
Assuming pure F
The 40Ca(18O,18Ne)40Ar case:
𝑑𝜎 𝑑Ω 𝐷𝐶𝐸 𝑞,𝜔 = 𝜎 𝛼 𝐷𝐶𝐸 𝐸 𝑝 ,𝐴 𝐹 𝛼 𝐷𝐶𝐸 𝑞,𝜔 𝐵 𝑇 𝐷𝐶𝐸 𝛼 𝐵 𝑃 𝐷𝐶𝐸 𝛼
39 μb/sr
0.77
0.36
To be compared to:
B2[F;18Ogs(0+) 18Fgs(1+)] * B2[F;40Cags(0+) 40K0-6MeV(1+)]
= 0.138
= 4.00
0.55
Y. Fujita private communication
D.J.Mercer et al. Phys. Rev. C 49 (1994) 3104

54. A quick historical background
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
The Higgs mechanism cannot explain the mass of neutrinos

55. Double β-decay
𝑍 𝐴 𝑋 𝑁 → 𝑍−2 𝐴 𝑌 𝑁+2 + 2𝑒 − + 2 𝜈
Process mediated by the weak interaction occurring in even-even nuclei where the single -decay is energetically forbidden
The role of the pairing force

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

57. Normal vs inverted hierarchy
Neutrino oscillation experiments sensitive to m

58. Matter vs Antimatter
Leptonic number = 0 at Big Bang
All the physics we know does conserve the leptonic number
Why the matter dominates over antimatter?
Majorana neutrinos can explain that since they do not conserve leptonic number!

59. From Jouni Suhonen, JYFL (Finland)

60. From Jouni Suhonen, JYFL (Finland)

61. Beyond the standard model
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

62. Moving towards hot-cases
Caveat
The (18O,18Ne) reaction is particularly advantageous, but it is of β+β+ kind;
None of the reactions of β-β- kind looks like as favourable as the (18O,18Ne).
(18Ne,18O) requires a radioactive beam
(20Ne,20O) or (12C,12Be) have smaller B(GT)
In some cases gas target will be necessary, e.g. 136Xe or 130Xe
In some cases the energy resolution is not enough to separate the g.s. from the excited states in the final nucleus  Coincident detection of -rays
A strong fragmentation of the double GT strength is known in the nuclei of interest compared to the 40Ca.

63. Major upgrade of LNS facilities
The CS accelerator current upgrade (from 100 W to 5-10 kW);
The MAGNEX focal plane detector will be upgraded from 1 khz to 100 khz
The MAGNEX maximum magnetic rigidity will be increased
An array of detectors for -rays measurement in coincidence with MAGNEX will be built
The beam transport line transmission efficiency will be upgraded from about 70% to nearly 100%
The target technology for intense heavy-ion beams will be developed

64. MAGNEX Focal Plane Detector
Entrance window
Ion trajectory
Silicon detectors
Cathode (-950V)
Frisch grid (0V)
Induction pads
DC wires (750V)
φfoc - +
57 Silicon Detectors
→ Eres
5 Proportional Wires
→ ΔE
4 Induction Strip
→ X1,X2,X3,X4
→ Xfoc,θfoc
4 Drift Chamber (DC)
→ Y1,Y2,Y3,Y4
→ Yfoc,φfoc
Ion identification
Ray-reconstruction
C.Boiano et al., IEEE 55 (2008) 3563
M.Cavallaro et al. EPJ A 48: 59 (2012)
D.Carbone et al. EPJ A 48: 60 (2012)
Section view

65. It works fine but it is limited to 1 kHz
We need to go to 100 kHz
A major upgrading is required but preserving the good tracking and particle identification

66. The proposed idea (gas tracker)
From To
GEM (THGEM, WALL, Micromega) gas tracker
Multiwire gas tracker
Ion trajectories
Long occupancy (0.5 ms)
Very high rate capability (few MHz/mm2)

67. Gas tracker with GEM readout
Preliminary study
Courtesy of G. Bencivenni INFN-LNF
Gas tracker with GEM readout
operated at low pressure (10 mbar*) and low gain (G~100)
drift length ~ 200 mm; TPC thickness ~ 50 mm; TPC length ~ 1000 mm
Gas mixture (tbd): Ar/CO2  Vdrift ~ 50 µm/ns
GEM foils 50x1000 mm2 (n. 3 amplification stages)
Readout PCB (resistive - tbd) segmented in 40 rows of pads (1x1 mm2, tbd)  40 kchs
XY space resolution (with analog readout – charge centroid - tbd)  σXY ~ 200 – 300 µm
Z space resolution (by drift time measurement : σT ~ ns)  σZ = Vdriftx σT ~ 500µm
Possible issues (to be studied carefully): gas mixture, resistive PCB segmentation, ion feedback, electronics sensitivity
* See for example arXiv: (Property of LCP-GEM in Pure Dimethyl Ether at Low Pressure): in 20 Torr DME, G~50-300

68. The proposed idea (PID wall)
From To
Wall of 60 stopping 7 X 5 cm2 silicon pad detectors
Wall of ~ X 1 cm2 telescopes of SiC – CsI detectors
PID function decoupled from gas tracker
Double-hit probability at 100 kHz < 1%
Acceptable uncertainties in the absolute cross section measurement
Much smaller maintenance cost
First irradiation tests successfully performed in collaboration with CNR
Double-hit probability at 100 kHz > 30%
Large uncertainties in the absolute cross section measurement
High-cost for breaking with localized exposure

69. The proposed idea - -ray calorimeter
MAGNEX to measure high resolution energy spectra for well identified reaction products
An array of scintillators (NaI, CsI, LaBr3…) to improve the energy resolution in the energy spectra, with good efficiency

70. The Phases of NUMEN project
LNS
Phase1: The experimental feasibility
Phase2: “hot” cases optimizing the experimental conditions and getting first results
Phase3: The facility Upgrade (Cyclotron, MAGNEX, beam line, …..):
Phase4 : The systematic experimental campaign
Preliminary time table
year
2013
2014
2015
2016
2017
2018
2019
2020
Phase1
Phase2
Phase3
Phase4

71. An intense experimental activity in phase 2

72. An intense R&D activity in phase 2

73. Attività NUMEN prevista 2015
Esperimento al CS (LNS) MAGNEX, richiesta tempo macchina per le prime reazioni: primo fascio febbraio
116Sn (18O,18Ne) 116Cd
116Cd (20Ne,20O) 116Sn
Sviluppo prototipi del tracciatore a gas su tecnologie GEM, THGEM, WELL, Micromega
Sviluppo prototipi del telescopio di identificazione su tecnologia SiC+CsI
Test di scintillatori
Sviluppo prototipi schede di elettronica di front-end e digitalizzazione
Technical Design Report per nuovi rivelatori
Sviluppo modelli teorici

74. A fundamental property
The complicated many-body heavy-ion scattering problem is largely simplified for direct quasi-elastic reactions
V (r ,) = U (r) + W(r ,)
Optical potential
Residual interaction
For charge exchange reactions the W(r ,) is ‘small’ and can be treated perturbatively
In addition the reactions are strongly localized at the surface of the colliding systems and consequently large overlap of nuclear densities are avoided
Accurate description in fully quantum approach, eg. Distorted Wave techniques
Microscopic derived double folding potentials are good choices for U (r)
Microscopic form factors work for charge exchange reactions