1. LNS Determining NME by Heavy-Ion Double Charge Exchange
Clementina Agodi - Laboratori Nazionali del Sud – INFN - Italy
Jason and the Golden Fleece
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

2. LNS
Introduction
Neutrinoless double beta decay is potentially the best resource to probe the Majorana or Dirac nature of neutrino and to extract its effective mass.
2ββ-decay predicted by the Standard Model
0ββ-decay forbidden by the Standard Model
Process mediated by the weak interaction occurring in even-even nuclei where the single -decay is energetically forbidden
The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

3. 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.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

4. New physics for the next decades!
LNS
The state of the art
New physics for the next decades!
The evaluation of NME:
Calculations (still sizeable uncertainties): QRPA, Large scale shell model, IBM …..
Giuliani and A. Poves, Adv. in High Energy Phys., (2012)
Measurements (still not conclusive for 0):
(+, -)
single charge exchange (3He,t)
electron capture
transfer reactions …
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)
F.Iachello et al. NPB (2013)
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)
D.Frekers et al. NPA 916 (2013)
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

5. A new esperimental tool: DCE
LNS
A new esperimental tool: DCE
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

6. HI Double Charge Exchange
LNS
HI Double Charge Exchange
HI Double charge exchange reactions are characterized by the transfer of two units of the isospin (ΔTz= ± 2) leaving the mass number unchanged
2 n
E-x = MeV
Direct mechanism: isospin-flip processes
18Ne+11Li
20Ne+18Li
2 p
E-x = MeV
2 p
E-x = MeV
direct
Heavy Ion DCE
16O+13B
18O+11B
2 n
E-x = -18 MeV
Sequential mechanism: two-proton plus two-neutron transfer or vice-versa
11B(18O,18Ne)11Li
D.R.Bes, O. Dragun, E.E. Maqueda, Nucl. Phys. A 405 (1983) 313.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

7. Heavy-ion DCE LNS 1 2 Sequential nucleon transfer mechanism 4th order:
Brink’s Kinematical matching conditions
D.M.Brink, et al., Phys. Lett. B 40 (1972) 37
Meson exchange mechanism 2nd order:
Momentum transfer correction of the GT unit cross- section 2
T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125
Direct DCE cross-section as the product of the two charge-exchange ones
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

8. LNS
0 vs 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.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

9. Factorization of the charge exchange cross-section
LNS
Factorization of the charge exchange cross-section
for single CEX:
-decay transition strengths
(reduced matrix elements)
α= Fermi (F)
or Gamow Teller (GT)
Mj(α) 2= B(α)
C.J Guess,et al, PRC (2011)
The factor F(q,) describes the shape of the cross-section distribution as a function of the linear momentum transfer and the excitation energy.
unit cross-section
T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125
In the hypothesis of a surface localized process (for direct quasi elastic processes):
generalization to DCE:
In analogy to the single charge-exchange, the dependence of the cross-section from q is represented by a Bessel function.
unit cross-section
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

10. This is what happens in single charge exchange :
LNS
The unit cross section
In the σ(Ep,A) the specificity of the single or double charge exchange is express through the volume integrals of the potentials: the other factors are general features of the scattering.
JST Volume integral of the VST potential
Single charge-exchange
Double charge-exchange
If known it would allow to determine the NME from DCE cross section measurement, whatever is the strenght fragmentation
This is what happens in single charge exchange :
B(GT;CEX)/B(GT;-decay)  1 within a few % especially for the strongest transitions
In a simple model one can assume that the DCE process is just a second order charge exchange, where projectile and target exchange two incorrelated isovector virtual mesons.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

11. 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

12. LNS
DCE at LNS
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

13. The experiment: 40Ca(18O,18Ne)40Ar@LNS
18O7+ beam from LNS 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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

14. The experimental SET-UP@ 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. Differential cross-section of the transition
LNS
Preliminary results
Measured energy spectrum of 40Ar at very forward angles with an energy resolution of FWHM ~ 0.5 MeV .
Differential cross-section of the transition
270 Mev
FWHM ~ 0.5 MeV !
preliminary
The 40Ar 0+ ground state is well separated from both the first excited state 40Ar 2+ at 1.46 MeV and the 18Ne excited state at MeV
The position of the minima is well described by a Bessel function : such an oscillation pattern is not expectd in complex multistep transfer reactions.
dσDCE /dΩ=11μb/sr at θcm=00
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

16. LNS
The NUMEN Project
C. Agodi, F. Cappuzzello, M. Bondì, L. Calabretta, 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;
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

17. LNS
Few “hot” cases
To optimize the experimental conditions to open a new and challenging research field, we propose an experimental campaign using, as probe, few targets of interest as candidate nuclei for the 0νββ decay such as 76Se, 76Ge, 116Cd, 130Te :
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

18. The experimental campaign
LNS
The experimental campaign
To perform the experimental campaign that we propose it is necessary a
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
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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

19. The Holy Graal: the unit cross section
LNS
The Holy Graal: the unit cross section
Studying if the σDCE is a smooth 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 challanges connected with the low cross sections and resolution requests
Goal N.1 for NUMEN
A new generation of DCE constrained 0 NME theoretical calculations
can emerge
The measured DCE cross sections provide a powerful tool for theory in order to give very stringent onstraints in the NME estimation The DCE processes can be artificially generated in the lab! (Few labs. as the LNS)
Goal N.2 for NUMEN
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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

20. 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!
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

22. Determination of nuclear matrix elements seems to be at our reach…
LNS
…experimental limits
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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

23. Check the validity of the factorization
LNS
Check the validity of the factorization
We deduce the unit cross section for the DCE process assuming a double GT
Transition. Taking into account single charge exchange data:
40Ca response to charge exchange
Courtesy of Prof. Y. Fujita
BGT=0.069(6)
About half of the total GT strenght goes to the 2.73 MeV state of 40K
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

24. Assuming incoherent sum of F + GT The 40Ca(18O,18Ne)40Ar case:
13 μb/sr
7 μb/sr
Here we estimated the uncertainty by checking the sensitivity of the results to the used parameters and found that it is is about a factor 2.
To be compared to:
Despite the approximations used and the simplified scheme considered these results indicate that the DCE unit cross section is at our reach,
in analogy to the single charge exchange!
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

25. 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

26. A fundamental property
LNS
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
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

27. 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

28. 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

29. The experimental feasibility
LNS
The experimental feasibility
PILOT experiment 270 MeV
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

30. Moving towards hot-cases
LNS
Moving towards hot-cases
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.
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

31. B2[GT;18Ogs(0+) 18Fgs(1+)] * B2[GT;40Cags(0+) 40K0-6MeV(1+)]
Assuming pure GT
LNS
In the 40Ca(18O,18Ne)40 case
0.15  0.07
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
corresponding to the product of the known B(GT) values
for the transitions in the projectile and target
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

32. Measured energy spectrum
LNS
Measured energy spectrum
Measured energy spectrum of 40Ar at very forward angles.
FWHM ~ 0.5 MeV !
The 40Ar 0+ ground state is well separated from both the first excited state 40Ar 2+ at 1.46 MeV and the 18Ne excited state at MeV
C. Agodi Roma - CSN3 31- Marzo 2014

33. Differential cross-section of the transition
LNS
Preliminary results
Differential cross-section of the transition
270 Mev
preliminary
The position of the minima is well described by a Bessel function : such an oscillation pattern is not expectd in complex multistep transfer reactions.
dσDCE /dΩ=11μb/sr at θcm=00
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014

34. B2[F;18Ogs(0+) 18Fgs(1+)] * B2[F;40Cags(0+) 40K0-6MeV(1+)]
LNS
Assuming pure F
The 40Ca(18O,18Ne)40Ar case:
0.77
32 μb/sr
0.44  0.2
B2[F;18Ogs(0+) 18Fgs(1+)] * B2[F;40Cags(0+) 40K0-6MeV(1+)]
To be compared to:
D.J.Mercer et al. Phys. Rev. C 49 (1994) 3104
Y. Fujita private communication
0.55
= 4.00
= 0.138
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

35. LNS 40Ca(18O,18Ne)40Ar @ 270 MeV Projectile Target 18O 18Ne
B(GT) = 3.27
B(GT) = 1.09
18O
18F
18Ne
Super-allowed transition
GT strength not fragmented
Projectile
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
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

36. 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.

37. 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

38. 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

39. Preliminary spectrum of 38Ar C. Agodi Roma - CSN3 31- Marzo 2014
LNS
Preliminary spectrum of 38Ar
270 MeV
counts
0°< θlab<10°
g.s. l = 0
g.s.* l = 2
Preliminary
E* (MeV)
l = 4
l = 6
l = 8
16O(18O,20Ne)14C
12C(18O,20Ne)10Be
Suppression of l = 0 in the transfer
C. Agodi Roma - CSN3 31- Marzo 2014

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

41. Few experimental attempts
LNS
Few 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
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014

42. 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

43. 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