jason and the golden fleece
DESCRIPTION
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. LNS. Introduction. - PowerPoint PPT PresentationTRANSCRIPT
Jason and the Golden Fleece
Determining NME by
Heavy-Ion Double Charge Exchange
Clementina Agodi - Laboratori Nazionali del Sud – INFN - Italy
LNSLNS
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
Introduction
Process mediated by the weak interaction occurring in even-even nuclei where the single -decay is energetically forbidden
LNSLNS
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
2ββ-decay predicted by the Standard Model
0ββ-decay forbidden by the Standard Model
The knowledge of the nuclear matrix elements for the neutrinoless double beta decay is fundamental for neutrino physics.
Neutrinoless double beta decay is potentially the best resource to probe the Majorana or Dirac nature of neutrino and to extract its effective mass.
The role of nuclear physics
220
010 )00(/12
1
em
mMGT
2020 0ˆ0 if OM
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 :
Thus, if the M0νββ nuclear matrix elements were known with sufficient precision, the neutrino mass could be established from 0νββ decay rate measurements.
LNSLNS
iii
iei emUm
2
A lot of new physics inside !
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
2020 ˆ
if OM
Calculations (still sizeable uncertainties): QRPA, Large scale shell model, IBM …..
A. Giuliani and A. Poves, Adv. in High Energy Phys., 857016 (2012) Measurements (still not conclusive for 0):
(+, -) single charge exchange (3He,t)electron capturetransfer reactions …
New physics for the next decades!New physics for the next decades!
N. Auerbach, Ann. Of Phys. 192 (1989) 77S.J. Freeman and J.P. Schiffer JPG 39 (2012) 124004D.Frekers, Prog. Part. Nucl. Phys. 64 (2010) 281J.P. Schiffer, et al., PRL 100 (2008) 112501D.Frekers et al. NPA 916 (2013)219 - 240
E. Caurier, et al., PRL 100 (2008) 052503N. L. Vaquero, et al., PRL 111 (2013) 142501J. Barea, PRC 87 (2013) 014315 T. R. Rodriguez, PLB 719 (2013) 174 F.Simkovic, PRC 77 (2008) 045503.F.Iachello et al. NPB 237-238 (2013) 21 - 23
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The state of the art
The evaluation of NME:
A new esperimental tool: A new esperimental tool: DCEDCE
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
HI Double Charge Exchange
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18Ne+11Li
16O+13B
20Ne+18Li
18O+11B2 n
E-x = -18 MeV
2 p
E-x = -10.8 MeV
2 p
E-x = -10.6 MeV
11B(18O,18Ne)11Li
2 n
E-x = -10.8 MeV
HI Double charge exchange reactions are characterized by the transfer of two
units of the isospin (ΔTz= ± 2) leaving the mass number unchanged
Heavy Ion DCE
Direct mechanism: isospin-flip processes
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.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
1 Sequential nucleon transfer mechanism 4th order:
Brink’s Kinematical matching conditionsD.M.Brink, et al., Phys. Lett. B 40 (1972) 37
2 Meson exchange mechanism 2nd order:
Momentum transfer correction of the GT unit cross- section
22
3
1exp)( rqq
T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125
Heavy-ion DCEHeavy-ion DCE
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
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Direct DCE cross-section as the product of the two charge-exchange ones
00 vs DCE vs DCE1. Initial and final states: Parent/daughter states of the 0ββ are the same as those of
the target/residual nuclei in the DCE;
2. 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;
3. Large momentum transfer: A linear momentum transfer as high as 100 MeV/c or so is characteristic of both processes;
4. 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;
5. In-medium processes: both processes happen in the same nuclear medium, thus quenching phenomena are expected to be similar;
6. Relevant off-shell propagation in the intermediate channel: both processes proceed via the same intermediate nuclei off-energy-shell even up to 100 MeV.
8
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
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Factorization of the Factorization of the charge exchange cross-section charge exchange cross-section
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for single CEX: -decay transition strengths (reduced matrix elements)
unit cross-section
generalization to DCE:
The factor F(q,) describes the shape of the cross-section distribution as a function of the linear momentum transfer and the excitation energy.
In the hypothesis of a surface localized process (for direct quasi elastic processes):
In analogy to the single charge-exchange, the dependence of the cross-section from q is represented by a Bessel function.
Mj(α) 2= B(α)
T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125
C.J Guess,et al, PRC 83 064318 (2011)
unit cross-section
α= Fermi (F) or Gamow Teller (GT)
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The unit cross sectionThe unit cross section
JST Volume integral of the VST potential
Single charge-exchange
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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 transitionsIn 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.
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.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
Past experimental attemptsPast experimental attempts
40Ca(14C,14O)40Ar @ 51 MeV 10° < θlab < 30° Q = -4.8 MeV
D.M.Drake, et al., Phys. Rev. Lett. 45 (1980) 1765
C.H.Dasso, et al., Phys. Rev. C 34 (1986) 743
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).
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C. Agodi Roma - CSN3 31- Marzo 2014
12
DCE at LNSDCE at LNS
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The experiment: 40Ca(18O,18Ne)40Ar@LNS
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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
The experimental SET-UP@ LNS:MAGNEX
LNSLNSMeasured Resolution:
Energy E/E 1/1000
Angle Δθ 0.3°
Mass Δm/m 1/160
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.
Preliminary results
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 1.887 MeV
FWHM ~ 0.5 MeV !
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Measured energy spectrum of 40Ar at very forward angles with an energy resolution of
FWHM ~ 0.5 MeV .
Differential cross-section of the transition 0Cag.s.(18O,18Ne)40Arg.s. @ 270 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.
preliminary
dσDCE /dΩ=11μb/sr at θcm=00
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The NUMEN ProjectThe NUMEN Project
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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
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 :
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The experimental campaignTo perform the experimental campaign that we propose it is necessary a
Facility Upgrade1.CS upgrade to give high beam intensity
2.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
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The Holy Graal:The Holy Graal:the unit cross sectionthe unit cross section
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Goal N.1 for NUMEN
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
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
Goal N.3 for NUMENClementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
This could impact in future development of the field.
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.
Summary
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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
…experimental limitsDetermination of nuclear matrix elements seems to be at our reach…
BUT :
1.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;
2.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;
3.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
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Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
40Ca response to charge exchange40Ca response to charge exchange
Courtesy of Prof. Y. Fujita
BGT=0.06
9(6)
About half of the total GT strenght goes to the 2.73 MeV state of 40K
Check the validity of the factorization
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We deduce the unit cross section for the DCE process assuming a double GT Transition. Taking into account single charge exchange data:
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The 40Ca(18O,18Ne)40Ar case:
13 μb/sr
To be compared to:
Assuming incoherent sum of F + GT
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.
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
Double charge exchange reactions at RCNP (Japan)
Double charge exchange reactions at RCNP (Japan)
12C(18O,18Ne)12Be @ 80 AMeV
Limitation: Energy resolution 1.2 MeV
• Grand Raiden spectrometer• Beam energy 80AMev• Beam intensity 25 pnA
T. Uesaka et al., Prog. of Theor. Phys. 196 (2012) 150H.Matsubara et al. Few Body Syst. 2013 DOI 10.1007/s00601-012-
0586-9
Interest for 48Ca (CANDLES)
A fundamental propertyA fundamental propertyThe complicated many-body heavy-ion scattering problem is largely
simplified for direct quasi-elastic reactions
V (r ,) = U (r) + W(r ,)
26
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 techniquesMicroscopic derived double folding potentials are good choices for U (r)
Microscopic form factors work for charge exchange reactions
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Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
Geometrical Parameters measured
at the FPD
Physical Parameters at the target
The reconstruction problemThe reconstruction problem
if XX
:1Ffi XX
:FInversion of the transport matrix
The image at the focus is meaningful if it can give us information about the object in
its position!To see means to reconstruct
The optical aberrations make this reconstruction
difficultF. Cappuzzello, et al., NIM A 638, (2011) 74
MAGNEX: a ray-reconstruction MAGNEX: a ray-reconstruction spectrometerspectrometer
Possible definition: spectrometer reconstructing a net image by an optically aberrated onePractically
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
if
iiiiiif
iiiiiif
iiiiiif
iiiiiif
iiiiiif
lyxFl
lyxF
lyxFy
lyxF
lyxFx
),,,,,(
),,,,,(
),,,,,(
),,,,,(
),,,,,(
5
4
3
2
1
),,,,(
),,,,(
),,,,(
),,,,(
),,,,(
'5
'4
'3
'2
'1
fffff
fffffi
fffffi
fffffi
fffffi
lyxF
lyxF
lyxFy
lyxF
lyxFx
inversion
Long learning step
The experimental feasibility
PILOT experiment 40Ca(18O,18Ne)40Ar @ 270 MeV
with the competing processes:
40Ca(18O,18F)40K single charge exchange40Ca(18O,20Ne)40Ar two-proton transfer
40Ca(18O,16O)42Ca two-neutron transfer.
21Ne22Ne20Ne
19Ne
18Ne
EC
Pco
rr (
Ch
)
Xfo
c (m
)
Eresid (Ch)Eresid (Ch)
FNe
Na
LNSLNS
C. Agodi Roma - CSN3 31- Marzo 2014
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.
Moving towards hot-casesMoving towards hot-cases
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Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
In the 40Ca(18O,18Ne)40 case0.15 0.07
B2[GT;18Ogs(0+) 18Fgs(1
+)] * B2[GT;40Cags(0+) 40K0-6MeV(1+)]
To be compared to:
D.J.Mercer et al. Phys. Rev. C 49 (1994) 3104
Y. Fujita private communication
corresponding to the product of the known B(GT) valuesfor the transitions in the projectile and target
= 3.56 = 0.0075
Assuming pure GT
0.098
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Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
Measured energy spectrum
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 1.887 MeV
FWHM ~ 0.5 MeV !
LNSLNS
C. Agodi Roma - CSN3 31- Marzo 2014
Measured energy spectrum of 40Ar at very forward angles.
Preliminary results
LNSLNS
Differential cross-section of the transition 0Cag.s.(18O,18Ne)40Arg.s. @ 270 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.
preliminary
dσDCE /dΩ=11μb/sr at θcm=00
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The 40Ca(18O,18Ne)40Ar case:
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 communication0.55
= 4.00 = 0.138
0.44 0.2
Assuming pure F
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Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
0.7732 μb/sr
40Ca(18O,18Ne)40Ar @ 270 MeV
B(GT) = 3.27 B(GT) = 1.09 18O
18F
18NeSuper-allowed transition
GT strength not fragmented
Projectile
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40Ar
40Ca
40K4-
1+2.73
g.s.
0+
0+g.s.g.s.
B(G
T)=0.069(6)
B(G
T)=
0.02
3
B(G
T)
total < 0.15
Target
GT strength not much fragmented
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
1s1/2
1p1/2
1p3/2
1d3/21d5/2
2s1/2
40Cag.s.
1f7/2
1f5/2
n p n p n p
40Kg.s.40Arg.s.
1s1/2
1p1/2
1p3/2
1d3/21d5/2
2s1/2
1f7/2
1f5/2
Double Charge Exchange on Double Charge Exchange on 4040Ca Ca ground stateground state
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
37
Major upgrade of LNS facilitiesMajor upgrade of LNS facilities
The Phases of NUMEN project
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
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year 2013 2014 2015 2016 2017 2018 2019 2020
Phase1
Phase2
Phase3
Phase4
Preliminary time table
cou
nts
0°< θlab<10°g.
s. l
= 0
g.s.
* + 2
.167
l =
2 Prelim
inary
E* (MeV)
l =
4
l =
6
l =
8
Preliminary spectrum of Preliminary spectrum of 3838Ar Ar 40Ca(18O,20Ne)38Ar @ 270 MeV
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16O(18O,20Ne)14C
12C(18O,20Ne)10Be
Suppression of l = 0 in the transfer
C. Agodi Roma - CSN3 31- Marzo 2014
24Mg(18O,18Ne)24Ne at 1.37GeV
J.Blomgren, et al., Phys. Lett. B 362 (1995) 34
Past experimental attemptsPast experimental attempts
Few experimental attemptsFew experimental attempts
40Ca(14C,14O)40Ar @ 51 MeV 10° < θlab < 30° Q = -4.8 MeV
D.M.Drake, et al., Phys. Rev. Lett. 45 (1980) 1765
C.H.Dasso, et al., Phys. Rev. C 34 (1986) 743
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).
LNSLNS
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
RD
D
mm
m00)(det 2
DR
RD
D mmmm
m
R
DR
DRR
m
mm
mmm 222
,2
4
Seesaw mechanism
R
D
m
m 2
Rm
R
D
m
m 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
Beyond the standard modelBeyond the standard modelBeyond the standard modelBeyond the standard model LNSLNS
C. Agodi Roma - CSN3 31- Marzo 2014
The role of the involved nuclei
)(
/
0/)(2
1
0//
2121
0
22
11
21012
22110
iiffeff
eff
ZZZZQQ
mvk
evenl
evenl
vRQRRkL
RRkk
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
LNSLNS
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.