jason and the golden fleece

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


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 !


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

LNSLNS


The state of the art

The evaluation of NME:

A new esperimental tool: A new esperimental tool: DCEDCE

LNSLNS


HI Double Charge Exchange

LNSLNS

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.


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


LNSLNS

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


LNSLNS

Factorization of the Factorization of the charge exchange cross-section charge exchange cross-section

LNSLNS

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)


The unit cross sectionThe unit cross section

JST Volume integral of the VST potential

Single charge-exchange

LNSLNS

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.


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).

LNSLNS

C. Agodi Roma - CSN3 31- Marzo 2014

12

DCE at LNSDCE at LNS

LNSLNS


The experiment: 40Ca(18O,18Ne)40Ar@LNS

LNSLNS

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


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 !

LNSLNS

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


The NUMEN ProjectThe NUMEN Project

LNSLNS

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;


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 :

LNSLNS


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

LNSLNS


The Holy Graal:The Holy Graal:the unit cross sectionthe unit cross section

LNSLNS

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

LNSLNS

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

LNSLNS


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

LNSLNS

We deduce the unit cross section for the DCE process assuming a double GT Transition. Taking into account single charge exchange data:


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!


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

LNSLNS


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


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

LNSLNS


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

LNSLNS


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


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


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

LNSLNS


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

LNSLNS

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


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

LNSLNS

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

LNSLNS

16O(18O,20Ne)14C

12C(18O,20Ne)10Be

Suppression of l = 0 in the transfer


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


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


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.

jason and the golden fleece

Documents

neutrino physics

neutrino mass

single decay

neutrinoless double

forbiddenclementina

dirac nature of neutrino

standard model0decay

decay rate measurements