Transcript Diapositiva 1 - INFN

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
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
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 :
2
0


1 / T 1 ( 0  0 )  G 01 M
 0
2
2
M
 0

2

0 f Oˆ
m
m

U ei
2
mie
i i
i
me
 0


A lot of new physics inside !
2
0i
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
LNS
The state of the art
New physics for the next decades!
The evaluation of NME:
M
 0

2

 0
 f Oˆ 
i
2
 Calculations (still sizeable uncertainties): QRPA, Large scale shell model, IBM …..
E. Caurier, et al., PRL 100 (2008) 052503
N. L. Vaquero, et al., PRL 111 (2013) 142501
J. 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
A. Giuliani and A. Poves, Adv. in High Energy Phys., 857016 (2012)
 Measurements (still not conclusive for 0):
(+, -)
single charge exchange (3He,t)
electron capture
transfer reactions …
N. Auerbach, Ann. Of Phys. 192 (1989) 77
S.J. Freeman and J.P. Schiffer JPG 39 (2012) 124004
D.Frekers, Prog. Part. Nucl. Phys. 64 (2010) 281
J.P. Schiffer, et al., PRL 100 (2008) 112501
D.Frekers et al. NPA 916 (2013)219 - 240
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
LNS
A new esperimental tool:
DCE
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
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
E-x = -10.8 MeV
18Ne+11Li
2n
20Ne+18Li
E-x = -10.6 MeV
Direct mechanism: isospin-flip processes
E-x = -10.8 MeV
2p
2p
16O+13B
2n
Heavy Ion DCE
18O+11B
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
LNS
Heavy-ion DCE
th
1 Sequential nucleon transfer mechanism 4 order:
 Brink’s Kinematical matching conditions
D.M.Brink, et al., Phys. Lett. B 40 (1972) 37
nd
2 Meson exchange mechanism 2 order:
 Momentum transfer correction of the GT unit cross- section

1

3
 ( q )  exp  
q
2
r
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
LNS
0 vs DCE
1.
Initial and final states: Parent/daughter states of the 0ββ are the same as those of
the target/residual nuclei in the DCE;
2.
Spin-Isospin mathematical structure of the transition operator: Fermi, GamowTeller 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 the8 same intermediate nuclei off-energy-shell even up to 100 MeV.
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
LNS
Factorization of the
charge exchange cross-section
-decay transition strengths
for single CEX:
(reduced matrix elements)
α= Fermi (F)
or Gamow Teller (GT)
Mj(α) 2= B(α)
C.J Guess,et al, PRC 83 064318 (2011)
unit cross-section
T.N.Taddeucci, et al, Nucl. Phys. A 469 (1987) 125
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):
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
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.
Single charge-exchange
Double charge-exchange
JST Volume integral of the
VST potential
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
LNS
Past experimental attempts
40Ca(14C,14O)40Ar
Few experimental attempts:
@ 51 MeV
10° < θlab < 30° Q = -4.8
MeV
 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
LNS
DCE at LNS
12
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
LNS
The experiment:
40Ca(18O,18Ne)40Ar@LNS

18O7+

40Ca

Ejectiles detected by the MAGNEX spectrometer

Angular setting
beam from LNS Cyclotron at 270 MeV (10 pnA)
solid target of 300 μg/cm2
qopt = 4°
16O
18O
+
40Ca
+
-2° < qlab <10°
42Ca
18F
+
40K
20Ne
+
38Ar
18Ne
+
40Ar
Measured
Not measured
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
Measured Resolution:
Energy E/E 1/1000
Angle Δθ 0.3°
Mass Δm/m 1/160
The experimental SET-UP@ LNS:
MAGNEX
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
LNS
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.
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
0Ca
18
18
40
g.s.( O, Ne) Arg.s. @ 270 Mev
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 1.887
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
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
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
LNS
The experimental campaign
To perform the experimental campaign that we propose it is necessary a
Facility Upgrade
1.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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
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
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
LNS
…experimental limits
Determination 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
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
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:
response to charge exchange
BGT=0.0
69(6)
40Ca
About half of the total GT strenght
goes to the 2.73 MeV state of 40K
Courtesy of Prof. Y. Fujita
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
The
40Ca(18O,18Ne)40Ar
case:
13 μb/sr
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.
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
Double charge exchange reactions
at RCNP (Japan)
12C(18O,18Ne)12Be
@ 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. 2013 DOI 10.1007/s00601-012-0586-9
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)
26
Microscopic
form factors work for charge exchange reactions
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
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

F : Xi


Xf
Inversion of the transport matrix
F
1

: Xf


Xi
Physical Parameters
at the target
The optical aberrations make
this reconstruction difficult
Geometrical
Parameters measured
at the FPD
F. Cappuzzello, et al., NIM A 638, (2011) 74
MAGNEX: a ray-reconstruction
spectrometer
Possible definition: spectrometer reconstructing a net image by an optically
aberrated one
Practically
x

y

l

f
 F1 ( x i ,  i , y i ,  i , l i ,  i )
f
 F2 ( x i , i , y i ,  i , l i ,  i )
f
 F3 ( x i , i , y i ,  i , l i ,  i )
f
 F4 ( x i , i , y i ,  i , l i ,  i )
inversion
 F5 ( x i , i , y i ,  i , l i ,  i )
f
f
 
i
 xi

 i

 yi

 i


 F1 ( x
f
,
f
, y
f
,
f
,l
f
)
 F2 ( x
f
,
f
, y
f
,
f
,l
f
)
 F3 ( x
f
,
f
, y
f
,
f
,l
f
)
 F4 ( x
f
,
f
, y
f
,
f
,l
f
)
 F5 ( x
f
,
f
, y
f
,
f
,l
f
)
'
'
'
'
'
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
Long learning step
LNS
The experimental feasibility
40Ca(18O,18Ne)40Ar
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.
1600
20
18
1400
0
30
-0.05
22Ne
20Ne
25
19Ne
-0.1
1200
18Ne
14
Xfoc (m)
ECPcorr (Ch)
16
21Ne
20
-0.15
1000
12
Na
10
800
8
Ne
600
-0.2
15
-0.25
10
6
F
-0.3
4
400
5
-0.35
2
200
1900
2000
2100
2200
2300
2400
2500
2600
2700
-0.4
1900
2000
2100
Eresid (Ch)
C. Agodi Roma - CSN3 31- Marzo 2014
2200
2300
Eresid (Ch)
2400
2500
2600
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.

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.
136Xe
or
130Xe
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
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+)]
= 0.0075
= 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
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
1.46 MeV and the 18Ne excited state at 1.887 MeV
C. Agodi Roma - CSN3 31- Marzo 2014
40Ar
2+ at
LNS
Preliminary results
Differential cross-section of the transition
0Ca
18
18
40
g.s.( O, Ne) Arg.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.
dσDCE /dΩ=11μb/sr
at θcm=00
Clementina Agodi, Neutrino Oscillation Workshop Conca Specchiulla (Otranto) -September 7-14, 2014
LNS
Assuming pure F
The
40Ca(18O,18Ne)40Ar
case:
32 μb/sr
0.77
0.44  0.2
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
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
LNS
40Ca(18O,18Ne)40Ar
@ 270 MeV
Projectile
18O
18Ne
Super-allowed transition
GT strength not fragmented
18F
g.s.
40K
40Ar
0+
GT strength not
much fragmented
4-
g.s.
g.s.
Target
1+
2.73
40Ca
0+
Neutrino Oscillation Workshop - Conca Specchiulla (Otranto, Lecce, Italy) -September 7-14, 2014
Double Charge Exchange on
ground state
40Ca
1f5/2
1f7/2
1d3/2
2s1/2
1d5/2
1p1/2
1p3/2
1s1/2
1f5/2
1f7/2
1d3/2
n
p
40Ca
g.s.
n
p
40K
g.s.
p
n
40Ar
g.s.
2s1/2
1d5/2
1p1/2
1p3/2
1s1/2
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
37
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
Phase1
Phase2
Phase3
Phase4
2013 2014
2015
2016
2017
2018
2019
2020
LNS
Preliminary spectrum of 38Ar
40Ca(18O,20Ne)38Ar
@ 270 MeV
16O(18O,20Ne)14C
0°<
θlab<10°
l=8
l=6
Suppression of l = 0 in
the transfer
l=4
g.s. l = 0
g.s.* + 2.167 l = 2
counts
12C(18O,20Ne)10Be
E* (MeV)
C. Agodi Roma - CSN3 31- Marzo 2014
Past experimental attempts
24Mg(18O,18Ne)24Ne
at 1.37GeV
J.Blomgren, et al., Phys. Lett. B 362 (1995) 34
LNS
Few experimental attempts
40Ca(14C,14O)40Ar
Few experimental attempts:
@ 51 MeV
10° < θlab < 30° Q = -4.8
MeV
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
Beyond the standard model
 0

 mD
 
mR 
 
det 
 mD
mD 

mR 
2
mR  4mD
2
LNS

2
   (   m R )  m D  0
mR   
mD
2
 mR ,
mD
2
mR
mD
mR
mR
m D 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
mR
C. Agodi Roma - CSN3 31- Marzo 2014
2
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.
 k  k 0   1 / R1   2 / R 2  0
 Brink’s matching conditions
D.M. Brink, Phys. Lett. B 40 (1972) 37-40
 L   2  1 
1
2
k 0 ( R 1  R 2 )  Q eff R /  v  0
l 1   1  even
l 2   2  even
k 0  mv / 
Q eff  Q  ( Z 1 Z 2  Z 1 Z 2 )
f
f
i
i
 The survival of a preformed pair in a transfer process is favoured when
the initial and final orbitals are the same