Dott. Antonio Botrugno
Ph.D. course
UNIVERSITY OF LECCE (ITALY)
DEPARTMENT OF PHYSICS
Inclusive cross section for neutrino
scattering off nuclei:
l  X  l 
A
Z 1
*
l  X  l 
A
Z 1
*
A
Z
A
Z


Y
Z
l  X l  X
*
l  X l  X
*
A
Z
A
Z
A
Z
A
Z
Charge
Current
Neutral
Current
• Above nucleon emission threshold.
• The state of the emitted nucleon is not observed.
SCHEMATIC REPRESENTATION OF
NUCLEAR RESPONSE:
A many-body theory to calculate
nuclear-responses at low and intermediate
transferred energy (10 - 300 MeV)
WHY NEUTRINO - NUCLEUS ?
NUCLEUS USED AS A
DETECTOR OF NEUTRINOS
Neutrino fluxes are sometimes not
well known:
- source uncertainty (solar, supernova,
and geophysic neutrinos)
- oscillation phenomena
We need an accurate knowledge
of the neutrino-nucleus cross
sections to better understand
detector response.
NEUTRINOS USED AS
PROBE TO STUDY
NUCLEAR STRUCTURE
Neutrinos are an ideal probe to
investigate nuclear structure
moreover
they are able to excite nuclear
modes not accessible to the
electomagnetic probes.
Cross Section:
Nuclear Models:
1. Mean Field (MF)
Microscopic
Models
2. Continuum Random Phase
Approximation (RPA)
3. Final State Interaction (FSI)
Phenomenological
Model
1) Mean Field Model
 MF
J i  p j h
f
Single particle excitations
E
Transferred
Energy
r
This model is inadequate in the Giant Resonance Region where
collective excitations are important.
INPUT 1 Wood-Saxon Potential:
2) Continuum Random Phase Approximation

RPA
f


J  i   X ph p j h  Yph h j p 

ph
  d p  X ph ( p ) p j h  Yph ( p ) h j p
ph
Collective excitations
E
Transferred
Energy
x

INPUT 2 Nucleon-Nucleon Interaction:
• Landau-Migdal Type 1 (LM1)
• Landau-Migdal Type 2 (LM2)
• Polarization Potential
(PP)
CC Processes
3) Final State Interaction
APPROXIMATION
Nuclear Response in a microscopic model:
• 1p-1h Correlations:
• np-nh Correlations:
3) Final State Interaction
APROXIMATION
INPUT 3
Constraints and Prediction Power
of the Models
• Photo-absorption.
to set the FSI parameters
• Electron scattering.
to test the prediction power of the model
• Sum rules
to test the consistence of the calculation
Photo-absorption
Data:
J. Ahrens et al.,
Nucl. Phys. A 251, (1975), 479
Constraints and Prediction Power
of the Models
• Photo-absorption.
to set the FSI parameters
• Electron scattering.
to test the prediction power of the model
• Sum rules
to test the consistence of the calculation
X (e, e' ) X
*
Energy Region: I)
Quasielastic Peak
FSI
RPA
12
12
C (e, e') C
*
Energy Region: II)
Giant Resonance
FSI
RPA
Constraints and Prediction Power
of the Models
• Photo-absorption.
to set the FSI parameters
• Electron scattering.
to test the prediction power of the model
• Sum rules
to test the consistence of the calculation
Comparison between electron and neutrino
scattering:
In electron scattering the value of the cross section decreases with increasing
incoming energy and/or scattering angle
In neutrino scattering the value of the cross section increases with increasing
incoming energy (and/or scattering angle in giant resonance region).
The shapes of the neutrino cross sections are very different to those of the
electron cross sections because:
1) the axial vector part of the weak current dominates in neutrino scattering.
2) the particle-hole transitions in CC processes are different to those of the
electron scattering.
I) Giant Resonance
16
16
O(e, e') O
O( , ') O
16
16
*
*
II) Quasielastic Peak
Comparison between electron and neutrino
scattering:
In electron scattering the value of the cross section decreases with increasing
incoming energy and/or scattering angle
In neutrino scattering the value of the cross section increases with increasing
incoming energy (and/or scattering angle in giant resonance region).
The shapes of the neutrino cross sections are very different to those of the
electron cross sections because:
1) the axial vector part of the weak current dominates in neutrino scattering.
2) the particle-hole transitions in CC processes are different to those of the
electron scattering.
Comparison between electron and neutrino scattering:
I) Giant Resonance
CRPA calculation
II) Quasielastic Peak
MF calculation
Conparison between electrons ed neutrinos
scattering:
In electron scattering the value of cross section decrease with increasing
incoming energy and/or scattering angle
In neutrino scattering the value of cross section increase with increasing
incoming energy (and/or scattering angle in giant resonance region).
Shapes of neutrinos cross sections are very different to electron cross section
because:
1) the axial vector part of the weak current dominates in neutrino scattering.
2) the particle-hole transition in CC processes are different to electron
scattering.
Caution in testing the prediction accuracy of neutrino
scattering using electron scattering.
Caution in using the response function extracted from
electron scattering to calculate neutrino cross sections.
Comparison between
various models
O( ,  ) F
16
 16
*
Nuclear Models
should be used only
in their range of
applicability.
CRPA has a large
energy range of
applicability.
FG: Model of Smith e Monitz.
Angular
distribution
16
O
Total cross section
including FSI effect
16
O
Landau-Migdal 1
Landau-Migdal 2
Polarization
Potential
The sensitivity of the
cross section to the
nucleon-nucleon
interaction is 10-12 %
in giant resonance
region.
The effect of FSI Model is a reduction of the cross section
of about 10 – 15 % on all neutrino processes.
Main results
• The sensitivity of the cross section to the nucleon-nucleon
interaction is 10-12 % in giant resonance region.
• The effect of FSI Model is a reduction of the cross section of
about 10 – 15 % on all neutrino processes.
Some important proposals for the
future
• Implementing the formalism for other nuclei.
• Application for know or expected neutrino fluxes: solar,
atmospheric, supernova, pion decay, beta-beam.
• Other processes at low energy: ZA X  , ' p ZA X *


Thomas-Reiche-Kuhn sum rules:
Total cross section
including FSI effect.
12
C
Landau-Migdal 1
Landau-Migdal 2
Polarization
Potential