dott. antonio botrugno ph.d. course university of lecce (italy) department of physics
TRANSCRIPT
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Dott. Antonio Botrugno
Ph.D. course
UNIVERSITY OF LECCE (ITALY)
DEPARTMENT OF PHYSICS
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*1
*1
ZlX
YlXA
ZAZl
AZ
AZl
*
*
XX
XXAZl
AZl
AZl
AZl
• Above nucleon emission threshold.
• The state of the emitted nucleon is not observed.
Charge Current
NeutralCurrent
Inclusive cross section for neutrino scattering off nuclei:
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A many-body theory to calculate nuclear-responses at low and intermediate
transferred energy (10 - 300 MeV)
SCHEMATIC REPRESENTATION OF NUCLEAR RESPONSE:
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Neutrinos are an ideal probe to investigate nuclear structure
moreover
they are able to excite nuclear modes not accessible to the electomagnetic probes.We need an accurate knowledge
of the neutrino-nucleus cross sections to better understand detector response.
WHY NEUTRINO - NUCLEUS ?
NUCLEUS USED AS A DETECTOR OF NEUTRINOS
NEUTRINOS USED AS PROBE TO STUDY NUCLEAR STRUCTURE
Neutrino fluxes are sometimes not well known:
- source uncertainty (solar, supernova, and geophysic neutrinos)
- oscillation phenomena
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Cross Section:
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Nuclear Models:
1. Mean Field (MF)
2. Continuum Random Phase Approximation (RPA)
3. Final State Interaction (FSI)
Microscopic Models
Phenomenological Model
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hjpJ iMFf
Single particle excitations
E
rTransferred Energy
1) Mean Field Model
This model is inadequate in the Giant Resonance Region where collective excitations are important.
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INPUT 1 Wood-Saxon Potential:
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E
xTransferred Energy
2) Continuum Random Phase Approximation
pjhYhjpXd
pjhYhjpXJ
pphph
pphp
phph
phiRPAf
)()(
Collective excitations
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INPUT 2 Nucleon-Nucleon Interaction:
• Landau-Migdal Type 1 (LM1)
• Landau-Migdal Type 2 (LM2)
• Polarization Potential (PP)
CC Processes
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APPROXIMATION
3) Final State Interaction
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Nuclear Response in a microscopic model:
• 1p-1h Correlations:
• np-nh Correlations:
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APROXIMATION
3) Final State Interaction
INPUT 3
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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
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Photo-absorption
Data:J. Ahrens et al.,Nucl. Phys. A 251, (1975), 479
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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
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*)',( XeeX
Energy Region: I) Quasielastic Peak
FSI
RPA
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*1212 '),( CeeC
Energy Region: II) Giant Resonance
FSI
RPA
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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
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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.
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*1616 '),( OeeO
*1616 '),( OO
I) Giant Resonance II) Quasielastic Peak
CRPA Calculation
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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.
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Comparison between electron and neutrino scattering:
I) Giant Resonance II) Quasielastic Peak
CRPA calculation MF calculation
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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.
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Comparison between various models
*1616 ),( FO
FG: Model of Smith e Monitz.
Nuclear Models should be used only in their range of applicability.
CRPA has a large energy range of applicability.
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O16
Angular distribution
CRPA Calculation
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O16
The sensitivity of the cross section to the nucleon-nucleon interaction is 10-12 % in giant resonance region.
Total cross section including FSI effect
Landau-Migdal 1
Landau-Migdal 2
Polarization Potential
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The effect of FSI Model is a reduction of the cross section of about 10 – 15 % on all neutrino processes.
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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: *', XpX AZ
AZ
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.
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Thomas-Reiche-Kuhn sum rules:
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C12
Total cross section including FSI effect.
Landau-Migdal 1
Landau-Migdal 2
Polarization Potential