Dott. Antonio Botrugno

Ph.D. course

UNIVERSITY OF LECCE (ITALY)

DEPARTMENT OF PHYSICS

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• Above nucleon emission threshold.

• The state of the emitted nucleon is not observed.

Charge Current

NeutralCurrent

Inclusive cross section for neutrino scattering off nuclei:

A many-body theory to calculate nuclear-responses at low and intermediate

transferred energy (10 - 300 MeV)

SCHEMATIC REPRESENTATION OF NUCLEAR RESPONSE:

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

Cross Section:

Nuclear Models:

1. Mean Field (MF)

2. Continuum Random Phase Approximation (RPA)

3. Final State Interaction (FSI)

Microscopic Models

Phenomenological Model

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.

INPUT 1 Wood-Saxon Potential:

E

xTransferred Energy

2) Continuum Random Phase Approximation

pjhYhjpXd

pjhYhjpXJ

pphph

pphp

phph

phiRPAf

)()(

Collective excitations

INPUT 2 Nucleon-Nucleon Interaction:

• Landau-Migdal Type 1 (LM1)

• Landau-Migdal Type 2 (LM2)

• Polarization Potential (PP)

CC Processes

APPROXIMATION

3) Final State Interaction

Nuclear Response in a microscopic model:

• 1p-1h Correlations:

• np-nh Correlations:

APROXIMATION

3) Final State Interaction

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

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Energy Region: I) Quasielastic Peak

FSI

RPA

*1212 '),( CeeC

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.

*1616 '),( OeeO

*1616 '),( OO

I) Giant Resonance II) Quasielastic Peak

CRPA 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.

Comparison between electron and neutrino scattering:

I) Giant Resonance II) Quasielastic Peak

CRPA calculation 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

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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.

O16

Angular distribution

CRPA Calculation

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

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: *', 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.

Thomas-Reiche-Kuhn sum rules:

C12

Total cross section including FSI effect.

Landau-Migdal 1

Landau-Migdal 2

Polarization Potential