FROM (e,e’p) TO NEUTRINO SCATTERING Carlotta …crex.fmf.uni-lj.si/eep17/Giusti_bled.pdf · FROM (e,e’p) TO NEUTRINO SCATTERING Carlotta Giusti Università and INFN Pavia

FROM (e,e’p) TO NEUTRINO SCATTERING

Carlotta Giusti

Università and INFN Pavia

International Workshop on (e,e’p) Processes, 2-6 July 2017, Bled

(e,e’p) QE

(e,e’p)

1pKO

both e’ and p detected

(A-1) in a bound or continuum state

Em missing energy (W*A-1 – WA)

discrete spectrum (low Em) peaks

continuum spectrum (larger Em)

for Em corresponding to a peak (A-1) in a discrete eigenstate

(e,e’p) discrete low-lying states

(e,e’p) in the continuum

EXCLUSIVE

QE

(e,e’p) (e,e’) QE

1pKO









EXCLUSIVE

(e,e’p)

only e’ detected

all final states included

discrete and continuum spectrum

INCLUSIVE

(e,e’) QE

1pKO









EXCLUSIVE

(e,e’p)

EXCLUSIVE

INCLUSIVE

proton-hole states

properties of bound protons

s.p. aspects of nuclear structure

validity and limitation of IPSM, MFA

nuclear correlations SRC

only e’ detected



INCLUSIVE

(e,e’) QE

(e,e’p)

EXCLUSIVE

INCLUSIVE

proton-hole states




nuclear correlations SRC short-range correlations

SRC

high Em beyond threshold for

the emission of a second N

two-nucleon knockout

only e’ detected



INCLUSIVE

(e,e’) QE

(e,e’p)

EXCLUSIVE

INCLUSIVE

proton-hole states





SRC




only e’ detected



INCLUSIVE

(e,e’) QE

NEUTRINO-NUCLEUS SCATTERING

(e,e’p)

EXCLUSIVE

INCLUSIVE

proton-hole states





SRC




only e’ detected



INCLUSIVE

(e,e’) QE

The work done for electron scattering can be exploited to describe nuclear effects in

neutrino-nucleus scattering This is very important for neutrino oscillation experiments where nuclei are used as neutrino detectors.

nuclear response to the electromagnetic probe

QE-peak


QE-peak

QE-peak dominated by one-nucleon knockout


QE-peak



QE-peak



QE-peak


B (A-1) (e,e’p)

A

missing energy

missing momentum

OPEA

Experimental data: Em and pm distributions

Experimental data: Em and pm distributions

For Em corresponding to a peak we assume that the residual nucleus is in a discrete eigenstate

ONE-HOLE SPECTRAL FUNCTION

exclusive reaction

joint probability of removing from the target a nucleon p1 leaving the residual nucleus in a state with energy Em

ONE-HOLE SPECTRAL FUNCTION

exclusive reaction

joint probability of removing from the target a nucleon p1 leaving the residual nucleus in a state with energy Em

inclusive reaction : one-body density

MOMENTUM DISTRIBUTION

probability of finding in the target a nucleon with momentum p1

A

B (A-1)

OPEA

A

B (A-1)

OPEA

A

B (A-1)

OPEA

hadron tensor

A

B (A-1)

OPEA

hadron tensor

A

B (A-1)

OPEA

hadron tensor

E0’

E0

,q

p n

0

(e,e’p)

exclusive reaction n

DKO mechanism: the probe interacts through a one-body current with one nucleon which is then emitted the remaining nucleons are spectators

impulse approximation IA |i >

|f >

,q

p n

0

(e,e’p)

|i >

|f >

FSI = 0


DKO mechanism: the probe interacts through a one-body current with one nucleon which is then emitted the remaining nucleons are spectators

impulse approximation IA

E0’

E0

PW

factorized cross section

PW FSI=0 PLANE-WAVE IMPULSE

APPROXIMATION

PWIA

spectral function

spectroscopic factor

overlap function

For each Em the mom. dependence of the SF is given by the mom. distr. of the quasi-hole states n produced in the target nucleus at that energy and described by the normalized OVF

The norm of the OVF, the spectroscopic factor gives the probability that n is a pure hole state in the target.

IPSM s.p. SM state

1 occupied SM states

0 empty SM states

There are correlations and the strength of the quasi-hole state is fragmented over a set of s.p. states

spectroscopic factor overlap function

,q

p n

0

DWIA (e,e’p)

|i >

|f >

FSI


DKO IA

FSI DWIA

unfactorized c.s.

non diagonal SF

DW

j one-body nuclear current

(-) s.p. scattering w.f. H+(+Em)

n s.p. bound state overlap function H(-Em)

n spectroscopic factor

(-) and consistently derived as eigenfunctions of a Feshbach optical model Hamiltonian

Direct knockout DWIA (e,e’p)

phenomenological ingredients usually adopted

(-) phenomenological optical potential

n phenomenological s.p. wave functions WS, HF MF (some calculations including correlations are available)

n extracted in comparison with data: reduction factor applied to the calculated c.s. to reproduce the magnitude of the experimental c.s.

DWIA-RDWIA calculations

phenomenological ingredients usually adopted

(-) phenomenological optical potential

n phenomenological s.p. wave functions WS, HF MF (some calculations including correlations are available)

n extracted in comparison with data: reduction factor applied to the calculated c.s. to reproduce the magnitude of the experimental c.s.

DWIA-RDWIA calculations

DWIA and RDWIA: excellent description of (e,e’p) data

NIKHEF data & CDWIA calculations

Experimental data: pm distribution

NIKHEF data & CDWIA calculations

reduction factors applied: spectroscopic factors

0.6 - 0.7

Experimental data: pm distribution

depletion due to NN correlations

different independent investigations:

SRC (Short-Range Correlations) account for only a few % of the depletion, up to 10-15 % with TC

LRC (Long-Range Correlations) main contribution to the depletion

LRC collective excitations of nucleons at the nuclear surface

SPECTROSCOPIC FACTORS and NN CORRELATIONS

account for only a small part of the depletion

depletion due to SRC compensated by the admixture of high-momentum components in the s.p. w.f.

SRC effects on (e,e’p) cross sections at high pm are small for low-lying states

calculations of the 1BDM and of the momentum distribution indicate that the missing strength due to SRC is found at large pm and Em, beyond the continuum threshold, where various processes involving more nucleons can be present

SRC

account for only a small part of the depletion

depletion due to SRC compensated by the admixture of high-momentum components in the s.p. w.f.

SRC effects on (e,e’p) cross sections at high pm are small for low-lying states

calculations of the 1BDM and of the momentum distribution indicate that the missing strength due to SRC is found at large pm and Em, beyond the continuum threshold, where various processes involving more nucleons can be present

(e,e’p) at high values of Em

SRC

16O(e,e’p) at high Em

N. Liyanage et al. PRL 86 (2001) 5670

<pm> = 50 MeV/c <pm> = 145 MeV/c <pm> = 280 MeV/c <pm> = 340 MeV/c



1p1/2 1p3/2


16O(e,e’p) RDWIA

JLab (,q) const kin E0=2445 MeV =439 MeV Tp= 435 MeV

diff opt.pot.

n = 0.7

A. Meucci, C. Giusti, F.D. Pacati PRC 64 (2001) 014604



1p1/2 1p3/2 1s1/2


RDWIA (J. Kelly).

2NKO (Ghent).



1p1/2 1p3/2 1s1/2


RDWIA (J. Kelly).

2NKO (Ghent).



1p1/2 1p3/2 1s1/2


RDWIA (J. Kelly).

2NKO (Ghent).



1p1/2 1p3/2 1s1/2


RDWIA (J. Kelly).

2NKO (Ghent).

the exp. c.s contains other contributions beyond 1NKO+2NKO.

DWIA

FSI

FSI described by a complex OP, the imaginary part gives a reduction of the calculated c.s. which is essential to reproduce (e,e’p) data for low Em (low-lying states)

DWIA

DWIA

FSI

FSI described by a complex OP, the imaginary part gives a reduction of the calculated c.s. which is essential to reproduce (e,e’p) data for low Em (low-lying states)

not suited to address the continuum

the OP describes elastic nucleon-nucleus scattering. The Im part accounts for the flux lost in the elastically scattered beam toward the inelastic channels that are open

DWIA: the Im part removes the contribution of inelastic channels

(e,e’p) at low Em : only the final-state channel n is considered, it can be correct to account for the flux lost in the considered channel. The main contribution comes from the 1pKO process where the outgoing proton scatters elastically with the residual nucleus in the state n.

inclusive (e,e’) all the final-state channels are included, the flux must be redistributed and conserved in the sum over all the channels. In every channel flux is lost toward the other channels and flux is gained due to the flux lost in the other channels toward the considered channel

inclusive scattering: GREEN’S FUNCTION MODEL

FSI and OPTICAL POTENTIAL

GREEN’S FUNCTION MODEL

Based on the IA: one-body current interacts with a nucleon that is then emitted. Sum over all the nucleons of the target

FSI are accounted for by the complex energy dependent OP: the formalism translates the flux lost toward inelastic channels, represented by the Im part of the OP, into the strength observed in inclusive reactions.

The OP is responsible for the redistribution of the flux in all the final-state channels and in the sum over all the channels the flux is conserved.

The OP becomes a powerful tool to include important inelastic contributions beyond 1NKO (multi-nucleon, rescattering, non-nucleonic…) not included in usual models based on the IA

GREEN’S FUNCTION MODEL

Based on the IA: one-body current interacts with a nucleon that is then emitted. Sum over all the nucleons of the target

FSI are accounted for by the complex energy dependent OP: the formalism translates the flux lost toward inelastic channels, represented by the Im part of the OP, into the strength observed in inclusive reactions.

The OP is responsible for the redistribution of the flux in all the final-state channels and in the sum over all the channels the flux is conserved.

The OP becomes a powerful tool to include important inelastic contributions beyond 1NKO (multi-nucleon, rescattering, non-nucleonic…) not included in usual models based on the IA

MODEL SUCCESSFULLY APPLIED TO QE (e,e’) and CCQE NCE

16O(e,e’)

data from Frascati NPA 602 405 (1996)

RPWIA

RGF

RDWIA

A. Meucci, F. Capuzzi, C. Giusti, F.D. Pacati PRC 67 (2003) 054601

(e,e’)

E0 = 1080 MeV # = 32o

E0 = 841 MeV # = 45.5o

E0 = 2020 MeV # = 20o

RGF

A. Meucci et al. PRC 87 (2013) 054620

FSI in (e,e’p)

DWIA not suited to address the continuum

at high Em and pm : contributions beyond 1pKO

removed in DWIA by the Im part of the OP and included by the Im part of the OP in the GF model

e.g. multi-scattering effects: the ejectile proton in its way through the nucleus undergoes secondary collisions where it can change direction and lose energy before being emitted and detected

FSI in (e,e’p)

DWIA not suited to address the continuum

at high Em and pm : contributions beyond 1pKO

removed in DWIA by the Im part of the OP and included by the Im part of the OP in the GF model

e.g. multi-scattering effects: the ejected proton in its way through the nucleus undergoes secondary collisions where it can change direction and lose energy before being emitted and detected

Multi-scattering effects in (e,e’p) knockout: P.Demetriou, S. Boffi, C. Giusti, F.D. Pacati, Nucl. Phys. A 625 (1997) 513

Multi-Scattering Effects in (e,e’p)

Improve the treatment of FSI The method follows the lines of the multi-step direct (MSD) scattering theory of Feshbach. Kerman, and Koonin which allows one to trace the secondary collisions of the emitted nucleon. The proton, following the initial elm int., is excited to the continuum and subsequently undergoes a series of 2-b interactions with the residual nucleus before being emitted. Thus there are a series of collisions leading to the excitation of intermediate states of increasing complexity. At each step a N can be emitted. The theory combines a QM treatment of multiple scattering with statistical assumptions that lead to the convolution nature of the multistep c.s. and enables the calculation of higher-order contributions which would be otherwise impracticable

(e,e’p) c.s. = 1-step + n-step terms

DWIA

n-step term convolution of 1NKO and 1-step MSD c.s. over all intermediate energies E1, E2 … and angles 1, 2…..

DWIA DWBA



The method follows the trace of the fast emitted proton but does not follow the fate of secondary nucleons

2NKO not included Pion contribution and reabsorption not included

Suited to study the continuum spectrum with not too high Em

P . Demetriou et al Nucl. Pys. A 625 (1997) 513

E0=497 MeV, µ=52.9o, != 140 MeV , Tp= 87 10 MeV

Em =28 MeV Em =43 MeV


tot

1-s

1-s

1-s 1-s

2-s

2-s

tot

3-s

tot tot

2-s

2-s

3-s

3-s

3-s 4-s

4-s

P . Demetriou et al Nucl. Phys. A 625 (1997) 513

E0=497 MeV, µ=52.9o, != 140 MeV , Tp= 87 10 MeV



tot

1-s

1-s

1-s 1-s

2-s

2-s

tot

3-s

tot tot

2-s

2-s

3-s

3-s

3-s 4-s

4-s

increasing Em 2-s and 3-s become gradually more important. The domination of multi-step processes at large scatt. angles is expected since the proton gradually loses memory of its initial direction yielding thus increasingly symm. ang. distribution

In the continuum effects and mechanisms beyond direct 1NKO may be important or even dominant Strong sensitivity to kinematic conditions. In electron scattering suitable kinematic conditions can be selected able to minimize or emphasize and therefore study specific contributions ELECTRON SCATTERING IS SELECTIVE

In the continuum effects and mechanisms beyond direct 1NKO may be important or even dominant Strong sensitivity to kinematic conditions. In electron scattering suitable kinematic conditions can be selected able to minimize or emphasize and therefore study specific contributions ELECTRON SCATTERING IS SELECTIVE

from e-nucleus to n-nucleus scattering

CCQE


CCQE


only final lepton detected inclusive CC

same model as for inclusive (e,e’)

CCQE




both final lepton and nucleon …. exclusive (e,e’N)

CCQE




both final lepton and nucleon …. exclusive (e,e’N)……

BUT

different exp. situation in electron and º scattering

electron scattering :

beam energy known, ! and q determined

neutrino scattering:

beam energy not known, ! and q not determined, flux averaged c.s.

calculations over the energy range relevant for the neutrino flux,

broader kinematic region


electron scattering :

beam energy known, ! and q determined

neutrino scattering:

beam energy not known ! and q not determined, flux averaged c.s.

calculations over the energy range relevant for the neutrino flux,

broader kinematic region


the flux-average procedure picks up contributions from different kinematic regions, not only QE, contributions other than direct 1-nucleon emission are more important than in (e,e’)

RGF

MiniBooNe CCQE data

RGF-EDAI

RGF-EDAD1

RGF-GRFOP

M.V. Ivanov et al. PRC 94 014608 (2016)

RPWIA

rROP

RGF EDAI

RGF-EDAD1

A. Meucci and C. Giusti PRD 85 (2012) 093002

Comparison with MiniBooNe CCQE data

CCQE


both final lepton and nucleon …. (e,e’p) where the incident electron energy is not know

calculations for different values of Eº , !, and in a certain range of Em

Experimental and theoretical work already done and that can be done for electron scattering extremely useful to provide reliable º-nucleus cross sections

Comparison with electron-scattering data test of the validity and predictive power of a nuclear model Electron scattering experiments in suitable kinematics can give information on the relevant reaction mechanisms, nuclear dynamics FSI, nuclear current (1-body, 2-body)…. Information on nuclear structure and correlations, contained in the spectral function, can be obtained from dedicated (e,e’p) experiments (e.g. JLab experiment on 40Ar)


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FROM (e,e’p) TO NEUTRINO SCATTERING Carlotta …crex.fmf.uni-lj.si/eep17/Giusti_bled.pdf · FROM (e,e’p) TO NEUTRINO SCATTERING Carlotta Giusti Università and INFN Pavia