Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing - - PowerPoint PPT Presentation

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Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing - - PowerPoint PPT Presentation

Mar 10, 2023 21 likes •182 views

Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing Lawrence Weinstein Old Dominion University N, Z and high momentum nucleons: 54-40 or Fight aka The CaFe Experiment Goal: understand pairing mechanisms in symmetric and

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SLIDE 1

Semi-Inclusive Reactions: N, Z, Nucleon momenta, and Pairing

Lawrence Weinstein Old Dominion University

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SLIDE 2

N, Z and high momentum nucleons:

“54-40 or Fight” aka “The CaFe Experiment”

  • Goal: understand pairing mechanisms in symmetric and

asymmetric nuclei

– Neutron skins – Connection to EMC effect

  • Method: Measure A(e,e’p) at low and hi missing momentum

at kinematics sensitive to n(k)

  • Targets: D, 12C, 40Ca, 48Ca, 54Fe

– Add p, n symmetrically from D to 12C to 40Ca – Add 8 neutrons from 40Ca to 48Ca – Add 6 protons from 48Ca to 54Fe

  • L. Weinstein, EMC SRC MIT 2016

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SLIDE 3

N, Z and high momentum nucleons:

“54-40 or Fight” aka “The CaFe Experiment”

  • Goal: understand pairing mechanisms in symmetric and

asymmetric nuclei

– Neutron skins – Connection to EMC effect

  • Method: Measure A(e,e’p) at low and hi missing momentum

at kinematics sensitive to n(k)

  • Targets: D, 12C, 40Ca, 48Ca, 54Fe

– Add p, n symmetrically from D to 12C to 40Ca – Add 8 neutrons from 40Ca to 48Ca – Add 6 protons from 48Ca to 54Fe

  • L. Weinstein, EMC SRC MIT 2016

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40Ca 54Fe

48Ca

  • 8 Neutrons

+ 6 Protons

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SLIDE 4

Adding neutrons to 40Ca

Two models:

  • More neutrons, similar volume larger pn
  • More neutrons, more np pairs larger pp
  • L. Weinstein, EMC SRC MIT 2016

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No Correlations With Correlations

48Ca

+8%

  • 12%

40Ca

  • M. Vanhalst, et al., J. Phys. G 42, 055104 (2015)
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SLIDE 5

Adding neutrons to 40Ca

Two models:

  • More neutrons, similar volume larger pn
  • More neutrons, more np pairs larger pp
  • L. Weinstein, EMC SRC MIT 2016

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0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01 1.00E+00 1.20E+00

0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01 1.00E+00 1.20E+00 1.40E+00 1.60E+00 1.80E+00 2.00E+00

Integrated momentum density

sum p sum n

2.0 1.0 0.0 0.5 1.5

neutrons protons Larger pn

Hagen et al, Nature Phys 12, p186 (2015)

N2LO saturation

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SLIDE 6

Focusing on 48Ca

0.15 – 0.3 fm

Coordinate space:

[CREX]

Momentum space:

[CaFe]

Adding correlations:

  • Reduce the radius.
  • Inverts the momentum

skin?

  • M. Vanhalst, et al., J. Phys. G 42, 055104 (2015)

Neutron Proton No SRC + np-SRC + nn-SRC Neutron Proton Neutron Proton

  • L. Weinstein, EMC SRC MIT 2016

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SLIDE 7

Focusing on 48Ca

0.15 – 0.3 fm

Coordinate space:

[CREX]

Momentum space:

[CaFe]

Adding correlations:

  • Reduce the radius.
  • Inverts the momentum

skin?

  • M. Vanhalst, et al., J. Phys. G 42, 055104 (2015)

Neutron Proton No SRC + np-SRC + nn-SRC Neutron Proton Neutron Proton

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Depends on pairing mechanisms in asymmetric nuclei!

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SLIDE 8

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40Ca 48Ca 54Fe

48Ca has a

40% neutron excess!!

The CaFe Triplet: A Lab for Asymmetric Nuclei

  • L. Weinstein, EMC SRC MIT 2016
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SLIDE 9

Nucleus Z N

40Ca

20 20 Symmetric double magic

48Ca

20 28 + Full neutron shell (1f7/2)

54Fe

26 28 Almost symmetric double magic

How do the neutrons from the

  • uter 1f7/2 shell correlate with

the 40Ca core?

The CaFe Triplet: A Lab for Asymmetric Nuclei

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  • L. Weinstein, EMC SRC MIT 2016

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SLIDE 10

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What do we already know?

(e,e’) cross-section ratios at xB>1 are sensitive to the TOTAL NUMBER OF SRC PAIRS:

=> 48Ca: + 20% nucleons, +20% SRC pairs!

  • Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861

1.44 1.2

0.96

  • Z. Ye, JLab Users Group Meeting Talk (2016)

~5% norm uncertainty not shown

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SLIDE 11
  • Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861
  • Z. Ye, JLab Users Group Meeting Talk (2016)

1.44 1.2 0.96

What do we already know?

The neutrons in the outer 1f7/2 shell (i.e. in the skin) are equally correlated as the nucleons in the 40Ca core!

(e,e’) cross-section ratios at xB>1 are sensitive to the TOTAL NUMBER OF SRC PAIRS:

Due to the extra 8 neutrons

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11

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SLIDE 12
  • Z. Ye Ph.D. Thesis, UVA. arXiv: 1408.5861
  • Z. Ye, JLab Users Group Meeting Talk (2016)

1.4 1.2 1.0

What do we already know?

The neutrons in the outer 1f7/2 shell (i.e. in the skin) are equally correlated as the nucleons in the 40Ca core!

(e,e’) cross-section ratios at xB>1 are sensitive to the TOTAL NUMBER OF SRC PAIRS:

Due to the extra 8 neutrons

The crust neutrons form MANY SRC pairs!

[What types? What’s their impact?]

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12

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SLIDE 13

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Cross section factorizes (in PWIA):

detect the proton (e,e’p)

  • L. Weinstein, EMC SRC MIT 2016

dσ dEedΩedTpdΩ p = KS( ! pmiss,Emiss) dσ free dΩ

Emiss = ν −Tp −TA−1 ! pmiss = ! q − ! pp = − ! pinitial Complications:

  • Rescattering of the outgoing proton.
  • Off-shell proton cross-section.
  • Meson Exchange Currents (MEC).
  • Delta production (i.e. IC).

=> Spectral function is not an observable! Compare cross sections for high (SRC) and low (MF) missing momentum protons in various nuclei

S D( ! pmiss,Emiss) = dσ dEedΩedTpdΩ p

/ K dσ free

dΩ

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SLIDE 14

Minimizing FSI

  • L. Weinstein, EMC SRC MIT 2016

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Pmiss (GeV/c) θnq= 35o θnq= 75o

PWIA Full 0.1 0.1 0.5 0.5 R = σFull / σPWIA

200 MeV/c

400 MeV/c 500 MeV/c

3He e,e' p

( )

θrq

20 40 100 120 60 80

d(e,e’p)

Boeglin et al., PRL 107 (2011) 262501

Sargsian Full = PWIA + FSI Θrq = angle between q and recoil

Avoid rescaaering peak at θrq ≈ 70o

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SLIDE 15

Optimizing (e,e’p) kinematics

  • L. Weinstein, EMC SRC MIT 2016

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  • Ebeam = 11 GeV @ 40 uA to maximize rates.
  • 1H, 2H, 12C, 40Ca, 48Ca, and 54Fe targets.
  • Q2 ≈ 3.5 GeV2

– Reduces non-nucleonic currents (MEC, IC). – Proton energies high enough for Glauber FSI calculahons.

  • xB = Q2/2mω > 1.2 to minimize non-nucleonic currents.
  • θrq < 50o to minimize FSI.
  • Two Kinemahcs:

– 350 < pmiss < 600 MeV/c (“SRC”) – pmiss < 250 MeV/c (“Mean-Field”)

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SLIDE 16

“Observables”

  • Distorted spectral funchons (i.e., reduced σ)

– Need theory support to interpret

  • Double rahos of

– extra SRC p from A1 to A2

  • e.g.: from 40 to 48Ca np pairs created by 8 more n

– Reduced transparency (FSI) correchons – Compare symmetric and asymmetric nuclei

  • 40 and 48Ca; 6 and 7Li
  • d, C, Ca, Fe
  • L. Weinstein, EMC SRC MIT 2016

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σ (SRC) /σ (MF)A1 σ (SRC) /σ (MF)A2