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Concettina Sfienti
Johannes Gutenberg-Universität - Institut für Kernphysik, Mainz
Neutron
Skin@Mainz:
Why? What?
How?
Where do the neutrons go?
Nuclear charge radii
Neutron Skin for beginner
Where do the neutrons go?
Pressure forces neutrons
out against surface tension
EOS
Neutron Skin for beginner
Where do the neutrons go?
Pressure forces neutrons
out against surface tension
EOS
Neutron Skin for beginner
Phases of Nuclear Matter
LRP Nuclear Science Advisory Committee(2008)
A heavy nucleus (like 208Pb)
is 18 orders of magnitu...
WHY?
Equation Of State
3/12
symmetry energy
slope parameter
curvature parameter
…
M. Thiel Bormio 2015
Equation Of State
3/12
symmetry energy
slope parameter
curvature parameter
…
Equation Of State
3/12
symmetry energy
slope ...
Pb Radius vs Neutron Star Radius
• The 208Pb radius constrains the
pressure of neutron matter at
subnuclear densities. Typ...
....did I made this plot in the first place?!?!
WHY?
....did I made this plot in the first place?!?!
ISI + FSI
FSI
(syst)theo??
(syst)theo??
WHY?
....did I made this plot in the first place?!?!
(syst)theo??
Intepretation
+
WHY?
....did I made this plot in the first place?!?!
WHY?
Neutron skin Radii: Where are we?
value and its uncertainty obtained from neutron skins wi
Ssw ¼ 0 is thus quite compatibl...
N
γ
dσ
dΩ ∝ |A|2 × ...
 nuclear effects  FSI  ...
meson - nu
interaction
coherent
γ
πo
A, ⃗q γ + A → πo + A
dσ
dΩ ∝ | A|2 ...
WHAT?t method: PV e- scattering
5/12
NN
N
2
NN
N
2
NN
N
2
NN
2
...since...
...to measure ...
N
....construct ....
Model Dependent? YES but only a bitt method: PV e- scattering
5/12
Rn#
Assume#surface#thickness#
good#to#25%#(MFT)#
Neutro...
HOW?
Concettina Sfienti
Johannes Gutenberg-Universität - Institut für Kernphysik, Mainz
NSkin measurement@MESA
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Neutron Skin Measurements at Mainz

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Extract of a longer presentation on the neutron skin measurement program at the Institute of Nuclear Physics, Mainz (Germany)

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Neutron Skin Measurements at Mainz

  1. 1. Concettina Sfienti Johannes Gutenberg-Universität - Institut für Kernphysik, Mainz Neutron Skin@Mainz: Why? What? How?
  2. 2. Where do the neutrons go? Nuclear charge radii Neutron Skin for beginner
  3. 3. Where do the neutrons go? Pressure forces neutrons out against surface tension EOS Neutron Skin for beginner
  4. 4. Where do the neutrons go? Pressure forces neutrons out against surface tension EOS Neutron Skin for beginner
  5. 5. Phases of Nuclear Matter LRP Nuclear Science Advisory Committee(2008) A heavy nucleus (like 208Pb) is 18 orders of magnitude smaller and 55 orders of magnitude lighter than a neutron star They are bounded by the same EOS
  6. 6. WHY? Equation Of State 3/12 symmetry energy slope parameter curvature parameter … M. Thiel Bormio 2015
  7. 7. Equation Of State 3/12 symmetry energy slope parameter curvature parameter … Equation Of State 3/12 symmetry energy slope parameter curvature parameter X. Roca-Maza et al., PRL 106 (2011) 252501 … WHY? M. Thiel
  8. 8. Pb Radius vs Neutron Star Radius • The 208Pb radius constrains the pressure of neutron matter at subnuclear densities. Typel + Brown find sharp correlation between P at 2/3 ρ0 and Rn. • The NS radius depends on the pressure at nuclear density and above. Central density of NS few to 10 x nuclear density. • Pb radius probes low density, NS radius medium density, and maximum NS mass probes high density equation of state. • An observed softening of EOS with density (smaller increase in pressure) could strongly suggest a transition to an exotic high density phase such as quark matter, strange matter, or a color superconductor… Chiral EFT calc. of pressure P of neutron matter by Hebeler et al. including three neutron forces (blue band) agree with PREX results but two nucleon only Neutron skins constraint the EOS[@low ρ] of ... Pressure @ low ρ Crust thickness Pressure @ high ρ from mass measurements WHY?
  9. 9. ....did I made this plot in the first place?!?! WHY?
  10. 10. ....did I made this plot in the first place?!?! ISI + FSI FSI (syst)theo?? (syst)theo?? WHY?
  11. 11. ....did I made this plot in the first place?!?! (syst)theo?? Intepretation + WHY?
  12. 12. ....did I made this plot in the first place?!?! WHY?
  13. 13. Neutron skin Radii: Where are we? value and its uncertainty obtained from neutron skins wi Ssw ¼ 0 is thus quite compatible with the quoted co straints from isospin diffusion and isoscaling observabl in HIC [6–8]. On the other hand, the symmetry term of t incompressibility of the nuclear EOS around equilibriu (K ¼ Kv þ K2 ) can be estimated using information the symmetry energy as K % Ksym À 6L [5–7]. The co straint K ¼ À500 Æ 50 MeV is found from isospin d fusion [6,7], whereas our study of neutron skins leads K ¼ À500þ125 À100 MeV. A value K ¼ À550 Æ 100 Me seems to be favored by the giant monopole resonan (GMR) measured in Sn isotopes as is described in [13 Even if the present analyses may not be called definitiv 0 0.1 0.2 I = (N−Ζ) /Α -0.1 0 0.1 0.2 0.3 S(fm) 40 20 Ca 58 28 Ni 54 26 Fe 60 28 Ni 56 26 Fe 59 27 Co 57 26 Fe 106 48 Cd 112 50 Sn 90 40 Zr 64 28 Ni 116 50 Sn 122 52 Te 124 52 Te 48 20 Ca 96 40 Zr 120 50 Sn 116 48 Cd 126 52 Te 128 52 Te 124 50 Sn 130 52 Te 209 83 Bi 208 82 Pb 232 90 Th 238 92 U experiment linear average of experiment prediction Eq. (2) FSUGold SLy4 FIG. 2 (color online). Comparison of the fit described in tM. Centelles, et al Phys. Rev. Lett. 102, 122502 (2009) 2 Weeks Program in 2016 (short Workshop in May) NSkin from antiprotonic-atoms Neutron radius is not directly measured ➜ strong dependence on theoretical models. We need this systematics! ☠ Are model dependences clearly understood? ☠ Ultimate 208Pb potential: ± 0.03 fm?
  14. 14. N γ dσ dΩ ∝ |A|2 × ... nuclear effects FSI ... meson - nu interaction coherent γ πo A, ⃗q γ + A → πo + A dσ dΩ ∝ | A|2 × F2(q2) × ... nuclear effects FSI ... nuclear for ∆ in-mediu spin/iso-sp meson - nu bound stat incoherent γ πo γ′ A, ⃗q γ + A → πo + A⋆ → πo + A + γ transition f ∆ in-mediu spin/iso-sp 58 116 120 124 208 QaD Method 1: Coherent π0 photoproduction WHAT? SaD Method: Polarizability (Compton scattering) Virtual or Real (3/02/2015) Virtual (4/02/2015) Virtual when MESA becomes real (5/02/2015) (Electric)*Dipole*Polarizability* External*Field* “Books serve to show a man that those original thoughts of his aren't very new after all.” Abraham Lincoln
  15. 15. WHAT?t method: PV e- scattering 5/12 NN N 2 NN N 2 NN N 2 NN 2 ...since... ...to measure ... N ....construct ....
  16. 16. Model Dependent? YES but only a bitt method: PV e- scattering 5/12 Rn# Assume#surface#thickness# good#to#25%#(MFT)# Neutron#density#at#one#Q2# Small#correcAons#for# ###############MEC# Weak#density#at#one#Q2# Correct#for#Coulomb# DistorAons# Measured#APV# PHYSICAL REVIEW C88, 034325 (2013) ATION CONTENT OF THE WEAK-CHARGE FORM . . . PHYSICAL REVIEW C 88, 034325 (2013) 0 0.4 0.8 1.2 1.6 q(fm-1) 0 0.2 0.4 0.6 0.8 1 Fw(q) SV-min FSUGold PREX qCREX 48 Ca 208 Pb Fw×10 . (Color online) Weak-charge form factors with corre- theoretical errors for 48 Ca and 208 Pb as predicted by nd FSUGold. Note that the theoretical error bars have cially increased by a factor of 10. Indicated in the figure lues of the momentum transfer appropriate for PREX-II 5 fm−1 ) and CREX (q = 0.778 fm−1 ). maintained at all q values, except for diffraction minima and maxima. Given the similar patterns predicted by SV-min and FSUGold, we suggest that the observed q dependence of the correlation with rn represents a generic model feature. Figure 4(b) displays the same correlation, but now we also include the experimental uncertainty on the strange-quark form factor. Although the strange-quark contribution to the electric form factor of the nucleon appears to be very small [47], there is an experimental error attached to it that we want to explore. For simplicity, only results using SV-min are shown with and without incorporating the experimental uncertainty on the s quark. We note that an almost perfect correlation at low-to-moderate momentum transfer gets diluted by about 6% as the uncertainty in the strange-quark contribution is included. Most interestingly, the difference almost disappears near the actual PREX point, lending confidence that the experimental conditions are ideal for the extraction of r208 n . Finally, given that the strong correlation between the neutron radius and the form factor is maintained up to the first diffraction minima (about q = 1.2 fm−1 in the case of 48 Ca), the CREX experimental point lies safely within this range (figure not shown). sponding theoretical errors for 48 Ca and 208 Pb as predicted by SV-min and FSUGold. Note that the theoretical error bars have been artificially increased by a factor of 10. Indicated in the figure are the values of the momentum transfer appropriate for PREX-II (q = 0.475 fm−1 ) and CREX (q = 0.778 fm−1 ). the (absolute value) of the correlation as predicted by SV- min and FSUGold. At small momentum transfer, the form factor behaves as FW (q) ≈ 1 − q2 r2 W /6 ≈ 1 − q2 r2 n/6 so the correlation coefficient is nearly 1. Note that we have used the fact that the weak-charge radius rW is approximately equal to rn [4]. Also note that, although at the momentum transfer of the PREX experiment the low-q expression is not valid, the strong correlation is still maintained. Indeed, the robust correlation is 0.6 0.7 0.8 0.9 1.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 q (fm-1 ) SV-min (b) no s with s 0.6 0.7 0.8 0.9 1.0 (a) SV-min FSU Crn,FW in208 Pb PREX-IIPREX-II FIG. 4. (Color online) Correlation coefficient (9) between r208 n and F208 W (q) as a function of the momentum transfer q. Panel (a) shows the absolute value of the correlation coefficient predicted by SV-min and FSUGold assuming no strange-quark contribution to the nucleon form factor. Panel (b) shows the impact of including the experimental uncertainty in the strange-quark contribution to the nucleon form factor. The arrow marks the PREX-II momentum transfer of q = conditions are ideal for the extraction of rn . Fi the strong correlation between the neutron radi factor is maintained up to the first diffraction q = 1.2 fm−1 in the case of 48 Ca), the CREX point lies safely within this range (figure not sh IV. CONCLUSIONS AND OUTLO In this survey, we have studied the potentia proposed PREX-II and CREX measurements o the isovector sector of the nuclear EDF. In explored correlations between the weak-char of both 48 Ca and 208 Pb, and a variety of observ to the symmetry energy. We wish to emphasiz chosen the weak-charge form factor rather tha quantities—such as the weak-charge (or neu since FW is directly accessed by experiment. To tions among observables, two different approa implemented. In both cases we relied exclusiv that were accurately calibrated to a variety of gr on finite nuclei. In the “trend analysis,” the pa optimal model were adjusted in order to system the symmetry energy, and the resulting imp observables was monitored. In the “covarianc obtained correlation coefficients by relying exc covariance (or error) matrix that was obtained of model optimization. From such combined a the following: (i) We verified that the neutron skin of 20 fundamental link to the equation of state matter. The landmark PREX experim very small systematic error on r208 n tha reaching the total error of ±0.06 fm PREX-II is realistic. (ii) We also concluded that an accurate de r208 skin is insufficient to constrain the n 48 Ca. Indeed, because of the significan the surface-to-volume ratio of these tw
  17. 17. HOW? Concettina Sfienti Johannes Gutenberg-Universität - Institut für Kernphysik, Mainz NSkin measurement@MESA Nomen Omen Smaller Faster MORE DANGEROUS? V-RAPTORP Full azimuthal coverage 4xstat ± 0.03 fm! t method: PV e- scattering 5/12 Open question: 48Ca, 124Sn, 208Pb? ➜ Resolve Elastic: 1st excited state (3.8-1.1-2.6 MeV)

Extract of a longer presentation on the neutron skin measurement program at the Institute of Nuclear Physics, Mainz (Germany)

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