1. Concettina Sfienti
Johannes Gutenberg-Universität - Institut für Kernphysik, Mainz
Neutron
Skin@Mainz:
Why? What?
How?

2. Where do the neutrons go?
Nuclear charge radii
Neutron Skin for beginner

3. Where do the neutrons go?
Pressure forces neutrons
out against surface tension
EOS
Neutron Skin for beginner

4. Where do the neutrons go?
Pressure forces neutrons
out against surface tension
EOS
Neutron Skin for beginner

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. WHY?
Equation Of State
3/12
symmetry energy
slope parameter
curvature parameter
…
M. Thiel Bormio 2015

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. 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. ....did I made this plot in the first place?!?!
WHY?

10. ....did I made this plot in the first place?!?!
ISI + FSI
FSI
(syst)theo??
(syst)theo??
WHY?

11. ....did I made this plot in the first place?!?!
(syst)theo??
Intepretation
+
WHY?

12. ....did I made this plot in the first place?!?!
WHY?

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. 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. 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. 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. 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)