Pr

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• - Two categories of magic numbers
• Harmonic Oscillator and Spin Orbit
• - The role of proton-neutron interactions
• Disappearance of magic numbers
• Appearance of new magic numbers
• What do we mean by SO magic numbers ?
• Influence of binding energy on nuclear force ?
• Note that
• Structural variations better seen in light
  nuclei
• Extract general empirical rules / symmetries
• -gt extrapolate to other regions

Mean-field approach for atomic nuclei
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The N20 shell closure A prototypical case of HO
shell number
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N20 magic number Disappears !
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2) Presence of intruder fp states, f and p
reversed ? 3) New magic number at N16 ?
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hole
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Nuclear interaction in the sd shell
A critical view Mechanism of inversion not
proven 02 not yet observed in 34Si and
32Mg Hard to get 28O unbound using standard
Vnn No direct (easy) determination of
Vd5/2d3/2 due to deformation So far monopole
assumed constant whatever neutron and proton
binding energy True or not ? Can we check it ?
Neutron
-gt Study of 26F
Utsuno, Otsuka et al.
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Empirical determination of Vd5/2d3/2
Exp monopole 600keV weaker than Shell Model !
continuum effects ?? Where is the 4 ? Isomer ?
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Generalization to other HO shell gaps
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O. S. , MG Porquet PPNP (2008)

• Same mechanism at play
• Drop in 2 energy at N8, 20 and 40
• Inversion between normal and intruder states at
  N40
• Search for a (super)deformed 02 in 68Ni
• Prove the extreme deformation of 64Cr

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Role of the p p3/2- n p1/2 interaction
Role of the p d5/2- n d3/2 interaction
SPIN FLIP Dl0 INTERACTION
Role of the p f7/2- n f5/2 interaction ?
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The making of SO magic numbers Which physics
? Which interactions ?
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Extracted from BEs, spectroscopy and SFs
In collab with MG Porquet
gt Same increase of the neutron shell gaps by
about 3 MeV ! gt Same mechanism at play to create
SO magic numbers -gt empirical rule to be used
to constraint these spacing for heavier nuclei
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46Ar
44S
42Si
gt Role of nuclear forces Modification of the
N28 shell gap ? SO and Tensor interaction ?
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Variation of single particle energies (SPE)
Evolution of SPEs from tensor part of the
proton-neutron interaction
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Role of the p d3/2 n f7/2 interaction
Decrease of the N28 gap by 1MeV for 6 protons
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Role of the p p1/2 n d5/2 interaction
Decrease of the N14 by 1.6 MeV for 2 protons
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The N50 shell closure at 78Ni50
 Monopole propose, quadrupole dispose  A. Zuker
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Some Conclusions
Robust effect of NN inteactions Proton
Neutron interaction DL0 plays an essential role
to modify HO shell gaps Proton Neutron
interaction DL1 plays an certain role to modify
SO shell gaps -gtPerhaps not strong enough to
supress the magicity in 78Ni50 Role of Vnn to
create SO magic numbers -gt Same increase of
neutron shell gap (3MeV) for all SO magic numbers
! Modification of Vpn due to the presence of
continuum ? Vpn d5/2d3/2 (26F) 60 of
canonical value only ! -gt Other candidates YES
!!!
Special thanks S. Grévy, L. Gaudefroy, D.
Sohler, Z. Dombradi, M. Stanoiu, M. G. Porquet,
F. Nowacki and F. Azaiez
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The N28 shell gap and the role of 3 body forces
Holt, Otsuka, Schwenk, Suzuki
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reduced by 330keV
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Development of collectivity in 42Si
f5/2
p1/2
p3/2
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Dl2
f7/2
(jngt)
neutrons
d3/2
(jplt)
s1/2
Dl2
14
d5/2
(jpgt)
protons
42Si
Doubly magic numbers originating from spin-orbit
interaction Mutual reductions proton and
neutron gaps depends on the strength the tensor
force The proton and neutron gaps are connected
by Dl2 connections with valence states
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in the N50 region
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-No change of np1/2-p3/2 splitting between 41Ca
and 37S after removal of 4 protons from
pd3/2 -Reduction of splitting due to ps1/2
p1/2
170keV per proton
p3/2
-85keV
0.66
s1/2
p
n
Central density dependence (Piekarewicz)
Gaudefroy et al. PRL 2007
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Probe the density dependence of the SO
interaction in 36S and 34Si
B.G Todd Rutel et al. PRC 69 (2004) 1301(R) M.
Grasso et al. NPA 2009
SO reduced
34Si
36S
RMF calculations using NL3 interaction Reduction
of the SO splitting by 70 MF / Skyrme or Gogny
forces Reduction of the SO splitting by 40 SM
calculations spdf-NR Reduction of SO splitting
by 30 Bare forces VlowK reduction by 7 only
36S
34Si
Analysis GANIL in progress
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Insert here one or two slides on the effect of
continuum
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Part I Properties of shell closures of HO
origin The N8 shell closure
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Role of the pp3/2-np1/2 interaction
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Summary - Two classes of shell closures (magic
numbers) HO and SO - Proton-neutron
interactions usually act to destroy them - Takes
root in NN bare forces link in progress -
Forces be strong enough to destroy shell closures
in heavy nuclei ? - Astrophysical consequences
expected - Extrapolation to superheavies or
unknown regions ?
The
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Searching for a new N16 shell closure
In-beam g-ray spectroscopy using double step
fragmentation
Size of N16 gt 4 MeV
No bound excited state in 23O and 24O
M. Stanoiu et al. PRC 69 (2004)
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After this point the talk is finished Extra
slides only !
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22O(d,p)23O reaction to probe the neutron N16,
20 shell closures
protons
d
qp
RIKEN
f7/2
d3/2
16
s1/2
14
d5/2
Elekes et al. PRL98 (2007) 102502
22O14
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Collapse of the N28 shell closure in 42Si
42Si
B. Bastin, S. Grévy et al., PRL 99 (2007)
20C
5
O
E(2) (MeV)
C
0
5
10
20
15
Neutron Number
M. Stanoiu submitted
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p3/2
fp
f7/2
20
2p-2h excitations
20
d3/2
16
s1/2
sd
14
14
d5/2
8
8
p1/2
n
n
at Z14
at Z12
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130Cd
pg9/2
Known T1/2
Need for good extrapolations far from known
regions Understand bulk evolution of
nucleus Always protons removed in the same g9/2
shell Proton(p)-neutron(n) interactions involving
the g9/2 orbit, e.g. pg9/2 - ng7/2
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Evolution of the N20 shell closure
s1/2
d3/2

• Evolution of BE shows that
• N20 gap remains large and constant as long as
• protons occupy d3/2 and s1/2 orbits
• pn interactions involved have similar strength
• Vpn(d3/2f7/2) ? Vpn(d3/2d3/2)
• Vpn(s1/2f7/2) ? Vpn(s1/2d3/2)

40Ca
34Si
28O
7/2-
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Large N/Z
19K
d3/2
d3/2
s1/2
s1/2

f7/2
f7/2
14
14
n
n
d5/2
d5/2
p
p
N20
N28
29Cu
f5/2
g9/2
p3/2
p3/2
f5/2
n

g9/2
SPIN-FLIP Dl1 INTERACTION
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28
n
f7/2
f7/2
p
p
N44
N40
51Sb
g7/2
d3/2
d3/2
d5/2
d5/2
g7/2
h11/2
h11/2

s1/2
50
s1/2
50
n
n
g9/2
g9/2
p
p
N70
N64
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5
O
E(2) (MeV)
C
0
5
d3/2
d3/2
d5/2
0
16
s1/2
Effective Single Particle Energy (MeV)
16
s1/2
d5/2
14
-5
5
10
20
10
5
15
15
20
Neutron Number
Neutron Number
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Simplified mean-field approach for atomic nuclei
How will proton-neutron interactions (Dlnp0,1)
change this picture ? For large N/Z ratios, the
L2 and L.S terms are expected to be reduced
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ESPE in N20 isotones and island of inversion
Vpn(d3/2d5/2) gtgt Vpn(d3/2d3/2)
d5/2
s1/2
d3/2
N20
0f7/2
Island of inversion
T. Otsuka EPJA (2004) 69
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Z8
Z20
Z14
p3/2
p3/2
p3/2
Dl 2
f7/2
f7/2
f7/2
d3/2
20
20
16
d3/2
d3/2
d3/2

d3/2
s1/2
s1/2
s1/2
s1/2
s1/2
14
14
14
d5/2
d5/2
d5/2


d5/2
d5/2
d5/2
p
p
p
n
n
n
unbound
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Ground state composition of Mg isotopes at N18,
20
occupancy
J. R. Terry et al., PRC 77 (2008) 014316.
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60NaI detectors, eg 20
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• From 14C to 12Be or 10He, the removal of p3/2
  protons
• provoke the breaking of the N8 shell gap,
  inferred from
• -energy of the 1/2-, 1/2 states
• 1-, 2 systematics,
• SFs derived from 1n neutron knock-out reaction
• Role of the proton-neutron interaction p3/2-p1/2

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No bound excited state in 23O and 24O
Doppler corrected
Raw spectra
Monte Carlo 20feeding
22O
23O
23000 nuclei
Sn 2.7(1) MeV
exp
23O
Monte Carlo 20feeding
24O
24O
exp
6671 nuclei
Sn4.19(10) MeV
4180
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Beta-decay of Mg isotopes
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Collapse of the N28 shell closure in 42Si
42Si
43P
41P