- two categories of magic numbers : harmonic oscillator and spin orbit

- 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…

-> extrapolate to other regions

40g9/2

H.O L2+

Experimental progresses and challenges in the evolution of shell closuresO. Sorlin (GANIL)

ESNT 2010 - Saclay

The N=20 shell closure A prototypical case of HO shell number

12 16 20 24Neutron Number

38Ar 36S 34Si 32Mg 30Ne40Ca

2016 24

Neutron Number N

36Ca 20

N=20 magic number Disappears !

36S32Mg

2) Presence of intruder fp states, f and p reversed ?

3) New magic number at N=16 ?

ESPE in N=20 isotones and island of inversion

T. Utsuno et al. PRC (1999)

d3/2s1/2d5/2

Role of the Vpnd5/2d3/2 and Vpnd5/2(fp) interactionsAttractive and repulsive tensor terms, respectively

1) Reduction of the N=20 shell gap

Occupancy of fp states grows at N=20

yJ. R. Terry et al., PRC 77 (2008) 014316.

20301680

W. Catford et al., PRL 2010

25Ne0.80

0.150.44

= 2, 3/2+

= 0, ½+

= 2, 5/2+ hole

= 1, 3/2-

( = 3),7/2-

- Proximity of f and p states to sd ones

- p and f states reversed, N=28 gap

24Ne(d,p)25Ne with TIARA+EXOGAM+VAMOS (GANIL)

Protons -> TIARAGammas -> ExogamNuclei -> Vamos

The ‘sizes’ of the N=20 and N=16 gaps in Oxygen (RIKEN)22O(d,p)23O reaction to probe the neutron N=16, 20 shell closures

N=20 : 1.3 MeV

N=16 : 4.0 MeV

5/2+ observed PRL99 (2007)Elekes et al. PRL98 (2007) 102502

Gated on neutrons Gated on 4 MeV neutron peak

34Si40Ca

d3/2s1/2d5/2

28O N=20

Utsuno, Otsuka et al.

A ‘critical’ view :

Mechanism of inversion not proven :

0+2 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 ?-> Study of 26F

Nuclear interaction in the sd shell N

Empirical determination of Vd5/2d3/2

183.46

26Ffree

24O 168.38

BE(MeV)

Vpn (d3/2d5/2)

Exp monopole ~ 600keV weakerthan Shell Model !

continuum effects … ??Where is the 4+ ? Isomer ?

interact

),()12(

2/32/52/32/5 J

Hoffman PRL 100(2008)Stanoiu thesis 2003,E(J=2)Jurado PLB 649 (2007)

Generalization to other HO shell gaps

Same mechanism at play : -Drop in 2+ energy at N=8, 20 and 40

-Inversion between normal and intruder states at N=40

- Search for a (super)deformed 0+2 in 68Ni

-Prove the extreme deformation of 64Cr

Great similarity between the three cases of HO shell numbers

N=8 N=20 N=40

O. S. , MG Porquet PPNP (2008)

N~20 p3/2

d3/2s1/2

p1/232

Large N/Z

N~40d5/2d5/2

N~8 s1/2

Evolution of Harmonic Oscillator shell closures

Role of the p3/2- p1/2 interaction

Role of the d5/2- d3/2 interaction

Role of the f7/2- f5/2 interaction ?

IN –

ION N=14

Small gaps

The making of ‘SO’ magic numbers

Which physics ? Which interactions ?

Neutrons

Evolution of neutron SPE in the Ca isotopic chain

20 28 20 28 Neutrons

Courtesy M.G Porquet

No increase of the N=28 shell gap when f7/2 is filled Same with realistic VlowK interaction -> 3 body ?

> Same increase of the neutron shell gaps by about 3 MeV !> Same mechanism at play to create SO magic numbers -> empirical rule to be used to constraint these spacing for heavier nuclei

Building SO magic numbers by neutron-neutron interactions

20 2822 24 26

Neutron number

- 840 42 44 46 48 50

68Ni 78Ni

From data around 90Zr

Neutron number

Extracted from BE’s, spectroscopy and SF’s

In collab with MG Porquet

Sn(23O)

Sn(22O)

Sn(17O)

E*(17O)

14s1/2

d5/2 [ ] [ ]

> Role of nuclear forces :Modification of the N=28 shell gap ?SO and Tensor interaction ?

j=2 j=2

Enhanced E2 collectivity due to j=2

N=28N=20

The study of the N=28 shell closure : a way to probe nuclear force

Ca, Z=20 48Ca

S, Z=16

Si, Z=14

1- compression of proton orbits

neutron f7/2 filling

2- Evolution of neutron orbits due to pn interactions

proton sd removed

49Ca47Ar

Variation of single particle energies (SPE)

Tensor interaction (Otsuka) d3/2 –( f7/2-f5/2 )

+280keV per proton added in d3/2

-210keV

Evolution of SPE’s from tensor part of the proton-neutron interaction

Use of 46Ar (d,p) transfer reaction

Size of the N=28 shell gap

Reduction of SO splitting

L. Gaudefroy et al. PRL 97 (2006),

28f7/2

eV) + 2

49Ca47Ar2018

Global trend of single particle energies between 49Ca and 43Si

derived from experimentally-constrained monopole variations

45S161443Si

-A shrink of SPE’s due to two-body p-n interactions…-Favor particle-hole excitations and E2 collectivity

- Spherical, shape coexistence in 44S and deformation in 42Si

Weak mixing between prolateand spherical shapes in the 0+

Qi ~ 55

Qi ~ 0

Electron spectroscopy to probe shape coexistence in 44S

Glasmacher et al., PLB 395 (97)

63(18)

BE2e2fm4

1365 2.62(2) s42(2)

C. Force, S. Grévy et al. to be published

Ee- (keV)

1365 keV

e- conv

(E0) = 8.7(5) 10-3

BE2(0+2 → 2+

1)BE2(0+

1 → 2+1)

f7/2d3/2s1/2

[ ] p3/2

42Si14

N=28p3/2

d3/2s1/2

[ ]28[ ]

48Ca20

Collapse of the N=28 shell closure in 42Si

B. Bastin, S. Grévy et al., PRL 99 (2007)

Role of the d3/2 – f7/2 interaction

Decrease of the N=28 gap by ~1MeV for 6 protons

N=14 shell closure in 22O and 20C

Thirolf et al. PLB 485 (2000) M. Stanoiu et al. PRC 69 (2004) and (2009)

s1/2 N=14

d5/2p1/2

[ ]14[ ]

d5/2s1/2

20C 6 20C 6

Role of the p1/2 – d5/2 interaction

Decrease of the N=14 by ~1.6 MeV for 2 protons

f7/2d3/2s1/2

[ ] p3/2

42Si14

s1/2 N=14

d5/2p1/2

[ ]14[ ]

d5/2s1/2

20C 6 20C 6

N=28p3/2

d3/2s1/2

[ ]28[ ]

48Ca20

N=50d5/2

f5/2p3/2

[ ][ ]

f5/2p3/2

78Ni50

N=50 ??

N=82f7/2

d5/2g7/2

[ ]82[ ]

d5/2g7/2

64 132Sn50

N=82 strong

48Ca40Ca

Occupation probability0 0.5 1

The N=50 shell closure at 78Ni50

« Monopole propose, quadrupole dispose »A. Zuker

Some Conclusions

Robust effect of NN inteactions :

Proton Neutron interaction L=0 plays an essential role to modify HO shell gaps

Proton Neutron interaction L=1 plays an certain role to modify SO shell gaps->Perhaps not strong enough to supress the magicity in 78Ni50

Role of Vnn to create SO magic numbers -> 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 ! -> Other candidates YES !!!

Special thanks : S. Grévy, L. Gaudefroy, D. Sohler, Z. Dombradi, M. Stanoiu, M. G. Porquet, F. Nowacki and F. Azaiez

V lowk NN

No N=28 shell gap formationwith realistic interactions !

The N=28 shell gap and the role of 3 body forces

Holt, Otsuka, Schwenk, Suzuki

: reduced by 330keV

Use of 46Ar (d,p) transfer reaction

Size of the N=28 shell gap

Reduction of SO splitting

L. Gaudefroy et al. PRL 97 (2006)

28f7/2

Evolution of the neutron SPE below 48Ca

(2J+1)C2S=1.7(2J+1)C2S=2.44

(2J+1)C2S=1.36C2Sf=0.64

C2Sg=0.34

neutrons

protons

42Si and 78Ni are ‘mirror’ systems

Development of collectivity in 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 ℓ=2 connections with valence states

neutrons

protons

28p3/2

42Siℓ

Role of proton-neutron forces in the N=28 region

Neutron Number

16s1/2

d3/2f7/2

40 5042 44 46 48

Neutron Number

32p3/2

Cu (Z=29)exp Around 78Ni

- ) (k

in the N=50 region

49Ca47Ar

Change of SO splitting for p orbits

Central density dependence (Piekarewicz)

s1/20.66

+170keVper proton

-85keV

-No change of p1/2-p3/2 splitting between 41Ca and 37S after removal of 4 protons from d3/2

-Reduction of splitting due to s1/2

Gaudefroy et al. PRL 2007

Probe the density dependence of the SO interaction in 36S and 34Si

RMF calculations using NL3 interactionReduction of the SO splitting by 70%

MF / Skyrme or Gogny forces Reduction of the SO splitting by 40%

SM calculations spdf-NRReduction of SO splitting by 30%Bare forces VlowK reduction by 7% only

SO reduced

N=16 disappears !

B.G Todd Rutel et al. PRC 69 (2004) 1301(R)M. Grasso et al. NPA 2009

Analysis GANIL in progress

36S 34Si

34Si36S

Insert here one or two slides on the effect of continuum…

Part I :Properties of shell closures of ‘HO’ origin

The N=8 shell closure

Quadrupole excitations favored in BeFirst ‘Island of inversion’ ?12Be g.s. strongly mixed (Navin et al PRL85; Pain et al. 96)

12Be : Iwasaki et al., PLB 481 (2000) 7

Evolution of the N=8 shell closure

8 6 4 2Z

-1-2-3-4-5

p1/2 p3/2

d5/2s1/2

Role of the p3/2-p1/2 interaction

Magic Numbers are a four-piece rock band from England comprising two pairs of brother and sister who previously went to The Cardinal Wiseman Roman Catholic High School in Greenford. The group was formed in 2002, releasing their critically acclaimed album titled The Magic Numbers in June 2005….

The Magic NumbersFrom Wikipedia, the free encyclopedia

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 ?

h11/2s1/2

p3/2h9/2

f5/2p1/2

Around 132Sn

N>>Z, drip-line

Nuclear Shell Structure Evolution

Mean field near stabilityStrong spin-orbit interaction

Reduced spin-orbit Tensor forcesMean field for N>>Z ?Effect of continuum ?

Adapted from J Dobaczewski

Major consequences :

1 : Reduction/disappearence of shell gaps -> modify the shape of r abundance peaks

2 : Change of g7/2 energy, increase the g7/2 → g9/2 GT transition, shorten -decay lifetimes

3 : The valence p states appear at weak excitation energy, favor neutron capure with n =0

No bound excited state in 23O and 24O

Size of N=16 > 4 MeV

Searching for a new N=16 shell closure

In-beam -ray spectroscopy using double step fragmentation

M. Stanoiu et al. PRC 69 (2004)

After this point the talk is finished…

Extra slides only !

Evidence of intruder configurations in neutron-rich Ne isotopes

Reduction of the N=20 shell gap ?

A. Obertelli Phys. Lett. B633 (2006)33

26Ne(d,p)27Ne in thick CD2 target 2 states at 765 and 885keVInclusive for 765keV, compatible with intruder

L=0L=1L=2

p// (Gev/c)

28Ne(-1n)27Netransition between 765 and 885keVIntruder state (765keV) has L1 from momentum distrib.

J.R. Terry, Phys. Lett. B 640 (2006) 86

CD240Ar

gammas23O

neutrons

14d5/2

protons

22O(d,p)23O reaction to probe the neutron N=16, 20 shell closures

Elekes et al. PRL98 (2007) 102502

B. Bastin, S. Grévy et al., PRL 99 (2007)

M. Stanoiu submitted

Knock-out reaction 12Be(-1n) to probe g.s. composition of 12Be

11Be1/2 +1/2 -

Navin et al., PRL 85 (2000) 266

E*(MeV) J

Confirms that the N=8 gap has collapsed

(5/2 +)

(3/2 -)

Almost equal SF values

Admixtures of s, p and d statesN=8 shell closure no longer present

Pain et al., PRL 96 (2006) 032502

11Be unbound1.8

Erel (MeV)

Large quadrupole deformation in the N=20 isotones below Z=14

Proton inelastic scatteringthick Liquid H target

Y. Yanagisa et al., PLB 566 (2003) 84

sdfpsd SM predictions

d3/2s1/2

at Z=14

at Z=12

2p-2h excitations

Known T1/2

h9/2p3/2f7/2

neutrons

protons

Need for good extrapolations far from known regionsUnderstand bulk evolution of nucleusAlways protons removed in the same g9/2 shellProton()-neutron() interactions involving the g9/2 orbit, e.g. g9/2 - g7/2

Evolution of the N=20 shell closure

d3/2s1/2d5/2

Onset of deformation around 32Mg

Specific role of the d5/2 – d3/2 and d5/2 – f7/2 interac.

No longer determine the size of the spherical N=20 gap

Some consequences …

Evolution of BE shows that :

N=20 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)

g9/2p3/2

d5/2d3/2

50 s1/2

d3/2 s1/2

p3/2f5/2

g7/2d5/2 d3/2

50 s1/2

N≤64

Large N/Z

10 15 20Neutron Number

d5/2s1/2

10 15 20Neutron Number

16d5/2

How will proton-neutron interactions (np=0,1)change this picture ? For large N/Z ratios, the L2 and L.S terms are expected to be reduced

Simplified mean-field approach for atomic nuclei

40g9/2

H.O L2+

d3/2s1/2

T. Otsuka EPJA (2004) 69

ESPE in N=20 isotones and island of inversion

Vpn(d3/2d5/2) >> Vpn(d3/2d3/2)

d5/2 d3/2s1/2

d3/2s1/2

d3/2 [ ]

d3/2s1/2

20s1/2

p3/2f7/2

p3/2p3/2 = 2

unbound

J. R. Terry et al., PRC 77 (2008) 014316.

Ground state composition of Mg isotopes at N=18, 20

60NaI detectors, = 20%

At N=20Constancy of B(E2) and E(2+) for Z=14-20Sudden drop of E(2+)Sudden rise of B(E2) at 32Mg Excitations to the neutron fp shells are required

012 16 20 24

Neutrons

12Mg16S

40Ca 38Ar 36S 34Si 32Mg 30Ne

From 14C to 12Be or 10He, the removal of p3/2 protons

provoke the breaking of the N=8 shell gap, inferred from -energy of the 1/2-, 1/2+ states

-1-, 2+ systematics,-SF’s derived from –1n neutron knock-out reaction

Role of the proton-neutron interaction p3/2-p1/2

s1/2 s1/2

Summary for the N=8 shell closure

Sn= 2.7(1) MeV

23000 nuclei

No bound excited state in 23O and 24O

Monte Carlo20%feeding

Doppler corrected

Raw spectra

6671 nuclei

Sn=4.19(10) MeV

Monte Carlo20%feedingexp

24O 24O

30Mg12

335(17)ms

log ft I

GT dominated by d3/2 d5/2

Large occupancy of d3/2 orbital

Beta-decay of Mg isotopes0+

32Mg12

86(5)ms

(4-)(4+)

log ft I

GT strength to g.s. much weaker

Missing occupancy of the d3/2 orbital

few %>7? (1-)

data S. Grévy (GANIL)

2 neutrons in d3/2

4 neutrons in d3/2

d5/214

d3/2s1/2

41P2643P28

- two categories of magic numbers : harmonic oscillator and spin orbit

neutron shell gaps

protonsthe n

neutron gaps

shell closure

sidoubly magic numbers

categories of magic

increase of neutron

p d32 n f72 interaction

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