Structure evolution towards 78 Ni :

61
Structure evolution towards 78 Ni : challenges in the interpretation of hard-won experimental data solved by simple means David Verney, IPN Orsay FUSTIPEN Topical Meeting -- « Recent Advances in the Nuclear Shell Model » -- June 19-20, 2014, GANIL, Caen • An introduction to the N=50 shell effect/evolution towards 78 Ni • How and why the subject was introduced in Orsay • What we have learned ? Selection of results (from Orsay and elsewhere) : collectivity and evidence of intruder states in the 78 Ni region

description

Structure evolution towards 78 Ni : challenges in the interpretation of hard-won experimental data solved by simple means David Verney, IPN Orsay. • An introduction to the N=50 shell effect/evolution towards 78 Ni. • How and why the subject was introduced in Orsay. - PowerPoint PPT Presentation

Transcript of Structure evolution towards 78 Ni :

Page 1: Structure evolution towards  78 Ni :

Structure evolution towards 78Ni : challenges in the interpretation of hard-won experimental data

solved by simple means

David Verney, IPN Orsay

FUSTIPEN Topical Meeting -- « Recent Advances in the Nuclear Shell Model » -- June 19-20, 2014, GANIL, Caen

• An introduction to the N=50 shell effect/evolution towards 78Ni

• How and why the subject was introduced in Orsay

• What we have learned ?Selection of results (from Orsay and elsewhere) :

collectivity and evidence of intruder states in the 78Ni region

Page 2: Structure evolution towards  78 Ni :

Page 2Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

• An introduction to the N=50 shell effect/evolution towards 78Ni

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Page 3Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

The 78Ni region in 2014: the final cut (?)

Age of the pionneers: mid 80’s

TRISTAN(Brookhaven)/OSIRIS(Studsvik)

“Is the region above 78Ni doubly magic ?”r-process consequences

Fogelberg, J.C. Hill, J.A. Winger and others

The final cut ? : ca 2014

RIKEN

direct study of 78Ni

By Kratz et al. PRC 38 (1988)

Waiting point nucleus at N=50 80Zn

«  »  very busy decade

dormance

Second golden age : ca 2004

Yrast (LNL,Euroball)/Coulomb exc. (ISOLDE,ORNL)

/Masses (JYFL,ISOLDE)/transfer (ORNL,ISOLDE)

/Radioactivity(ORNL,Orsay)“Is N=50 a good magic number?”

r-process + structure consequences

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The persistence of N=50: the core-breaking states

32

p1/2

g9/2

d5/2

neutrons

50

O. Sorlin, M.G. Porquet

Prog. Part. Nucl. Phys. 61 (2008) 602

N=50 gap extrapolation → 78Ni =3.0(5) MeV

After a decade : no (serious) evidence was found for shell quenching down to Z=30 in the low energy data (radioactivity and coulomb excitations studies). But:

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The question of the size of the gap at N=50: what masses sayusing data taken from AME2012[including Hakala et al. PRL101 052502 (2008)]

collective origintheoretically : Bender et al. Phys. Rev. C 78, 054312 (2008)

maximum influence of beyond mean-field correlations

D = S2n(52)-S2n(50)

extracted from

Bender et al. Phys. Rev. C 78, 054312 (2008)e

d 5/2 –

eg 9/

2 (M

eV)

Ni Zn Ge Se Kr Sr

Duflo Zuker gap PRC59 (1999) 90Zr =4,7 MeV

Duflo Zuker gap 78Ni =5,7 MeV

« standard »« graphical »

loca

l min

imum

at Z

=32

Zr

K. Heyde et al. Phys. Let. B176 (1986) NPA466 (1987) 189

« standard »

« graphical »

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K. Sieja and F. Nowacki, Phys. Rev. C 85, 051301R (2012)

minimum in gap D

The question of the size of the gap at N=50: shell model

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Page 7Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

NPA466 (1987) 189

Z

Sn(Z,N)-Sn(Z,N+1)

Sn(Z,N)-Sn(Z,Nextr)

N N+1 N+3 N+5 N+7neutron number

(Koopmans theorem)

gap in the single particle levels

n

50ej’n

ejn

-ej’n= Sn(Z,N)

but Sn(Z,N+1) is not a good prescription for

for the evaluation of ejn

one has to estimate ej’n and ej n in the same nucleus

ejn—ej’n = Sn(Z,N) —Sn(Z,Nextr) then the good prescription becomes :

The question of the size of the gap at N=50: back to core-breaking states

p1/2

g9/2

d5/2

neutrons

50

K. Heyde et al. graphical methodNPA466 (1987) 189

There are more things than monopole effects in the red curve …

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Page 8Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

K. Sieja and F. Nowacki, Phys. Rev. C 85, 051301R (2012)

The question of the size of the gap at N=50: back to core-breaking states

Fusion-fission experiment accepted for AGATA@GANIL campaign (spokespersons G. Duchêne and G. De Angelis)search for core-breaking Yrast states in 80Zn

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figures taken from Bender et al. Phys. Rev. C 78, 054312 (2008)

N=50 vs Z=50 situations

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• How and why the subject was introduced in Orsay

(experimental context)

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Zn81

Present limit of structure knowledge(at least few excited states are known)

hot plasma ionization(1 µA deuteron primary beam)O. Perru PhD – def. 10th December 2004Eur. Phys. J. A 28, 307 (2006)+PhD A. Etile CSNSM ongoing

surface ionization (2-4 µA electron primary beam)M. Lebois PhD – def. 23th September 2008PRC 80, 044308 (2009) B. Tastet PhD – def. 13th May 2011PRC 87, 054307 (2013)D. Testov PhD – def. 17th January 2014

laser ionization(10 µA electron primary beam)K. Kolos PhD – def. September 2012PRC 88, 047301 (2013)

Ga84Ga83Ga82 Ga85Ga80Ga79

Ge80Ge79 Ge81 Ge85 Ge86

As82

hot plasma ionization(1 µA deuteron primary beam)PRC 76 (2007) 054312

-decay spectroscopyat the PARRNe mass separator (Tandem/ALTO)

Zn82

And “spin-off” elsewhere: -LNL :Plunger + AGATA + PRISMA-RIKEN: EURICA, MINOS campaignsaccepted : GANIL Plunger + AGATA + VAMOS LoI: SPES, SPIRAL2 phase 2

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Tandem building Institut de Physique Nucléaire Campus of the Paris Sud University Orsay (France)

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ALTO=ISOL installation based on photo-fission (the first of its kind in the world)

PARRNe mass separator

e-LINAC 10 µA 50MeV

(former 1st section of the

CERN LEP injector)

TIS vault>~1.10^11 fissions/s

Target Ion-source ensemble

kicker - bender

secondary beam lines

POLAREXnuclear

orientation on line

identification station

BEDObeta decay

spectroscopy

and the only facility in France providing fission fragments as mass separated RIBs (prefiguring for a time SPIRAL2.2)

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plastic scintilator

Large volume Ge detector(EUROGAM-1 French-UK loan pool)

Ge CLOVER (proto EXOGAM )

Mylar tape

beam

etotal(photo-peak 1.3MeV)~2%

T1/2 measurement: tape motion cyclingTriggerless DAQ 400ps resolution time stamping

time

decayion beam deviated

build upion collection

Detection setup and movable tape

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β energy loss

Compton

collection point

Ge

GeGe

plastic scintillator

4π-β

Ge

ancilaryplastic

BGO

4p beta

BEDO : BEta Decay studies at OrsayStrategy for optimal detection Compact geometry (max γ efficiency)

γ background suppression

BGO crystals

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BEDO : BEta Decay studies at Orsay construction completed – commissioning beam time in 2012

Anti-Compton belt

4 EXOGAM small prototypesSource-cap distance = 5 cmevaluated e g (1 MeV) = 3-4 % (previous system 1-2%)

sensitivity 0.1 pps

up to 5 Ge detectors

6 plastic detectors

beam entrance

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• What we have learned ?Selection of results,

collectivity and evidence of intruder states in the 78Ni region

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Page 18Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

Zn81

surface ionizationB. Tastet PhD – def. 13th May 2011PRC 87, 054307 (2013)laser ionization(10 µA electron primary beam)K. Kolos PhD – def. September 2012PRC 88, 047301 (2013)D. Testov PhD – def. 17th January 2014

Ga84Ga83Ga82 Ga85Ga80Ga79

Ge80Ge79 Ge81 Ge85 Ge86

As82

Zn82

-decay spectroscopyaround the Z=32 “curiosity”

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isomerism in the N=49 line

(3-5) Hoff & Fogelberg NPA368 (1981)

8+6+

4+

2+

0+

(ng9/2-2)8+ seniority isomer

populated in DIC●Makishima et al PRC 59 (1999)●Podolyak et al Int. J. Mod phys E 13 (2004)●H. Mach et al J. Phys. G 31 (2005)

→ T1/2=2.95(6) ns

existence of second beta decaying state with I~7 suspected

ISOLDE experiment, laser spectroscopy : two long lived states in 80Ga I=3 and I=6 (negative parity from shell model)B. Cheal et al., PRC 82 (2010) 051302R

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Study of 80Ga→80Ge beta decayhi

ts p

er 0

.5 k

eV

Energy (keV)

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etc…Over the 75 γ-rays previously attributed to the 80Ga decay, the decay time of 67 individual β-delayed γ-activities were measured

the apparent half life of 30 levels could be determined

Study of 80Ga→80Ge beta decay

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measured half-life in seconds

T1/2=1.6870.011s Singh Nuclear Data sheets 105 (2005) 223

apparent half-life of the 80Ge levels

longer lived

shorter livedHoff & Fogelberg 235U

ALTO

238 U

Study of 80Ga→80Ge beta decay

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80Galonger

shorter

80Ge

lA (apparent half life)

lL

longer lived state contribution

shorter lived state contribution

levels of 80Ge

lS

1 0,8 0,6 0,4 0,2 0

lF (indirect feeding apparent half life)

Study of 80Ga→80Ge beta decay

Page 24: Structure evolution towards  78 Ni :

Page 24Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

80Galonger

shorter

T1/2= 1.90.1 s

T1/2= 1.30.2 s3―

6―

Study of 80Ga→80Ge beta decay

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Page 25Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

M. Honma et al., Phys. Rev. C 80, 064323 (2009)

B.A. Brown private communication, as first used in D. V. et al. Phys. Rev. C 76, 054312 (2007)

JUN45 JJ4B

multipletsclose to the 0(6) limit of IBM

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Kumar model-independent n-body moments

[Kumar PRL28, 249 (1972)]

intrinsic shapes of SM eigenstates

JUN45 JJ4B

shell model calculations and transcription into intrinsic shapes

Page 27: Structure evolution towards  78 Ni :

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microscopic origin of the collective features

JUN45 JJ4B

f5/2

p3/2

p1/2

g9/2

p n

f5/2

p3/2

p1/2

g9/2

p n

collective gamma-soft configurations

f5/2

p3/2

p1/2

g9/2

p n

non-collectivequasi-particle like

configurations

Dℓ=2

quadrupole components of the interaction

pairing components of the interaction

►the energy proximity of f5/2 and p orbits (Dℓ=2) seems to be the key ingredient

energy separation between f5/2 and p3/2 in 79Cu :~1 MeV in JUN45 390 keV in JJ4B

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Triaxiality at Z=32

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76Ge

0+2 ?

Triaxiality at Z=32 and possible intruder 2p-2h 0+ states at N=48

“triaxial features” evolution of the 0+2 state energy

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80Ge 80Ge

from M. Honma et al., Phys. Rev. C 80, 064323 (2009)

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Zn81

laser ionization(10 µA electron primary beam)K. Kolos PhD – def. September 2012PRC 88, 047301 (2013)

Ga84Ga83Ga82 Ga85Ga80Ga79

Ge80Ge79 Ge81 Ge85 Ge86

As82

Zn82

-decay spectroscopyaround the Z=32 “curiosity”

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Lebois et al.

Kolos et al.

Study of 84Ga5384Ge52 decay

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(0—,1—)

Study of 84Ga5384Ge52 decay

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84Ga5384Ge52 : addressing the collectivity development beyond N=50

0 0+

2+710

1744 4+

6+3095

1542 22+

1934 02+

2838 23+

HFB-5DCH Gogny D1S Delaroche et al. Bruyères-le-Châtel, available online, S. Hilaire M. Girod

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0 0+

2+769

1584 4+

6+2900

1530 22+

42+21302002 31+

2812 51+

1768 02+

2150 24+

2603 43+

1873 23+

2360 32+

346

370

405

269

166

229231

599

77

137

145

0 0+

2+

(1+,2+)

(0+,1+,2+)

3502 (1+,2+)

EXP

2228

1389

624

JJ4B(proton-proton)+Sieja et al PRC 79, 064310 (2009)

g (°)

b =

0 0+

2+710

1744 4+

6+3095

1542 22+

1934 02+

2838 23+

HFB-5DCH Gogny D1S

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Page 37Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

A bit deeper into the problem of intruder states: odd isotones N=49

• What we have learned ?Selection of resultscollectivity and evidence of intruder states in the 78Ni region

Page 37: Structure evolution towards  78 Ni :

Page 38Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

Zn81

Ga84Ga83Ga82 Ga85Ga80Ga79

Ge80Ge79 Ge81 Ge85 Ge86

As82

Zn82

PhD A. Etile (CSNSM Orsay) ongoingfirst data taken with the new -decay spectroscopy setup BEDO(BEDO commissioning)

odd-odd nuclei:- detailed spectroscopy: stopped beam experiments- -decay very selective as allowed GT transitions e-e→o-o practically exclusively 0+→1+

A bit deeper into the problem of intruder states: the case of the odd-odd N=49 isotones

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By Kratz et al. PRC 38 (1988)

Waiting point nucleus at N=50 80Zn

By Winger et al. PRC 36 (1987)

«  » 

The anomalous occurrence of low lying 1+ states in the odd-odd N=49 isotone 80Ga → historically launched the problematic of a possible vanishing of the N=50 shell effect

Page 39: Structure evolution towards  78 Ni :

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Winger et al. PRC 36 (1987) Fig. taken from Kratz et al. PRC 38 (1988)

RPA calculations, with significant quadrupole deformation (ε2=0.26) produce naturally an enormous amount of 1+ states (2QP states, Nilsson labeled), which was found satisfactory (!)

in a similar study Winger et al removed the parenthesis only at much higher energy

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In the observation of the beta decay of an even-even to an odd-odd nucleus : one cannot (in principle) “miss” the lowest 1+ states (only 0+→1+ beta transitions are allowed in n-rich nuclei)

Q window

Eidens et al (1970)

Hoff & Fogelberg (1981)

Winger et al(1987)

note the huge increase in the number of states populated by beta decay between 82As and 80Ga-- is it real ? is there an important structure effect at play ?

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H. Gausemel et al., Phys. Rev. C 70, 037301 (2004)

3.4(9)

80(20)

1.6(5)

0.35(9)

B(%) log ft

5.7(2)

4.2(2)

5.3(2)

5.8(2)

3.5(

5)8.

50(6

)

1.45

(2)

<1<1

100(

3)

(0-,1-)

(0,1)

(0,1)

Study of 82Ge→82As beta decay

(Still a bit preliminary)

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what are the proton-neutron configurations one can expect at low energy ?→ let’s start with the zero-order coupling

O-ν

even-even semi-magic core

O-O O-π

E-Eproton open shell(proton quasi-particles)

neutron closed shell(neutron holes and intruder states)

odd-proton N=50 nucleus(taken from experimental level scheme)

odd-neutron N=49 nucleus(taken from experimental level scheme)

odd-odd N=49 nucleus(we hope to describe)

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Neutron statesOmnipresence of positive parity (intruder) statesFirst hinted at from transfer reaction data [e.g. Detorie et al PRC18 (1978)]First systematics proposed by Hoff & Fogelberg NPA 368 (1981)emphasized in Meyer et al. PRC 25 (1982) since then everybody has been quiet on the subject

1p-2h states2+ p1/2

-1 or f5/2-1,p3/2

-1 ?

78Zn(d,p) R. Orlandi et al. (REX-ISOLDE)79-80Cu -decay M. Niikura (EURICA RIKEN)

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A. Pfeiffer et al. NPA 455 (1986) 381

Proton states

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from beta-decayD.V. et al. PRC 76, 054312 (2007)

Proton states

5/2 assignment to ground state unambiguously confirmed from laser spectroscopy measurementsCheal et al PRL 104, 252502 (2010) N.B. We will know more soon:

79Cu has been populated in 80Zn(p,2p) reaction at RIKEN recently (PhD work in Orsay under the supervision of S. Franchoo)

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0

500

1000

1500

2000

2500

3000

3500

4000

86Rb 84Br 82As 80Ga

Ener

gy (k

eV)

f5*p3(+)

f5*f5(+)

p3*p1(+)

p3*p3(+)

p3*f5(+)

p1*p1(+)

p1*p3(+)

g9*g9(+)

0

500

1000

1500

2000

2500

3000

3500

4000

86Rb 84Br 82As 80Ga

Ener

gy (k

eV)

f5*d5(-)

f5*d3(-)

p3*d5(-)

p3*s1(-)

p3*d3(-)

p1*s1(-)

p1*d3(-)

82As is the first N=49 isotone for which low-spin negative parity (0- and 1-) states appear below the first 1+ state

Unperturbed positions of the proton-neutron configurations in the odd-odd N=49 isotones

normal positive parity intruder negative parity

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Include 2d5/2, 3s1/2, 2d3/2 on top of the fp-g valence space → very challenging for shell model, not yet available

→ what can be done ?

→ in a first approach, one can use a much less computationally demanding solution:core-particle coupling model

→ our job was facilitated and encouraged by :(1) The description of odd N=49 nuclei down to 85Kr, including 2d5/2, 3s1/2, 2d3/2 has already been

done: Kitching Z. Phys. 258 (1973) ; Bhattacharya & Basu J. Phys. G 5 (1979)

(2) Hoffmann-Pinther & Adams [NPA229 (1974)] have already treated the odd-odd case within the Thankappan-True [Phys. Rev. 137 (1965)] schematic approach

Core QP π QP ν C - π

C - ν

π-ν interactionexperimental values fit to the odd nucleistrength adjusted on

86Rb

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experimental

coupled to 0+

coupled to 2+

in agreement with identifications made by Dawson et al. Phys. Rev. 181 (1969)

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experimental

coupled to 0+

coupled to 2+

3.4(9)

80(20)

1.6(5)

0.35(9)

B(%) log ft

5.7(2)

4.2(2)

5.3(2)

5.8(2)

3.5(

5)8.

50(6

)

1.45

(2)

<1<1

100(

3)

(0-,1-)

(0,1)

(0,1)only states coupled to 2+

2+ core coupled states ?

(clearly) π p3/2 ν p1/2-1

intruder π f5/2 ν d5/2

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Winger et al. PRC 36 (1987) Fig. taken from Kratz et al. PRC 38 (1988)

RPA calculations, with significant quadrupole deformation (ε2=0.26) produce naturally an enormous amount of 1+ states (2QP states, Nilsson labeled), which was found satisfactory (!)

in a similar study Winger et al removed the parenthesis only at much higher energy

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The 78Ni region in 2014: the final cut (?)

Age of the pionneers: mid 80’s

TRISTAN(Brookhaven)/OSIRIS(Studsvik)

“Is the region above 78Ni doubly magic ?”r-process consequences

Fogelberg, J.C. Hill, J.A. Winger and others

Second golden age : ca 2004

Yrast (LNL+Euroball)/Coulomb exc. (ISOLDE,ORNL)

/Masses (JYFL+ISOLDE)/transfer (ORNL,ISOLDE)

/Radioactivity(ORNL+Orsay)“Is N=50 a good magic number?”

r-process + structure consequences

Third golden age : ca 2014

RIKEN + elsewhere

direct study of 78Ni + around

very busy decade

dormance

towards an even busier decade

Conclusions• the question of the gap minimum Z=32, its microscopic origin and general consequences : we have just scratched the subject

• rapid energy increase of the p1/2 hole states below Z=32 (N=40 gap)

• Below Z=32, even at low energy, there is no hope shell model calculations can do a good job without including some external orbits (obvious statement but cruel necessity for experimentalists’ interpretations)

importance of the triaxial degree of freedom

AND the intruder states

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backup slides

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90’s ending, beginning 2000’s, ISOL activity back at IPN: PARRNe

converter(C)

deuteron beam(1µA 26 MeV)

fast neutrons

1+

ionsource

FissionFragments

target (10^9 fissions/s)

238U

fission

mass separator

detection

from P.W.Lisowski et al, OECD/NEA Report NEANDC-305 'U' 1991 p.177

Thesis Nicolas PauwelsIPN Orsay

initially a R&D test bench for the SPIRAL2 project

« Production d’Atomes Radioactifs Riches en Neutrons »

it all began with…

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Page 56Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

exploratory photofission experiment at CERN

arrival of the LINAC cavity from decommissioned LEP injector

construction of the LINAC bunker

RF system

First e-beam extracted

UCx target on line with e-beam– production yields measurements

Commissioning : tests and radiation safety measurements

TIS vault

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

1999

1998

building of the low energy beam lines + laser ion source

2011

2012

2013

green light from French nuclear safety authorities

BEDO commissioning

first laser ionized RIB

83Ga -> 83Ge b-decay

81Zn -> 81Ga b-decay

84Ga -> 84Ge b-decay

initial idea of a R&D test bench for the SPIRAL2 project at the Orsay Tandem

INAUGURATION

ISOL available at TANDEM PARRNe mass-separator on line

Page 56: Structure evolution towards  78 Ni :

Page 57Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

BEDO

LINOlaser spectroscopy

POLAREX

TAS

TETRA

nuclear orientation on line (CSNSM)

Total Absorption Spectroscopy(Subatech Nantes, IFIC Valencia)

Pn measurements(IPN/FLNR)

The ISOL installation at ALTO short and medium term projects

Page 57: Structure evolution towards  78 Ni :

Page 58Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

first experimental hint of proton evolution towards 78Nialong the N=50 linevery temptative, preliminary etc

p3/2

f5/2

28 29 30 31 32 33 34 35 36 37 38 39 40 41

-25

-20

-15

-10

-5

0

exactly consistent withPfeiffer et al. NPA 455 (1986) 381who provided sp energies, QP energies and v2.

prot

on E

SPS

(MeV

)

Z (N=50)

g9/2p1/2 Fermi level

f7/2

allows to explain the Jp of 80Ga and 80mGaISOLDE experiment, laser spectroscopy : two long lived states in 80Ga J=3 and J=6B. Cheal et al., PRC 82 (2010) 051302

extrapolation

Ga As BrCu Rb

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Page 59Verney – IPN Orsay FUSTIPEN Topical Meeting –Caen June 19-20, 2014

0

1

2

3

4

5

6

7

8

f5p3p1g9

PRO

TON

SPE

(MeV

)

p3/2

f5/2

g9/2

p1/2

JW Lis JUN45 JJ4B

Ji et Wildenthal Phys. Rev. C 38, 2849 (1988)

A.F. Lisetskiy et alPhys. Rev. C 70, 044314 (2004)

M. Honma et alPhys. Rev. C 80, 064323 (2009)

A. Brown priv. com.used inVerney et al Phys. Rev. C 76, 054312 (2007)

may be useful for shell model calculations in the 78Ni region

fitted SPE

result from monopole migration (realistic N-N interactions)

Sieja & Nowacki Phys. Rev. C 81, 061303(R) (2010)

SN this work

Page 59/Verney – IPN Orsay Shell Model as Unified View of Nuclear Structure – 8-10 Oct. 2012

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ng9/2np1/2

Z=37

Z=35

Z=33

Z=31

Z=29

N=49

78Ni

78Cu

80Ga

82As

84Br

86Rb

N=50

p3

f5 ●● ●● ●●●●● ○

p3

f5 ●● ●● ●●●

p3

f5 ●● ●● ●○

p3

f5 ●

○ ○○

p3

f5 ●● ●○ ○○

Z=38 88Sr

pp 3/

2p

f 5/2

90Zr

pp 1/

2p

g 9/2

nd5/2 ns1/2 nd3/2

np3/2

nf5/2 86Rb Dawson et al. Phys. Rev. 181 (1969)

2,3,4,5,6,7

3,4,5,6

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ng9/2np1/2

Z=37

Z=35

Z=33

Z=31

Z=29

N=49

78Ni

78Cu

80Ga

82As

84Br

86Rb

N=50

pf5/2-1ng9/2

-1

pp3/2-1ng9/2

-1

pf5/2-1ng9/2

-1

pp3/2+1ng9/2

-1

pf5/2-1ng9/2

-1

pp3/2+1ng9/2

-1

pf5/2+1ng9/2

-1

pp3/2+1ng9/2

-1

pf5/2+1ng9/2

-1

pp3/2+1ng9/2

-1

p3

f5 ●● ●● ●●●●● ○

p3

f5 ●● ●● ●●●

p3

f5 ●● ●● ●○

p3

f5 ●

○ ○○

p3

f5 ●● ●○ ○○

p3/2 turns into particle character

f5/2 turns into particle character

Z=38 88Sr

pp 3/

2p

f 5/2

90Zr

pp 1/

2p

g 9/2

N=49

nd5/2 ns1/2 nd3/2

np3/2

nf5/2