evolution of n=50 towards 78 ni: recent inputs from experiments

Evolution of N=50 towards 78Ni: recent inputs from experiments

Workshop Espace de Structure Nucléaire Théorique Saclay 3-5 May 2010

Position of the problem : why should we worry about N=50 ?1

N=50 shell gap evolution: salient features from experimental data2

deeper into nuclear structure close to 78Ni : valence space, single particle state effective sequence

3

D. Verney, IPN Orsay

0 Introduction: recent progress in experiment north north-east to 78Ni

0 Introduction: recent progress in experiment north north-east to 78Ni

N=50 : recent experimental breakthrough

(d,3He)

-decay

« border » of the knowledge on nuclear structure

fission

(t,p)

Zendel et alInorg Nucl Chem 42, 1387 (1980)

Kratz et alNucl Phys A

250, 13 (1975)

Del Marmol et alNucl Phys A

194, 140 (1972)

Hoff -FogelbergNucl Phys A

368, 210 (1981)Ge83

Experimental status in year 2003

Sr88

Rb87

Kr86

Br85

Se84

As83

Ge82

Ga81

Zn80

Cu79

Ni78Ni77Ni71 Ni72 Ni73 Ni74 Ni75 Ni76Ni70Ni69Ni68Ni67Ni66Ni65Ni64

Ge76Ge74Ge72

Y89

Zr90 Z=40

28

N=40 50

Cu65

Zn66 Zn67 Zn68 Zn70

Ga69 Ga71

Ge70 Ge73

As75

Se76Se74 Se77 Se78 Se80 Se82

Br79 Br81

Kr78 Kr80 Kr82 Kr83 Kr84

Rb85

Sr86 Sr87Sr84

Zr91

Se75 Se79 Se81 Se83

Kr85

Cu74

Zn75 Zn76 Zn77 Zn78

Ga79 Ga80fra

gmentation

Winger et alPhys Rev C

36, 758 (1987)

Beginning of -decay studies at PARRNe

OSIRIS /Studsvik

TRISTAN /Brookhaven

On

-lin

e m

as

s

se

pa

rati

on

Ch

imic

al

se

pa

rati

on

First structure data (’s) came from -decay (for N=50)1

Fission + ISOL technique

ESNT Workshop – Saclay – 3-5 May 2010 D. Verney

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main nuclear mechanisms used :

-fragmentation of stable beams

-fission

Sr88

Rb87

Kr86

Br85

Se84

As83

Ge82

Ga81

Zn80

Cu79

Ni78Ni77Ni71 Ni72 Ni73 Ni74 Ni75 Ni76Ni70Ni69Ni68Ni67Ni66Ni65Ni64

Ge76Ge74Ge72

Y89

Zr90 Z=40

28

50

Cu65

Zn66 Zn67 Zn68 Zn70

Ga69 Ga71

Ge70 Ge73

As75

Se76Se74 Se77 Se78 Se80 Se82

Br79 Br81

Kr78 Kr80 Kr82 Kr83 Kr84

Rb85

Sr86 Sr87Sr84

Zr91

Ge84Ge83

isomeric decay: LISE-GANIL

radioactive beam: REX ISOLDECu77

Zn78 Zn79

As84

Se85 Se86

-decay Orsay direct reaction in inverse kinematics :

Oak Ridge

DIC at Legnaro

ISOLDE laser

Experimental status in year 2010

-decay is still in the competition, good complementarities with DIC2

Fission + ISOL technique + post acceleration

BE(2)

Spectroscopic factors

DIC at Legnaro

Fusion-fission

Spontaneous fission

JYFLTRAP IGISOL

-decay Orsay

N=50 : recent experimental breakthrough

main nuclear mechanisms used :

-fragmentation of stable beams

-fission

-deep inelastic collisions


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Position of the problem : why should we worry about N=50 ?1

Why should we worry about N=50 ?

Historically from astrophysical considerations (and -decay experiments)

By Kratz et al. PRC 38 (1988)

Waiting point nucleus at N=50 80Zn

By Winger et al. PRC 36 (1987)

« »

« it’s a joke » M. Bernas, private communication (2001)

1


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ground state of 42Si N=28 is observed deformedB. Bastin et al., Phys. Rev. Lett. 99 (2007) 022503

spin-orbit origin



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“A full treatment of Hm shows no magicity at30Ne and 32Mg, while 34Si (or any other Si isotope)exhibits a clear shell effect. It just so happens that the fullHm reproduces the observed robustness of the SO closures,and the fragility of those of other origins. Whetherthey survive or not depends mainly on the possibility ofdeveloping quadrupole coherence in a given space.”

A.P. Zuker PRL 91 (2003)

O. Sorlin, M. Porquet Prog. Part. Nucl. Phys. 61 (2008) 602

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

100Sn

78Ni

from binding energies of the states below and above Z=28 and N=50

78Ni

56Ni

Z=28 gap extrapolation → 78Ni =2.5 MeV


44 46 48 50


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T. Otsuka et al. PRL95, 232502 (2005)



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extracted from J. Van de Walle et al PRC 70 (2009) 014309

Their is a N=50 shell effect with strong influence on nuclear structure close to 78Ni

Now, the real question becomes : how the shell gap associated to the N=50 magic number evolves towards 78Nior is there any evolution at all ?

N=50 shell gap evolution: prominent features from experimental data2

Evolution of the N=50 shell gap


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A Prévost et al. EPJ A 22 (2004) 391Medium/high spin states obtained from fusion/fission at the Vivitron (Euroball IV)

conclusion : N=50 shell gap decrease : yes

-

f7/2

p3/2

p1/2

f5/2

g9/2

28

50

40

f7/2

p1/2

g9/2

d5/2

p3/2f5/2

protons neutrons

-

+

+ +

Yrast structure studies (fusion-fission mechanism)

Yrast structure studies (spontaneous fission mechanism)

2 levels added : one of the two “must be” 1p-1h across N=50

T. Rza˛ca-Urban et al. PRC 76 (2007) 027302Medium/high spin states fed in 248Cm spontaneous fission

conclusion : N=50 shell gap decrease : yes


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32

Y.H. Zhang et al. PRC 70 (2004) 024301Medium/high spin states fed in DIC at Legnaro (GASP)conclusion : N=50 shell gap decrease : no(same conclusion as Kamila)

84Se

SM calculation proton valence space

SM calculation proton valence space + neutron 1ph

f7/2

p3/2

p1/2

f5/2

g9/2

28

p1/2

g9/2

d5/2

protons neutrons

504 MeV

The gap used in the calculation has the good size

Yrast structure studies (deep inelastic mechanism)


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Mass measurements (IGISOL Jyvaskyla)



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Local minimum at Z=32

=S2n(52)-S2n(50)

(this quantity is the one traditionnally used to extract shell gaps from mass measurements)

Mass measurements (IGISOL Jyvaskyla)



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Koopmans theorem :

gap in the single particle levels

50

j’

j

j’= Sn(Z,N)

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

for for the evaluation of j

one has to estimate j’ and jin the same

nucleus

NPA466 (1987) 189

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

Mass measurements : what quantity is truly relevant for nuclear structure



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Z

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

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

N N+1 N+3 N+5 N+7

neutron number

using data taken from mass evaluation 2010 with kind authorization by G. Audi (AME2010 unpublished - G. Audi private communication)

d5/

2 –

g9/

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

gap

« rough »

« prescripted »

gap

pairi

ng g

ain(

MeV

)

neutron pairing gain = 2Sn(Z,N+1) —S2n(Z,N+2)

Ni Zn Ge Se Kr Sr

AME2010 extrapolation

Mass measurements : what quantity is truly relevant for nuclear structure


loca

l min

imu

m a

t Z

=3

2


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conclusion : N=50 becomes somewhat “porous” relative to pair promotions (towards 78Ni)• what will be the result on structure? • what is the microscopic mechanism at play which could explain this local minimum ?

Zr

32



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in particular : could provide a simple explanation to the Yrast structure behavior

Local minimum, not at mid distance Z=28-40

REX-ISOLDE

J. Van de Walle et al.PRL 99, 142501 (2007)

80Zn 82Ge84Se

86Kr

88Sr

90Zr


and also the peculiar evolution of the E(2+) of the even-even N=50 isotones


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from -decay at ALTO



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52

N=42

0.1 0.2 0.3 0.40

N=44

0.1 0.2 0.3 0.40

N=46

0.1 0.2 0.3 0.40

N=48

0.1 0.2 0.3 0.40

Ge isotopic chain


and connection with collectivity

N=50

0.1 0.2 0.3 0.40

N=52

0.1 0.2 0.3 0.40

N=54

0.1 0.2 0.3 0.40

O Perru thesis Paris-Sud XI (2004) & J. Libert and M. Girod

private communicationD1S Gogny HFB calculation

GCM Bohr dynamics


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Ge

HFB + GCM (GOA)




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Collectivity close to 78Ni N=52 even-even nuclei

Z=

28 s

hell

closu

re

Z=

40 s

ubsh

ell

eff

ect

N=52




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deeper into nuclear structure close to 78Ni : valence space, single particle state effective sequence

3

Proton structure above 78Ni

K. Flanagan et al.

N=40 N=42 N=44 N=46 N=48 N=50

but already hinted at in the 80’s !!(from shell model, empirical interaction)

E (MeV)

-14,386

-13,233

-11,831

-7,121

40

f5/2

p3/2

p1/2

g9/2

Proton single particles

From Ji et Wildenthal Phys. Rev. C 38, 2849

(1988)

28

50


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shell model calculation :

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

TBME and SP energies fitted to the data


E (MeV)

-14,386

-13,233

-11,831

-7,121

40

f5/2

p3/2

p1/2

g9/2


28

50

Zn GeSe

Kr


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



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E (MeV)

-14,386

-13,233

-11,831

-7,121

40

f5/2

p3/2

p1/2

g9/2



(1988)

28

50

1236(9/2-)

hot subject - -decay experiment redone at ISOLDE and Oak Ridge

(same lines as us)

observed in -decay at Orsay (PARRNe)

D. Verney et al PRC 76 (2007) 054312

observed in DIC experiments at LegnaroG. De Angelis et al. NPA 787

(2007) 74c

Zn81

Sr88

Rb87

Kr86

Br85

Se84

As83

Ge82

Ga81

Zn80

Cu79

Ni78

Y89

Zr90

50

Zr91 Zr93Zr92 Zr92 Zr93 Zr94 Zr95 Zr96

Se85 Se86

As84

Ge83 Ge84

3 protons out of a 78Ni core

PARRNe



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0

200

400

600

800

1000

1200

1400

1600

1800

keV

3/2-5/2- 64 keV

0 keV

679 keV3/2-

1279 keV1/2-5/2- 1368 keV

3/2- 1897 keV

81Ga Z=31 N=50

351.1 keV

0 keV

802.8 keV

1236 keV

Experiment

empirical effective interaction : fit on a series of carefully selected states

Valence space N=50 closed & Z=28 closed (the doubly magical nature of 78Ni is assumed)The valence space is reduced to proton orbitals

Theory

Ji & Wildenthal, PRC 40, 389 (1989)

306.51 keV

83As Z=33 N=50

0 keV

711.66 keV

1193.7 keV1196.53 keV1256.76 keV1329.87 keV1415.11 keV1434.92 keV1525.52 keV

1804.76 keV

1977.9 keV

Experiment

(3/2-)

(5/2-)

Winger et al, PRC 38, 285 (1988)

1/2-

0 keV

189 keV

353 keV

589 keV

990 keV

1115 keV

1253 keV

1382 keV1455 keV

1643 keV

1845 keV1857 keV1879 keV1985 keV

5/2-

3/2-1/2-

3/2-

7/2-5/2-3/2-1/2-

5/2-9/2-

3/2-7/2-

9/2-

Theory

351.

1 ke

V45

1.7

keV

(5/2-)

(3/2-)

(3/2-)

(9/2-)



/52



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what to do ?

remember the textbooks and assume 1f5/2 is indeed the first proton orbit filled above 78Ni

formule générale

V J j n a b c n an n 1( )

2 b J( ) J 1( ) n j j 1( )[ ] c

n 2

2 j 3 n Talmi : <VJ>=

single particle (binding) energy

number of particles in the configuration

seniority number

for identical particles in j<=7/2 there exists a closed formula expressing the configuration energy (by Talmi)

82Ge 81Ga 80Zn

n=4, =00+

5/2+

3/2+

0+

2+

n=3, =1

n=3, =31492 keV

803 keV

n=2, =2

n=2, =0

BE(f5/2)= -13.576 MeV………JW give -14.386 MeV

E(9/2-) in 81Ga=1250 keV ……experiment :1236 keV

E(4+) in 80Zn=1809 keV ………experiment :?

1f5/2)4 1f5/2)3 1f5/2)2

but also extract : <f5/2f5/2|V|f5/2f5/2>J=0

<f5/2f5/2|V|f5/2f5/2>J=2 <f5/2f5/2|V|f5/2f5/2>J=4


f5/2 f5/2 f5/2 f5/2

f5/2 f5/2 f5/2 f5/2

f5/2 f5/2 f5/2 f5/2

pairing looks small !

back to the Ji Wildenthal proton-proton residual interaction :

Is it possible to find a simple cure to the interaction ?


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A.F. Lisetskiy et al.,

PRC 70 (2004)

Ji & Wildenthal,

PRC 40, 389 (1989)Z=31 N=50

JW+rustine



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1qp f5/2

1qp p3/2

v=3(f5/2)3

A.F. Lisetskiy et al.,

PRC 70 (2004)

Ji & Wildenthal,

PRC 40, 389 (1989)

Z=33 N=50

711 keV

JW+rustine



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1qp f5/2

1qp p3/2

1qp p1/2

Z=35 N=50

JW+rustineESNT Workshop – Saclay – 3-5 May 2010

D. Verney /52

1qp f5/2

1qp p3/2

1qp p1/2


2p3/2

1f5/2

81Ga Z=31 N=50

2p3/2

1f5/2

83As Z=33 N=50

2p3/2

1f5/2

85Br Z=35 N=50

2p1/22p1/2 2p1/2

the conclusion is : this proton sequence is confirmed

E (MeV)

-14,386

-13,233

-11,831

-7,121

40

f5/2

p3/2

p1/2

g9/2



(1988)

28

50

and the observed structure of the odd-proton N=50 isotones simply (and naturally) reflects the change of the Fermi level



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Neutron structure above 78Ni


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O. Sorlin, M. Porquet Prog. Part. Nucl. Phys. 61 (2008) 602

centroides from (d,p)

g7/2 goes up

91Zr

89Srg7/2 nearly constant

K. Sieja et al. PRC 79, 064310 (2009)EXPERIMENT

THEORY (SM)

g7/2 goes down

SM calculations in valence space above 78Ni

From Duflo Zuker

PRC 59, R2347 (1999)

E (MeV)

0.00

1.00

2.453.04

82

Neutron single particles

From T.A. Hughes

Phys. Rev. 181, 1586 (1969)

d5/2

d3/2

s1/2

g7/2

50

in 89Sr

? h11/2

but in fact the problem of the position of h11/2 remains unsolved → need for the observation of negative parity Yrast states in N=51



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experiment and theory agree close to stability

Ga84

247.81/2+

observé en2H(82Ge,p)83Ge à Oak

RidgeThomas et al.

PRC 71 (2005) 021302

observé en décroissance -decay à PARRNe

O. Perru et al.EPJ A 28 (2006) 307

et thèse Paris 11

Ga83

Sr88

Rb87

Kr86

Br85

Se84

As83

Ge82

Ga81

Zn80

Cu79

Ni78

Y89

Zr90

50

Zr91 Zr93Zr92 Zr92 Zr93 Zr94 Zr95 Zr96

Se85 Se86

As84

Ge83 Ge84

4 protons + 1 neutron au dessus de 78Ni

observé en décroissance n avec ALTO

M. Lebois et al.PRC 80 (2009) 044308

et thèse Paris 11

2d5/2

3s1/2

(3/2,5/2+)

7/2+


experiment and theory agree close to stability ?


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(1/2+)?

E(2+) of the even-even core(semi-magic N=50)


systematics for the odd-neutron N=51 isotones


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Even-even semi-magic core

single particle

Q>0Q=0 Q<0

2+1 2d5/2

J=1/2

J=3/2 J=9/2

J=5/2

J=7/2



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(1/2+)?

N=51

E(2+) of the even-even core(semi-magic N=50)



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(1/2+)?

S=0.84

non-stripped

S=0.49

S=0.016

d3/2

g7/2

S=0.06±0.02S=0.77±0.27

from J. S. Thomas et al. PRC 76, 044302 (2007)

not observed in (d,p)



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first 7/2 state is 2+*d5/2 coupled state, g7/2 is higher in energy

(1/2+)?

s1/2

d’après J. S. Thomas et al. PRC 76, 044302 (2007)

S=0.905

S=0.46S=0.31

S=0.18non-stripped

not observed (dp)

S=0.52s1/2 s1/2

s1/2

down sloping of the s1/2 is firmly established



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Core – particle coupling model

Even-even semi-magic core

L. S. Kisslinger & R. A. Sorensen Rev. Mod. Phys., 35, 853, (1963)

Thankappan & TruePhys. Rev. B, 137, 793 (1965)

Neutron single particle

Core excitation energies taken from experiment : E(2+)

Parameters :

Vector space :0+1 2d5/22+1 2d5/22+1 3s1/2Etc…

= =

Quadrupole moment of the 2+ state

Phenomenological model with a clear underlying physical image. All parameters with straightforward interpretation:

Example : harmonic vibrator : Q2+=0 2=0

how to extract (at least approximately) effective single particle energies when no direct reaction data is available ? use a simple empirical model



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unperturbed theory experiment

0+ d5/2

0+ s1/2

2+ d5/2

0+ d3/2

0+ g7/2

02+ d5/2

22+ d5/2

2+ s1/2

52

12

32

72

52

12

32

52

72

92

52

52

72

12

72

72

52

52

32

92 3

2

92

32

32

12

72

12

32

52

72

92

12

0.26ps

0.19ps0.10ps0.21ps

0.11ps

0.16ps

0.02ps0.09ps

1.85ps

S=0.79

S=0.905

S=0.091

S=0.46

S=0.34

S=0.74

S=0.88

S=0.78

S=0.016

S=0.053S=0.64

S=0.15

S=0.84

89Sr3

25

2

>1 ps

1/2 calculated assuming only M1 and E2 transitions

e()=1 and gs=0.6 gsfree

2=0.56 (M1+E2)

2=0.87 (M1+E2)

Qexp= -0.28(3) eb / -0.32(2) eb exp= -1.1481 n.m.

Qcalc= -0.27 eb calc= -1.020 n.m.

experimentcore-particle couplingnot included in the model space


0+ d5/2 52

52

52S=0.90 S=0.56

0+ s1/2 12

2+ d5/2 12

32

52

72

92

0+ d3/2 32

0+ g7/2 72

4+ d5/2 32

52

72

92 2

112

13

22+ d5/2 1

23

25

27

29

2

2+ s1/23

25

2

12

32

92

72

52

32

12

72

52

S=0.68

S=0.20

S=0.02

S=0.06

S=0.43

S=0.27

S=0.84

S=0.03

72

32

52

92

S=0.4612

S=0.23

92

32

52S=0.02

32

52

S=0.0912S=0.18

112

32

52S=0.3

S=0.49 72

87Kr

85Se

0+ d5/2

0+ s1/2

2+ d5/2 12

32

52

72

92

02+ d5/2

12

52

52

4+ d5/2 32

52

72

92 2

112

13

2+ s1/2 32

52

0+ d3/2

0+ g7/2

32 7

2

12

52


72

92

52

32

32

72

12

52

12

72

92

32

52

12 ?

12

92

72 ?-

112

32

52

32

12

92

32

52

72

112

132

32

52

72?

?

?

S=0.38

S=0.31

S=0.77 or 0.06

S=0.90

S=0.86

S=0.09

g7/2

d3/2

d5/2

s1/2


on the overall neutron single particle sequence appears to be :


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d5/2

s1/2

d3/2

g7/2

MeV

N=

58

?

if we extract the effective single particle energies using the core-particle coupling model :



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conclusion : appearance of a new neutron subshell gap close to 78Ni ?

d5/2

s1/2

d3/2

g7/2

MeV

?

N=

58

?

is there a simple explanation to the s1/2 down sloping ?



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80 10060is there a simple explanation to the s1/2 down sloping ?



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s1/2 s1/2s1/2

s1/2s1/2

g7/2

d3/2


K. Sieja private communication (yesterday)


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d5/2

d3/2

s1/2

g7/2

Neutron single particles

f5/2

p3/2

p1/2

g9/2

Single particle sequence in 78Ni mean-

field

Conclusion

What we think we have understood :

1

2 the N=50 shell gap is effective towards 78Nithough it varies a little in amplitude impact on collectivity


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evolution of n=50 towards 78 ni: recent inputs from experiments

Documents

evolution of n

shell gap evolution

decay studies

nuclear structure close

gap extrapolation

bdecay experiments

recent progress

shell effect