Shell evolution in the neutron rich N=20, N=28 and Z=28 ...brown/EFES-2010/pdf/neyens.pdfNuclear...
Transcript of Shell evolution in the neutron rich N=20, N=28 and Z=28 ...brown/EFES-2010/pdf/neyens.pdfNuclear...
Shell evolution in the neutron rich Shell evolution in the neutron rich
N=20, N=28 and Z=28 regions
from measurements of moments and spinsGerda Neyens, IKS, K.U. Leuven, Belgium
Belgian Research Initiative on eXotic nuclei
1
regions of interest
Along magic numbers: • Below 40Ca, along N=20 island of inversion due to
reduction of N=20 gap
• Below 48Ca, along N=28 shape coexistence due to
reduction of N=28 and Z=16
• Along Z=28, from N=28 up to N=50 softness of 56Ni core,
56
Along Z 28, from N 28 up to N 50 softness of Ni core,
monopole migration
onset of collectivityνp3/2f5/2p1/2 g9/2νf7/2
Z=20
Z=28 78Ni56Ni
40Ca 48Ca
πf7/2
Z=8 N=28N=50
16O
πd5/2s1/2d3/2πs1/2d3/2
N=8
N=20
2
Experiments at ISOL and fragmentation facilities
The COLLAPS collaboration at CERN‐ISOLDE Leuven – Mainz – Heidelberg – Manchester ‐ …
‐ collinear laser spectroscopy on bunched beams: I, μ, Q measuredp py , μ, Q61Cu ‐ 75Cu (Z=29, from N=32 to N=46) odd‐even and odd‐odd67Ga ‐ 81Ga (Z=31, from N=36 to N=50) odd‐even and odd‐odd
β NMR and laser spectroscopy on laser polarized beams I g measured‐ β‐NMR and laser spectroscopy on laser‐polarized beams: I, g, μ measured21Mg ‐ 33Mg (Z=12, from N=9 to N=21) even‐odd only
The β‐NMR collaboration at LISE‐GANIL Leuven – GANIL – Bruyères‐le‐Chatel – Tokyo …
‐ β‐NMR spectroscopy on reaction‐polarized beams: |g| and |Q| measured, I deduced31Al‐34Al (Z=13 from N=18 to N=21) odd‐even and odd‐oddAl‐ Al (Z=13, from N=18 to N=21) odd‐even and odd‐odd44Cl (Z=17, N=27)
Other input from: ‐ in‐source laser spectroscopy at LISOL@CRC Louvain‐la‐Neuve: 57Cu (μ)Other input from: in source laser spectroscopy at LISOL@CRC Louvain la Neuve: Cu (μ)‐ TDPAD on isomeric states at GANIL: 43S (Z=16, N=27) (|g|)
3
Nuclear moments near magic shells
very sensitive to nuclear wave function !y
Magnetic moment of odd‐even, even‐odd and odd‐odd isotopes (μ=g.I) near closed shells:
g‐factor is determined by the orbital occupied by unpaired valence protons and/or neutrons
‐ depends on spin and orbital g‐factors for protons and neutrons (gsπ, gl
π, gsν, gl
ν)
‐ depends on orbital momentum l and spin j of orbit occupied by unpaired nucleons
sign of g determines the parity of the wave function !!
‐ g‐factor is not depending on the number of unpaired nucleons in an orbit
57Cu = 56Ni + p 57Cu = 40Ca + 9p+8n
Comparing experimental and calculated g‐factors: ‐ confirm the proposed wave function‐ in some cases: assign spin and/or parity‐ test the shell model interaction and used model space‐ find deviations from ‘normal’ shell model configurations
4
Nuclear moments near magic shells
very sensitive to nuclear wave function !y
Quadrupole moments of odd‐even, even‐odd and odd‐odd isotopes
Q‐moment is determined by the spin j and the <r2> of the orbit occupied by unpaired valence protons ‐ neutrons are not charged but induce core polarization through p‐n interaction
iti t ll ti it i th f ti‐more sensitive to collectivity in the wave function
Comparing experimental and calculated Q‐moments near closed shells: ‐ probing the proton‐neutron interaction
57Cu = 56Ni + p 57Cu = 40Ca + 9p+8n
‐ study the softness of a core as a function of N and/or Z‐ study effects of core polarization ‐ study shape coexistence in nuclei‐ confirm the proposed wave functionconfirm the proposed wave function‐ test the shell model interaction‐ find deviations from ‘normal’ shell model configurations
5
The “island of inversion”
active neutron orbits around N 20
fp‐shell20
f7/2p3/2
d
P35
S36
active neutron orbits around N=20
sd‐shell
8
d3/2
d5/2s1/2
Si29
Si30
Si31
Si32
Si33
Si34
Si35
Si36
Si37
Al28
Al29
Al30
Al31
Al32
Al33
Al34
Al35
Al36
Mg Mg Mg Mg Mg Mg Mg Mg Mg 12
13
14
g πd
5/2
f
27 28 29 30 31 32 33 34 35
Na26
Na27
Na28
Na29
Na30
Na31
Na32
Na33
Na34
Ne25
Ne26
Ne27
Ne28
Ne29
Ne30
Ne32
12
11
emptying
influence of particle‐hole excitationsIn the ground state wave functions ?
pf
sd
20
F
24
F
25
F
26
F
27
F
2922
201816
hi N 20
Experimental challenge: how large is this ‘region of inversion’ ?
approaching N=20
Study transition region difficult to make theoretical predictions !
6
g-factors of Al isotopes ground states dominated by πd5/2-1
P. Himpe et al., Phys. Lett. B ( ) Z 13 hole in d orbital643 (2006) 257–262 Z=13: hole in πd5/2 orbital
Iπ = 5/2+ expected for odd‐Al isotopeswave function and spin confirmed by g‐factor
etry
33Al(Si)
through comparison with calculated μ=g.I insd‐shell model (USD – 0p0h)sdf7/2p3/2 shell model space
SDPF M (MCSM mixed)
βas
ymm
e
‐ SDPF‐M (MCSM, mixed)‐ sdpf‐interaction (2p2h)
(free‐nucleon g‐factors)B (gauss)
Conclusion for 33Al (N=20):4
4,2
μ (μN) 0p-0h
exp
Iπ=5/2+
small (<25‐30 %) intruder admixture in the 33Al ground state.
3,6
3,8 MCSM(50% intruder)
3,4
10 12 14 16 18 20 22 24N
2p-2h
Y. Utsuno et al., PRC 64, 011301R, 2001
7
M. De Rydt et al., PLB 678, 344
quadrupole moments of 31,33Al more sensitive to neutron excitations
Error bars smaller than dot size !31Al(Al203)y , ,
(2009) Q(31Al)
2p‐2h
T. Nagatomo, et al., EPJA 42,
Error bars smaller than dot size !Al(Al203)
g383–385 (2009) Q(33Al)
to be continued !
exp
ν (kHz)Calculations in sdp3/2f7/2‐shell:
0p‐0h
νQ(kHz)3/ /
* SDPF‐M interaction (MCSM)Otsuka, Utsuno et al., private communication
* sdpf‐NR interaction (ANTOINE code)Nummela et al., PRC63 (2001)
very good agreement for 27,31Alwith proton effective charge :
e = 1 1 e
33Al has a mixed g.s. configuration: ν(sd)‐2(fp)2 contribution in wave function !
Nummela et al., PRC63 (2001)
ep = 1.1 eneutron effective charge:
en = 0.5e
To determine amount of mixing: need more precise Q‐moment value ! Experiment at GANIL, july 2010
8
M. De Rydt et al., PLB 678, 344 (2009)
Fitted effective charges using all known sd‐shell Q‐moments
Compare Q of sd shell isotopes (errorsy , , ( ) Compare Qexp of sd‐shell isotopes (errors smaller than dot‐size)with calculated values in sdp3/2f7/2‐space using sdpf effective interaction
eπeff=1.3e
odd‐Z quadrupole moments
sdpf effective interaction
M. Depuydt, M. De Rydt, G. Neyens, to be published
χ2=3.4
33 sd‐shell Q‐momentssdpf‐U effective interaction(Nowacki and Poves, PRC79, 014310 (2009))
eπeff=1.1e
χ2=1.5sd‐shell proton effective charge: ep = 1.12 e
neutron effective charge: en= 1.45 e9
G Neyens et al PRL 94 022501 (2005)G Neyens et al PRL 94 022501 (2005)20
g‐factor (+ sign) and spin of the 31,33Mg ground state
G. Neyens et al., PRL 94, 022501 (2005)G. Neyens et al., PRL 94, 022501 (2005)D. Yordanov et al., PRL 99, 212501 (2007)D. Yordanov et al., PRL 99, 212501 (2007)
Measured spin 31Mg and 33MgF i f f t it
Al28
Al29
Al30
Al31
Al32
Al33
Al34
Al35
Al36
Mg27
Mg28
Mg29
Mg30
Mg31
Mg32
Mg33
Mg34
Mg35
20
From sign of g-factor parity
31Mg, Iπ = 1/2+ ν(sd)-3 (fp)2
33Mg, Iπ = 3/2- ν(sd)-2(fp)3
νd3/2+
νf7/2−
REAL d t t fi tig, ( ) ( p)
pure 2p-2h intruder ground states !
pf
REAL ground state configurations:
31Mg (N=19) 33Mg (N=21)
31Mg (N=19) 33Mg (N=21)
f
Normal ground state configurations:pf
sd
20d3/2
20
20d3/2
20f7/2
Iπ=1/2+
ν(s )(d 2) (fp)2
Iπ=3/2‐
ν(d -2) (f σ=3)3
Iπ=3/2+ Iπ=7/2‐
ν(s1/2)(d3/2 )0(fp) 0
[ν(d3/2)π(sd)2+]1/2(fp)20
ν(d3/2 )0(f7/2,σ=3) 3/2
ν(d3/2-2)0(f2)0p3/2
10
Spin/parity of the 33Mg ground state in the shell model
Look at the g‐factors of isotones with similar configurationLook at the g factors of isotones with similar configuration
N=21 isotone: 35SiN=19 isotone: 33Si
Iπ=7/2‐f7/220
p3/228p3/2
f7/220
28
Iπ=3/2+d3/2 Si Si Si
P35
S36
normal ground state in 33Mg
sd
1p1h intruder ground state
s1/233 34 35
Al32
Al33
Al34
Mg31
Mg32
Mg33 normal ground state in 33Mg
same g-factor (particle in f7/2) as 35Si1p1h intruder ground state in 33Mg same g-factor as 33Si
g(35Si) = -0.47g(33Si) = +0.76
212019
2p2h ground state in 33Mgsimilar g-factor as 35Si (3 particles in f7/2)
(f7/2)33/2
gexp(33Mg) = -0.4971(4)
G. Neyens et al., PRL 94, 022501 (2005)G. Neyens et al., PRL 94, 022501 (2005)D. Yordanov et al., PRL 99, 212501 (2007)D. Yordanov et al., PRL 99, 212501 (2007)
2 neutron holes in sd act as spectators (paired)gsdpf(3/2+) = +0.78 (1p1h)gsdpf(3/2-) = -0.47 (2p2h)
11
Spin/parity of the 33Mg ground state in Nilsson model
D. Yordanov et al., comment to PRL, acceptedD. Yordanov et al., comment to PRL, accepted
gHamamoto, PRC76, 054319 (2007)
gexp(33Mg) = - 0.4971(4)‐0.51+0.56‐0.21‐1.98‐1.72
Interpretation in Nilsson Model:31Mg ground state:g gbuild on ½+[200] g= -1.72 (exp=-1.7671)
33Mg ground state:and on 3/2 [321] g= 0 21 (exp= 0 4971)and on 3/2-[321] g= -0.21 (exp= -0.4971)
3/2-[330] g= -0.51 (exp= -0.4971)
12
Summary: “island of inversion” around 32Mg
Present status of the “Island of inversion”as deduced from static and dynamic moments measurements
P. Himpe et al., Phys. Lett. B. 658, 203 (2008)
All intruder g.s. configurationsare of the 2p‐2h type !!
(two neutrons excited across N=20)
Utsuno et al., PRC70,0044307,2004 13
Evolution of the proton single particle states above Z=28
4466Ga67Ga 68Ga 70Ga 71Ga72Ga73Ga 74Ga75Ga 76Ga69Ga 4477Ga78Ga 79Ga80Ga 81Ga82Ga
62Cu 63Cu 64Cu65Cu 66Cu67Cu 68Cu 70Cu 71Cu 72Cu73Cu 74Cu75Cu76Cu69Cu
64Zn 65Zn 66Zn 67Zn 69Zn 70Zn 71Zn 72Zn 73Zn 74Zn 75Zn68Zn
77Cu 78Cu 79Cu
44Ga Ga Ga Ga Ga Ga Ga Ga Ga GaGa 44Ga Ga
61Cu
Ga
N=40 N=50ν1g9/2ν(p3/2,f5/2p1/2) 46 48
64Ni 65Ni 66Ni 67Ni 68Ni 69Ni 70Ni 71Ni 72Ni 73Ni 74Ni 75Ni 76NiZ=28 77Ni 78Ni
5/2-1/2-
Evolution of the experimental 5/2‐ and 1/2‐ energies in Cu isotopes πp1/2
N 40 N=50g9/2 3/ 5/ / 46 48
5/2
1 5 μs200 ns
πf5/2
57Cu 59Cu 61Cu 63Cu 65Cu 67Cu 69Cu 71Cu 73Cu 75Cu3/2-
1.5 μsπp3/2
h l ( ) S f l PRL 100 112502 (2008)
N=28 N=40S. Franchoo et al., PRC 64, 054308 (2001) Stefanescu et al., PRL 100, 112502 (2008)
J.M. Daugas, Ph.D. Thesis, GANIL
Steep decrease of the 5/2- and 1/2- levels when νg9/2 is filledExperiment: g.s. spin assigned up to 73Cu (3/2‐) from β‐decay14
Ground state spin of 71,73,75Cu
K.T. Flanagan et al., PRL 103, 142501 (2009)
73Cu, I=3/2
g ( )
g.s. spins measured with laser spectroscopyspins assigned to isomeric levels in 75Cu
(based on measured lifetimes)
75Cu, I=5/2
(based on measured lifetimes)
Theory reproduces lowering of 5/2‐ correctlytheory overestimates the 1/2‐ energy
from 69Cu to 75Cu !!!
Model space: 56Ni core +f p p g
JJ4b, Brownf5/2 p3/2 p1/2 g9/2
Effective interaction: Lisetsky and Brownbased on A. F. Lisetskiy et al., Phys. Rev. C 70, 044314 (2004)
15
Ground state spin of 72,74Cu
72Cu, I=2
Ratio of A factors should be constant
74Cu I=2
Ratio of A‐factors should be constant,if the hyperfine structure is fitted with correct spin value(input in fit: I, Au, Ad, Bu, IS)
Cu, I=2
Ground state spins I=2, withmore than 4 sigma confidence level
16
Ground state parity and structure of 72Cu
72Cu expected low‐energy levels: use Paar’s ruleCu expected low energy levels:
1g9/2 1g9/2
Z=29 N=43 (πp3/2 νp1/2−1g9/2
4) (1,2)+
neutron excitation across N=40
use Paar s rule
40
1f5/2
2p1/2
1g9/240
1f5/2
2p1/2
1g9/2
(πf5/2 νg9/23) (2,…,7)‐
proton excited to the f5/2 orbital
2p3/2 2p3/2 (πp3/2 νg9/23) (3,4,5,6)‐
J.C. Thomas et al., PRC74, 054309, 2006
(1+)
270
376
(6‐) t1/2=1.76μs
, , ,
Ground state has spin I=2But what is the parity ??
2+
2‐1+
387418431
(3‐)
(4‐)
137
219
270(6‐) 1/2 μ
Can we assign parity based on measuredmagnetic moment ?
??
4‐
5‐
140
235
Experiment
0(2)
magnetic moment ?μ = ‐1.3451(6) μN
Realistic interaction
3‐6‐
016
17
Ground state parity and structure of 72Cu: Iπ = 2‐ !!
Use additivity rules for proton‐neutron configurations:
Main negative parity configuration: μ(πf5/2 νg9/23; 2‐) μfree(2‐) = ‐2.13 μN
μemp (2‐) = ‐1.94 μN
1 4
y p g
Main positive parity configuration: μ(πp3/2 νp1/2−1g9/2
4; 2+) μfree(2+) = +4.44 μN
μemp (2+) = +1.44 μN
Conclusion: the measured SIGN of the moment, μ = ‐1.3451(6) μN, is crucial to decideConclusion: the measured SIGN of the moment, μ 1.3451(6) μN, is crucial to decide on the parity !
in absolute value it is in agreement with 2+however, a negative sign is only compatible with a proton in f5/2 orbital
2+
2‐1+
387418431(1+)
270
376
(6‐) t1/2=1.76μs
4‐
5‐
140
235
(3‐)
(4‐)
137
219
270(6‐) 1/2 μ
Realistic interaction
3‐6‐
016
Experiment
0(2‐)
18
Magnetic moments of odd‐Cu isotopes from N=28 to N=40
Compare performance large scale shell model calculations:GXPF1 40Ca core + full pf‐shell (f7/2p3/2f5/2p1/2)GXPF1A same
T. Cocolios et al., PRL 103 102501 (2009)
Conclusions:
(1) Effective g = 0 9g free close to free
PRL 103, 102501 (2009)
Iπ = 3/2‐
P. Vingerhoets et al., in preparation
(1) Effective gs = 0.9gsfree , close to free‐
nucleon value (because model space includes all pf levels)
(2) Softness of 56Ni core well reproduced(g with 56Ni core: 1.997)
(3) GXPF1 reproduces all values perfectly(3) GXPF1 reproduces all values perfectly, except for 69Cu
shows the need to include νg9/2in the model space
(4) GXPF1A slightly underestimates the values for 63,65,67Cu (N=34,36,38)
19
Quadrupole moments of odd‐Cu isotopes up to N=40
CONCLUSIONS:
(1) Effective charges are from a chi^2 fit toIπ=3/2‐
P. Vingerhoets et al., in preparation
(1) Effective charges are from a chi 2 fit to both odd‐odd and odd‐even Cuquadrupole moments
(2) Quadrupole moments are very similar with GXPF1 and GXPF1A
(3) the g‐factor is more sensitive to small(3) the g factor is more sensitive to small admixtures in the wave function
(4) 68Ni core is more stiff than 56Ni core in this i t ti d d l (binteraction and model space (because no excitations across N=40 included)
to verify experimentally if neutron excitations to g9/2 reduce the core stiffness of 68Ni, we need to compare Qexp for 57Cu to 69Cu
20
g‐factors of (1,2)+ states in odd‐odd Cu isotopes
C t i i l l f k li l l ti f
very sensitive to purity of the configuration and small effects of fi ti i i !
Compare to empirical values from weak coupling calculations for puresingle particle configurations
configuration mixing !
P. Vingerhoets et al., in preparation
Isomeric 1+ state
Note: the experimental sign of 66Cu was wrong in literature !!
21
g‐factors and Q‐moments of odd‐odd Cu isotopes: GXPF1 and GXPF1A
πp3/2νp1/2
πp3/2νp3/2
πp3/2νf5/2
Conclusions: (1) the experimental g‐factors agree well with single particle estimatesfor rather pure π−ν configurations with normal filling of the νp3/2f5/2 p1/2 orbits
(2) GXPF1 does overall rather well for μ and Q(2) GXPF1 does overall rather well for μ and Q (3) GXPF1A strongly deviates at N=35 and N=37 (64,66Cu) for g and Q !!!
most likely too much νp1/2 into the g.s. wave function ??OVERALL CONCLUSION: GXPF1A has a problem between N=34 and N=38 22
Magnetic moments of odd‐Cu isotopes from N=28 to N=46
T Cocolios et al PRL 103 102501 (2009) K T Flanagan et al PRL 103 142501 (2009)T. Cocolios et al., PRL 103, 102501 (2009)
Calculations:
Model space (56Ni core) + f p p g
K.T. Flanagan et al., PRL 103, 142501 (2009)
Model space (56Ni core) + f5/2 p3/2 p1/2 g9/2Effective Interactions:* JUN45, Honma et al., PRC80, 064323, 2009* jj4b, Brown, private communication
Conclusions:(1) 69Cu magnetic moment very close to the
reduced single particle valuereduced single particle value
(2) used gs = 0.7 gsfree (56Ni core, no f7/2)
(3) Towards N=28: both π and ν f7/2 core excitations needed to reproduce core softness!
(4) Beyond N=40: * 75Cu, 5/2 g‐factor well reproduced (because nearly pure πf5/2 wave function)* 71,73Cu, 3/2 values largely overestimated need more mixing with (πf5/2⊗2+)3/2 23
Quadrupole moments of odd‐Cu isotopes from N=32 to N=46
Conclusions:
(1) Effective charges are adapted to get best overall agreement (fit to all)
(2) jj4b i d i ll t l ll !!(2) jj4b is doing overall extremely well !!
(3) JUN45 does not very well reproduce the strong core‐polarization observed when adding or removing neutrons to/from 69Cu.
related to the too high 5/2 below N=40too high 1/2 above N=40too high 1/2 above N=40
(4) a better precision on 61Cu and a value for 59Cu will be a very clear proof for the softness of the 56Ni core !
JUN45, Honma et al., PRC80, 064323, 2009jj4b, Brown, private communication
24
g‐factors of odd‐odd Cu isotopes from N=29 to N=45
Conclusions:
(1) Overall trend best reproduced by jj4b
29 31 33 35 37 39 41 43 45
πp3/2νp1/2 (1) Overall trend best reproduced by jj4b
(2) g‐factor is very sensitive to the l di fi ti i thleading configuration in the wave function
(3) Both overestimate the 66Cu value
πp3/2νp3/2
( )leading configuration is coupling to νf5/2, not to νp1/2
(4) Leading proton configuration in
πp3/2νf5/2(4) Leading proton configuration in
72,74Cu is πf5/2 !!(πf5/2νg9/2, 2‐)
JUN45, Honma et al., PRC80, 064323, 2009jj4b, Brown, private communication
The 2‐ appears at 264/211 keV !!!
25
quadrupole moments of odd‐odd Cu isotopes from N=29 to N=43
26
Energy levels of odd‐Cu isotopes from N=28 to N=50
5/210281106 1/2-
914
7/2-1399
970
7/2-1311
962
7/2-1327
1/210965/2-1116
7/2-1482 7/2-1670
5/2-11151170(1/2-) 5/2-1214
981 961
ExperimentN=40N=28
57Cu3/2-
5/2-1028
59Cu3/2-
61Cu3/2-
63Cu3/2-
65Cu3/2-
67Cu3/2-
69Cu3/2-
71Cu3/2-
73Cu3/2-
75Cu5/2-
1/2-491
5/2-914
1/2-475
5/2-970
1/2-670
5/2-9621/2-771
1/2-
1/2-454534 5/2-
5/2 5/27/2-981
(1/2-)135166 5/2-
(7/2-)961
62(3/2-)
(1/2-)128
JUN45 Below N=40:
5/2-1119
5/2-1655
1/2-1989
7/2-1457
640
13877/2-
5/2-1397
1/2-824
7/2-149416355/2-
1/2-931
15167/2-
5/2-1570
1213 1/2-
5/2-1372
16997/2-
13135/2-
1/2-1470
7/2-1153
5/2-794
1/2-12857/2-1562
1/2-1039
7/2-1422
1/2-963
7/2-1401
JUN45 Below N 40:•5/2- level ~500 keV high•½- rather OK, not in 57Cu
Above N=40:
57Cu3/2-
59Cu3/2-
61Cu3/2-
63Cu3/2-
65Cu3/2-
67Cu3/2-
69Cu3/2-
71Cu3/2-
73Cu3/2-
75Cu5/2-
1/2-4221/2-640
5/2-3013/2-136
1965jj4b
Above N 40:• 5/2- level rather OK• ½- > 800 keV too high
Below N=40:
5/2371
1/2-1388
1/2-4195/2-681
7/2-1530
1/2384
5/2-841
7/2-1512
1/2373
5/2-900
7/2-1311
1/2-6735/2-909
7/2-1551
5/2-8689771/2-
7/2-1647
5/2-9161/2-1177
7/2-1965
253
1/2-584
7/2-1626
221/2-430
7/2-1410
1/2-679
7/2-1436
Below N 40:•5/2- level in 57Cu too low !•5/2- level ~ 200 keV too low•½- rather OK
57Cu3/2-
59Cu3/2-
61Cu3/2-
63Cu3/2-
65Cu3/2-
67Cu3/2-
69Cu3/2-
71Cu3/2-
73Cu3/2-
75Cu5/2-
5/2-371 1/2-38 1/2-3735/2-253 22 5/2- 1/2-145
Above N=40:• 5/2- level rather OK• ½- bit too high in 73,75Cu
3
27
Energy levels Cu isotopes beyond N=42
(πf5/2νg9/2)2‐7
(πp3/2νg9/2)3‐6(πp3/2νg9/2)3 6
28
Ground state spins in odd‐Ga isotopes
62C 63C 64C 65C 66C 67C 68C 70C 71C 72C 73C 74C 75C 76C69C
64Zn 65Zn 66Zn 67Zn 69Zn 70Zn 71Zn 72Zn 73Zn 74Zn 75Zn68Zn
77Cu 78Cu 79Cu
4466Ga67Ga 68Ga 70Ga 71Ga72Ga73Ga 74Ga75Ga 76Ga69Ga 4477Ga78Ga 79Ga80Ga 81Ga
61C
82Ga
( f )
62Cu 63Cu 64Cu65Cu 66Cu67Cu 68Cu 70Cu 71Cu 72Cu73Cu 74Cu75Cu76Cu69Cu
64Ni 65Ni 66Ni 67Ni 68Ni 69Ni 70Ni 71Ni 72Ni 73Ni 74Ni 75Ni 76NiZ=28 77Ni 78Ni
77Cu 78Cu 79Cu61Cu
N=40 N=50ν1g9/2 ν(p3/2,f5/2p1/2) 46 48
Normal ground state configuration of odd‐Ga isotopes: π(p3/23)3/2‐
Prior to our work: firmly assigned 3/2‐ value up to 75Ga tentatively assigned 3/2‐ for 77,79Gano assignment for 81Ga
This work: measured all g.s. spins from 67Ga up to 81Ga !!
g
S i h i 73G (I 1/2) d 81G (I 5/2) !!
B. Cheal et al., in preparation
Spin changes in 73Ga (I=1/2) and 81Ga (I=5/2) !!
Need the magnetic and quadrupole moment to understand the structure change !29
I Stefanescu et al PRC 79 064302 (2009)
Odd‐Ga level systematics
N=38 N=46 I. Stefanescu et al. PRC 79, 064302 (2009)
N=40 N=44Dip in 9/2+ energy at 73Ga (N=42)(intruder πg9/2 leading to onset of deformation around neutron mid-shell at N = 42)
N=42
No low-lying spin-1/2 state observed in 73Ga before
at N 42)
in 73Ga before.
3/2- seen in 73Ga seen in (p,t) reaction study (Vergnes et al., PRC19, 1276, 1971)
½- g.s. must be near-degenerate with this 3/2- state (less than 1 keVwith this 3/2- state (less than 1 keVaccording to Stefanescu)!!
30
g-factors of odd-Ga isotopes
B Cheal et al in preparationg-factors
g.s. wave function dominated by unpaired πp3/2 (seniority σ=1), in 67,69,71Ga and in 75 77Ga
B. Cheal et al., in preparation
75,77Ga
g.s. dominated by π(f5/2) configurations in
I=3/2 I=5/2
81Ga, having spin 5/2, but also in 79Ga having spin 3/2 (with mixed π(p3/22f5/2)⊗ν2+ and π(f5/23, σ=3)3/2 as leading configurations)!!
N=40 N=50I=1/2
/ /
g.s very mixed in 73Ga: π(p3/23, σ=3)1/2 with πp1/2 and πf5/2⊗2+
the 73Ga g.s. g‐factor gexp=0.418(4) is very close to gR ~ Z/A ~ 0.44)
31
quadrupole moments of odd-Ga isotopes
B Cheal et al in preparationQsShape changes
(1) around 73Ga
B. Cheal et al., in preparation
( )
•Below N=42 (36,38,40): Q > 0main configuration: Q(p3/2
3) = Q(p3/2‐1 )(hole configuration has a positive Q‐moment)
•Above N=42 (44,46) : Q < 0+1 (f )2
N=40 N=50
main configuration: p3/2+1 (f5/2p1/2)
2
(particle configuration has a negative Q‐moment)
(2) In 79Gapositive Q‐moment: particle‐like must be the leading configuration
mixing between ((p3/2)2πf5/2 ⊗ 2+)3/2 and (f5/2)33/2 configurations
32
Comparing magnetic moments to JUN45 and jj4b
B. Cheal et al., in preparation
JUN45
jj4b
B. Cheal et al., in preparation
jj4b
Second 3/2‐ in calculations !!
Both interactions predict g.s. structure of 79Ga around 250‐300 keV !
33
Comparing quadrupole moments to JUN45 and jj4b
B. Cheal et al., in preparation
JUN45
jj4bSecond 3/2‐ in l l i !!
p p
jj4bcalculations !!
Conclusions: (1) jj4b has better overall agreement for the magnetic moments !(2) in jj4b the quadrupole moment of 69Ga and 71Ga has wrong sign
too fast emptying of the p3/2 orbital ?(indeed, lowest 3/2‐ has leading p3/2f5/2
2 configuration,while the first‐excited 3/2 has a leading p3/23 configuration)
check if this Q‐moment and mu‐moment better fit data !!34
Comparing experimental levels to JUN45 and jj4b
Real ground state !
Real ground state ???To be checked by moments !To be checked by moments !
35
Reduction of the N=28 gap below 48Ca
N=28νf7/2 νpN=20
N 28
40Ca 41Ca
42K 43K
45Ca
44K 45K
47Ca
46K 47K
39Ca
38K
42Ca 43Ca 44Ca 46Ca 48Ca39K 40K 41K
Z=20
νf7/2 νp3/2
Evidence for N=28 gap reductionbelow 48Ca in
39Ar
38Cl 39Cl
41Ar
40Cl
42Ar
41Cl
43Ar
42Cl
44Ar
43Cl
45Ar
44Cl
46Ar
45Cl
37Ar
36Cl
40Ar38Ar
37Cl
below 8Ca, in ‐ in Ar isotopes‐ in S isotopes
35P
37S
36P
38S
37P
39S
38P
40S
39P
41S
40P
42S
41P
43S
42P
44S
43P
35S
34P
36SN=27 isotones
Experimental 7/2‐ and 3/2‐
νp3/2
From Gaudefroy et al., PRL 102 (2009):7/2‐ isomer in 43S is dominated by νf7/2 (from g‐factor)7/2 isomer in S is dominated by νf7/2 (from g factor)very good agreement with sdpf‐U interactionsuggested g.s. of 43S: a collective 3/2‐ state
dominated by νp3/2
νf7/244Cl between 45Ar and 43S
36
Near‐degeneracy of πs1/2 and πd3/2 near N=28
Z 20 νf7/2 43Cl and 45Cl have probably 1/2+ Z=20 νf7/2
ground state (A. Gade, PRC 74(2006)034322)
πd3/2N=28N=22 N=24 N=26
44Cl is in between 43Cl and 45Cl
44Cl ground statepresumably dominated
πs1/2
presumably dominated by πs1/2 configurations
Hardly no experimental information available on 44Cl ‐ knock‐out reaction from 45Cl (PRC79, 2009) suggests 2‐ g.s. with significant contribution from νp / in the wave functioncontribution from νp3/2 in the wave function‐ no excited states known.
Normal 44Cl g.s. configuration = (πd3/2νf7/2‐1) 2,3,4,5‐Mixed with (πd νp ) 0 1 2 3‐Mixed with (πd3/2νp3/2) 0,1,2,3
(πs1/2νp3/2) 1,2‐ pushes 2- down in energylowers the g-factor
37
g‐factor and g.s. structure of 44Cl
Fragmentation of 48Ca beam 2 μAβ‐NMR on 44Cl(NaCl)
|g|=0.27487(16)
Fragmentation of 48Ca beam, 2 μAselect polarized beams at LISE‐GANIL
for β‐Nuclear Magnetic Resonance
M. De Rydt et al., PRC 2010, submitted
Calculation: sdpf‐U interaction (Nowacki and Poves, PRC79 (2009))
protons in sd orbitsprotons in sd orbits neutrons in pf orbitsgs
eff=0.75gs
GOOD AGREEMENT :Ground state spin 2 confirmedVERY MIXED WAVE FUNCTION CONFIRMED
38
Conclusions
(1) Knowing magnetic moments and quadrupole moments in a series of isotopes or isotonesis extremely helpful to understand the structural changes inis extremely helpful to understand the structural changes in isotopes far from stability !
(2)Measurements of the g.s. spin is needed in these exotic(2) Measurements of the g.s. spin is needed in these exotic regions, because theories are not sufficiently well developed to make predictions !
(3) Measured g.s. spin values are crucial for further assigning spins of excited levels.
(4) Measuring the sign of the g‐factor (magnetic moment) is crucial for interpretation of the mixed g.s. structures (less critical for isomeric states that are mostly of single particle t )nature)
39
T. Nagatomo, H. Ueno et al., preliminary
M. De Rydt et al., PLB 678, 344 (2009)
31Al(Al 0 )
33Al NQR
g p y31Al(Al203)
34Al f t
P. Himpe et al., Phys. Lett. B 643 (2006) 257–262
34Al g factor
νQ(kHz)
40