Shell evolution in the neutron rich N=20, N=28 and Z=28 regions from measurements of moments and spins

Transcription

1 hell evolution in the neutron rich N=, N=28 and Z=28 regions from measurements of moments and spins Gerda Neyens, IK, K.U. Leuven, Belgium Belgian Research Initiative on exotic nuclei 1 regions of interest ong magic numbers: Below 40 Ca, along N= island of inversion due to reduction of N= gap Below 48 Ca, along N=28 shape coexistence due to reduction of N=28 and Z=16 ong Z=28, from N=28 up to N=50 softness of 56 Ni core, νf 7/2 56 Z=28 Ni 78 Ni monopole migration νp 3/2 f 5/2 p 1/2 g 9/2 onset of collectivity Z= πf 7/2 40 Ca 48 Ca πd 5/2 s 1/2 d 3/2 πs 1/2 d 3/2 Z=8 16 O N=28 N= N=50 N=8 2

2 Experiments at IOL and fragmentation facilities The COLLA collaboration at CERN IOLDE Leuven Mainz Heidelberg Manchester collinear laser spectroscopy py on bunched beams: I, μ, Q measured (Z=29, from N=32 to N=46) odd even and odd odd 67 Ga 81 Ga (Z=, from N=36 to N=50) odd even and odd odd β NMR NMRand laser spectroscopy on laser polarized beams: I, g, μ measured 21 (Z=12, from N=9 to N=21) even odd only The β NMR collaboration at LIE GANIL Leuven GANIL Bruyères le Chatel Tokyo β NMR spectroscopy on reaction polarized beams: g and Q measured, I deduced 34 (Z=13, from N=18 to N=21) odd even and odd odd 44 Cl (Z=17, N=27) Other input from: in source laser spectroscopy at LIOL@CRC Louvain la Neuve: 57 (μ) TDAD on isomeric states at GANIL: 43 (Z=16, N=27) ( g ) 3 Nuclear moments near magic shells very sensitive to nuclear wave function! 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 (g sπ, g lπ, g sν, g lν ) 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 Comparing experimental and calculated g factors: confirm the proposed wave function in some cases: assign spin and/or parity 57 = 56 Ni + p 57 = 40 Ca + 9p+8n test the shell model interaction and used model space find deviations from normal shell model configurations 4

3 Nuclear moments near magic shells very sensitive to nuclear wave function! Quadrupole moments of odd even, even odd and odd odd isotopes Q moment is determined by the spin j and the <r 2 > of the orbit occupied by unpaired valence protons neutrons are not charged but induce core polarization through p n interaction more sensitive to collectivity it in the wave function Comparing experimental and calculated Q moments near closed shells: probing the proton neutron interaction study the softness of a core as a function of N and/or Z study effects of core polarization study shape coexistence in nuclei 57 = Ni + p = 40 Ca + 9p+8n confirm the proposed wave function test the shell model interaction find deviations from normal shell model configurations 5 The island of inversion i i i 30 i 32 i i 34 i i i Na 26 Ne 25 F 24 Na 27 Ne 26 F Na 28 Ne 27 F 26 Na 29 Ne 28 F Na 30 Ne 29 Na Ne 30 F 29 Na 32 Na Ne approaching N N= Na emptying πd 5/2 activeneutron orbits around N= 8 p 3/2 f 7/2 d 3/2 s 1/2 d 5/2 pf fp shell sd shell influence of particle hole excitations In the ground state wave functions? sd Experimental challenge: how large is this region of inversion? tudy transition region difficult to make theoretical predictions! 6

4 g-factors of isotopes ground states dominated by πd 5/2-1. Himpe et al., hys. Lett. B 643 (06) Z=13: Z13 hole in πdd 5/2 orbital β asymme etry (i) B (gauss) I π = 5/2 + expected for odd isotopes wave function and spin confirmed by g factor through comparison with calculated μ=g.i in sd shell model (UD 0p0h) sdf 7/2 p 3/2 shell model space DF M (MCM, mixed) sdpf interaction (2p2h) (free nucleon g factors) μ (μ N ) 4,2 4 3,8 I π =5/2 + 0p-0h exp MCM (50% intruder) 3,6 2p-2h 3, N Conclusion for (N=): small (<25 30 %) intruder admixture in the ground state. Y. Utsuno et al., RC 64, R, 01 7 quadrupole moments of, more sensitive to neutron excitations M. De Rydt et al., LB 678, 344 (09) Q() T. Nagatomo, et al., EJA 42, (09) Q() to be continued! ( ) Error bars smaller than dot size! 2p 2h exp Calculations in sdp 3/2 f 7/2 shell: ν Q (khz) * DF M interaction (MCM) Otsuka, Utsuno et al., private communication * sdpf NR interaction (ANTOINE code) Nummela et al., RC63 (01) very good agreement for 27, with proton effective charge : e p = e neutron effective charge: e n = 0.5e 0p 0h has a mixed g.s. configuration: ν(sd) 2 (fp) 2 contribution in wave function! To determine amount of mixing: need more precise Q moment value! Experiment at GANIL, july 10 8

5 Fitted effective charges using all known sd shell Q moments M. De Rydt et al., LB 678, 344 (09) y,, ( ) Compare Q of sd shell shell isotopes (errors exp odd Z quadrupole moments smaller than dot size) e eff with calculated values in sdp 3/2 f 7/2 space using π =1.3e sdpfeffective interaction M. Depuydt, M. De Rydt, G. Neyens, to be published χ 2 =3.4 sd shell Q moments sdpf U effective interaction (Nowacki and oves, RC79, 0140 (09)) e π eff =1.1e χ 2 =1.5 sd shell proton effective charge: e p = 1.12 e neutron effective charge: e n = 1.45 e 9 g factor (+ sign) and spin of the, ground state νd 3/ νf 7/ REAL ground state tt configurations: (N=19) (N=21) I π =1/2 + pf d 3/2 sd I π =3/2 G. Neyens et al., RL 94, (05) D. Yordanov et al., RL 99, (07) Measured spin and From sign of g-factor parity, I π = 1/2+ ν(sd) -3 (fp) 2, I π = 3/2- ν(sd) ( ) -2 (fp) 3 pure 2p-2h intruder ground states! Normal ground state configurations: (N=19) (N=21) f 7/2 d 3/2 ν(s 2 2 1/2 )(d 3/2 ) 0 (fp) 0 [ν(d 3/2 )π(sd) 2+ ] 1/2 (fp) 2 0 ν(d /2 ) 0 (f 7/2,σ=3) 3/2 ν(d -2 I π =3/2 + I π =7/2 3/2 ) 0 (f 2 ) 0 p 3/2 10

6 pin/parity of the ground state in the shell model Look at the g factors of isotones with similar configuration N=19 isotone: i 28 p 3/2 36 f 7/2 35 d 3/2 I π =3/2 + i i i s 1/ p1h intruder ground state in same g-factor as i g( i) = N=21 isotone: 35 i 28 p 3/2 f 7/2 I π =7/2 sd normal ground state in same g-factor (particle in f 7/2 ) as 35 i g( 35 i) = g exp ( ) = (4) g sdpf (3/2+) = (1p1h) g sdpf (3/2-) = (2p2h) 2p2h ground state in similar g-factor as 35 i (3 particles in f 7/2 ) (f 7/2 ) 3 3/2 2 neutron holes in sd act as spectators (paired) G. Neyens et al., RL 94, (05) D. Yordanov et al., RL 99, (07) 11 pin/parity of the ground state in Nilsson model D. Yordanov et al., comment to RL, accepted g Hamamoto, RC76, 0549 (07) g exp ( ) = (4) Interpretation in Nilsson Model: gground state: build on ½+[0] g= (exp= ) ground state: and on 3/2-[321] g= (exp= ) 3/2-[0] g= (exp= ) 12

7 ummary: island of inversion around 32 resent status of the Island of inversion as deduced from static and dynamic moments measurements. Himpe et al., hys. Lett. B. 658, 3 (08) l intruder g.s. configurations are of the 2p 2h type!! (two neutrons excited across N=) Utsuno et al., RC70, , Evolution of the proton single particle states above Z= Ga Ga Ga Ga Ga Ga Ga Ga Ga 44 Ga Ga Ga 78 Ga 79 Ga Ga 81 Ga 82 Ga 64 Zn 65 Zn 66 Zn 67 Zn 68 Zn 69 Zn 70 Zn 71 Zn 72 Zn 73 Zn 74 Zn 75 Zn Ni 65 Ni 66 Ni 67 Ni 68 Ni 69 Ni 70 Ni 71 Ni 72 Ni 73 Ni 74 Ni 75 Ni Z=28 Ni Ni 78 Ni ν(p 3/2,f 5/2 p 1/2 ) N=40 N40 ν1gg 9/ N=50 πp 1/2 πf 5/2 1/2 - Evolution of the experimental 5/2 and 1/2 energies in isotopes 5/2 - πp 3/2 0 ns 15μs 1.5 3/ h l ( ) f l RL (08) N=28 N=40. Franchoo et al., RC 64, (01) tefanescu et al., RL 100, (08) J.M. Daugas, h.d. Thesis, GANIL teep decrease of the 5/2- and 1/2- levels when νg 9/2 is filled Experiment: g.s. spin assigned up to 73 (3/2 ) from β decay14

8 Ground state spin of 71,73,75 K.T. Flanagan et al., RL 103, (09) 73, I=3/2 g.s. spins measured with laser spectroscopy spins assigned to isomeric levels in 75 (based on measured lifetimes) 75, I=5/2 Theory reproduces lowering of 5/2 correctly theory overestimates the 1/2 energy from 69 to 75!!! Model space: 56 Ni core + f 5/2 p 3/2 p 1/2 g 9/2 Effective interaction: Lisetsky and Brown based on A. F. Lisetskiy et al., hys. Rev. C 70, 0444 (04) JJ4b, Brown 15 Ground state spin of 72,74 72, I=2 74, 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, I) Ground state spins I=2, with more than 4 sigma confidence level 16

9 Ground state parity and structure of expected low energy levels: use aar s rule Z=29 N=43 (πp 3/2 νp 1 1/2 g 9/24 ) (1,2) + 1g 9/2 1g 9/2 neutron excitation across N= p (πf5/2 νg9/2 3 1/2 2p ) (2,,7) 1/2 proton excited to the f 5/2 orbital 1f 5/2 1f 5/2 2p 3/2 2p 3/2 (πp 3/2 νg 9/23 ) (3,4,5,6) (1+) t =1.76μs (6 ) 1/2 μ (4 ) (3 ) (2) J.C. Thomas et al., RC74, , 06 Experiment ?? Realistic interaction Ground state has spin I=2 But what is the parity?? Can we assign parity based on measured magnetic moment? μ = (6) μ N 17 Ground state parity and structure of 72 : I π = 2!! Use additivity rules for proton neutron configurations: Main negative parity configuration: μ(πf 5/2 νg 9/23 ; 2 ) μ free (2 ) = 2.13 μ N μ emp (2 ) = 1.94 μ N Main positive parity configuration: μ(πp 4 3/2 νp 1 1/2 g 9/24 ; 2 + ) μ free (2 + ) = μ N μ emp (2 + ) = μ N Conclusion: themeasuredignofthemoment, moment, μ = (6) μ N, 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 f 5/2 orbital (1+) t =1.76μs (6 ) 1/2 μ (4 ) (3 ) (2 ) Experiment Realistic interaction 18

10 Magnetic moments of odd isotopes from N=28 to N=40 T. Cocolios et al., RL 103, (09) Compare performance large scale shell model calculations: GXF1 40 Ca core + full pf shell (f 7/2 p 3/2 f5/2p 1/2 ) GXF1A same. Vingerhoets et al., in preparation I π = 3/2 Conclusions: (1) Effective g 09g s = 0.9g free s, close to freenucleon value (because model space includes all pf levels) (2) oftness of 56 Ni core well reproduced (g with 56 Ni core: 1.997) (3) GXF1 reproduces all values perfectly, except for 69 shows the need to include νg 9/2 in the model space (4) GXF1A slightly underestimates the values for 63,65,67 (N=34,36,38) 19 Quadrupole moments of odd isotopes up to N=40 CONCLUION: (1) Effective charges are from a chi^2 fit to both odd odd and odd even quadrupole moments. Vingerhoets et al., in preparation I π =3/2 (2) Quadrupole moments are very similar with GXF1 and GXF1A (3) the g factor is more sensitive to small admixtures in the wave function (4) 68 Ni core is more stiff than 56 Ni core in this interaction ti and model dl space (because no excitations across N=40 included) to verify experimentally if neutron excitations to g9/2 reduce the core stiffness of 68 Ni, we need to compare Qexp for 57 to 69

11 g factors of (1,2)+ states in odd odd isotopes Compare to empirical ii values from weak coupling calculations l for pure single particle configurations very sensitive to purity of the configuration and small effects of configuration mixing ii!. Vingerhoets et al., in preparation Isomeric 1+ state Note: the experimental sign of 66 was wrong in literature!! 21 g factors and Q moments of odd odd isotopes: GXF1 and GXF1A πp 3/2 νp 1/2 πp 3/2 νp 3/2 πp 3/2 νf 5/2 Conclusions: (1) the experimental g factors agree well with single particle estimates for rather pure π ν configurations with normal filling of the νp 3/2 f 5/2 p 1/2 orbits (2) GXF1 does overall rather well for μ and Q (3) GXF1A strongly deviates at N=35 and N=37 ( 64,66 ) for g and Q!!! most likely too much νp 1/2 into the g.s. wave function?? OVERALL CONCLUION: GXF1A has a problem between N=34 and N=38 22

12 Magnetic moments of odd isotopes from N=28 to N=46 T. Cocolios et al., RL 103, (09) K.T. KT Flanagan et al., RL 103, (09) Calculations: Model space ( 56 Ni core) + f 5/2 p 3/2 p 1/2 g 9/2 Effective Interactions: * JUN45, Honma et al., RC80, , 09 * jj4b, Brown, private communication Conclusions: (1) 69 magnetic moment very close to the reduced single particle value (2) used g s = 0.7 g s free (56Ni core, no f7/2) (3) Towards N=28: both π and ν f 7/2 core excitations needed to reproduce core softness! (4) Beyond N=40: * 75, 5/2 g factor well reproduced (because nearly pure πf 5/2 wave function) * 71,73, 3/2 values largely overestimated need more mixing with (πf 5/2 2 + ) 3/2 23 Quadrupole moments of odd isotopes from N=32 to N=46 Conclusions: (1) Effective charges are adapted to get best overall agreement (fit to all) (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 69. related to the too high 5/2 below N=40 too high 1/2above N=40 (4) a better precision on 61 and a value for 59 will be a very clear proof for the softness of the 56 Ni core! JUN45, Honma et al., RC80, , 09 jj4b, Brown, private communication 24

13 g factors of odd odd isotopes from N=29 to N= πp 3/2 νp 1/2 Conclusions: (1) Overall trend best reproduced by jj4b πp 3/2 νp 3/2 (2) g factor is very sensitive to the leading configuration in the wave function πp 3/2 νf 5/2 (πf 5/2 νg 9/2, 2 ) (3) Both overestimate the 66 value leading configuration is coupling to νf 5/2, not to νp 1/2 (4) Leading proton configuration in 72,74 is πf5/2!! The 2 appears at 264/211 kev!!! JUN45, Honma et al., RC80, , 09 jj4b, Brown, private communication 25 quadrupole moments of odd odd isotopes from N=29 to N=43 26

14 Energy levels of odd isotopes from N=28 to N=50 N=28 N=40 Experiment / / / /2-57 3/ / / /2-11 7/ / / / / / /2-7/ (1/2-) 12145/ / / / / /2-961 (7/2-) 534 5/ / /2-135 (1/2-) 128 (1/2-) 62 (3/2-) 59 3/2-61 3/2-63 3/2-65 3/2-67 3/2-69 3/2-71 3/2-73 3/2-75 5/ / / / / / / / / / / /2-9 1/ / / / /2-13 5/ / / /2-1/ / / /2- Below N=40: JUN45 5/2 - level ~500 kev high ½- rather OK, not in / / /2-57 3/2-59 3/2-61 3/2-63 3/2-65 3/2-67 3/2-69 3/2-71 3/2-73 3/2-75 5/ / / / / / / / / / / /2-11 7/ /2-1/ / / / / / / / /2- jj4b 373 1/ /2-1/ / /2-22 5/ /2-57 3/2-59 3/2-61 3/2-63 3/2-65 3/2-67 3/2-69 3/2-71 3/2-73 3/2-75 5/2 - Above N=40: 5/2- level rather OK ½- > 800 kev too high Below N=40: 5/2 - level in 57 too low! 5/2- level ~ 0 kev too low ½- rather OK Above N=40: 5/2- level rather OK ½- bit too high in 73,75 27 Energy levels isotopes beyond N=42 (πf 5/2 νg 9/2 )2 7 (πp 3/2 νg 9/2 )3 6 28

15 Ground state spins in odd Ga isotopes Ga 67 Ga 68 Ga Ga 71 Ga 72 Ga 73 Ga 74 Ga Ga Ga Ga Ga 78 Ga 79 Ga Ga 81 Ga 64 Zn 65 Zn 66 Zn 67 Zn 68 Zn 69 Zn 70 Zn 71 Zn 72 Zn 73 Zn 74 Zn 75 Zn Z=28 64 Ni 65 Ni 66 Ni 67 Ni 68 Ni 69 Ni 70 Ni 71 Ni 72 Ni 73 Ni 74 Ni 75 Ni Ni Ni 78 Ni ν(p 3/2,f 5/2 p 1/2 ) N=40 ν1g 9/ N=50 Normal ground state configuration of odd Ga isotopes: π(p 3/23 )3/2 rior to our work: firmly assigned 3/2 value up to 75Ga tentatively assigned 3/2 for 77,79Ga no assignment for 81Ga This work: measured all g.s. spins from 67Ga up to 81Ga!! pin changes in 73Ga (I=1/2) and 81Ga (I=5/2)!! 82 Ga B. Cheal et al., in preparation Need the magnetic and quadrupole moment to understand the structure change! 29 Odd Ga level systematics N=38 N=46 I. tefanescu et al. RC 79, (09) N=40 N=44 N=42 Dip in 9/2+ energy at 73 Ga (N=42) (intruder πg 9/2 leading to onset of deformation around neutron mid-shell at N = 42) No low-lying spin-1/2 state observed in 73 Ga before. 3/2- seen in 73Ga seen in (p,t) reaction study (Vergnes et al., RC19, 1276, 1971) ½- g.s. must be near-degenerate with this 3/2- state (less than 1 kev according to tefanescu)!! 30

16 g-factors of odd-ga isotopes g-factors B. Cheal et al., in preparation g.s. wave function dominated by unpaired πp 3/2 (seniority σ=1), in 67,69,71Ga and in 75,77Ga77Ga I=3/2 I=5/2 I=1/2 N=40 N=50 g.s. dominated by π(f 5/2 ) configurations in 81Ga, having spin 5/2, but also in 79Ga having spin 3/2 (with mixed π(p 3/22 f 5/2 ) ν2 + and π(f 5/23, σ=3) 3/2 as leading configurations)!! g.s very mixed in 73 Ga: π(p 3/23, σ=3) 1/2 with πp 1/2 and πf 5/2 2+ the 73 Ga g.s. g factor g exp =0.418(4) is very close to g R ~ Z/A ~ 0.44) quadrupole moments of odd-ga isotopes hape changes (1) around 73Ga B. Cheal et al., in preparation Qs Below N=42 (36,38,40): Q > 0 main configuration: Q(p 3/23 ) = Q(p 3/2 1 ) (hole configuration has a positive Q moment) Above N=42 (44,46) : Q < 0 main configuration: p +1 3/2 (f 5/2 p 1/2 ) 2 (particle configuration has a negative Q moment) N=40 N=50 (2) In 79Ga positive Q moment: particle like must be the leading configuration mixing between ((p 3/2 ) 2 πf 5/2 2+) 3/2 and (f5/2) 3 3/2 configurations 32

17 Comparing magnetic moments to JUN45 and jj4b B. Cheal et al., in preparation JUN45 jj4b econd 3/2 in calculations!! Both interactions predict g.s. structure of 79 Ga around kev! Comparing quadrupole moments to JUN45 and jj4b B. Cheal et al., in preparation p econd 3/2 in calculations l!! JUN45 jj4b 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 p 3/2 f 5/22 configuration, while the first excited 3/2 has a leading p3/2 3 configuration) check if this Q moment and mu moment better fit data!! 34

18 Comparing experimental levels to JUN45 and jj4b Real ground state! Real ground state??? To be checked by moments! 35 Z= 39 Ca 38 K 37 Ar 36 Cl N= Reduction of the N=28 gap below 48 Ca νf 7/2 N=28 νp 3/2 40 Ca 41 Ca 42 Ca 43 Ca 44 Ca 45 Ca 46 Ca 47 Ca 48 Ca 39 K 40 K 41 K 38 Ar 37 Cl 39 Ar 40 Ar 38 Cl 39 Cl 42 K 43 K 41 Ar 40 Cl 42 Ar 41 Cl 44 K 45 K 43 Ar 42 Cl 44 Ar 43 Cl 46 K 47 K 45 Ar 44 Cl 46 Ar 45 Cl Evidence for N=28 gap reduction below 48 Ca, in in Ar isotopes in isotopes N=27 isotones Experimental 7/2 and 3/2 νp 3/2 From Gaudefroy et al., RL 102 (09): 7/2 isomer in 43 is dominated by νf 7/2 (from g factor) very good agreement with sdpf U interaction suggested g.s. of 43 : a collective 3/2 state dominated by νp3/2 44Cl between 45Ar and 43 νf 7/2 36

19 Near degeneracy of πs1/2 and πd3/2 near N=28 Z= νf 43Cl and 45Cl have probably 1/2+ 7/2 ground state (A. Gade, RC 74(06)034322) πd 3/2 N=22 N=24 N=26 N=28 44 Cl ground state presumably dominated by πs 1/2 configurations 44 Cl is in between 43 Cl and 45 Cl πs 1/2 Hardly no experimental information available on 44 Cl knock out reaction from 45 Cl (RC79, 09) suggests 2 g.s. with significant contribution from νp 3/2 in the wave function no excited states known. Normal 44 Cl g.s. configuration = (πd 3/2 νf 1 7/2 ) 2,3,4,5 Mixed with (πd 012 3/2 νp 3/2 ) 0,1,2,3 (πs 1/2 νp 3/2 ) 1,2 pushes 2- down in energy lowers the g-factor 37 g factor and g.s. structure of 44 Cl β NMR on 44 Cl(NaCl) g = (16) Fragmentation of 48 Ca beam, 2 μa select polarized beams at LIE GANIL for β Nuclear Magnetic Resonance M. De Rydt et al., RC 10, submitted Calculation: sdpf U interaction (Nowacki and oves, RC79 (09)) protonsin sd orbits neutrons in pf orbits g eff s =0.75g s GOOD AGREEMENT : Ground state spin 2 confirmed VERY MIXED WAVE FUNCTION CONFIRMED 38

20 Conclusions (1) Knowing magnetic moments and quadrupole moments in a series of isotopes or isotones is extremely helpful to understand the structural changes in isotopes far from stability! (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 nature) 39 M. De Rydt et al., LB 678, 344 (09) ( ) T. Nagatomo, H. Ueno et al., preliminary NQR. Himpe et al., hys. Lett. B 643 (06) g factor ν Q (khz) 40