The race for 100Sn – History and status of experimental and shell model approach

Topics:

• History: the past 50 years

• Experimental approach

• Spin gap isomerism and seniority in the g9/2 hole space

• Excitation of the 100Sn core and large scale shell model

• Super Gamow-Teller decay of 100Sn

• Z=N=50 shell gaps

• The doubly-magic neighbours 56Ni, 78Ni and 132Sn

• The future has started !

H. Grawe, M. Górska, T. Faestermann SMUV Strasbourg 8. – 10. 10. 2012

(cf. FGG, Progr. in Part. Nucl. Phys., in print)

2d5/2,1g7/2,3s1/2,1h11/2,2d3/2

2d5/2,3s1/2,2d3/2,1g7/2,1h11/2

1f5/2,2p3/2,2p1/2,1g9/2

On the road to 100Sn

88Sr,89Y, 90Zr, 92Mo

"classical" and "new‘‘

doubly-magic and

"almost" magic nuclei

The Start !

The race for 100Sn – landmarks part I – the start 1958 90Zr up to (0-8)+ N.H. Lazar et al., PR 110, 513(58)

1960 89Y,90Zr,91Nb, excited states ESM analysis I.Talmi, I.Unna, NPA19, 225 (60)

1965 88Sr - 92Mo binding energies, 8+ isomers N. Auerbach, I. Talmi, NPA64, 458(65)

TBME in proton (p1/2,g9/2) space yield 100Sn Sp=1.83 MeV

1970-75 NaI(Tl) replaced by Ge -detectors, (4He/3He,xn) by (HI,xn yp z) reactions

1976 ESM in pn (p1/2,g9/2) space, seniority conservation Sp=2.92 MeV

F.J.D Serduke, R.D. Lawson, D.H. Gloeckner, NPA 256, 45 (76)

R. Gross, A. Frenkel 267, 85 (76)

Excited states (Ex) and binding energies (BE) for N=48-50 and Z < 43 (Tc)

1980-85 (g9/2)n mid-shell nuclei Ru-Pd studied in ISOL and in-beam

seniority breaking in 95Rh: E. Nolte et al., ZPA 298, 191 (80); A. Amusa,

R.D.Lawson, ZPA 307,333(82) ; J.Blomqvist, L.Rydström, Phys. Scr. 31,31(85)

1985-90 Multi-detector arrays for , n, p, OSIRIS, NORDBALL, EUROGAM

OXBASH shell model code B.A. Brown et al., MSU-NSCL report No. 524 (85)

(a very personal view)

The race for 100Sn - part II – detector arrays and shell model analysis

1990-95 97Ag -3, 104Sn 4, 100Cd -22 closest approach in-beam and excited states

98Cd Gamow-Teller -decay @ISOLDE A. Plochocki et al., ZPA 342,43(92)

100Sn: SPE/SHE, gaps: 5.92 (Z=50)/6.80 (N=50) MeV H.G. et al.,Phys.Scr.T56,71(95)

SM summary in (p1/2,g9/2) D. Rudolph et al., NPA 597, 298(96)

Z=50,N=50 GT review K.Rykaczewski et al., IOP Conf. Ser. No. 132, 215(93)

Fragmentation and in-flight separators FRS/GSI, LISE/GANIL

1994 Identification of 100Sn @GANIL and GSI M. Lewitowicz et al., PLB 332, 20(94)

in projectile fragmentation R. Schneider et al., ZPA 348, 241 (94)

GAMMSPHERE, GASP, EUROBALL I-IV + ancillaries, fusion-evaporation

and fragmentation for isomers R. Grzywacz et al., PLB 355,439(97)

1995-99 98Cd, 8+ isomer -2 M. Górska et al., PRL 79, 2415 (97)

102Sn, 6+ isomer 2 M. Lipoglavšek et al., PLB 440, 246 (98)

G-matrix based realistic interactions M. Hjorth-Jensen et al., PR 261,125(95)

ANTOINE and NATHAN E.Caurier, F.Nowacki, Acta Phys. Pol. B30, 705(99)

The race for 100Sn - part III – the new century 2000-05 103Sn prompt (d5/2,g7/2) C. Fahlander et al., PRC 63, 021307(R) (01)

99Cd core excitation M. Lipoglavšek et al., PRC 66,011302(R) (02)

98Cd core excited 12+ isomer, N=50 gap A. Blazhev et al., PRC 69, 064304(04)

based on LSSM 100Sn core excitation F. Nowacki, NPA 704, 223c(02)

2005-11 106-110Sn 2+ Coulex @GSI, MSU, REX-ISOLDE A.Banu et al.,PRC 72,061305(05)

C. Vaman et al., PRL 99,162501 (07), A.Ekström et al., PRL 101, 012502 (08)

106Te next to 100Sn in recoil - tagging B. Hadinia et al., PRC 72, 041303 (05)

101Sn (d5/2,g7/2) in 105Te -decay, sequence still disputed

D. Seweryniak et al., PRL 99, 022504 (07), I.G. Darby et al., PRL 105, 162502 (10)

96Cd 16+ spin trap -decay and 96Ag 19+ core excited isomer, LSSM

B.S. Nara Singh et al., PRL 107, 172502 (11), P. Boutachkov et al., PRC 84, 044311 (11)

2012 100Sn Super-GT decay, , coinc., QEC Ch. Hinke et al., Nature 486, 341 (12)

LSSM ; Z=50, N=50 robust shell closure verified !! (K. Sieja, F. Nowacki)

Quenching of GT operator ~0.75

108Sn / 197Au v/c = 0.45 P/B ~ 1-2

108Sn / 58Ni v/c = 0.08 P/B ~ 4-5

114Sn / 58Ni v/c = 0.07 P/B ~ 40

2+→

0+

2+→

0+

2+→

0+

58Ni

GSI/RISING

REX/ISOLDE

GSI/UNILAC

Coulex of radioactive and stable beams @ relativistic and „safe“ energy

A. Banu et al., PRC 72, 061305 (2005)

A. Ekström et al., PRL 101, 012502 (2008)

P. Doornenbal et al., PRC 78, 031303 (2008)

108In

8+ 8+

6+

4+

2+

6+

4+ 2+

12+!!Sum (4207)

Valence and core excited isomers in N=50 98Cd

NORDBALL+2 EUROBALL cluster EUROBALL IV @ Strasbourg

t1/2(8+)=0.48(16)s t1/2(8+)=0.17(+6 -4) s

t1/2(12+)=0.23(+4 -3) s

M. Górska et al., PRL 79, 2415

(1997)A. Blazhev et al., PRC 69, 064304

(2004)

8+ 8+

6+

4+

2+

6+

4+ 2+

12+!!Sum (4207)

Valence and core excited isomers in N=50 98Cd

NORDBALL+2 EUROBALL cluster EUROBALL IV @ Strasbourg

t1/2(8+)=0.48(16)s t1/2(8+)=0.17(+6 -4) s

t1/2(12+)=0.23(+4 -3) s

M. Górska et al., PRL 79, 2415

(1997)A. Blazhev et al., PRC 69, 064304

(2004)

A. Blazhev et al., J. Phys. Conf. Ser. 205, 012035

RISING@GSI (2010)B(E2; 8+→ 6+) = 1.2(3) W.u.B(E2;12+→10+)=2.2(8) W.u.B(E4;12+→ 8+)=3.0(8) W.u.

See Andrey Blazhev‘s talk

100Sn

Identification Z vs. A/Z124Xe fragmentation

spectrum

100In levels

100Sn Super Gamow-Teller decay (I)Ch. Hinke et al., Nature 486, 341 (2012)

Close-up view of the 100Sn region

• proton – neutron

hole-hole interaction

in g9/2-n

• core excitation in

large-scale SM

in g9/2-1 (d5/2

,g7/2)1

Spin gap isomers

below N = Z = 50

@ RISING, GSI – ISOL and EUROBALL IV

?

<jn,v,J|OL|jn,v,J> ~ const

<jn,v,J|V|jn,v,J> ~ const + (n-v)/2

<jn,v,J|OL|jn,v-2,J´>2 ~ f(1-f)

<jn,v,J|OL|jn,v,J´> ~ (1-2f)

<jn,v,J|V|jn,v-2,J> ~ (1-2f)√f(1-f)

1 – body, L=odd, v - v e.g. M1,

2 - body, odd, v - v , e.g. interaction

1 – body, L=even,v - v-2 e.g. B(E2)

1 – body, L=even, v – v, e.g. E2, Q

2 – body, even, v – v-2

N=50 isotones g9/2n

schematic experiment g9/2(+p1/2)by core excitation

corex!

The g9/2n seniority scheme and distortion

Symmetry rules in the seniority scheme

• Excitation energies are independent of shell occupation n

• Matrix elements of even-tensor one- and two particle operators change sign in mid-shell, i.e. they vanish for n = (2j+1)/2

• Odd-tensor one- and two particle operators are diagonal in v

• Proton-neutron interaction, e.g T=0 core excitations, break seniority

A. De Shalit, I. Talmi, Nuclear Shell Theory, Academic Press, New York, 1963R.F.Casten, Nuclear Structure from a Simple Perspective, Oxford University Press, 2000H. G., The Euroschool Lectures on Physics with Exotic Beams, Vol. I, Lect. Notes Phys.

651, 33 (2004)A. Amusa, R.D. Lawson, ZPA 307, 333 (1982)H. Grawe et al., EPJA 27, s01, 257 (2006)H. Mach et al., Proc. Int. Symposium A New Era of Nuclear Structure Physics, Niigata, Japan 2003, World Scientific, Singapore, 2004, p.277F. Nowacki, priv. comm. A. Escuderos, L. Zamick, PRC73, 044302 (2006) P. Van Isacker, Int. J. Mod. Phys. E20, 191 (2011)

}95Rh

96Pd94Ru

Z=28

N=50

Valence mirror g9/2n nuclei in Z=28 isotopes

and

N=50 isotones The 8+ isomers disappear in mid-shell Ni isotopes due to stronger I= 2+ two-body matrix element (Ex(2+)

~1.0 vs. 1.5 MeV), which shifts the seniority v=4, 6+ state (*) below the v=2, 8+ enabling a strong v=2 B(E2)H.G. et al., NPA 704, 211c (2002)

A. Lisetskiy et al., PRC 70, 044314 (2004)

8+ isomers !

No 8+ isomers !

A. Blazhev et al., PRC 69, 064304

preliminary !

100Sn core excitation

•LSSM smoothly converged at t=5 (F. Nowacki, E. Caurier)

• 100Sn neutron shell gap N=50 inferred 6.46 (15) MeV• remaining E2,E4 deficiency is due to interaction and/or proton gap Z=50• effective E2 charge will not help !

Valence statesg9/2

-2

ph statesg9/2

-2g9/2-t (d5/2,g7/2)t

pairing

• Valence excitation energy increases with t• ph excitation energy decreases with t• Exception t=2 : pairing overbinds valence states

E2

E2

E4

98Cd

A. Blazhev et al., PRC 69, 064304 (04)

96Pd

First core excited odd-parity isomer in N=50 96Pd

• = + states well reproduced in LSSM @t=5 in gds space

• = - states calculated @ t=1 for neutrons in fpgd5/2

M. Palacz et al., PRC 86, 014318 (2012)

valence

corex

96Ag

Valence and core excited isomers in N=49

96Ag

P. Boutachkov et al., PRC 84, 044311 (2011) see A. Blazhev !

valence isomers

core excited isomer

SMf5/2,p,g9/2

LSSM gds

100Sn excited states predictions from shell model and mean field

I= 6+ isomer?2+, 3- position?B(E2;2+→0+) ~ 10 W.u.LSSM:gds, “Tokyo“ interaction, t=4M. Hjorth-Jensen, et al., PR 261,125(95)monopole tunedF. Nowacki, NPA 704,223(2000)by Etienne Caurier ! (2005)SM:gd5/2 , H7B interaction, t=3A. Hosaka et al., NPA 244,76(1985) monopole tuned by H.G.HF-RPA:V.I. Isakov, K.I. Erokhina, Phys. At. Nucl. 65,1431(2002)RQRPA:A. Ansari, P. Ring,PRC 74,054313(2006)

100Sn Super Gamow-Teller decay (II)Ch. Hinke et al., Nature 486, 341 (2012)

QEC = 4.35(-17 +19) MeVT1/2 = 1.09 (18) s

LSSM 100In EXP

g9/2-1 g7/2) 1+ log(ft) = 2.62(+0.13

-0.11) record low !

B(GT) = 9.3 (+2.3-3.0)

record high ! Single 1+ feeding

+

Ch. Hinke et al., Nature 486, 341 (2012)

100Sn

LSSM in gdsK. Sieja, F. Nowacki

LSSM guided correction:3 more 1+ states fed with B(GT)>0.1

B(GT) = 9.9 (+2.8-3.2)

B(GT;1+1) = 7.6 (+2.2 -2.5)

LSSM value 5.7 robust shell gaps >6 MeV q~0.75 quenching of GT operator confirmed

Why “Super“ ?

B(GT) =160/9 × 1 × 1for g9/2 → g7/2 spin-flip transition Unique in the Segrè chart !

100Sn Super Gamow-Teller decay (III)

Monopole driven shell structureSingle particle/hole energies (SPE/SHE) and shell gaps from extrapolation of experimental data from known CS´to next CS

e.g. N=50

99,100,101Sn99In

90,91,92Nb89,90,91Zr

92Mo

Two-body matrix elements (TBME) and monopoles from binding energies (BE),SPE/SHE () and excitation energies (Ex)within each multiplet j´j for particle-particle andj´k for particle-hole

See FGG !

Exp. gaps from separation energies S1n,S2n

ESPE from exp. multipletscorrected for occupation

theoretical monopoleT. Otsuka et al., PRL104,012501 (10)

SM in valence space, no corex

100Sn : 6.35(13) MeV for d5/2 g.s.3.9(5)/3.0(3) MeV for d5/2/g7/2 g.s.O. Sorlin, M.-G. Porquet, PPNP 61, 602 (08)

robust shell gaps !

78Ni : 4.05(18) MeV for d5/2 g.s.3.4 MeV for d5/2 g.s.M.-G. Porquet, O. Sorlin,PRC 85, 014307(12)

4.7 from LSSM and d5/2 g.s.K. Sieja, F. Nowacki, PRC 85,051301(R) (12)

Shell gap along N=50

100Sn and 56Ni SPE/SHE and g7/2 monopole migration

d5/2, g7/2 problem in 101SnAnalogy of N=3, 4 HO shells andintruders from N=4, 5100Sn gaps: 5.96(20) () and 6.35(13) () MeV

D. Seweryniak et al., PRL 99, 022504(07) (ANL)I.G. Darby et al.,PRL105, 162502(10) (ORNL)

Extrapolation “safe“ for g9/2d5/2 multiplet (92Nb)g9/2g7/2 monopole from G-matrix (MHJ)modified to fit N=51 single particle states (MHJm)

100Sn extrapolated SPE vs. SM and global predictions (just a selection from many)

“EX“: extrapolated H.G.SKX : Skyrme B.A. Brown PRC 58,220(98)

PL40: RMF K. Rutz et al., NPA 634,67 (98)DZ: SM based global monopole scalingJ. Duflo, A.P Zuker, PRC 59, R2347(99)

100Sn and its magic neighbours 56,78Ni and 132Sn

f5/2(p) − g9/2: gap increase from 56Ni to 78Ni /100Sn and decrease from 100Sn to 132Sn due to strong monopole; Z=40 subshell at N=82?f5/2(p)g9/2 – g7/2(ds)h11/2: N=4 intruder g9/2 well separated N=40 subshell in Ni´s N=5 intruder h11/2 embedded in s1/2,d3/2 orbits no subshells in Sn´s

56Ni vs. 100Sn – fp vs. gds structure analogies - Why and why not?

(a)valence states Imax = 6+ vs. 8+

B(E2) = 3.3 vs. 1.2 W.u.

core excited isomers I= 10+ vs. 12+ = Imax + 4 B(E2) = 1.7 vs. 2.2 W.u.B(E4) = 0.8 vs. 3.0 W.u.

correspondence principle ! (Jan Blomqvist)(b)valence statesImax = 11+ vs. 15+ Imax-2 = 9+ (!) vs. 13+

Isomer destroyed !9+2 needs p3/2 !No core excited isomers due to proximity to proton mid-shell

LSSM80Zr

Z=50 shell gap for 100-132Sn and B(E2;0+→2+)

SM 100Sn core onlyLSSM 80/90Zr core A. Banu et al., PRC 72,

061305 (2005)

RQRPAA. Ansari et al., PLB 623, 37

(2005)EXP: ENSDF

AMDC sys

Extrapolated• B(E2) enhanced below A~114• correlation with reduced Z=50 shell gap and g9/2

-1d5/2 E2 excitation?• B(E2) evolution below N=56 ?

B(E2; 0+ → 2+)

E(2+) and B(E2;2+ 0+) in semi-magicvalence mirrors fpg and gdsh nuclei Experiment and shell model (SM/LSSM)

Moderate N=40 and Z=(38),40 gaps No N=64,66 nor 70 gapsbetween p1/2 and g9/2 orbits due to closely packed g7/2dsh11/2 orbits SM: A. Lisetskiy et al., PRC 70, 044314 (04) SM and

LSSM: O. Kenn et al., PRC 63,064306(01) LSSM: A. Banu et al., PRC 72 ,061305(05) O. Sorlin et al., PRL 88,092501(02) S. Lenzi et al., PRC 82,054301(10)

Z=28 N=50 Z=50

p,f5/2 g9/2p,f5/2 g9/2 s,d,g7/2 h11/2

No gap !

Apparent scaling of effective g9/22 two-body matrix

elements

S S S

• S = E(8+)-E(2+) ~ A-1 ?

• valence space pf5/2g9/2 ~ A-1/3

• Coulomb and pairing negligible

• Cross shell excitation different N=3, N=4, N=5 HO shells !

• Quadrupole interaction scales as EQ = O(D-1 A-1/3) , Degeneracy D M. Dufour and A. P.

Zuker, PRC54, 1641 (1996)

• Normalise to 98Cd LSSM in gds Frederic Nowacki, priv. comm.

Normalised to 2+ to minimise effect of

p1/2, Coulomb and pairing

9848Cd50

LSSM EXP

t=0 1 2 3 4 5

EX D A-1 A-1/3

76Ni 1428 1353 1336 1128

98Cd 1036 1036 1036 1036 (reference)

130Cd 803 785 781 943

Summary of status and outlook

• g9/2 isomerism, interaction, seniority scheme and distortions • core excitation across Z,N=50 and E2/E4 isomerism and strength• super Gamow-Teller decay and implication for shell structure• verification of general GT quenching factor ~0.75 for N=4 HO shell• robustness of Z=N=50 shells 3 MeV from the proton dripline • monopole driven evolution of single particle energies • shell structure evolution towards HO shell neighbours• A-1 scaling of empirical TBME• masses and half lives along the rp path• super-allowed decay close to N=Z

• experimental verification 100Sn gaps and single particle/hole energies• excited states and mirror symmetry in, below and beyond 100Sn• precision masses and GT strength along the rp path• precision studies of super-allowed Fermi decay and CVC hypothesis• proton emission below Z=50• super-allowed -decay at N=Z• realistic interaction beyond 0 ħ• consistent LSSM description of excitation and masses

Done:

To do:

Collaborations

EUROBALL I-IV, the home of European Gamma Arrays

RISING Rare ISotope INvestigation at GSI

EURICA EUroball Riken Cluster Array

PreSPEC Pre- (HI-DE-SPEC) campaign @GSI plus

AGATA Advanced Gamma Tracking Array

SM2 Strasbourg-Madrid Shell Model

Special thanks go to: A. Blazhev, P. Boutachkov, B.A. Brown, E. Caurier, T. Faestermann, M. Górska, Ch. Hinke, M. Hjorth-Jensen, G. Martinez-Pinedo, B.S. Nara Singh, F. Nowacki, T.

Otsuka, K. Sieja