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Shell model studies along the N~126 line Zsolt Podolyák

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“Shell-model” nuclei Shape transition, triaxiality N Z L.M. Robledo et al., J. Phys. G. 36, (2009). H. Grawe, K. Langanke, G. Martinez-Pinedo, Rep.Progr.Phys.70 (2007)1525.

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Isomeric states around 208 Pb 208 Hg, 209 Tl N. Aldahan et al., PRC80, (R) (2009). Isomeric state RISING: isomeric decays S. Steer et al., Int. J. Mod. Phys. E18, 759 (2009) and to be published ■ ■ * A. Gottardo et al.

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In box: E(4 + )/E(2 + ) ratio Even-even nuclei around 208 Pb

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π ν In the beta decay of the r-process path nuclei: The FF ν i 13/2 -> πh 11/2 dominates; also GT νh 9/2 ->πh 11/2

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Zs. Podolyák et al., Phys. Lett. B 672 (2009) 116. Internal charged particle decay Internal gamma decay 205 Au: three proton-hole nucleus Gammas following beta decay AIDA will do much better with conversion electrons

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Shell-model calculations (M.Górska, H.Grawe, H. Maier, A.Brown) (a)and (d):TBME from L.Rydstrom et al, NPA512(1990)217 (based on Kuo-Brown interaction) (b) and (c): three TBMEs modified Δ(d 3/2 h 11/2 ; d 3/2 h 11/2 ) 7- = +135 keV Δ(s 1/2 d 5/2 ; s 1/2 d 5/2 ) 2+,3+ =+230 keV (monopole only) Δ(d 3/2 h 11/2 ; s 1/2 h 11/2 ) 6- changed to MeV (fit for B(E2) Good description of energies and B(EL)s S.Steer et al., Phys. Rev C78 (2008) (R)

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Variation of key non-diagonal TBME to fit E2 strengths. The effective proton charge used in the SM is 1.35 e which is smaller than the adopted value of 1.5 e. Note that the upper experimental limit for the 7- → 5- is increased by a factor of about five if the (unknown) transition energy is below the Pt M edge. The vertical dashed line represents the adopted TBME value, which is given in MeV.

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203Ir b) modified; a) original

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Effective charges: 1.5e for E2 and 2.0e for E3 (to reproduce 206Hg) Transition strengths in N=126 nuclei Good description of N=126 nuclei after small modifications of TBMEs 203Ir B(E2:23/2+->19/2+) 0.02(1) b)

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N=125; Z= Pt

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Structure: N=126 nuclei ( 205 Au, 204 Pt, 203 Ir) changes in TBME helps/needed N=128 nuclei ( 208 Hg, 209 Tl) agreement with shell model N<126 nuclei ( 203 Pt etc) shell model has difficulties Conclusions

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Approved experiment on the book 205 Au: beta decay from 205 Pt => will fix the πs 1/2 orbital 203 Ir: beta decay from 203 Os (νg 9/2 ) => will fix the πd 3/2,πs 1/2,πh 11/2 202 Os: isomeric decay I=(5),(7),(10) 202 Os: beta decay of 203 Ir (νg 9/2 ) 3/2+ 0 1/ / Au 202 Os shell model +fast-timing measurements: 206 Hg: 7 - -> 5 - ~1.2ns(1W.u.) … Future

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Shell-model calc. (H. Grawe) TBME: from E.K. Warburton, PRC44, (1991) 233; are based on the Kuo-Herling realistic int. Single particle energies: 207 Tl and 209 Pb exp.

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( νg 2 9/2 ) states; 2 + mixed with πs -1 1/2 d -1 3/2 B(E2)=1.22 W.u. SM B(E2)=1.95(39)-1.58(22) W.u. exp. 208 Hg: Isomer: 8 + ( νg 2 9/2 )

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209 Tl : Isomer: 17/2 + ; ( νg 2 9/2 ) (πs -1 1/2 ) 17/2 + ->13/2 + Δ 13/2 + ->9/ keV 9/2 + ->7/2 + Δ, allowed M1 7/2 + ->3/ keV 3/2 + ->1/ keV E2(+M1) B(E2)=0.96 W.u. SM B(E2)=1.87(22)-1.51(18) W.u. exp. 209Tl: previously from (t,α) and alpha decay. (t,α): C. Ellegaard, P.D. Barnes and E.R. Flynn, Nucl. Phys. A259 (1976) 435.

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N. Aldahan et al., Phys. Rev. C80, (R) (2009).Theory: H. Grawe N=128 nuclei: energies in 208 Hg, 209 Tl are OK problems with transition strengths

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-single-particle energies are taken from the experimental spectra of 207Tl and 209Pb. -TBME are from E.K. Warburton, Phys. Rev. C44, (1991) 233 ; are based on the Kuo-Herling realistic interaction for pp and nn TBME derived from a free nucleon-nucleon (NN) potential with core polarisation renormalisation due to the finite model space. Standard shell-model calculations for N≥126,Z≤82 Problems: -energies and ordering of states in 204 Pt, 205 Au and others -problems with transition strengths in 204 Pt, 205 Au, 208 Hg, 209 Tl

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Aim: measure B(E2; 0+->2+) via Coulomb excitation

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H. Grawe, K. Langanke, G. Martinez-Pinedo, Rep. Prog. Phys. 70, 1525 (2007) The FF ν i 13/2 -> πh 11/2 dominates; also GT νh 9/2 ->πh 11/2 Half-lives of neutron-rich N~126 nuclei N=126 r-process path nuclei

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( νg 2 9/2 ) states; 2 + mixed with πs -1 1/2 d -1 3/2 B(E2)=1.22 W.u. SM B(E2)=1.95(39)-1.58(22) W.u. exp. N=128 nucleus 208 Hg: Isomer: 8 + ( νg 2 9/2 ) Shell-model calc. (H. Grawe) TBME: from E.K. Warburton, PRC44, (1991) 233; based on the Kuo-Herling realistic int. Single particle energies: 207 Tl and 209 Pb exp.

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N=128 nucleus 209 Tl : Isomer: 17/2 + ; ( νg 2 9/2 ) (πs -1 1/2 ) 17/2 + ->13/2 + Δ 13/2 + ->9/ keV 9/2 + ->7/2 + Δ, allowed M1 7/2 + ->3/ keV 3/2 + ->1/ keV E2(+M1) B(E2)=0.96 W.u. SM B(E2)=1.87(22)-1.51(18) W.u. exp. 209Tl: previously from (t,α) and alpha decay. (t,α): C. Ellegaard, P.D. Barnes and E.R. Flynn, Nucl. Phys. A259 (1976) 435.

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N. Al-Dahan et al., Phys. Rev. C80, (R) (2009).Theory: H. Grawe energies in 208 Hg, 209 Tl are OK small (?) problems with transition strengths => Good description of N=128 nuclei

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~1/(Δl+Δn) N>126, Z<82 nuclei Mass measurement of 208 Hg (GSI storage ring) L. Chen et al., PRL102 (2009) proton neutron i13/2 i11/2 g9/2 Z=82 N=126 s1/2 p1/2 d3/2 f5/2

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Shell-model calculations (M.Górska, H.Grawe, H. Maier, A.Brown) (a)and (d):TBME from L.Rydstrom et al, NPA512(1990)217 (based on Kuo-Brown interaction) (b) and (c): three TBMEs modified Δ(d 3/2 h 11/2 ; d 3/2 h 11/2 ) 7- = +135 keV Δ(s 1/2 d 5/2 ; s 1/2 d 5/2 ) 2+,3+ =+230 keV (monopole only) Δ(d 3/2 h 11/2 ; s 1/2 h 11/2 ) 6- changed to MeV (fit for B(E2)) Good description of energies and B(EL)s if TBMEs modified S.J. Steer et al., Phys. Rev C78 (2008) (R)

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Protons Neutrons Z =126 i

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