Neutron-rich lead isotopes provide hints on the role of the effective three-body forces

Jose Javier Valiente Dobón

Laboratori Nazionali di Legnaro (INFN), Italia

Overview

• Neutron-rich Pb nuclei beyond N=126• Experimental setup and challenges• Seniority Pb isomers the B(E2) probes• Effective 3-body forces• A puzzle: 210Hg• Summary

The Z=82 and beyond N=126

216Pb216Pb212Pb212Pb

218Pb218Pb

g9/2g9/2

.Taking advantage of these isomers we want to study the developmet of nuclear structure from 212Pb up to 218Pb and nearby nuclei

.Taking advantage of these isomers we want to study the developmet of nuclear structure from 212Pb up to 218Pb and nearby nuclei

• 5x106 pps• 2 HPGe detectors (Effγ=1%)• 350 ions implanted

GSI

M. Pfutzner, PLB 444 (1998) 32

Difficult region to explore: only fragmentation possible, primary

beam charge states!

Experimental challenges

FRS-Rising at GSI: stopped beam campaign

Target 2.5 g/cm2 Be

Deg. S1: Al 2.0 g/cm2

MONOCHROMATICDeg S2: Al 758 mg/cm2

S1

S2S3 S4

15 CLUSTERs x 7 crystals

εγ = 11% at 1.3MeV

Beam: 238U @ 1GevA

9 DSSSD, 1mm thick, 5x5 cm2 16x16 x-y strips

Experimental setup

• Fragment position: TPC, MWPC, Scintillators

• Time Of Flight TOF: Scintillators

• Atomic number: MUSIC

~70 m H. Geissel et al., Nucl. Instr. Meth. B70, 286 (1992)

Experimental setup II

90+

91+92+

212Pb

238U

238U

212Pb

S1S1

S2S2

S2

92+91+

90+

Charge state problem

Mocadi simulations

1 GeVA 238U beam from UNILAC-SIS at 109 pps

206Hg 210Hg209Tl 213Tl

212Pb 218Pb215Bi 219Bi

A/q

Z

Nuclei populated in the fragmentation

212,214,216Pb: 8+ isomer

214Pb: γγ coincidences

210Pb

The 8+ isomer is a seniority isomer, involving neutrons in the 2g9/2

214Pb212Pb 216Pb8+ X

8+ X

Ductu naturae

2g9/2

1i11/2

1j15/2

3d5/2

3d3/2

4s1/2

2g7/2

-3.94

-2.37-2.51

-3.16

-1.45-1.90

-1.40

S.p. energies (MeV) Shells

208Pb is the core (Z=82, N=126).

•For neutron-rich Lead isotopes, the N=6 major shell is involved

•No shells beyond the magic numbers for neutrons

N=126

N=184

N=7 major shell

Kuo-Herling interaction: Valence space

E.K. Warburton and B.A. Brown PRC43, 602 (1991).

th. expth. exp.

Calculations with Antoine and Nathan codes and K-H interaction

E.K. Warburton and B.A. Brown PRC43, 602 (1991).

th. th.exp.

210Pb

exp.

212Pb216Pb

214Pb

Shell Model calculations Kuo-Herling

218Pb

th.

K.-H:200nsK.-H:200ns

The neutron 2g9/2 shell has a dominant role for the 8+ isomeric state. 1i11/2 , 1j15/2 and 3d5/2 also play a role

210Pbn = 2

212Pbn = 4

214Pbn = 6

216Pbn = 8

218Pbn = 10

2g9/2 1.99 3.39 4.78 6.21 6.96

1i11/2 0.005 0.33 0.68 1.04 2.16

1j15/2 0.002 0.16 0.32 0.43 0.59

3d5/2 0.0008 0.04 0.08 0.11 0.14

8+ state wave functions: occupational numbers show quite pure wave functions

The ground state wave functions are in general more fragmented, with the 1i11/2 shell around 25 - 30 %

Occupationalnum

bersWave functions from Kuo-Herling

B(E2) calculated considering internal conversion coefficients, and a 20-90 keV energy interval for unknown transitions.

Reduced transition prob. B(E2)

B(E

2; 8

+ -

> 6

+)

A (Lead)

eν=0.8eν=0.8

Large discrepencies factor ~ 5

Large discrepencies factor ~ 5

210Pb 212Pb 214Pb 216Pb

Isomer t1/2 (μs) 0.20 (2) 6.0 (8) 6.2 (3) 0.40 (4)

B(E2) e2fm4 Exp. 47(4) 1.8(3) 1.4-1.9 24.7-30.5

B(E2) e2fm4 KH 41 8 0.26 16.4

Upper limit 90 keV based on Kα X rays intensity (K

electrons bound ~88 keV)

B(E2) ~ Eγ-5 (1+α)-1τ-1B(E2) ~ Eγ-5 (1+α)-1τ-1

• The results are roughly independent of the interaction used: KH, CD-Bonn, etc.

• One possibility is the mixing of states 6+ with different seniorites, but requires too large change of the realistic interaction Is not the case

• Seniority mixing with g9/2 seniority isomers also for the first g9/2

( neutrons: 70Ni - 76Ni, protons: 92Mo - 98Cd)

Origin of discrepancies

Seniority Mixing

Calculations by P. Van Isacker

ν=2ν=2ν=4ν=4

• The results are roughly independent of the interaction used: KH, CD-Bonn, Delta, Gaussian

• One possibility is the mixing of states 6+ with different seniorites, but requires too large change of the realistic interaction Is not the case

• Seniority mixing with g9/2 seniority isomers also for the first g9/2

( neutrons: 70Ni - 76Ni, protons: 92Mo - 98Cd)

So …..

• Need to introduce state-dependent effective charges?

• Caution when using renormalised interactions

Origin of discrepancies

Theory of effective interactions

Theory of effective interactions

Realistic collective nuclear H

Unified view

Effective 3 body interactions

Two body Three bodyUsually neglected!

One body

Effective 3-body terms appear naturally in the renormalization process, but they are NOT included in shell-model codes (ANTOINE and NATHAN):•Two-body operators (H) become effective 3-body operators•One-body transition operators (B(E2)) become effective 2-body operators

Effective three-body forces

Z=82 N=126h11/2 i13/2

2f7/22g9/2

π ν

In a perturbative approach, the bare g9/2 is «dressed» with p-h excitations from the 208Pb core

In a perturbative approach, the bare g9/2 is «dressed» with p-h excitations from the 208Pb core

...... ν shells above N=126π shells above Z=82

The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body force and 2-body operators is to diagonalize usign the dressed wave function. Expectation value of the Hamiltonian and of the transition operators is calculated directly between the dressed wave functions, thus also including the many-body terms otherwise neglected.

The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body force and 2-body operators is to diagonalize usign the dressed wave function. Expectation value of the Hamiltonian and of the transition operators is calculated directly between the dressed wave functions, thus also including the many-body terms otherwise neglected.

By allowing relevant p-h excitations from the core to the g9/2 shell to neutron shells above, we include the previuosly neglected terms

By allowing relevant p-h excitations from the core to the g9/2 shell to neutron shells above, we include the previuosly neglected terms

quasi-SU3quasi-SU3

Exp. data

g9/2(n-1) + ν shells

above + core exc.

g9/2(n-1) + ν shells above

g9/2

Standard eff. charges:

eν = 0.5, eπ = 1.5

Standard eff. charges:

eν = 0.5, eπ = 1.5

Effective 3-body interaction: Results

The explicit coupling to the core restores the conjugation

symmetry

The explicit coupling to the core restores the conjugation

symmetry

Kahana Lee Scott (KLS) interactionS. Kahana, Scott, Lee Phys. Rev. 185 (1969).A. Abzouzi, E. Caurier, and A.P. Zuker, Phys. Rev. Lett. 66, 1134,(1991).M. Dufour and A.P. Zuker PRC54 1641 (1996)

Bi-isomer in 210Hg

643

0

1196

663

• E3 (663keV) and E1 (20 keV) 106 suppression in the E1

643

553

663

(0+)

(2+)

(6+)(4+)

1366(8+)

?

T1/2 ~1 μs

Puzzle 210Hg

208Hg interaction: Al-Dahan et al., PRC80, 061302(R) (2009).

3- calculated particle-vibration coupling models.

1+? s1/2 d3/2: SM: 1.5 MeV

• Experiment with radioactive beam, with the in-flight technique. Several experimental challenges overcome.

• The neutron-rich region along Z = 82 was populated, enabling to study the nuclear structure in this region up to now unknown due to experimental difficulties

• The observed shell structure seems to follow a seniority scheme. However, a closer look reveals that the B(E2) values have an unexpected behaviour. B(E2) values are a sensitive probe to understand in detail the features of the nuclear force The mechanism of effective 3-body forces is general, and could be relevant also for other parts of the nuclide chart.

• Puzzle of the 210Hg Need of further studies

• Many more isomers: 217Bi, 211-213Tl, 213Pb and remeasured: 208Hg

Summary

A. Gottardo, G. Benzoni, J.J.V.D., R. Nicolini, E. Maglione, A.P. Zuker, F. Nowacki

A. Gadea, S.Lunardi, G. de Angelis, A. Bracco, D. Mengoni, A.I. Morales, F. Recchia, P. Boutachkov, L. Cortes, C. Domingo-Prado,F. Farinon, F.C.L. CrespiH. Geissel, , S. Leoni, B. Million, O. Wieland,

D.R. Napoli, E. Sahin, R. Menegazzo,J. Gerl, N. Goel, M. Gorska, J. Grebosz, E. Gregor, T.Haberman,I. Kojouharov, N. Kurz, C. Nociforo, S. Pietri, A. Corsi, A. Prochazka, W.Prokopowicz, H.

Schaffner,A. Sharma, F. Camera, H. Weick, H-J.Wollersheim, A.M. Bruce, A.M. Denis Bacelar, A. Algora, M. Pf¨utzner, Zs. Podolyak, N. Al-Dahan, N. Alkhomashi, M. Bowry, M. Bunce,A. Deo, G.F. Farrelly, M.W. Reed, P.H. Regan, T.P.D. Swan, P.M. Walker, K. Eppinger,S. Klupp, K. Steger, J.

Alcantara Nunez, Y. Ayyad, J. Benlliure, Zs.Dombradi E. Casarejos,R. Janik,B. Sitar, P. Strmen, I. Szarka, M. Doncel, S.Mandal, D. Siwal, F. Naqvi,T. Pissulla,D. Rudolph,R. Hoischen, P.R.P. Allegro,

R.V.Ribas, and the Rising collaboration

Università di Padova e INFN sezione di Padova, Padova, I; INFN-LNL, Legnaro (Pd), I; Università degli Studi e INFN sezione di Milano, Milano, I; University of the West of Scotland, Paisley, UK; GSI, Darmstadt, D; Univ. Of Brighton, Brighton, UK; IFIC,

Valencia, E; University of Warsaw, Warsaw, Pl; Universiy of Surrey, Guildford, UK; TU Munich, Munich, D; University of Santiago de Compostela, S. de Compostela, E; Univ. Of Salamanca, Salamanca, E; Univ. of Delhi, Delhi, IND; IKP Koeln, Koeln, D; Lund

University, Lund, S; Univ. Of Sao Paulo, Sao Paulo, Br; ATOMKI, Debrecen, H.

Collaboration

Reduced transition prob. B(E2)

PRC 80, 061302(R)208Hg

210Hg

Change in structure ?

Energy (keV)

210Hg isomers (1)

• Mixing between one ν=2 and two ν=4 states in 212,214Pb. The quadrupole matrix element to ν=4 states is more than five times the one to ν=2, and opposite in sign

• Even a small mixing (few %) would be enough to correct the B(E2) value for 212Pb

• One possibility is the mixing of states (6+) with seniority 4: need to modify the interaction

Seniority mixing?

ν=2ν=2ν=4ν=4

Calculations by P. Van Isacker

Building up collectivity

Quadrupole deformation can be generated by using a quadrupole force with the central field in the subspace spanned by a sequence of j = 2 orbits that come lowest by the spin-orbit splitting representing this relevant subspace a quasi-SU3. In the Cr region it happens something similar to what happens in the Island of inversion 32Mg.

32Mg20sd

p3/2f7/220

Cr40pf

d5/2g9/240

quasi-SU3

Effective 3-body forces

The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body forces and 2-body transition operators is

to diagonalize using the dressed wave function

The only way to include in a standard shell-model calculation (ANTOINE, NATHAN) the effective 3-body forces and 2-body transition operators is

to diagonalize using the dressed wave function

By allowing p-h excitations from the core to the g9/2 shell, we include the previuosly neglected terms

By allowing p-h excitations from the core to the g9/2 shell, we include the previuosly neglected terms

nnn gigg 2/912/13

12/92/9

02/7

12/11

12/7

02/7 fhff

N = 126 core break

Z = 82 core break

GQR

+coupling to 2+ (and 3-) excitations from

the core

Constant eν = 0.5, eπ = 1.5

Effective 3-body interactions

We «dress» the bare g9/2 with p-h excitations

from the 208Pb core

We «dress» the bare g9/2 with p-h excitations

from the 208Pb core

nnn gigg 2/912/13

12/92/9

02/7

12/11

12/7

02/7 fhff

N = 126 core break

Z = 82 core break

The only way to include in a standard shell-model calculation (ANTOINE,

NATHAN) the effective 3-body force and 2-body operators is to

diagonalize usign the dressed wave function

The only way to include in a standard shell-model calculation (ANTOINE,

NATHAN) the effective 3-body force and 2-body operators is to

diagonalize usign the dressed wave function

By allowing p-h excitations from the core to the g9/2 shell to neutron shells above, we include the previuosly neglected

terms

By allowing p-h excitations from the core to the g9/2 shell to neutron shells above, we include the previuosly neglected

terms

Two body

Three body

Usually neglected!

One body

• The neutron-rich Pb were populated, enabling to study the nuclear structure in this region up to now unknown due to experimental difficulties

• The observed shell structure seems to follow a seniority scheme: However, a closer look reveals that the B(E2) values have an unexpected behaviour. B(E2) values might be a sensitive probe to understand in detail the features of the nuclear force Seniority mixing; 3N forces, relevant valence space

• Future: Measurement of B(E2) of the 2+0+ in Pb and Hg using transfer reactions and DSAM (backing target)

Conclusions

BLF

TLF

PRISMA207Pb:TLF

Beam

Nucleons in a valence jn configuration behave according to a seniority scheme: the states can be labelled by their seniority ν

For even-even nuclei, the 0+ ground state has seniority ν = 0, while the 2+, 4+, 6+, 8+ states have ν = 2

In a pure seniority scheme, the relative level energies do not depend on the number of particles in the shell j

0+

2+

6+8+

4+

(2g9/2)20+

2+

(2g9/2)40+

2+

(2g9/2)60+

2+

(2g9/2)8ν = 0

ν = 2

SENIORITY SCHEME

6+8+

4+6+8+

4+6+8+

4+

The seniority scheme

Another possibility is the inclusion of 2p-2h excitations from the N=126 core. Calculations in BCS, but unable to reproduce results with shell-model codes

210Pb (νg9/2)4 same sign of (νg9/2)2,but smaller Slightly smaller B(E2)

212Pb (νg9/2)6 opposite sign of (νg9/2)4, same magnitude

Smaller B(E2): close exp. value

214Pb (νg9/2)8 same sign of (νg9/2)6, but 3 time larger

Larger B(E2): too large ?

Core excitations below N=126

Developing a new interaction with A. Zuker and F. Nowacki to break up the N=126 shell gap.

3N forces in the 208Pb region

215Pb_sett

Br1 - Br2

Z

217Pb_sett

Formation of many charge states owing to interactions with materialsIsotope identification is more complicated Need to disentangle nuclei that change their charge state after S2 deg.

(Br)Ta-S2 – (Br)S2-S4

DQ=0

DQ=+1

DQ=-1

DQ=-2

Br1 - Br2

Charge state selection

210Pb 212Pb 214Pb 216Pb

Isomer t1/2 (μs) 0.20 (2) 6.0 (8) 6.2 (3) 0.40 (4)

B(E2) e2fm4 Exp. 47(4) 1.8(3) 1.4-1.9 24.7-30.5

B(E2) e2fm4 KH 41 8 0.26 16.4

B(E2) calculated considering internal conversion coefficients, and a 20-90 keV energy interval for unknown transitions.

Reduced transition prob. B(E2)

Large discrepancies: -Seniority scheme-Shell model KH

Large discrepancies: -Seniority scheme-Shell model KH

Pure seniority scheme for g9/2

9 : 1 : 1 : 9

PLB 606, 34 (2005) ?

eν = 0.8

Theory of effective interactions

Instead of applying the perturbation theory to the operators involved in the problems, it is the wave function that is developed in a perturbative

manner. The idea is to start from a bare many-body state and then dress it, giving origin to a quasiconguration.

Nuclear shell theory Amos-de-Shalit I. Talmi

In una singola j-shell la seniorità si mescola solo se si mescolano le seniorità 1 e 3. Tuttavia nelle j-shell minori di 9/2 è impossibile avere due stati con lo stesso momento angolare e seniorità 1 e 3, per cui non ci può essere mescolamento fra queste due seniorità e quindi fra nessuna seniorità sotto j=9/2.

R-process pathR-process path

The Z=82 and beyond N=126

I.N. Borzov PRC67, 025802 (2003)

Experimental β-decay data needed around 208Pb to validate theoretical models.

Experimental β-decay data needed around 208Pb to validate theoretical models.

Beta-decay spectroscopy

• Background sources: δ-electrons, β-decay electroncs from other sources, “false” β decays/implantations

• Standard exponential fits/novel numerical procedure [1]

[1] T. Kurtukian-Nieto et al., NIMA 67, 055802 (2008)

Uncorrelated events are determined from backward

time-beta correlations

Beta-decay spectroscopy

New spectroscopic data on 219Po.

New spectroscopic data on 219Po.

FRDM+QRPA and(selfconsistent) DF3 + QRPA

models are in agreement with experimental data.

FRDM+QRPA and(selfconsistent) DF3 + QRPA

models are in agreement with experimental data.