through nuclear moment measurements Studies of the structure of exotic nuclei Dimiter L. BALABANSKI

Dimiter L. BALABANSKI

Studies of the structure of exotic nuclei through nuclear moment measurements

• results from g-RISING at GSI

• “the island of inversion” at GANIL

• towards studies with ISOL beams at ISOLDE

Nuclear moment measurements

magnetic moment (  ) quadrupole moment (Q)

single-particle configuration (configuration mixing)

collective properties

(deformation, effective charges)

Spin-oriented beams

nuclear electromagnetic moments

What do we learn from these experiments ?

Spin-aligned and spin-polarized beams

definitions

m

-2 –1 0 +1 +2

spin-alignment

m

-2 –1 0 +1 +2

spin-polarization

Hyperfine interactions

Information about the interaction

of the probe with the lattice.

basic definitions

Nuclear magnetic dipole moment

 = g I 

_N

 = <j, m=j | 

_z

| j,m=j>

 = g

_l

.l + g

_s

.s

 ( I ) = < I , m= I | (

^li

.

^{zi si}

.

^iz

)

i

g l  g s

 | I ,m= I >

π: g

_s

= 5.585, g

_l

= 1

ν: g

_s

= 3.826, g

_l

= 0

 = <j, m=j | 

_z

| j,m=j>

 (j= l + 1/2) =       j  1 2    g

^l

 1 2 g

^s

   

^N

 (j= l -1/2) =

3 1

1 2

^l

2

^{s N}

j j g g

j                

some more definitions

Magnetic dipole moment in atomic nuclei

Z.Phys. 106, 358 (1937)

Deformed nuclei

prolate core polarization oblate core polarization

yet more definitions

Electric quadrupole moment in atomic nuclei

2 2

(3. )

i i i

i

e z  r

 =

^{i i}

2 2 ( ,

^{i i}

)

i

e r Y  



^.

Q =

I m ,  I Q

₂⁰

I m ,  I

Q( j ) =

2 1

2

2( 1)

j j

e j r

j

 



theory

The Nilsson model

The spherical shell model provides an excellent description of nuclei close to closed shells. However, the large body of evidence that points toward the existence of deformed nuclei necessitates a model that uses a deformed nuclear potential. One such potential is the modified harmonic- oscillator potential, which was first used by Nilsson to investigate the effect of deformation on the single-

particle orbits.

Fragmentation at relativistic energies

abrasion ablation

v/c > 0.3

(GANIL, RIKEN, MSU)

What are the magic numbers far away from stability ?

or

• Does the spin-orbit change ?

• Does other terms of the

nucleon-nucleon potential

Example I:

The “island of inversion” around 32 Mg

GANIL, Caen (Normandie)

Fundamental nuclear properties:

moments and spins of exotic nuclei

three major developments in the 90

^ies

:

1. Production andspin-orientation

via projectile fragmentation

K. Asahi et al., PLB 251 (1990) 488 K. Asahi et al., PRC 43 (1991) 456

2. Selection via high-resolution in-flight separation

LISE, RIPS, A1200, …

3. Ab initio calculations of EFGs, Hyperfine Fields, …

WIEN97

P. Blaha et al., HFI 96/97 (1996)3

Fragmentation at intermediate energies

NMR experimental set up TDPAD set up

Oriented and polarized spin ensembles

m

-2 –1 0 +1 +2

m

-2 –1 0 +1 +2

spin-alignment

spin-polarization

definitions

Basic principles for moment measurements

(ground states of nuclei)

how to approach

Principle of nuclear magnetic resonance

the “island of inversion”

35 Si

Example II:

Experiments at relativistic energies (gRISING @ GSI)

1. Spin-alignment in projectile fission and g-factors around

¹³²

Sn

(Gerda Neyens and Gary Simpson)

EXPERIMENTS performed Oct – Dec. 2005

Sn

238U-fragmentation at 1 GeV/u

238U-fission at 750 MeV/u

2. Spin-alignment and g-factor of isomers in the neutron deficient Pb-region.

(Adam Maj and Juergen Gerl)

3. Spin-alignment and g-factors of isomers in

^127,128

Sn from fragmentation of a

136

Xe beam. (Dimiter Balabanski and Michael Hass)

136Xe-fagmentation at 700 MeV/u

Ilie et al, PL B687, 305 (2010)

Atanasova et al, EPL 91, 420 (2010)

THE EXPERIMENTAL SET-UP AT GSI: g-RISING

Spin-aligned secondary beam selected (S2 slits + position selection in SC21)

SC41 gives t=0 signal for -decay time measurement Implantation: plexiglass degrader + 2 mm Cu (annealed)

SC42 and SC43 validates the event

MW1

MW2 music

SC43 veto Al degrader

SC41 start slits

Pb-wall

BEAM

Ge clusters

Principle

Fragmentation :

~300

⁴³

S/sec

B

I(t)

H = - µ B H = g.I B

R(t)

G - B G + B

R(t) = A cos( w t+ f ) w = -gB

FRS@GSI

LISE@GANIL

BigRIPS@RIKEN

PROJECTILE FRAGMENTATION selection in longitudinal momentum + (slits in FRS or via ion-correlation)

The experimental method

61Fe YIELD

61Fe

ALIGNMENT(%)

+6.2(7)%

-15.9(8)%

61Fe

61Fe

CONDITION:

STRIPPED FRAGMENTS !

Part II: GANIL experiments

The

¹³⁶

Xe fragmentation experiment

Z

₁₂₇

Sn

128Sn

127Sn 4.5(3) s

-ray spectra gated on 127 Sn

1095 keV 715 keV

FFT TDPAD

715 keV

Structure of the 19/2

⁺

isomer in

¹²⁷

Sn

• the spin-parity assignment of the 19/2

⁺

isomer is based on energy systematics

J. Pinston et al., PRC 61, 024312 (2000)

• suggested configuration: (ν h

_11/2^{ 1}

 5

^

)

_19/2

+; g

_exp

( h

_11/2

) = 0.24

• the 5

^

isomers in even-even Sn isotopes take experimental values: g

_exp

(5

^

)  0.06 and are understood as an admixture of (ν h

_11/2^{ 1}

d

_3/2^{ 1}

)

₅

- with g

_emp

= 0.26

(ν h

_11/2^{ 1}

s

_1/2^{ 1}

)

₅

- with g

_emp

= 0.09

• for the structure of the 19/2

⁺

isomer an admixture with the ν g

_7/2^{ 1}

h

_11/2^{ 2}

configuration is suggested in order to explain the l -forbidden M 2 isomer-decay transition.

g

_emp

(ν s

_1/2^{ 1}

h

_11/2^{ 2}

) = 0.15

g

_emp

(ν g

_7/2^{ 1}

h

_11/2^{ 2}

) = 0.23

g (

¹²⁷

Sn; 19/2

⁺

) = 0.17(2)

g (

¹²⁸

Sn; 10

⁺

) = + 0.20(4)

SM I SM II

Example III:

Towards experiments with ISOL beams

Why transfer reactions ?

98

Mo

⁹⁹

Mo

100

Tc

100

Mo

¹⁰¹

Mo

102

Tc

63

Cu

⁶⁴

Cu

65

Zn

65

Cu

⁶⁶

Cu

67

Zn

P P

Principle investigators:

Georgi Georiev (Orsay) and DLB (Sofia)

The future: Moments in transfer reactions with RIBs

(d,p) reaction, Tandem-ALTO, Orsay

Q

_s

(

⁶¹

Fe; 9/2

⁺

)= 41(6); 

₂

> 0

Q

_s

(

⁶⁵

Cu; 3/2

⁻

) = −19.5(4); 

₂

< 0

Q add = Q  Q  = 21.5(60) efm 2

quadrupole moments in transfer

R. Lozeva et al, PLB 694, 316 (2011)

classical view quantum-mechanical view

Pop ulat io n

I = 2

E

m =2 m =1 m =0

m =-1 m =-2

I=2 ensemble

Necessary to induce polarization of the beam prior the measurement

ISOL снопове

ISOLDE – CERN

SPIRAL2 – GANIL

Studies of nuclear moments with ISOL

beams at ISOLDE at CERN

Rex-ISOLDE @ CERN

Polarized post-accelerated ISOL

beams? – Why not…

Polarized beams at HIE-ISOLDE – from dreams to reality.

G. Georgiev¹, M. Hass², A. Herlert³, D.L. Balabanski⁴, L. Hemmingsen⁵, K. Johnston³, M. Lindroos³, K. Riisager⁶, J. Van de Walle³, D. Voulot³, F. Wenander³, W.-D. Zeitz⁷

1. CSNSM, Orsay, France; 2. The Weizmann Institute, Rehovot, Israel; 3. ISOLDE, CERN, Geneva, Switzerland;

4. INRNE, BAS, Sofia, Bulgaria; 5. IGM, LIFE, University of Copenhagen, Denmark; 6. Department of Physics and Astronomy, University of Aarhus, Denmark; 7. Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Germany

Polarized beams – WHY?







 





 







 











 





 





 





 

d p p d

d d

d d d

d A_y









Precise test of the nuclear models for exotic nuclei:

• transfer reactions (analyzing power)

• Coulomb excitation – spin/parity;

multiplicity assignments etc.

• nuclear moments – proton/neutron character, angular momentum j

12





 j 

Can one do it and how?

Tilted Foils - the principles:

• atomic polarization  nuclear polarization

• higher nuclear spins  higher polarization (>10% achieved so far)

• strong velocity dependence

(poorly studied up to now)

- unique opportunity

What do we need to achieve it?

3 MeV/u and 0.3 MeV/u

-NMR setup from HMI Berlin transferred to ISOLDE

• gain of complete control on the TF polarization

• nuclear structure (moments, reactions …),

nuclear methods in the solid-state physics,

biophysics etc. …

This work wouldn’t have been possible without the efforts of my friends

Georgi Georgiev (Orsay),

Radomira Lozeva (Strasburg), Deyan Yordanov (CERN),

Gerda Neyens (Leuven),

Micha Hass (Rehovot), and