In-source laser spectroscopy at ISOLDE and IRIS (Gatchina): New results and the problem of

hyperfine structure anomaly

A. BarzakhPetersburg Nuclear Physics Institute, Gatchina, Russia

on behalf of Windmill-ISOLTRAP-RILIS collaboration

In-source laser spectroscopy at ISOLDE and IRIS

1. Brief review of the last results in lead region (At, Bi, Au, Hg chains)

2. Reminder on the HFA problem and the recently proposed method of experimental HFA study

3. HFA in Tl: first attempt to measure HFA rather far from stability4. HFA in Au and Bi: some problems5. HFA in Fr: determination of HFA6. Urgent theoretical and experimental task to be solved

Pre-2003: Charge radii in the lPre-2003: Charge radii in the lead region

?

? 85At ?

Pre-2012: Charge radii in the lPre-2012: Charge radii in the lead region

preliminary results!

?

?

IRIS, Bi isotopes: radii

big isomer shift:different deformation for g.s. and m.s. (intruder states)

big odd-even staggering;start of departure from spherical trend?

1 2 1 1 2

1 2 2

1A A a I

a I

HFA:

Hyperfine structure anomaly

(1 )pointa a 1 2

1 2( )A AA A

0

0

0 0

(1 )A AA AA A

A A

I a

I a

atomic part: independent of A (b-factor) nuclear configuration part

22 2( ) ( ) ( )s m mA b k r A d A Theory:

A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)

notation: — RHFA1 2A A

notation: ε — HFA

22 2( ) ( ) ( )s m mA b k r A d A

factorization:

J.R. Persson, ADNDT 99 (2013) 62

1 1

1 1 2 2

2 2

,

An lA

n l n l An l

a

a

DHFA:

1

1 1 2 21 1 2 2 1 2 1 2

1 2 2

1 1 2 2

,

1 1 2 2

,

1 ( ) ( )An l n ln l n l A A A A

A A An l n l

n l n l

Ratio may have a different value for different isotopes because the atomic states with different n, l have different sensitivity to the nuclear magnetization distribution.

1 1 2 2,An l n l

Differential hyperfine structure anomaly

Tl: we have studiedstate with p1/2 valence electron;previously state with s1/2 valence electron has been studied

DHFAJ. R. Persson, Eur. Phys. J. A 2, 3 (1998)J. S. Grossman, et al., Phys. Rev. Lett. 83, 935 (1999)J. Zhang, et al., PRL 115, 042501 (2015)

1 2

1 2

1 1

2 2

( )

( )

A A

A A

n l

n l

1 1 2 2

1 21 22 2( )

1

n l n lA AA A n l

pure atomic value!Independent on A

Differential hyperfine structure anomaly

determination of RHFA without independent high-accuracy μ-measurements

η(Tl; 7p3/2, 6p1/2)exp= -15.6(2)

η(Tl; 7p3/2, 6p1/2)theor= -17

admixture of 6s6p7s configuration!

η(Tl; 7s1/2, 6p1/2)exp= 4.4(15)

η(Tl; 7s1/2, 6p1/2)theor= 3.1

Differential hyperfine structure anomalyDifferential hyperfine structure anomalyDHFA RHFA μ correction

0

0

0 0

(1 )A AA AA A

A A

I a

I a

185 187 189 191 193 195 197

3.7

3.8

3.9

4.0

4.1

4.2

literature data lit. data corrected on HFA new data (with HFA correction)

, n

.m.

A

Magnetic moments for Tl isomers with I=9/2

205205

205 205

( )(1 )

( )AA A

A nl

I a nl

I a nl

HFA in Tl: μ correction

42036

205 10)15(050.12/1

P

1/2

205 ( 9/2) 27 ( ) 2.3(5) 10A IS exp

two orders of magnitude!

1/2

205 189 ( 9/2) 27 ( ) 1.8 10IS theor

A. E. Barzakh et al. Phys. Rev. C 86, 014311 (2012)

reasonable agreement of theory (Mårtensson-Pendrill) and experiment

DHFA: Au

RHFA in Au may be greater than 10%. To extract μ properly one needs in

calculation/measurement of η-factor. Measurement of η is possible for 196,198,199Au where precise independent μ-values are available ( RHFA).

DHFA: Bi

M. R. Pearson, et al., J. Phys. G, 26 (2000) 1829

very strange behaviour; usually RHFA for identical nuclear configuration with close μ’s is of order 10-3÷10-4. Sharp increase of atomic factor for atomic open p-shell (6p36p2 7s)? Or some “nuclear physics”?

RHFA: Fr, experiment

1. RHFA for odd isotopes is of order 0.5-1% — comparable to the μ-errors (1%). Should be taken into account!

22 2( ) ( ) ( )s m mA b k r A d A

2. Marked difference in ρ (i.e. in Δ) for odd and even isotopes was found previously in: J. S. Grossman, et al., Phys. Rev. Lett. 82, 935 (1999). It was attributed to the larger radial magnetization distribution of the unpaired neutrons, i.e. to the change in <r2>m:

22 2( ) ( ) ( )s m mA b k r A d A

1. Precise hfs-data: 7s1/2, 7p1/2, 7p3/2, 8p1/2, 8p3/2

(7p1/2: R. Collister, et al., PR A 90, 052502 (2014); J. Zhang, et al., PRL 115,

042501 (2015) & 7s1/2: A. Voss et al., PR C 91, 044307 (2015) )

2. Atomic calculations (for 7s1/2, 7p1/2 states)

(A.-M. Mårtensson-Pendrill, Hfi 127 (2000) 41: scaling Tl results!)

η(Fr; 7s1/2, 7p1/2 )theor=3.0 & ρexp experimental 210ΔA

Calculation with MP-atomic constants and simple one-configuration approximation for nuclear part, with assumption <r2>m= <r2>c.

RHFA: Fr, theory

Odd-even Δ-staggering is fairly explained without assumptions of the larger radial magnetization distribution for neutrons.

Deviations may be connected with the oversimplification of the nuclear part and/or with the nuclear configuration mixing for odd-odd nuclei.

prediction: 210Δ201(I=9/2)=-0.8%

210Δ201(I=1/2)=+1.5%

22 2( ) ( ) ( )s m mA b k r A d A

DHFA: Fr, 7p3/2 vs 7p1/2

excluded from mean

Ratio sΔp3/2/ sΔp1/2

should be independent on A due to atomic-nuclear factorization

Mean: sΔp3/2/ sΔp1/2

=-3.65(42)

η(7p3/2,7p1/2)=10.3(1.3)

with η(7s,7p1/2)=3.0

HFA for p3/2 state is ten times greater than for p1/2 state!

(cf. similar increase in Tl; some configuration mixing in Fr too?)

This systematics also points to the necessity to remeasure a(7p3/2) for 207,221Fr to check dropdown points on this plot

RHFA: Ra, experiment

Data for a(7s1/2) and a(7p1/2) in Ra II were used;

η(Ra II; 7s1/2, 7p1/2) was fixed to η(Fr; 7s1/2, 7p1/2)= 3

Direct measurement:213Δ225(7s1/2)=-0.8(4)%

Extracted from ρ:213Δ225(7s1/2)=-0.80(27)%

η(Ra II; 7s1/2, 7p1/2)exp=3(3)

S.A. Ahmad, et al., Nucl. Phys. A483, 244–268 (1988) W. Neu, et al., Z. Phys. D 11, 105–111 (1989)

HFA: urgent theoretical & experimental tasks

Atomic theory Experiment

AuLarge-scale atomic calculations of η(6s 2S1/2, 6p 2P1/2) and b-factors for 6s 2S1/2, 6p 2P1/2 states

Determination of a(6p 2P1/2) for 196,198,199Au with the accuracy less than 2÷3 MHz ( η with the accuracy of 5÷10%).

Tl

Determination of a(7s 2S1/2) for 203,205Tl with the accuracy less than 0.5 MHz ( η with the accuracy of 10÷15%).

BiLarge-scale atomic calculations of b-factors for 6p3 4S3/2, 6p27s 4P1/2 states

Check the unusual behaviour of ρ(6p3 4S3/2, 6p2 7s 4P1/2) for 205,213Bi

At

Large-scale atomic calculations of b-factors for 6p5 2P3/2, 6p4 7s 4P3/2 (46234 cm-1), 6p4 7p (?) (J=3/2, 58805 cm-1) states

Experiments with better resolution to determine ρ’s with better accuracy

FrLarge-scale atomic calculations of η(7s, 7p1/2), η(7s, 7p3/2) and b-factors for 7s, 7p1/2, 7p3/2 states

Measurements of a(7p3/2) for 207,221Fr to check dropdown points (and for some other isotopes with unrealistic

sΔp3/2: 205,210Fr)

Fr & Ra: η determination

Ratio of the electron density at the nucleus for s1/2 and p1/2 states:

1/(αZ)2=2.9 for Z=81(Tl).

Bohr & Weisskopf one-electron formulas:

η(Tl; s1/2, p1/2)BW=3.0 — fairly corresponds to Mårtensson many-

body calculations: η(Tl; s1/2, p1/2)M=3.1.

η(Fr; s1/2, p1/2)BW=2.51 (rather than 3.0 as quoted in: Hfi 127

(2000) 41 — should be checked!)

η(Ra+; s1/2, p1/2)BW=2.43

Au: μ determination

Previously empirical Moskowitz-Lombardi rule was used for HFA estimation in Au (and, therefore, μ determination) :

P. A. Moskowitz and M. Lombardi, Phys. Lett. 46B (1973) 334

2

1 1, , ,

2 2

1.2 10 ( )

I l odd neutron I l odd proton

Au

However, it was shown recently that this rule is (at least) not universal: J. R. Persson, Hfi 162, 139 (2005).Therefore, all previously determined hfs-μ values should be revised taking into account experimentally measured DHFA( RHFA).

42 24 4

2 2 22 2

, 1 ss m m m m m

s

b d rb d r k r

b d r

I

I

4

32

Ls

LI

I

ss gg

gg

g

gC

DHFA calculationAtomic part: atomic many-body technique

(relativistic “coupled-cluster” approach) by A.-M. Mårtensson-Pendrill

2

2 31 1 .2 3 2 3n s s

nd C C

n n

Single shell-modelconfiguration:

(in Tl case: pure h9/2 intruder state)

A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)

Odd-odd nuclei:

, ,I I

I I

g g g g g g

g g g g g g