In-source laser spectroscopy
at ISOLDE and IRIS (Gatchina):
New results and the problem of
hyperfine structure anomaly
A. Barzakh
Petersburg 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 stability
4. HFA in Au and Bi: some problems
5. HFA in Fr: determination of HFA
6. Urgent theoretical and experimental task to be solved
Pre-2003: Charge radii in the lead region
Pre-2012:
? 85At ?
?
?
?
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?
Hyperfine structure anomaly
HFA:
A1

A2

a  a point (1   )
a1  I1
1

2
a2  I 2
A1

A2
notation:
 ( A1   A2 )
I A aA
 A   A0  
 (1 
I A0 a A0
Theory:
1
A0
A1

A2
— RHFA
notation: ε — HFA
 A)
 ( A)  b2 s  km   r 2 m ( A)  d 2 ( A)
factorization:
atomic part: independent of A (b-factor)
nuclear configuration part
A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)
J.R. Persson, ADNDT 99 (2013) 62
Differential
DHFA:

A
n1l1 , n2 l2
hyperfine structure anomaly

Ratio n1l1 ,n2l2 may have a different
value for different isotopes because
the atomic states with different n, l
have different sensitivity to the nuclear
magnetization distribution.
A
A
n1l1
A
n2 l2
a
a
Tl: we have studied
state with p1/2 valence electron;
previously state with s1/2 valence
electron has been studied
nAl ,n l
1
n1l1
A1
 nA22l2 
11
nAl ,n l
2
11
DHFA
2 2
 1  A1  A2 (n1l1 )  A1  A2 (n2l2 )
2 2
J. 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)
Differential RHFA
DHFA
hyperfine structure
μ correction
anomaly
 (n1l1 )
  A1 A2
 (n2l2 )
A1
A2
pure atomic value!
Independent on A
A1
 A2 (n2l2 ) 
n1l1
A1
 nA22l2
 1
determination of RHFA without independent
high-accuracy μ-measurements
I A aA
 A   A0  
 (1 
I A0 a A0
A0
 A)
η(Tl; 7s1/2, 6p1/2)exp= 4.4(15)
η(Tl; 7p3/2, 6p1/2)exp= -15.6(2)
η(Tl; 7s1/2, 6p1/2)theor= 3.1
η(Tl; 7p3/2, 6p1/2)theor= -17
admixture of 6s6p7s configuration!
HFA in Tl: μ correction
Magnetic moments for Tl isomers with I=9/2
4.2
literature data
lit. data corrected on HFA
new data (with HFA correction)
, n.m.
4.1
205 203
 6 P1 / 2
4.0
205
3.9
 1.050(15) 10 4
7AS(1/2I 9/2) (exp)  2.3(5) 102
two orders of magnitude!
3.8
205
3.7
185
187
189
191
( I 9/2)
2
189
(
theor
)


1.8

10
7 S1/2
reasonable agreement of theory
(Mårtensson-Pendrill)
and experiment
193
195
197
A
I A a A (nl )
205 A
 A  205 

 (1   nl )
I 205 a205 (nl )
A. E. Barzakh et al. Phys. Rev. C 86, 014311 (2012)
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
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 (6p36p2 7s)? Or some “nuclear physics”?
M. R. Pearson, et al., J. Phys. G, 26 (2000) 1829
RHFA: Fr, experiment
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
1. RHFA for odd isotopes is of order 0.51% — comparable to the μ-errors (1%).
Should be taken into account!
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:
 ( A)  b2 s  km   r 2 m ( A)  d 2 ( A)
RHFA: Fr, theory
Calculation with MP-atomic constants and simple one-configuration
approximation for nuclear part, with assumption <r2>m= <r2>c.
 ( A)  b2 s  km   r 2 m ( A)  d 2 ( A)
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%
DHFA: Fr, 7p3/2 vs 7p1/2
Ratio sΔp3/2/ sΔp1/2 should be independent on A due to atomic-nuclear factorization
excluded from mean
Mean: sΔp3/2/ sΔp1/2=-3.65(42)
with η(7s,7p1/2)=3.0
η(7p3/2,7p1/2)=10.3(1.3)
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(7s )=-0.8(4)%
1/2
Extracted from ρ:
213Δ225(7s )=-0.80(27)%
1/2
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
Au
Large-scale atomic calculations of
η(6s 2S1/2, 6p 2P1/2) and b-factors for
6s 2S1/2, 6p 2P1/2 states
Experiment
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%).
Determination of a(7s 2S1/2) for
203,205Tl with the accuracy less than
0.5 MHz ( η with the accuracy of
10÷15%).
Tl
Bi
Large-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
Fr
Measurements of a(7p3/2) for
Large-scale atomic calculations of
207,221Fr to check dropdown points
η(7s, 7p1/2), η(7s, 7p3/2) and b-factors for
(and for some other isotopes with
7s, 7p1/2, 7p3/2 states
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 manybody 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) :



, I l
1
odd neutron, I  l
2
1
odd proton,
2
  1.2 102 ( 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).
P. A. Moskowitz and M. Lombardi, Phys. Lett. 46B (1973) 334
DHFA calculation
Atomic part: atomic many-body technique
(relativistic “coupled-cluster” approach) by A.-M. Mårtensson-Pendrill
 b4 s  d4  r 4 
  b2 s  m  d2 , m  r m  1 
 2 
 b2 s  d2  r 
2
Single shell-model
configuration:
(in Tl case:
pure h9/2 intruder state)

2

k


r
m
 m

2n
3


d 2 n  Cs   1 
  
 1  Cs  .
 2n  3  2n  3
gs gI  gL
2I  3

Cs 

4I
gI gs  gL
Odd-odd nuclei:
g g I  g
g g I  g
           ,    
,   
g I g  g
g I g  g
A.-M. Mårtensson-Pendrill, Phys. Rev. Lett. 74, 2184 (1995)