Transcript Charge radii of medium-mass nuclei using the atomic physics

below
Charge radii of medium-mass nuclei
using the atomic physics input
Magdalena Kowalska
CERN, PH-Dept.
[email protected]
Outline
Laser spectroscopy on radioactive nuclei
Optical isotope shifts
A long way from isotope shifts to charge radii
Take-home message
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Charge radii from optical transitions
 A, A'  ( K NMS  K SMS ) 
m A'  m A
 F  r 2
m A' m A
Atomic factors: (normal and specific mass shift, F-factor
(main source of uncertainties)
Cocolios et al,
Phys. Rev. Lett,
106, 052503 (2011)
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A, A '
Laser spectroscopy on radionuclides
Blue – since 1995
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Collinear laser spectroscopy
Why collinear? Ions at RIB facilities come out as a beam,
so laser-ion interaction is longest in (anti) collinear geometry
Laser beam,
Laser on fixed frequency
Charge exchange region
(if needed)
Ion beam
Retardation zone
Excitation / Observation region
Electrostatic
deflection
Detection method depends on chemical element
or even isotope => optimised for best S/N ratio:
- photon detection: all nuclei
- beta asymmetry: short-lived nuclei
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- collision reionisation: noble gases
Review: B Cheal and K T Flanagan 2010 J.
Phys. G: Nucl. Part. Phys. 37 113101
Optical isotope shifts
What is measured? (independently for each isotopes)
 Laser frequency of resonance (including HFS) in laboratory frame (often: moving
ions/atoms)
 Or accelerating high voltage at which ion/atom beam is in resonance with laser
What is needed to extract differences in charge radii?
 Frequency difference (HFS centroid) for 2 isotopes at rest
Conversion for ion beams (Collinear laser spectroscopy):
 Uncertainty in all input values contributes
 Statistical – collected statistics, quality of fit (especially for HFS)
 Systematic: precision and accuracy of atomic masses and measuring devices (laser
frequency and accelerating voltage)
set laser frequency (Wavemeter or frequency comb)
Accelerating voltage
(voltage divider + voltmeter)
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atomic masses
Optical isotope shifts - uncertainties
Uncertainties:
 Statistical – collected statistics, quality of fit (especially for HFS)
 Systematic: precision and accuracy of atomic masses and measuring devices
set laser frequency (Wavemeter or frequency comb)
Accelerating voltage
(usually voltage divider +
voltmeter)
atomic masses
Mg+, 2006 data
Systematic uncertainties
much larger than statistical
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From isotope shifts to charge radii
 A, A'  ( K NMS  K SMS ) 
Due to reduced mass of nucleus-e- system
and correlations between e-’s.
m A'  m A
 F  r 2
m A' m A
A, A '
Proportional to (change in) e- density at nucleus.
Semi-empirical or ab initio methods.
Ab initio methods or “King plot”.
 From HFS: all inner e’s are paired off in alkali-like atom and make no contribution to
magnetic HFS. HFS directly proportional to density of ns e- at point nucleus
A: HFS constant for ns e: correction for finite size of nucleus
e – HFS anomaly
g’ – reduced g factor of nucleus
 Goudsmit-Fermi-Segre formula:
ns electron density at nucleus is related to effective quantum number of ns level
Screening effects:
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K_MS: Modified King plot
When data for at least 3 isotopes exists (i.e stable isotopes) partial help is there!
 Combine absolute radii (transitions in muonic atoms or electron scattering) and
isotope shifts in optical transition
Usually resulting uncertainties too large -> so use F from semi-empirical or ab
ignition approaches
e.g. for Ne
A good side effect:
offset in accelerating voltage
 Scales with mass like mass shift
 -> can incorporate it in K_MS
Result: Determine K_MS and F
 usually too large uncertainties
 So: use calculated F
Modified isotope shift
Offset: K_MS
Slope: F
A, A’
A, A’’
0
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Modified difference in charge radii
From isotope shifts to charge radii
It is not that easy:
Many correlated systematic effects
 In IS – accelerating voltage
 In King-plot: Muonic data
Inconsistent values from ab initio atomic theory and other approaches
Large uncertainties in F and K_MS, whichever approach taken
Which F and K_MS to use?
Resulting radii trend must be the final judge:
 Consistent with radii trends of neighbouring chains
 Consistent with nuclear structure known from other observables
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Some examples
Below medium-mass nuclei
The lucky cases with at least 3 stable nuclei + K with 2 stable isotopes
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Laser spectroscopy on Mg isotopes
Mg+:
Detection via:
HFS structure of 21Mg
observed in b-decay asymmetry
(D1 line)
 Fluorescence photos
 Or beta-decay asymmetry
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From Mg isotope shifts to charge radii
F factor
F [MHz/
fm2]
Semi-empirical
Ab initio
GFS
HFS
[Tor85]
[Saf01]
[Ber03]
[Sah12]
s->p1/2
-158
-148
-117
-125.81
-127
-126.221
s->p3/2
-158
-148
-117
-126.821
-127
-126.324
20% difference,
seen also in other elements
10% error assumed
Specific mass shift
K_SMS
[GHz/u]
Ab initio
[Saf01]
[Ber03]
[Sah12]
[Sah12]
s->p1/2
-362
-379
-390.1
-398.8
s->p3/2
-361
-373
-386.1
-389.9
[Tor85] G. Torbohm, B. Fricke, A. Rosen, PRA 31, 2038 (‘85)
[Saf01] M.S. Safronova & W.R. Johnson, PRA 64, 052501 (‘01)
[Ber03] J.C. Berengut, V.A. Dzuba, V.V. Flambaum, PRA 68,
022502 (‘03)
[Sah12] B.K. Sahoo, J. Phys. B 43 231001 (’10)
Large differences or uncertainties -> let’s try a King plot (need Muonic data)
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Mg charge radii from muonic transitions
Large corrections and many systematic uncertainties
Fricke et al,
PRC 45, 81 (’92)
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Can they be determined more
accurately nowadays?
Mg modified King plot
Differences in radii from Muonic data vs electron scattering
Uncertainties:
from transition energy +
10% of larger nucl.
polarization uncert.
d
Too large
uncertainties
to be used
syst error 1: uncertainty in nuclear polarisation
correction (30% of total nuclear polarization)
Syst error 2: due to choice of skin thickness t
of Fermi distribution
Mg+, 24,25,26Mg
Syst error in IS would lead to additional 5 GHz u uncertainty in KMS
K_NMS = 365 GHz u
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Resulting charge radii
King plot
d<r2> (fm2)
Uncertainties in atomic factors are
equally important as central values
[Saf01]
Which atomic factors should I use?
The resulting nuclear physics
interpretation will tell me …
King plot
[Ber03]
[Sah10]
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Best nuclear physics
description from
King plot:
In general radii
increase
Minimum radii
for 24,26Mg
(new sub-shell
closures)
Radii around
N=20 larger
than around
N=8
Charge radius (fm)
Mg charge radii and nuclear structure
Uncertainty of the slope due to atomic
F factor uncertainty not included
N=14
N=20
Atomic number, A
Smallest radius at N=14, not N=20:
Migration of the shell closure
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D. Yordanov et al,
Phys. Rev. Lett. 108, 042504 (2012)
Laser spectroscopy of Ne isotopes
Ne atoms
Special type of setup:
 Excitation to a meta-stable level (neutralization)
 Laser excitation from this state
 Detection after reionization – ions or beta counts
Acceleration-voltage calibration:
 Use of (anti-) collinear laser
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Charge radii of Ne isotopes
 A, A'  ( K NMS  K SMS ) 
m A'  m A
 F  r 2
m A' m A
A, A '
1 GHz
10 MHz
F determined from semi-empirical approaches:
 Goudsmit-Fermi-Segre: F=-40(4) MHz/fm2 (assuming 10% uncertainty)
 HSF: F= -38 (4) MHz/fm2 (also, assuming 10% uncertainty)
 Any ab initio calculations existing for this transition?
Mass shift from modified King plot
 Muonic radii for 20,21,22Ne
 With fixed F
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Ne charge radii and nuclear structure
Determined trend in radii can be explained by nuclear models
Wealth of structures revealed:
 Presence and disappearance of shells, clustering, onset of halo formation
Intrinsic density distributions of
dominant proton FMD configurations
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Geithner et al, PRL 101, 252502 (‘08)
Marinova et al, PRC 84, 034313 (‘11)
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Laser spectroscopy of Ar isotopes
Ar atom
Technique: the same as later used for Ne (including energy calibration)
Determination of F – semi-empirical approach: F= - 104(10) MHZ/fm2
Determination of mass shift constant: modified King plot
 With fixed F
Any ab initio calculations?
Muonic data
Talmi – Zamick formula
HF calculation, A. Klein et al,
Nucl. Phys. A 607 (1996) 1.
K. Blaum et al, NPA 799, 30 (2008)
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Laser spectroscopy of K isotopes
Collinear laser spectroscopy on atoms
 Detection via fluorescence photons
 Bunched ion beam (to lower laser background)
K_SMS and F determined from ab initio calculations (only 2 data points from
muonic atoms)
 A.-M. Martensson-Pendrill, et al., JPB 23, 1749 (‘90) – reliable results for Ca
 K_SMS = −15.4(3.8) GHz u
 F =−110(3) MHz/fm2
N=28 shell closure well visible
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Charge radii of Ar and K isotopes
Resulting trends in radii make sense from nuclear structure point of view
 N=28 shell closure visible (but not N=20)
 Rather consistent with radii trends in neighbouring chains – although strong Z
dependence is clearly visible
Systematic errors in trends due
to F uncertainty not shown
K
Ar
K. Kreim et al, PLB 731, 97 (‘14)
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Take-away message
Optical isotope shifts are sensitive to small changes in nuclear charge radii
The art
 lies in determining the proportionality (atomic) factors with both enough
precision and enough accuracy to provide a quantitative relation and
 to provide nuclear radii which make sense from the nuclear physics point of view
Have to rely a lot on semi-empirical approaches and muonic data with large
corrections calculated with limited computer power
Hopefully ab initio approaches are catching up
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Collinear-anticollinear
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Modified King plot
Isotope
pair A, A’
slope
Isotope
pair A,A’’
0
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King plot for 2 optical transitions
In Mg+ s->p1/2 (D1) and s->p3/2 (D2)
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From optical isotope shifts to radii
Mass shift in spectra of many-electron atoms
Normal mass shift
First order field shift
Specific mass shift,
Due to e- correlations
 1st order perturbation theory (finite nucleus as
perturb to point-like nucleus)
 1st approach
 Then corrections
 For distribution
nonrelativistic probability density of e- at point nucleus
s-1 close to 1 for light isotopes, close to 0.1, 0.2 for heavy -> changes slowly with r, so can use
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From optical isotope shifts to radii
Electronic factor
nonrelativistic probability density of e- at point nucleus,
but it should be rather change in probability density
Determination of density of ns electron at point-like nucleus
Ab initio atomic calculations
Semi-empirical approaches:
 From HFS: all inner e’s are paired off in alkali-like atom and make no contribution to
magnetic HFS. HFS directly proportional to density of ns e- at point nucleus
A: HFS constant for ns e: correction for finite size of nucleus
e – HFS anomaly
g’ – reduced g factor of nucleus
 Goudsmit-Fermi-Segre formula: ns electron density at nucleus is related to effective
quantum number of ns level
Screening effects:
F for Mg+ from GFS
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F for Mg+ from HFS
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Field shift according to Seltzer
Seltzer
 A, A'  ( K NMS  K SMS ) 
m A'  m A
 F  r 2
m A' m A
A, A '
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2nd order field shifts
Due to 2nd-order contributions and from relativistic effects
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Nuclear radii
Which radius? Depends on the used probe
Charge radius – studied via Coulomb interaction of a charged particle with nucleus
Matter radius – studied via strong interaction of nuclei and particles
Nuclei don’t have abrupt boundaries - useful two parameters:
 Mean radius – where density is 50% of maximum
 Diffuseness/“skin thickness” – distance where density drops from near max to near min
Mean square radius of charge distribution
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Modified King plot
When data for at least 3 isotopes exists (i.e stable isotopes) partial help is there!
 Combine absolute radii (transitions in muonic atoms or electron scattering) and isotope
shifts in optical transitions
A
A
A
A
A
A
A
Isotope
pair A, A’
A
A
slope
A
A
A
A
A
A
Isotope
pair A,A’’
A
0
A
A
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But if there are
fewer stable
isotopes …
See Na, Mn, Cu, Ga
…
Lasers + ion traps: n-def Hg & Au isotopes
RILIS, Windmill, ISOLTRAP teams
Bonn et al., PLB38 (1972) 308
Ulm et al., Z Physik A 325 (1986) 247
Several techniques combined
RILIS lasers to probe the hyperfine
structure of Hg & Au isotopes
Detection:
 Alpha spectroscopy with Windmill
 Selective ion counting in MR-ToF
Au
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Resulting charge radii
King plot
King plot only
K_MS + error
K_MS - error
Too large uncertainties
d<r2> (fm2)
Middle values
[Saf01]
King plot
[Ber03]
[Sah10]
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Zamick
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Electron scattering
Diffraction with radiation of wavelength smaller than the object – high-energy eLambda < 10 fm -> p> 100 MeV (e.g 100 MeV to 1 GeV e-)
Result: rms radius: <r2>1/2
Diffraction minima
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Electron transitions
Nuclei are not point-like particles -> atoms electrons can penetrate inside and probe
the nuclear distribution (K X-ray transitions, especially 1s electrons)
Biggest penetration into nucleus for 1s eMuch easier to compare distibutions of two neighbouring isotopes (than determine
size of 1 radius absolutely)
K X-ray isotope shifts – relatively large
Optical isotope shifts in valence e-: much smaller penetration and thus smaller shift
Both are still very small effects – due to a small size of nucleus compared to e- orbits
optical transition
1e-7 effect
X-ray transition
1e-6 effect
J. Bonn et al, Z. Phys. A
276, 203 (1976)
P. Lee et al Phys Rev C
17, 1859 (1978)
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Muonic atoms
Muon’s mass = 200 e- mass -> Bohr
(atomic) radius 200 smaller
E.g. in 208Pb: muon’s mean radius is inside
the nucleus
Isotope shifts – factor 1-2 (vs 1e-4 – 1e-6
for e-)
Technique:
 Muons produced at accelerators (in decay
of pi mesons), e.g at PSI-Zurich
 Bombard target made of isotope(s) of
interest
 Muons are captured in high-n orbits and
cascade down to 1s orbits
 Emitted photons (of MeV energy) are
detected
 Obtain directly charge-distribution
parameters (although analysis is complex)
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