What we learned from Lecture 1 - University of...
Transcript of What we learned from Lecture 1 - University of...
What we learned from Lecture 1
Sizes
Spins
Qs
μ
Model Independent
(measured)
Lecture II
Doppler-free laser spectroscopy
2.1 Introduction to lasers and laser spectroscopy
2.2 The crossed beams method and fast beams collinear laser spectroscopy
2.3 The structure of K isotopes & the shell model
2.4 The N = 60 region and nuclear deformation
Simple principles of laser spectroscopy
ν1
ν0
t~10-30 ns
The absorption cross section of a photon by an atom and subsequent relaxation is given by a Lorentzian
function:
detector
σ ≈λ2/2π
When νl = ν0, resonant absorption.
This is an enormous dimension and highlights the effectiveness of laser spectroscopy!
Images of trapped Ba+ ions
A trapped Ba+ ion cloud with estimated number <50 ions
in the cloud
W. Neuhauser et al, PRL 41 (1978) 233
Individual trapped laser-cooled Ba+ ions
(Courtesy of the TRIµP group)
Tunable CW dye lasers (the workhorse)
The dye laser was developed in 1966, using organic dye as a lasing medium.
• Wavelengths from 400 nm – IR • Can be frequency doubled
• Bandwidth <1 MHz
The natural linewidth of an atomic state due to Heisenberg uncertainty principle (1/2πΤ) is 16 MHz for a 10 ns lifetime.
POLIISI
Doppler shift
Laser
The main problem in laser spectroscopy
The observed transition linewidth can be broadened by Doppler effects
)1(' 0c
vff
Thermal motion is a Maxwell-Boltzmann probability distribution. Causes a spread of frequencies observed by atoms
dfTfk
ffmcdffP
b
)2
)(exp()(
2
0
2
0
2 20
2ln8
mc
Tkf b
FWHM
Doppler broadening
232Th
Example of Doppler broadening: 232Th
• Hot cavity • Crossed beams
Natural linewidth 35 MHz; spectral linewidth 2.4 GHz (in oven), 170 MHz (crossed beams configuration)
The Doppler broadening is often comparable or greater than HFS or IS!
Crossed atomic beam laser spectroscopy
Incident laser beam interacts perpendicularly with a collimated beam of atoms. Resonant photons are detected orthogonally.
T~2500K
Ta tube (1.6 mm)
D.H. Forest et al., J. Phys. G 41 (2014) 025106
• 5 even-even isotopes • 2 odd-A isotopes (15 HF components each)
Ru (Z=44)
PMT
30-60kV
Collinear-beams laser spectroscopy
In a collinear geometry, light, whether co- or counter-propagating with the ion beam,
interacts with accelerated ionic ensembles.
Doppler broadening
𝐸 = 𝑒𝑉 = ½𝑚𝑣2
1. Accelerate all ions to energy E
c
vD 0
2. The energy spread δE (from source) remains constant
.)2
(2
constvmvmv
E
3. The corresponding velocity spread is decreased and we obtain the Doppler width:
20
2eVmc
ED
S.L. Kaufmann, Opt. Comm. 17 (1976) 309 W.H. Wing et al., PRL 36 (1976) 1488
The effect of the velocity compression
Courtesy: A. Voss
Typical ion source energy spreads are ~1 eV. Acceleration of medium-A nuclei to 30 keV produces a 3 order of magnitude velocity compression
T=2000 K
reduction in Doppler
broadening
Collinear-beams laser spectroscopy II
0
Applied Doppler tuning voltage
PMT
Charge exchange Ion
Source
Separator electrostatic acceleration (30-60 kV)
CW tunable laser
178g,mHf
(isomer 8- spin)
Doppler-shifted (relative) frequency
Tuning voltage adjusts ion velocity to Doppler shift it to resonance with locked laser
Laser frequency “locked” to a reference for long-term stability
Segmented PMT (16-fold)
The laser-ion interaction region
Photon-ion coincidence technique
D.A. Eastham et al., Opt. Commun. 82 (1-2) (1991) 23
Accept photons in delayed coincidence with the corresponding ion (or atom). Position sensitivity along the detection region can enhance the time resolution (to ~20 ns).
RF-multipole structure A. Nieminen, JYFL
F. Herfurth, ISOLTRAP
D. Lunney, MISTRAL cooler
Emittance few p mm mrad
Energy spread <1eV
Bunch width few µs
Transmission ~70 % RF
Radio-frequency quadrupole traps
More recently, a powerful and now popular variant of collinear spectroscopy exploits the availability of gas-filled, quadrupole traps
Ion
beam
cooler
Light
collection
region (Laser resonance fluorescence)
Reduces energy-spread of ion beam
Improves emittance of ion beam
Trap and accumulates ions – typically for 300 ms
Releases ions in a 15 µs bunch
Laser beams
+40 kV
39.9 kV
• Helium-filled radio-frequency trap
• Ion beam accumulated for 100 ms
• Released as a 5μs bunch
5μs
z En
d p
late
po
ten
tia
l
Accumulate
Release
Reacceleration
potential
PMT
Bunched beam spectroscopy
Accept photons in a time window during which the bunched beam passes. Temporal background compressions of ~104 routinely achieved.
P. Campbell et al., PRL 89 (2002) 082501
80Ga
B. Cheal et al., PRC 82 (2010) 051302(R)
(Dipole transition: F = 0, +/- 1)
At most 6 peaks expected.
I=3 (isomer)
I=6 (gs)
Discovery potential of laser spectroscopy
Laser spectroscopy is able to reveal new nuclear states which may be too long-lived for decay spectroscopic methods, half-lives too similar, too low-lying in energy to separate with modern Penning trap techniques.
J=3/2 → J=1/2
From lecture 1:
J. Hakala et al., PRL 101 (2008) 052502
• Half life of isomer must be >200 ms
• Negative parity based on shell model arguements • Not seen in high precision
mass measurements (states within 50 keV)
Complimentary nuclear spectroscopy
Verney et al., PRC 87 (2013) 054307: - used ALTO ISOL facility (surface ionization for 80Ga)
- collect on moveable tape, conventional β and γ detection setup - Measured half-lives. Higher spin 6- state: 1.9s, lower spin 3-: 1.3s
R. Lică et al., PRC 90 (2014) 014320: - used ISOLDE facility (resonance ionization of Zn) - excited states in 80Ga populated in β decay of 80Zn
- fast response β detector, LaBr3 γ detectors, HPGe detectors
β- decay study firmly assigned the spin and parity of the ground state to be 6-. The unknown energy of the isomer discovered by laser spectroscopy fixed at 22.4 keV
Bunched-beam spectroscopy: test of the nuclear wavefunction, the K isotope chain
2522
2753 2788
855
975 980
345 334
474
672 715
561 Exci
tati
on
en
erg
y [
keV
]
Exp. NR U Exp. Exp. Exp. NR NR NR U U U
39K 41K 43K 45K
- Measurement of ground-state spins and magnetic moments of K isotopes - Interplay of theory and experiment to improve effective shell-model
interactions
20
2s1/2
1d3/2
20
2p3/2
1f7/2
Shell model interactions: “NR” (SDPF-NR) “U” (SDPF-U)
3/2+
1/2+
320 312 360
Exp. NR U
47K
I = 1/2 I = 3/2
81
466
74 78
Exp. Exp. NR NR U U
49K 51K
I = ?
Spin assignments of 49,51K
3 peaks => I = 1/2
49K
51K 4 peaks => I > 1/2
I = 3/2 from relative height of peaks
J. Papuga et al., PRL 110 (2013) 172503
Nuclear spins and magnetic moments
I = 3/2
Odd-A K (odd-even) isotopes (gs wavefunction dominated by proton hole in the Z=20 shell).
20
2s1/2
1d3/2
20
2p3/2
1f7/2
Effective single-particle g factor 0.85eff free
s sg g 1.15lgp 0.15lg
J. Papuga et al., PRL 110 (2013) 172503
Exp. g factors of 39-45K close to effective value for a hole in
π1d3/2 orbit. This is dominant component
in ground state wavefunction.
47K SDPF-NR SDPF-U
13% 13%
49K SDPF-NR SDPF-U
1
3/2 2( )d fpp
21% 15%
1
3/2 2( )d fpp
Nuclear spins and magnetic moments
For 45,47K (spin ½), 47K g factor is close to effective value for hole in the π2s1/2 configuration. 49K, with same spin, has a rather mixed wave
function.
Effective single-particle g factor
I = 1/2
J. Papuga et al., PRL 110 (2013) 172503
20
2s1/2
1d3/2
20
2p3/2
1f7/2
Nuclear spins and magnetic moments
Once more, the dominant component in the ground-state wave function for 51K is a π1d3/2 hole. This supports the spin assignment of 3/2.
Effective single-particle g factor
J. Papuga et al., PRL 110 (2013) 172503
I = 3/2
20
2s1/2
1d3/2
20
2p3/2
1f7/2
More information extracted from the odd-odd isotopes (PhD thesis work of J. Papuga, published in
PRC 2014).
Evolution of the proton s1/2 – d3/2 gap
The inversion of the nuclear spin from I=3/2 to I=1/2 at N = 28 and the reinversion back at N = 32 is related to the evolution of the proton sd
orbitals as different neutron orbitals are filled.
- Up to N = 28, both shell model interactions are in
agreement with experiment
- Deviation beyond N = 28
- 49K, both interactions predict 75 keV energy
difference, but only one gets the gs spin correct
- both predict correct gs spin for 51K, however no data on
first excited state
J. Papuga et al., PRC 90 (2014) 034321
Ab initio calculations in mid-mass nuclei also available!
Nuclear charge radii of K isotopes (+ others) ',
2''
'
' AAAAAA rF
AA
AAK
Specific mass shift and electronic factor F calculated.
Strong shell closure effect at N=28 common to all
elements
Above N=28 the δ<r2> values show steep increasing slope
(volume-induced δ<r2> )
A
Ar
A
Arr
rARr
SphSph
Sph
2
0
22
2
03
2
2
0
2
5
2
3
2
5
3
5
3
To date, no single theoretical model has fully described the Z-dependent behaviour of radii across Z=20 K. Kreim et al., PLB 731 (2014) 97
Comparison with theory (mean field)
K. Kreim et al., PLB 731 (2014) 97
Non-relativistic and relativistic approaches considered (they give rise to different descriptions of the spin-orbit field)
Skyrme HFB model (Goriely et al, PRC 88 (2013)
Rel. mean field (Lalazissis et al, PRC 71 (2005)
40Zr δ<r2>
N=50 shell closure
Laser spectroscopy and collectivity: Z=40, N=60 region
Radius of spherical nucleus of same volume
Quadrupole deformation parameter
...
4
51 2
3
2
20
22 p
rr
2
2
0
22
4
51
i
irr p
Expand a deformed charge distribution in terms of spherical harmonics
2
2
2
By comparison, probes dynamic nature of deformation
40 45 50 55 60 65
0
1
2
3
4
5
Kr
Rb
Sr
Y
Zr
Nb**
Mo*
<
r2>
50,N
(fm
2)
N
Z = 36 to 42
*F.C. Charwood et al., Phys. Lett. B 674 (2009) 23 **B. Cheal et al., Phys. Rev. Lett. 102 (2009) 222501
Complementary binding energy data
N
http://research.jyu.fi/igisol/JYFLTRAP_masses/
http://isoltrap.web.cern.ch/isoltrap/database/isodb.asp
B. Cheal et al., Phys. Rev. Lett. 102 (2009) 222501
89Y+
Metastable state spectroscopy
When going to Y and Nb, the ground state ionic spin J=0 - this does not allow an independent measure of nuclear spin I
- transitions may be inaccessible to CW lasers - transitions may be inefficient
An Electrostatic ConeTrap
X
R ear Electrode
front electrode
[1] HT Schmidt et al., Nuclear Instruments and Methods in
Physics Research B173 (2001) 523-527.
[2] P. Reinhed et al., Nuclear Instruments and Methods in Physics
Research A621 (2010) 83–90.
Adjustable resolution spectroscopy…
Systematics of the overall region
Ru measured using crossed beams (only
stable isotopes)
Peak of deformation occurs in odd-Z 39Y chain – symmetric in onset and loss of collectivity around Y. From Qs, N = 60 shape changes moves to rigid prolate
Due to increase in mean- square deformation
N=Z 74Rb; superallowed β
emitter. Charge radius
required for isospin- symmetry breaking correction terms
Recent theoretical efforts
R. Rodriguez-Guzman et al., PRC 83 (2011) 044307
R. Rodriguez-Guzman et al., PLB 691 (2010) 202
The important message(s) from Lecture 2
• In addition to determining I, µ, Qs and δ<r2>, laser spectroscopy has the potential to discover new states
• Important to gain resolution – use Doppler-free techniques. At on-
line facilities, collinear laser spectroscopy is the workhorse. Background reduction is necessary.
• Access to spin and magnetic moments probes single-particle effects,
identifies quantum states and can test shell model interactions
• Laser spectroscopy offers a complementary probe to collective effects via quadrupole moments and charge radii. The latter show
extreme sensitivity to changes in the nuclear shape
• Complete spectroscopy (γ-ray, laser, decay spec, masses…) coupled with theoretical support provides a complete picture
End of Lecture 2