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