Lecture Series: Atomic Physics Tools in Nuclear Physics

Euroschool on Physics with Exotic Beams, Mainz 2005

Lecture Series: Atomic Physics Tools in Nuclear Physics Klaus Blaum Johannes Gutenberg-University Mainz and GSI Darmstadt, Germany Email: [email protected] www.quantum.physik.uni-mainz.de/mats

www.quantum.physik.uni-mainz.de/mats/

Content n Atomic physics tools in nuclear physics: Basics ¾ Laser spectroscopy ¾ Ion trapping (Paul, Penning, and atom trap) o Cooling and detection of (charged) particles ¾ buffer gas, resistive, laser cooling ¾ TOF detection, FT-ICR detection p Laser spectroscopy experiments ¾ Collinear laser spectroscopy ¾ Resonance ionization laser spectroscopy ¾ Atom trap laser spectroscopy q Atomic mass measurements ¾ Penning trap mass spectrometry www.quantum.physik.uni-mainz.de/mats/

Nuclear Ground State Properties Direct mass measurements and laser spectroscopy allow to determine fundamental properties of nuclei in ground or long-lived isomeric states: masses, spins, moments and radii What do we learn? Masses

nuclear binding energy basic test of nuclear models nuclear structure: shell closures, pairing, onset of deformation, drip lines, halos

Spins, Moments

microscopic nuclear structure: wave functions, coupling of nucleons, configuration mixing, shell structure macroscopic nuclear structure: deformation

Charge Radii

nuclear structure: nuclear charge distribution, deformation

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A Perfect Example: 11Li – A Neutron Halo

Nuclear Radius [fm]

11

Li

3,5

Neutron Halo

11Li

3,0

Stable nuclei 2,5

7

8

Li

6

Li 9

8

208Pb

Li

10

Mass [amu] 9Li

3/2 -

+2n

11Li

~350 keV 0 keV

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How to probe that 11Li is a neutron halo? Mass measurements Æ Two-neutron separation energy Laser spectroscopy Æ Nuclear charge radii I. Tanihata, J. Phys. G 22, 157 (1996).

Principle of Laser Spectroscopy Resonant step-wise excitation of one (or more) electrons in the electron shell of the atom. The transition frequencies (wavelengths) are unique like a fingerprint for elements and isotopes. Varying the laser frequency allows to probe different isotopes and elements. www.quantum.physik.uni-mainz.de/mats/

Laser excitation/ionization

Basic Theory of Laser Spectroscopy

What can we get out of atomic spectra ? (mostly) ground state properties: Isotopic shift: - distribution of nuclear charge Hyperfine structure: - HFS A-factor ⇒ dipole moment - HFS B-factor ⇒ quadrupole moment - spin of the nucleus

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Isotope Shift = Frequency difference in an electronic transition between two isotopes

∆νIS = ∆νMS + ∆νFS

A − A' A >> 1 1 ⎯⎯⎯→ 2 MS ∝ AA' A

Field Shift

r

V(r)

Mass Effect ∆νMS ~ (A-A')/AA'

2πZ |ψ(0)|2 δ r2 3

Z2 FS ∝ 3 A

n What is the origin of the MASS SHIFT and the FIELD SHIFT? www.quantum.physik.uni-mainz.de/mats/

Charge Radius Determination for Light Elements

∆νIS = ∆νMS + ∆νFS 2πZ ∆|ψ(0)|2 3

δr

2

THEORY

EXPERIMENT Charge Radius : δ r 2

A,A'

=

A, A' A, A' - ∆νMS, ∆νmeasured Theory

C Field effect for light atoms on the order of 1 MHz, mass effect some 10 GHz High Accuracy in Experiment and Theory required! www.quantum.physik.uni-mainz.de/mats/

Isotope Shift for Many-Electron System

∆νIS = ∆νMS + ∆νFS 2πZ |ψ(0)|2 δ r2 3

∆νNMS + ∆νSMS

Normal Mass Shift - easy to calculate m MNMS = me u

ν

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Field Shift

A-A‘ = (MNMS+MSMS) AA‘ Specific Mass Shift - due to electron correlations - no analytical expression - calculable only for 2- and 3electron systems

Fundamental: Accurate Theory non-relativistic ground state energy of atomic ground states Helium : Lithium:

2.903 724 377 034 119 598 311 (1) Rel. Accuracy: 5 × 10-22 7.478 060 323 650 3 (71) Rel. Accuracy: 1 × 10-12 G.W.F. Drake et al., PRA 65, 054501 (2002) Yan, Z.-C. and G.W.F. Drake, PRA 66, 042504 (2002)

Example of an Isotope Shift Calculation: µ/m 11454.668 801 ± 0.000 029 (µ/m)2 -1.793 864 ± 0.000 004 0.190 ± 0.055 α2 µ/m α3 µ/m, 1 e-0.078 ± 0.005 α3 µ/m, 2 e0.011 2 ± 0.000 2 Total MS

11453.00

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± 0.06 MHz

2s 2S1/2 – 3s 2S1/2 transition mass shift calculation for 7Li – 6Li Yan, Z.-C. and G.W.F. Drake, PRA 66, 042504 (2002)

Isotope Shift Measurement in Gd 5

Ionenzählrate Ion count rate / 0.3 0.3 s

10

160

158

156 157

155

IP

154

4

10

363.8 nm 6s6p

9F 3

152 422.7 nm

3

10

6s2 9D2

2

10

1

10

0

2000

4000

ν -ν

160

6000

8000

10000

@ 422.7 nm [MHz]

o Which effects determine the width of the resonances? www.quantum.physik.uni-mainz.de/mats/

Hyperfine Structure = Splitting of fine structure levels due to coupling of electron spin Splitting of fine structure levels due to coupling of electron spin and nuclear multipole moments: and nuclear multipole moments K ( K + 1) − I ( I + 1) J ( J + 1) A W (F ) = K + B 2 2(2 I − 1)(2 J − 1) I ⋅ J where K = F ( F + 1) − I ( I + 1) − J ( J + 1) 3 4

1/4 B 5/2 5/2 A

5/2 A + 5/4 B

W(J) J=1 I=3/2

Constant A:- magnetic dipole coupling

A=

µ I H e ( 0)

, I ⋅J H e (0) = magnetic field at site of nucleus - access to nuclear parameters I (number of lines) and µI (size of splitting)

Constant B: - electric quadrupole coupling

B = eQsϕ jj (0), 3/2

-B 3/2 A

Example: 201Hg

3/2 A - 9/4 B +5/4 B

1/2 www.quantum.physik.uni-mainz.de/mats/

ϕ jj (0) = electric field gradient at the site of the nucleus - access to spectroscopic quadrupole moment Qs ⇒ nuclear deformation parameters

Principle of Trapping Radial force

electric fields

Harmonic potential

Cooling

harmonic oscillation

damping of oscillation amplitudes

magnetic fields light fields

2 or 3 independent eigen frequencies “infinite” storage time

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minimization of trap imperfections

Why trapping? ¾ effective use of rare species ¾ easy manipulation of trapped particles ¾ q/m-separation ¾ extended observation & manipulation time

EFFICIENCY

¾ accumulation & bunching

ACCURACY

¾ charge breeding and post-acceleration

SENSITIVITY

¾ polarization ¾ increase of luminosity ¾ backing free samples for decay studies www.quantum.physik.uni-mainz.de/mats/

Trapping and Storage Devices Storage ring

Atom trap

Penning and Paul trap

B

U

0

relativistic particles

5

10 cm

0

0.5

1 cm

particles at nearly rest in space

∗ ion cooling ∗ “infinite“ storage time ∗ single-ion sensitivity ∗ high accuracy ∗ mass spectrometric capabilities

Large number of applications in atomic and nuclear physics. www.quantum.physik.uni-mainz.de/mats/

H.-J. Kluge et al., Phys. Scripta T104, 176 (2003)

Historic Details

Wolfgang Paul Mass seperation with high frequency electric quadrupole field: two dimensional focussing of particles with a dipole moment.

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Frans Michel Penning Superposition of an electric 3D multipole field with a magnetic dipole field: B field captures particle in radial, E field in the axial direction. Penning discharge.

Hans G. Dehmelt Implemented electric quadrupole field via applying dc voltage two hyperbolic electrodes, B field in z direction. Named trap to honor F. Penning.

Storage of Charged Particles required: desired:

potential minimum in 3 dimensions harmonic force in direction of trap centre → F~-r → harmonic oscillations

⇒

F = -e∇φ ~ - r

⇒

φ = Ax 2 + By 2 + Cz 2

∆φ = 0

in addition:

(Laplace equation) z

simplification:

y

rotational symmetry (z-axis)

φ φ φ = (x + y − 2z ) = (ρ − 2z d d

x

2

⇒

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0

2

2

2

2

2

2

0

0

2

)

Storage of Charged Particles in a Paul/Penning Trap BUT: sign of r different ! no simultaneous trapping in 3 dimensions possible by purely electrostatic potentials SOLUTION: a: superposition of magnetic field in z-direction:

b: time varying voltage (RF) between ring electrode and endcaps:

Penning trap

Paul trap

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Paul Trap Geometries The linear RFQ trap

URF

ring electrode end cap www.quantum.physik.uni-mainz.de/mats/

potential

3D confinement

The Penning Trap • Trapping of particle via motion in electro-magnetic field • Strong homogeneous magnetic field in z direction, particle moves with cyclotron frequency q ω c = Bz m → bound in radial direction

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The Penning Trap • Trapping of particle via motion in em field • Strong homogeneous magnetic field in z direction, particle moves with cyclotron frequency q ω c = Bz m → bound in radial direction

• Weak, electrostatic quadrupole potential

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The Penning Trap • Trapping of particle via motion in electro-magnetic field • Strong homogeneous magnetic field in z direction, particle moves with cyclotron frequency q ω c = Bz m → bound in radial direction

• Weak, electrostatic quadrupole potential V ( z, ρ ) =

U DC 2 1 2 (z − 2 ρ ) 2d 2

• Equations of motion in 3D:

d = (z + 2

··

F = −e0(∇φ(r)+v×B) + mr = 0 www.quantum.physik.uni-mainz.de/mats/

1 2

2 0

ρ 02 2

)

Geometry parameter

Solutions of the Equation of Motion axial oscillation

2e0U 0 md 02

⋅ z + mz·· z= =0 0

2e0U 0

ωz =

z or axial frequency

md 02

radial oscillation substitution:

ω+ =

u = x + iy e ωc = 0 B m

2 ω u· = iωcu· −- z u + u =00 2

u (t ) = u0e − iωt

ω− =

ωc 2

ωc 2

+

ω c2

−

ω c2

4

4

−

ω z2

−

ω z2

2

2

modified cyclotron frequency magnetron frequency

p What is the minimum magnetic field required to balance the radial component of the applied electric field? www.quantum.physik.uni-mainz.de/mats/

Ion Motion in a Penning Trap Motion of an ion is the superposition of three characteristic harmonic motions: – axial motion (frequency fz) – magnetron motion (frequency f–) – modified cyclotron motion (frequency f+) magnetron motion (f-) z r

rr+

modified cyclotron motion (f+)

Typical frequencies q = e, m = 100 u, B =6T ⇒ f- ≈ 1 kHz f+ ≈ 1 MHz

axial motion (fz)

The frequencies of the radial motions obey the relation L.S. Brown, G. Gabrielse, f+ + f- = fc

Rev. Mod. Phys. 58, 233 (1986).

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Excitation of Radial Ion Motions Dipolar azimuthal excitation Either of the ion's radial motions can be excited by use of an electric dipole field in resonance with the motion (RF excitation) ⇒ amplitude of motion increases without bounds Magnetron excitation: ρ−

Ud r r0

+Ud

-Ud

Cyclotron excitation: ρ+

Uq

-Uq

r r0

+Uq

Quadrupolar azimuthal excitation If the two radial motions are excited at their sum frequency, they are coupled ⇒ they are continuously converted into each other www.quantum.physik.uni-mainz.de/mats/

-Uq

+Uq

Landau Levels of an Ion in a Penning Trap Energy of harmonic oscillators:

n+

3

E = hω+(n++1/2) + hωz(nz+1/2) - hω-(n-+1/2)

amplitudes: 2

∼ 1

0

⇒

nz 2 1 0

n+

0

1 2

magnetron motion is unstable !

n+

n_ modified cyclotron frequency

axial frequency

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magnetron frequency

q How can cooling or excitation of the ion motion be explained in the picture of the Landau levels?

Real Traps • Deviation from ideal quadrupole potential caused by: – – – – –

truncation of electrodes imperfect electrode shapes misalignment contact potentials because of disposal at electrodes space charge of ion clouds

• Consequences: – Electric and magnetic field errors – Trapping potential is modified – Broadening and displacement of resonance curves Restriction to achievable precision ! r In high-precision mass spectrometry with ion traps only Penning traps are in use. Why? www.quantum.physik.uni-mainz.de/mats/

Real Penning Trap Configurations Hyperbolical Penning trap

Cylindrical Penning trap

Potential distribution 100

50 mm 10

mm 100

0

5 0

50

-50

0

-100

main electrodes correction electrodes

main electrodes correction electrodes www.quantum.physik.uni-mainz.de/mats/

0

40 80 Uz (V)

Summary of Lecture I We addressed the following topics:

• Nuclear ground state properties and their access. • Explanation of the principles of laser excitation • • •

and ion trapping. Theory of isotope shift and hyperfine structure. Theory of ion motion in a Penning trap. Energy diagram of a trapped charged particle.

Thanks a lot for your attention. And do not forget to answer my questions! www.quantum.physik.uni-mainz.de/mats/