Precision Nuclear Mass Measurements - Arunaaruna.physics.fsu.edu/ebss_lectures/F_Lecture3.pdf · Precision Nuclear Mass Measurements ... - Precision requirements - Physics motivation

Precision Nuclear Mass Measurements Matthew Redshaw

Exotic Beam Summer School, Florida State University Aug 7th 2015

• WHAT are we measuring? - Nuclear/atomic masses

• WHY do we need/want to measure it? - Precision requirements

- Physics motivation

• HOW do we measure it? - Precision measurement techniques

Outline

What is the mass of an atom with Z protons and electrons and N neutrons?

protons neutrons

electrons

The Mass of an Atom WHAT

What is the mass of an atom with Z protons and electrons and N neutrons?

Need to account for the binding energy

protons neutrons

electrons

The Mass of an Atom

What is the mass of an atom with Z protons and electrons and N neutrons?

Need to account for the binding energy

protons neutrons

electrons

The Mass of an Atom

What is the binding energy of a nucleus?

Binding energy ≈ 8 MeV/N (~1% of the atom’s mass)

Answer: It depends on the nucleus!

Binding energy and therefore atomic mass is a unique, fundamental property of a nucleus

Binding Energy of Stable Nuclei

Binding energy ≈ 8 MeV/N (~1% of the atom’s mass)

Answer: It depends on the nucleus!

Binding energy and therefore atomic mass is a unique, fundamental property of a nucleus

Binding Energy of Stable Nuclei

Nuclear masses can tell us something about nuclear structure and forces.

Nuclear masses are needed as inputs for understanding physical processes

Unified Atomic Mass Unit WHAT

The atomic mass unit is defined as 1/12th of the mass of 12C in its ground state

1 𝑢 = 𝑚𝑢 =1

12𝑚( C12 )

Unified Atomic Mass Unit WHAT

The atomic mass unit is defined as 1/12th of the mass of 12C in its ground state

1 𝑢 = 𝑚𝑢 =1

12𝑚( C12 )

(not amu, please)

Unified Atomic Mass Unit WHAT

The atomic mass unit is defined as 1/12th of the mass of 12C in its ground state

1 𝑢 = 𝑚𝑢 =1

12𝑚( C12 )

Conversion to keV 1 𝑢 = 931,494.0954 57 keV

1 𝑢 ≈ 𝑚𝑝 ≈ 𝑚𝑛 ≈ 1 GeV

Mass Excess 𝑀𝐸 = Δ = 𝑀[ 𝑋]𝐴 − 𝐴 × 931,494.0954 57 keV/u

in u a number

The Atomic Mass Evaluation (AME) WHY

The 2012 Atomic Mass Evaluation G. Audi, et al, Chinese Physics C 36, 1287 (2012) M. Wang, et al, Chinese Physics C 36, 1603 (2012) http://ribll.impcas.ac.cn/ame/evaluation/data2012/data/mass.mas12

AME initiated ~1955 by A. H. Wapstra

Mass Models

Theoretical mass predictions for Cs isotopes

From: Blaum, Phys. Rep. 425, 1 (2006) doi:10.1016/j.physrep.2005.10.011

Mass Excess/nucleon

Z=20 (Ca)

Nuclear Structure: Shell Structure

𝑀𝐸 = Δ = 𝑀[ 𝑋]𝐴 − 𝐴 × 931,494.0954 57 keV/u

Nuclear Structure: Shell Structure

Neutron separation energy

𝑆𝑛 = 𝑀 𝑋𝑍𝑍+𝑁−1 −𝑀( 𝑋) + 𝑚𝑛𝑍

𝑍+𝑁

Nuclear Structure: Shell Structure

Two neutron separation energy

Nuclear Structure: Shell Structure

Two neutron separation energy

Interpolated!!

Nuclear Structure: Shell Structure

Two neutron separation energy

F. Weinholtz, et al, Nature 498, 346 (2013) doi:10.1038/nature12226 A.T. Gallant, et al, PRL 109, 032506 (2012) doi:10.1103/PhysRevLett.109.032506 Mass measurements of 51-54Ca:

Nuclear Structure: 3N Forces

Three nucleon forces are naturally arise in chiral effective field theory.

F. Weinholtz, et al, Nature 498, 346 (2013) doi:10.1038/nature12226 A.T. Gallant, et al, PRL 109, 032506 (2012) doi:10.1103/PhysRevLett.109.032506

Nuclear Structure: Halo Nuclei

11Li: Borremean two neutron halo nucleus

• Halo nuclei are a very weakly bound systems • Mass (binding energy) measurements provide: - stringent tests of nuclear models - data for charge radius determination (along with laser spectroscopy data)

Nuclear Structure: Halo Nuclei

M. Smith, et al, PRL 101, 202501 (2008)

• Halo nuclei are a very weakly bound systems • Mass (binding energy) measurements provide: - stringent tests of nuclear models - data for charge radius determination (along with laser spectroscopy data)

Precision of 0.64 keV (t1/2 = 8.8 ms)

Nuclear Structure: Halo Nuclei

M. Smith, et al, PRL 101, 202501 (2008)

Precision of 0.64 keV (t1/2 = 8.8 ms)

W. Geithner, et al, PRL 101, 252502 (2008)

• Halo nuclei are a very weakly bound systems • Mass (binding energy) measurements provide: - stringent tests of nuclear models - data for charge radius determination (along with laser spectroscopy data)

Nuclear Astrophysics: rp-process and r-process

Masses of “waiting point” nuclei in rp-process e.g. 64Ge, 68Se, 72Kr

Q-values required for evaluating rp and r-process paths 𝑄 = 𝑀𝑝𝑎𝑟𝑒𝑛𝑡 −𝑀𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟 𝑐2

Masses of nuclei involved in r-process required for network calculations.

Fundamental Symmetries: Superallowed -decay

Pure Fermi decay from J = 0+ (parent) 0+ (daughter) T = 1 analog states

Collectively, these transitions: - Provide a test of the CVC hypothesis - Set limits on presence of scalar currents - Provide a test of CKM matrix unitarity

Fundamental Symmetries: Superallowed -decay

Pure Fermi decay from J = 0+ (parent) 0+ (daughter) T = 1 analog states

- Test of the CVC hypothesis That the weak vector coupling constant, GV is not renormalized in the nuclear medium

constant theoretical correction

Statistical rate function - depends on BR, t1/2, Q

J.C. Hardy and I.S. Towner, PRC 91, 025501 (2015)

Fundamental Symmetries: Superallowed -decay

Pure Fermi decay from J = 0+ (parent) 0+ (daughter) T = 1 analog states

- Limits on presence of scalar currents Standard model weak interaction is V A (no scalar currents)

Scalar current additional term in Ft: 1 + 𝑏𝐹𝛾1/𝑄

A.A. Valverde, et al, PRL 114, 232502 (2015)

Fundamental Symmetries: Superallowed -decay

Pure Fermi decay from J = 0+ (parent) 0+ (daughter) T = 1 analog states

- Provide a test of CKM matrix unitarity

𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏

CKM matrix

unitarity

𝑉𝑢2 =0.99978(55)

Summary of required precisions

Field Application Precision

Nuclear Astrophysics r, rp, s processes 106 – 107

Nuclear Physics Mass Models 106 – 108

Nuclear Structure 106 – 108

Fundamental Interactions 108 – 109

Neutrino Physics -decay 108 – 109

-decay, Electron Capture 1010 – 1012

Metrology -ray standard calibrations 1010 – 1011

Fundamental Constants 1010 – 1012

Test of E = mc2 1010 – 1012

Atomic Mass Measurements HOW

Historically, three main methods:

Electromagnetic spectographs and spectrometers

G. Audi, IJMS 251, 85 (2006) doi:10.1016/j.ijms.2006.01.048

Time of flight

RF spectrometer

J.J. Thomson (1913)

Atomic Mass Measurements HOW

Currently, three main (high-precision) methods for exotic isotopes:

Penning trap

Multi-reflection time of flight

Storage ring

The Penning Trap

What physical quantity can be most precisely measured? • Velocity

• Energy

• Frequency

• Charge

• Voltage

The Penning Trap

What physical quantity can be most precisely measured? • Velocity

• Energy

• Frequency

• Charge

• Voltage

The Penning Trap

νc = cyclotron frequency

m = mass q = charge B = magnetic field strength

+

Uniform B-Field

Convert the mass measurement into a (cyclotron) frequency measurement

𝐵 = 𝐵0𝑧

𝜈𝑐 =1

2𝜋

𝑞𝐵

𝑚

The Penning Trap

νc = cyclotron frequency

m = mass q = charge B = magnetic field strength

+

Uniform B-Field

Convert the mass measurement into a (cyclotron) frequency measurement

𝐵 = 𝐵0𝑧

𝜈𝑐 =1

2𝜋

𝑞𝐵

𝑚

Radial Confinement

The Penning Trap

+

Quadrupole E-Field

𝜑 𝑧, 𝜌 =𝑉

2𝑑2𝑧2 −

𝜌2

2

Provides a linear restoring force:

Simple Harmonic Motion Frequency independent of amplitude

+ -

𝜈𝑧 =1

2𝜋

𝑞𝑉

𝑚𝑑2

Axial Oscillation Frequency

+

+

end-cap

ring

end-cap

Superconducting Magnet

𝜈𝑐 =1

2𝜋

𝑞𝐵

𝑚

The Penning Trap

Hyperbolic Electrodes

Uniform B-Field Quadrupole E-Field

Hyperbolic surfaces are equipotentials of the potential we wish to create.

Higher B-field Higher precision (for a given measurement precision, Δ𝜈𝑐)

Δ𝑚

𝑚=Δ𝜈𝑐𝜈𝑐

+ +

Uniform B-Field Quadrupole E-Field

+ =

3 Normal Modes

ν+

ν- νz

True cyclotron frequency is related to the trap-mode frequencies via

Motion in the Penning Trap

𝜈𝑧 =1

2𝜋

𝑞𝑉

𝑚𝑑2 𝜈𝑐 =

1

2𝜋

𝑞𝐵

𝑚

+ -

Driving the Normal Modes Coupling the Normal Modes

+ +

Dipole rf field at rf = ± will excite radial motion

+

-

+

+

-

-

Quadrupole rf field at rf = + + - will couple radial motions

+

+

Manipulating the Motion of the Ion

Driving the Normal Modes Coupling the Normal Modes

+ +

Dipole rf field at rf = ± will excite radial motion

+

-

+

+

-

-

Quadrupole rf field at rf = + + - will couple radial motions

+

Manipulating the Motion of the Ion

pulseMagnetron Cyclotron

t

Coupling the Normal Modes

+

+

+

-

-

+

+

-

-

+

+

Manipulating the Motion of the Ion

Drive radial motion

Convert - + Radial energy gain

Cyclotron Frequency Measurement

Inhomogeneous part

of magnetic field

B

z

Drive radial motion

Eject Ions from Trap

Trap MCP

Convert - + Radial energy gain

Convert Er Ez Axial energy gain

Time of Flight Technique

Cyclotron Frequency Measurement

Inhomogeneous part

of magnetic field

B

z

Detector

Drive radial motion

Record TOF to MCP Eject Ions from Trap

Trap MCP

Convert - + Radial energy gain

Convert Er Ez Axial energy gain

Minimum when

Time of Flight Technique

Cyclotron Frequency Measurement

Detector

Mass Ratio Measurement

Penning Trap Facilities World Wide

TITAN, TRIUMF ISOL

CPT, ARGONNE 252Cf fission fragments

LEBIT, NSCL Projectile Fragmentation

SMILETRAP Highly-charged stable isotopes

JYFLTRAP, Jyvaskyla IGISOL

TRIGA-TRAP, MPI Nuclear reactor fission products

SHIPTRAP, GSI Superheavy Elements

ISOLTRAP, ISOLDE/CERN ISOL

MIT-FSU Trap High-precision (Stable Isotopes)

Storage Ring Mass Spectrometry

Measure frequency at which ions go around the ring But, velocity spread frequency spread

∆𝑓

𝑓= −

1

𝛾𝑡2

∆𝑚 𝑞

𝑚 𝑞 +∆𝑣

𝑣1 −

𝛾2

𝛾𝑡2 t describes detour of

particles due to dispersion

Storage Ring Mass Spectrometry

Advantages: • High sensitivity – single 208Hg79+ ion • Good resolution

• Fast – half-lives down to 10 s (not demonstrated yet)

Precisions ~10-6

Multi-Reflection Time-of-Flight

Time of flight: 𝑡 ∝ 𝑚 𝑞 Resolution: 𝑅 = 𝑡/2∆𝑡

Advantages: • High R in short time. • Can handle high levels

of contamination. • High sensitivity. • “Cheap”

Precisions ~10-6 - 10-7

Challenges and outlook for mass measurements with exotic isotopes

Challenges

• Extremely low rates • Short half-lives

• Background contamination

• High-precision requirements

Solutions

• Efficient transport to trap • New tools - MR-TOF

• New techniques

- Phase Imaging - Image Charge Detection

• Optimizing beam time

The World’s Most Precise Penning Trap

PI: Ed Myers

Tours available today (5 – 5:30 pm), Collins building