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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
