Download Precision Nuclear Mass Measurements

Precision Nuclear Mass Measurements
Matthew Redshaw
Exotic Beam Summer School, Florida State University Aug 7th 2015
Outline
• 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
WHAT
The Mass of an Atom
What is the mass of an atom with Z protons and electrons and N neutrons?
protons
electrons
neutrons
The Mass of an Atom
What is the mass of an atom with Z protons and electrons and N neutrons?
protons
electrons
Need to account for the binding energy
neutrons
The Mass of an Atom
What is the mass of an atom with Z protons and electrons and N neutrons?
protons
neutrons
electrons
Need to account for the binding energy
What is the binding energy of a nucleus?
Binding Energy of Stable Nuclei
Answer: It depends on the nucleus!
Binding energy ≈ 8 MeV/N
(~1% of the atom’s mass)
Binding energy and therefore atomic mass is
a unique, fundamental property of a nucleus
Binding Energy of Stable Nuclei
Answer: It depends on the nucleus!
Binding energy ≈ 8 MeV/N
(~1% of the atom’s mass)
Nuclear masses can tell us
something about nuclear
structure and forces.
Nuclear masses are needed
as inputs for understanding
physical processes
Binding energy and therefore atomic mass is
a unique, fundamental property of a nucleus
WHAT
Unified Atomic Mass Unit
The atomic mass unit is defined as 1/12th
of the mass of 12C in its ground state
1 𝑢 = 𝑚𝑢 =
1
𝑚( 12C)
12
WHAT
Unified Atomic Mass Unit
The atomic mass unit is defined as 1/12th
of the mass of 12C in its ground state
1 𝑢 = 𝑚𝑢 =
1
𝑚( 12C)
12
(not amu, please)
WHAT
Unified Atomic Mass Unit
The atomic mass unit is defined as 1/12th
of the mass of 12C in its ground state
1 𝑢 = 𝑚𝑢 =
Conversion to keV
1
𝑚( 12C)
12
1 𝑢 = 931,494.0954 57 keV
1 𝑢 ≈ 𝑚𝑝 ≈ 𝑚𝑛 ≈ 1 GeV
Mass Excess
𝑀𝐸 = Δ = 𝑀[ 𝐴𝑋] − 𝐴 × 931,494.0954 57 keV/u
in u
a number
WHY
The Atomic Mass Evaluation (AME)
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
Nuclear Structure:
Shell Structure
Mass Excess/nucleon
Z=20 (Ca)
𝑀𝐸 = Δ = 𝑀[ 𝐴𝑋] − 𝐴 × 931,494.0954 57 keV/u
Nuclear Structure:
Shell Structure
Neutron separation energy
𝑆𝑛 = 𝑀
𝑍+𝑁−1
𝑍𝑋
− 𝑀( 𝑍+𝑁𝑍𝑋) + 𝑚𝑛
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
Mass measurements of 51-54Ca:
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:
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
Precision of 0.64 keV (t1/2 = 8.8 ms)
•
•
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)
M. Smith, et al, PRL 101, 202501 (2008)
Nuclear Structure:
Halo Nuclei
W. Geithner, et al, PRL 101, 252502 (2008)
Precision of 0.64 keV (t1/2 = 8.8 ms)
•
•
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)
M. Smith, et al, PRL 101, 202501 (2008)
Nuclear Astrophysics:
rp-process and r-process
Q-values required for evaluating rp and r-process paths
𝑄 = 𝑀𝑝𝑎𝑟𝑒𝑛𝑡 − 𝑀𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟 𝑐 2
Masses of “waiting point” nuclei in rp-process
e.g. 64Ge, 68Se, 72Kr
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
theoretical
correction
constant
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 + 𝑏𝐹 𝛾1 /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
CKM matrix
𝑉𝑢𝑑
𝑉𝑐𝑑
𝑉𝑡𝑑
𝑉𝑢𝑠
𝑉𝑐𝑠
𝑉𝑡𝑠
𝑉𝑢𝑏
𝑉𝑐𝑏
𝑉𝑡𝑏
unitarity
𝑉𝑢
2
=0.99978(55)
Summary of required precisions
Field
Application
Precision
Nuclear Astrophysics
r, rp, s processes
106 – 107
Nuclear Physics
Mass Models
106 – 108
Nuclear Structure
106 – 108
Fundamental Interactions
108 – 109
-decay
108 – 109
-decay, Electron Capture
1010 – 1012
-ray standard calibrations
1010 – 1011
Fundamental Constants
1010 – 1012
Test of E = mc2
1010 – 1012
Neutrino Physics
Metrology
HOW
Atomic Mass Measurements
Historically, three main methods:
Electromagnetic spectographs
and spectrometers
Time of flight
RF spectrometer
J.J. Thomson (1913)
G. Audi, IJMS 251, 85 (2006) doi:10.1016/j.ijms.2006.01.048
HOW
Atomic Mass Measurements
Currently, three main (high-precision) methods for exotic isotopes:
Penning trap
Storage ring
Multi-reflection time of flight
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
Uniform B-Field
𝐵 = 𝐵0 𝑧
+
1 𝑞𝐵
𝜈𝑐 =
2𝜋 𝑚
νc = cyclotron frequency
m = mass
q = charge
B = magnetic field strength
Convert the mass measurement into a (cyclotron) frequency measurement
The Penning Trap
Uniform B-Field
𝐵 = 𝐵0 𝑧
+
1 𝑞𝐵
𝜈𝑐 =
2𝜋 𝑚
νc = cyclotron frequency
m = mass
q = charge
B = magnetic field strength
Radial Confinement
Convert the mass measurement into a (cyclotron) frequency measurement
The Penning Trap
Quadrupole E-Field
end-cap
Provides a linear restoring force:
+
+
-
+
ring
 Simple Harmonic Motion
 Frequency independent of amplitude
+
end-cap
𝜌2
𝑉
𝜑 𝑧, 𝜌 = 2 𝑧 2 −
2𝑑
2
Axial Oscillation Frequency
1
𝑞𝑉
𝜈𝑧 =
2𝜋 𝑚𝑑 2
The Penning Trap
Uniform B-Field
Quadrupole E-Field
Superconducting Magnet
Hyperbolic Electrodes
1 𝑞𝐵
𝜈𝑐 =
2𝜋 𝑚
Higher B-field  Higher precision
(for a given measurement precision, Δ𝜈𝑐 )
Δ𝑚 Δ𝜈𝑐
=
𝑚
𝜈𝑐
Hyperbolic surfaces are equipotentials
of the potential we wish to create.
Motion in the Penning Trap
Uniform B-Field
+
3 Normal Modes
Quadrupole E-Field
+
+
-
+
=
ν-
νz
ν+
1 𝑞𝐵
𝜈𝑐 =
2𝜋 𝑚
1
𝑞𝑉
𝜈𝑧 =
2𝜋 𝑚𝑑 2
True cyclotron frequency is related
to the trap-mode frequencies via
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
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
Coupling the Normal Modes
-
+
-
+
+
+
+
-
+
-
+
t

pulse
Magnetron
Cyclotron
Cyclotron Frequency Measurement
Drive radial motion
Convert -  +
Radial energy gain
Cyclotron Frequency Measurement
Time of Flight Technique
B
Inhomogeneous part
of magnetic field
z
Drive radial motion
Trap
MCP
Eject Ions from Trap
Convert -  +
Radial energy gain
Convert Er  Ez
Axial energy gain
Cyclotron Frequency Measurement
Time of Flight Technique
B
Inhomogeneous part
of magnetic field
z
Detector
Drive radial motion
Trap
MCP
Eject Ions from Trap
Convert -  +
Radial energy gain
Convert Er  Ez
Axial energy gain
Record TOF to MCP
Minimum when
Mass Ratio Measurement
Detector
Penning Trap Facilities World Wide
LEBIT, NSCL
Projectile Fragmentation
SMILETRAP
Highly-charged
stable isotopes
TRIGA-TRAP, MPI
Nuclear reactor
fission products
TITAN, TRIUMF
ISOL
ISOLTRAP, ISOLDE/CERN
ISOL
CPT, ARGONNE
252Cf fission fragments
MIT-FSU Trap
High-precision
(Stable Isotopes)
JYFLTRAP, Jyvaskyla
IGISOL
SHIPTRAP, GSI
Superheavy Elements
Storage Ring Mass Spectrometry
Measure frequency at which ions go around the ring
But, velocity spread  frequency spread
∆𝑓
1 ∆𝑚 𝑞 ∆𝑣
𝛾2
=− 2
+
1− 2
𝑓
𝛾𝑡 𝑚 𝑞
𝑣
𝛾𝑡
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
Solutions
• Extremely low rates
• Efficient transport to trap
• Short half-lives
• New tools
- MR-TOF
• Background contamination
• High-precision requirements
• 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