Precision Nuclear Mass Measurements Matthew Redshaw Exotic Beam Summer School, Florida State University Aug 7 th 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 neutrons electrons
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
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. Binding energy and therefore atomic mass is a unique, fundamental property of a nucleus Nuclear masses are needed as inputs for understanding physical processes
WHAT Unified Atomic Mass Unit The atomic mass unit is defined as 1/12 th of the mass of 12 C in its ground state 1 u = m u = 1 12 m( 12 C )
WHAT Unified Atomic Mass Unit The atomic mass unit is defined as 1/12 th of the mass of 12 C in its ground state 1 u = m u = 1 12 m( 12 C ) (not amu, please)
WHAT Unified Atomic Mass Unit The atomic mass unit is defined as 1/12 th of the mass of 12 C in its ground state 1 u = m u = 1 12 m( 12 C ) Conversion to kev 1 u = 931,494.0954 57 kev 1 u m p m n 1 GeV Mass Excess ME = Δ = M[ A X] 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[ A X] A 931,494.0954 57 kev/u
Nuclear Structure: Shell Structure Neutron separation energy S n = M ZN 1 ZN M( X) m n X Z Z
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 51-54 Ca: 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 11 Li: 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 (t 1/2 = 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 (t 1/2 = 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 = M parent M daughter c 2 Masses of waiting point nuclei in rp-process e.g. 64 Ge, 68 Se, 72 Kr 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, G V is not renormalized in the nuclear medium theoretical correction constant Statistical rate function - depends on BR, t 1/2, 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 b F γ 1 /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 V ud V us V ub V cd V cs V cb V td V ts V tb unitarity V u 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 Neutrino Physics -decay 10 8 10 9 -decay, Electron Capture 10 10 10 12 Metrology -ray standard calibrations 10 10 10 11 Fundamental Constants 10 10 10 12 Test of E = mc 2 10 10 10 12
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 = B 0 z ν c = 1 qb 2π m ν c = 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 = B 0 z ν c = 1 qb 2π m ν c = 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 φ z, ρ = V 2d 2 z2 ρ2 2 Axial Oscillation Frequency ν z = 1 2π qv md 2
The Penning Trap Uniform B-Field Superconducting Magnet Quadrupole E-Field Hyperbolic Electrodes ν c = 1 qb 2π m Hyperbolic surfaces are equipotentials of the potential we wish to create. Higher B-field Higher precision (for a given measurement precision, Δν c ) Δm m = Δν c ν c
Motion in the Penning Trap Uniform B-Field Quadrupole E-Field 3 Normal Modes - = ν - ν z ν ν c = 1 qb 2π m ν z = 1 2π qv md 2 True cyclotron frequency is related to the trap-mode frequencies via
Manipulating the Motion of the Ion Driving the Normal Modes Dipole rf field at rf = ± will excite radial motion - Coupling the Normal Modes - 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 Eject Ions from Trap MCP Convert - Radial energy gain Convert E r E z Axial energy gain
Cyclotron Frequency Measurement Time of Flight Technique B Inhomogeneous part of magnetic field z Drive radial motion Trap Eject Ions from Trap MCP Detector Record TOF to MCP Convert - Radial energy gain Convert E r E z Axial energy gain Minimum when
Mass Ratio Measurement Detector
Penning Trap Facilities World Wide LEBIT, NSCL Projectile Fragmentation SMILETRAP Highly-charged stable isotopes JYFLTRAP, Jyvaskyla IGISOL TITAN, TRIUMF ISOL TRIGA-TRAP, MPI Nuclear reactor fission products ISOLTRAP, ISOLDE/CERN ISOL SHIPTRAP, GSI Superheavy Elements CPT, ARGONNE 252 Cf fission fragments 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 m q γ 2 t m q v v 1 γ2 γ t 2 t describes detour of particles due to dispersion
Storage Ring Mass Spectrometry Advantages: High sensitivity single 208 Hg 79 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