DOCSLIB.ORG

Comments on Units in Magnetism*

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Comments on Units in Magnetism* JOURNAL OF RESEARCH of the National Bureau of Standards Vo lume 83, No.1 , Jonuary- February 1978 Comments on Units in Magnetism* L. H. Bennett, C. H. Page, and L. J. Swartzendruber Institute for Materials Research, National Bureau of Standards, Washington, D.C. 20234 (August 26, 1977) Suggestions are give n on how to express magne ti c qua ntities in 51 units . Key words: Magneti sm; units . 1. Introduction mass s usceptibility for y-Fe in cmJ/g, and the rationalized volume susceptibility for Li (d im e nsionless). Since these Perus in g the 1974 M3 Co nference Proceedings indicates differences in units are not li sted in the table, a n unsus pect­ that, at the present time, Systeme Internationale (S l) units ing user could eas il y be mi sled. As most commonl y used are avo id ed by most lead in g scientis ts and engineers in the with sr, the re la ti on be tween B, H, and M is defin ed as B = fi eld of magneti sm. Throughout the Proceedings, almost /1-0 (H + M) , X = M/H. Some a uthors [3] exh ibit the /1-0 universal preference is di s played for th e cgs e lectromagneti c assoc iated with the sr explic itly by re plac in g, H by B//1-o , system (or for the Gaussian system, whic h gives an equ ivalent giving X = /1-oM / B. This is, of course, approximately correct description of magneti c quantities). However, usage of SI for th e small s usceptibilities found in most diamagneti c and units in the fi eld of magneti sm will undoubtedly in crease paramagneti c mate ri als, but could be mi sappl ied to super­ with time. One barrier to in creased usage is the present lack paramagneti c or fe rromagneti c materi als. of standardized and agreed upon relationships be tween magne ti c quantities within the SI. In this paper we will 3. Recommendations tentatively propose notati on and definiti ons for those relation­ ships most freque ntl y used by experimentalists, with the In orde r to ease conversion from Gaussian (and cgs emu) hope that this will help stimulate the magneti sm community to SJ units, the names, definitions, and symbols for magneti c to make their vi ews known on preferred definitions. quantities should be s tandardized. This requires agreement within the magneti sm community. Our curre nt recomme nda­ 2. Some Considerations on the Two Systems tions are summarized in the tables. Table 1 lists recommend ed symbols a nd names for mag­ One major property of the Gaussian (and the cgs emu) neti c quantities in SI a nd cgs emu. Whe n using SI units to system, considered an advantage by some and a disadvantage express susceptibility, we believe it would be useful to label by others, is that Band H have the same numeri cal va lue in it 'rationalized' and give it the sy mbol K , reserving X for the empty s pace. Changing to the SI , whe re not only do Band non-rationalized cgs e mu system. What we have labeled the H have different units in empty space, but also different "volume susceptibility" in table 1 is ofte n referred to simply numerical magnitudes, puts one somewhat in the position of as just "susceptibility." The introduc ti on of the symbol J Casimir's [1 p mythical tangenometrists who decided that, (where J = /1-oM) in the SI is useful due to the controversy " The volumetric displacement of empty space - although [4] over wh ether one s hould defin e B = /1-0 (H + M) or B = equal to unity - had the dimension Archimedes per Euclid." /1- 0 H + M. Furthe r, the symbol J and the associated name The Sl is a "rationalized" syste m, wh ereas the Gaussian ' magnetic polarization', are in current use [5]. is unrationalized. Thus, when magneti c susceptibilities are Table 2 compares several of the more important equations converted between the two systems a fac tor of 47T is involved. in the fi e ld of magneti sm. Equations (1) and (2) define the Fut·th er factors of 10 are involved de pending on wh ether recommended usage of the symbols M and J in sr, as vo lume, mass, or molar s usceptibility is in question. This mentioned above. In both Gaussian and SI units, the volume gives consid erable latitude for errors and ambiguities in data susceptibility, defin ed by eq (3), is dime nsionless and is the compilations, handbooks, and treati ses which attempt to ratio of M to H , (both with magnitudes which will change by convert existing numeri cal values to SI units, and numerous a factor of 47T upon rationalization). Equation (4) giv es the examples of such e rrors can be found . For example, in the force on a material placed in a magnetic field gradient. recent treatise on magne ti c materials by Heck [2], who (This equation involves certain assumptions and is most endeavors to use SI units as much as possible, a table of useful for small samples with small susceptibilties.) Equation paramagnetic susceptibilties apparently gives the rational­ (5) gives the energy of a (point) magnetic moment in a ized mass susceptibility for Pt in cm3/g, the unrationalized magnetic field , and eq (6) gives the volume energy density associated with a magneto static fi eld. * Reprinlt:d from AlP Conference Preceedings, No. 29, (2 1st Annual Conference- Philadelphia), Table 3 gives numerical factors for converting between beca use of il s interest 10 lIsers of magnetic un its. 1 Figures in brackets indicate the litera ture references at the e nd of th is paper. the two unit systems. The conversions for flux density, B, 9 TABLE I TABLE 2 Symbols and names for magneti c quantities in S I a nd cgs, Gaussian (or Corresponding equation s in SI and cgs Gaussian (o r cgs e mu). In this cgs emu). table, F refers to force, W refers to the e ne rgy of a magneti c dipole in a fi led , w refe rs to the volume e nergy densit y. Othe r symbols are defined in Name table 1. Symbol cgs emu S I Gaussian (or cgs e mu) Sl B nux de nsity magneti c nux densit y (magnetic induc- B = H + 47TM B = /1-0 (H + M) (1) induction tion) B = /1-o H + J (2) x = M/ H K = M/ H (3) H magnet ic field s tre ngt h magnetic field stre ngth iiH F = /1-oKVH aH/iix (4) F= XVH - ax M magnetization magnetization W = - mBcosli W = - mBcos li (5) BH w = ~BH (6) magn etic polarization w= 8 7T x vo lume susceptibility K rat iona lized volume susce pti­ and s usceptibility, X and K, are inde pende nt of the conven­ bility tions adopted, i. e. whether B = H + M, B = JLo H + M, mass susceptibility etc. Other conversions will depend on these conve ntions . One problem for th ose not thoroughly fam ilar with current rationalized mass susce ptibil­ magnetic unit usage is that 'emu' is not reall y a unit but it y rathe r a nag to describe the unit system be ing used. Often, Xmole molal' susceptibilit y though not always, a dimensional anayls is on s usceptibility units may be performed if 'emu' is re placed by c m3. Another Kmole rational ized mo lar suscept i­ problem which undoubtedly gives further difficulty to the bility uninitiated is the variety of units used for the same quantity m magneti e moment magn et ie mom ent in the Gaussian sys tem. For example, in the 1974 M3 conference proceedings we find the following units used for /1-B Bohr magneton Bohr magneton " magnetization": G, Oe, emu/g, JLB/atom, B.M./FORMULA TABLE 3. Conve rsion from. Gaussian to 51 Units Multipl y the Numbe r for To Obtain the Number for by Gaussian Quantity Un it SI Quantity Un it nux densit y, B G 10 4 nux de nsity, B T( = Wb/ m' = Vs/m2) magneti c field strength, H Oe 1Q3/4 7T magneti c fi eld stre ngth, H A/ m volume susceptibility, X e mu/c lII 3 (dime ns ionless) 47T rationalized vo lume susce pti- dimension less b ilit y, K mass susceptibilit y, Xp e mu/g (=cm3/g) 4 7T . 10- 3 rat iona} izecl mass susceptibil- m3/ kg ity, Kp molar suscept ibility, * Xmole e mu/ mol ( = c Ill3/ mol) 4 7T · 1O- 6 rationalized molar susceptibil- m3/ mol ity, Km ul e G or Oe 10 3 magnetization, M Aim magnetization, M 4 7T . 10- 4 magnetic polari zation, J T G 01' Oe 10"/47T magnetization, M Aim magneti zation,47TM 10- 4 magnetic polarization, J T /1-B /atom or /1- B/ fol'm. unit, I magnetization, M /1-B /atom or magnetization, M elc . ** /1-B /form. un it , e tc . ** magneti c moment of a e rglG 10- 3 magneti c moment of a J/T (= An?) dipole, m clipole, m dimensionless 1/47T rati onalized de magnetizing fac- d imensionless de magnetizing fac tor. N tor, N a Also called atomi c susceptibil it y. Molar suscepllbillty IS preferred s ince atomiC suscepti bi lity has also been used to refe r to the susceptibility pe r atom. ** " Natura l" units, inde pende nt of unit syste m.
Load more

Recommended publications
  • Magnetism, Magnetic Properties, Magnetochemistry
    Magnetism, Magnetic Properties, Magnetochemistry 1 Magnetism All matter is electronic Positive/negative charges - bound by Coulombic forces Result of electric field E between charges, electric dipole Electric and magnetic fields = the electromagnetic interaction (Oersted, Maxwell) Electric field = electric +/ charges, electric dipole Magnetic field ??No source?? No magnetic charges, N-S No magnetic monopole Magnetic field = motion of electric charges (electric current, atomic motions) Magnetic dipole – magnetic moment = i A [A m2] 2 Electromagnetic Fields 3 Magnetism Magnetic field = motion of electric charges • Macro - electric current • Micro - spin + orbital momentum Ampère 1822 Poisson model Magnetic dipole – magnetic (dipole) moment [A m2] i A 4 Ampere model Magnetism Microscopic explanation of source of magnetism = Fundamental quantum magnets Unpaired electrons = spins (Bohr 1913) Atomic building blocks (protons, neutrons and electrons = fermions) possess an intrinsic magnetic moment Relativistic quantum theory (P. Dirac 1928) SPIN (quantum property ~ rotation of charged particles) Spin (½ for all fermions) gives rise to a magnetic moment 5 Atomic Motions of Electric Charges The origins for the magnetic moment of a free atom Motions of Electric Charges: 1) The spins of the electrons S. Unpaired spins give a paramagnetic contribution. Paired spins give a diamagnetic contribution. 2) The orbital angular momentum L of the electrons about the nucleus, degenerate orbitals, paramagnetic contribution. The change in the orbital moment
    [Show full text]
  • Experiment QM2: NMR Measurement of Nuclear Magnetic Moments
    Physics 440 Spring (3) 2018 Experiment QM2: NMR Measurement of Nuclear Magnetic Moments Theoretical Background: Elementary particles are characterized by a set of properties including mass m, electric charge q, and magnetic moment µ. These same properties are also used to characterize bound collections of elementary particles such as the proton and neutron (which are built from quarks) and atomic nuclei (which are built from protons and neutrons). A particle's magnetic moment can be written in terms of spin as µ = g (q/2m) S where g is the "g-factor" for the particle and S is the particle spin. [Note 2 that for a classical rotating ball of charge S = (2mR /5) ω and g = 1]. For a nucleus, it is conventional to express the magnetic moment as µ A = gA µN IA /! where IA is the "spin", gA is the nuclear g-factor of nucleus A, and the constant µN = e!/2mp (where mp= proton mass) is known as the nuclear magneton. In a magnetic field (oriented in the z-direction) a spin-I nucleus can take on 2I+1 orientations with Iz = mI! where –I ≤ mI ≤ I. Such a nucleus experiences an orientation- dependent interaction energy of VB = –µ A•B = –(gA µN mI)Bz. Note that for a nucleus with positive g- factor the low energy state is the one in which the spin is aligned parallel to the magnetic field. For a spin-1/2 nucleus there are two allowed spin orientations, denoted spin-up and spin-down, and the up down energy difference between these states is simply given by |ΔVB| = VB −VB = 2µABz.
    [Show full text]
  • Lecture #4, Matter/Energy Interactions, Emissions Spectra, Quantum Numbers
    Welcome to 3.091 Lecture 4 September 16, 2009 Matter/Energy Interactions: Atomic Spectra 3.091 Periodic Table Quiz 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Name Grade /10 Image by MIT OpenCourseWare. Rutherford-Geiger-Marsden experiment Image by MIT OpenCourseWare. Bohr Postulates for the Hydrogen Atom 1. Rutherford atom is correct 2. Classical EM theory not applicable to orbiting e- 3. Newtonian mechanics applicable to orbiting e- 4. Eelectron = Ekinetic + Epotential 5. e- energy quantized through its angular momentum: L = mvr = nh/2π, n = 1, 2, 3,… 6. Planck-Einstein relation applies to e- transitions: ΔE = Ef - Ei = hν = hc/λ c = νλ _ _ 24 1 18 Bohr magneton µΒ = eh/2me 9.274 015 4(31) X 10 J T 0.34 _ _ 27 1 19 Nuclear magneton µΝ = eh/2mp 5.050 786 6(17) X 10 J T 0.34 _ 2 3 20 Fine structure constant α = µ0ce /2h 7.297 353 08(33) X 10 0.045 21 Inverse fine structure constant 1/α 137.035 989 5(61) 0.045 _ 2 1 22 Rydberg constant R¥ = mecα /2h 10 973 731.534(13) m 0.0012 23 Rydberg constant in eV R¥ hc/{e} 13.605 698 1(40) eV 0.30 _ 10 24 Bohr radius a0 = a/4πR¥ 0.529 177 249(24) X 10 m 0.045 _ _ 4 2 1 25 Quantum of circulation h/2me 3.636 948 07(33) X 10 m s 0.089 _ 11 1 26 Electron specific charge -e/me -1.758 819 62(53) X 10 C kg 0.30 _ 12 27 Electron Compton wavelength λC = h/mec 2.426 310 58(22) X 10 m 0.089 _ 2 15 28 Electron classical radius re = α a0 2.817 940 92(38) X 10 m 0.13 _ _ 26 1 29 Electron magnetic moment` µe 928.477 01(31) X 10 J T 0.34 _ _ 3 30 Electron mag.
    [Show full text]
  • The G Factor of Proton
    The g factor of proton Savely G. Karshenboim a,b and Vladimir G. Ivanov c,a aD. I. Mendeleev Institute for Metrology (VNIIM), St. Petersburg 198005, Russia bMax-Planck-Institut f¨ur Quantenoptik, 85748 Garching, Germany cPulkovo Observatory, 196140, St. Petersburg, Russia Abstract We consider higher order corrections to the g factor of a bound proton in hydrogen atom and their consequences for a magnetic moment of free and bound proton and deuteron as well as some other objects. Key words: Nuclear magnetic moments, Quantum electrodynamics, g factor, Two-body atoms PACS: 12.20.Ds, 14.20.Dh, 31.30.Jv, 32.10.Dk Investigation of electromagnetic properties of particles and nuclei provides important information on fundamental constants. In addition, one can also learn about interactions of bound particles within atoms and interactions of atomic (molecular) composites with the media where the atom (molecule) is located. Since the magnetic interaction is weak, it can be used as a probe to arXiv:hep-ph/0306015v1 2 Jun 2003 learn about atomic and molecular composites without destroying the atom or molecule. In particular, an important quantity to study is a magnetic moment for either a bare nucleus or a nucleus surrounded by electrons. The Hamiltonian for the interaction of a magnetic moment µ with a homoge- neous magnetic field B has a well known form Hmagn = −µ · B , (1) which corresponds to a spin precession frequency µ hν = B , (2) spin I Email address: [email protected] (Savely G. Karshenboim). Preprint submitted to Elsevier Science 1 February 2008 where I is the related spin equal to either 1/2 or 1 for particles and nuclei under consideration in this paper.
    [Show full text]
  • 1. Physical Constants 1 1
    1. Physical constants 1 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 1998 by B.N. Taylor (NIST). Based mainly on the “1986 Adjustment of the Fundamental Physical Constants” by E.R. Cohen and B.N. Taylor, Rev. Mod. Phys. 59, 1121 (1987). The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard- deviation uncertainties in the last digits; the corresponding uncertainties in parts per million (ppm) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). Since the 1986 adjustment, new experiments have yielded improved values for a number of constants, including the Rydberg constant R∞, the Planck constant h, the fine- structure constant α, and the molar gas constant R,and hence also for constants directly derived from these, such as the Boltzmann constant k and Stefan-Boltzmann constant σ. The new results and their impact on the 1986 recommended values are discussed extensively in “Recommended Values of the Fundamental Physical Constants: A Status Report,” B.N. Taylor and E.R. Cohen, J. Res. Natl. Inst. Stand. Technol. 95, 497 (1990); see also E.R. Cohen and B.N. Taylor, “The Fundamental Physical Constants,” Phys. Today, August 1997 Part 2, BG7. In general, the new results give uncertainties for the affected constants that are 5 to 7 times smaller than the 1986 uncertainties, but the changes in the values themselves are smaller than twice the 1986 uncertainties.
    [Show full text]
  • Magnetism in Transition Metal Complexes
    Magnetism for Chemists I. Introduction to Magnetism II. Survey of Magnetic Behavior III. Van Vleck’s Equation III. Applications A. Complexed ions and SOC B. Inter-Atomic Magnetic “Exchange” Interactions © 2012, K.S. Suslick Magnetism Intro 1. Magnetic properties depend on # of unpaired e- and how they interact with one another. 2. Magnetic susceptibility measures ease of alignment of electron spins in an external magnetic field . 3. Magnetic response of e- to an external magnetic field ~ 1000 times that of even the most magnetic nuclei. 4. Best definition of a magnet: a solid in which more electrons point in one direction than in any other direction © 2012, K.S. Suslick 1 Uses of Magnetic Susceptibility 1. Determine # of unpaired e- 2. Magnitude of Spin-Orbit Coupling. 3. Thermal populations of low lying excited states (e.g., spin-crossover complexes). 4. Intra- and Inter- Molecular magnetic exchange interactions. © 2012, K.S. Suslick Response to a Magnetic Field • For a given Hexternal, the magnetic field in the material is B B = Magnetic Induction (tesla) inside the material current I • Magnetic susceptibility, (dimensionless) B > 0 measures the vacuum = 0 material response < 0 relative to a vacuum. H © 2012, K.S. Suslick 2 Magnetic field definitions B – magnetic induction Two quantities H – magnetic intensity describing a magnetic field (Système Internationale, SI) In vacuum: B = µ0H -7 -2 µ0 = 4π · 10 N A - the permeability of free space (the permeability constant) B = H (cgs: centimeter, gram, second) © 2012, K.S. Suslick Magnetism: Definitions The magnetic field inside a substance differs from the free- space value of the applied field: → → → H = H0 + ∆H inside sample applied field shielding/deshielding due to induced internal field Usually, this equation is rewritten as (physicists use B for H): → → → B = H0 + 4 π M magnetic induction magnetization (mag.
    [Show full text]
  • Deuterium Magnetic Resonance: Theory and Application to Lipid Membranes
    Quarterly Reviews of Biophysics 10, 3 (1977), pp. 353-418. Printed in Great Britain Deuterium magnetic resonance: theory and application to lipid membranes JOACHIM SEELIG Department of Biophysical Chemistry, Biocenter of the University of Basel, Klingelbergstrasse 70, C//-4056 Basel, Switzerland I. INTRODUCTION 345 II. THEORY OF DEUTERIUM MAGNETIC RESONANCE 358 A. Deuterium magnetic resonance in the absence of molecular motion 358 1. General theory 358 2. Rotation of the coordinate system 359 3. Principal coordinate system 360 4. Energy levels 362 5. Lineshapes of polycrystalline samples 364 B. Deuterium magnetic resonance of liquid crystals 369 1. Anisotropic motions in liquid crystals 369 2. Deuterium-order parameters in planar-oriented liquid crystals 373 3. Lineshapes for random and cylindrical distributions of liquid crystalline microdomains 377 4. Anisotropic rotation of CD2 and CD3 groups 383 5. Deuterium quadrupole relaxation in anisotropic media 386 III. APPLICATION OF DEUTERIUM MAGNETIC RESONANCE TO LIPID MEMBRANES 388 A. Lipid bilayers composed of soap molecules 388 B. Phospholipid bilayers 393 1. Hydrocarbon region 394 2. Structure and flexibility of the polar head groups 405 REFERENCES 411 23-2 Downloaded from https://www.cambridge.org/core. WWZ Bibliothek, on 14 Nov 2017 at 10:27:10, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0033583500002948 354 J- SEELIG I. INTRODUCTION Proton and carbon-13 nmr spectra of unsonicated lipid bilayers and biological membranes are generally dominated by strong proton-proton and proton-carbon dipolar interactions. As a result the spectra contain a large number of overlapping resonances and are rather difficult to analyse.
    [Show full text]
  • 1. Physical Constants 101
    1. Physical constants 101 1. PHYSICAL CONSTANTS Table 1.1. Reviewed 2010 by P.J. Mohr (NIST). Mainly from the “CODATA Recommended Values of the Fundamental Physical Constants: 2006” by P.J. Mohr, B.N. Taylor, and D.B. Newell in Rev. Mod. Phys. 80 (2008) 633. The last group of constants (beginning with the Fermi coupling constant) comes from the Particle Data Group. The figures in parentheses after the values give the 1-standard-deviation uncertainties in the last digits; the corresponding fractional uncertainties in parts per 109 (ppb) are given in the last column. This set of constants (aside from the last group) is recommended for international use by CODATA (the Committee on Data for Science and Technology). The full 2006 CODATA set of constants may be found at http://physics.nist.gov/constants. See also P.J. Mohr and D.B. Newell, “Resource Letter FC-1: The Physics of Fundamental Constants,” Am. J. Phys, 78 (2010) 338. Quantity Symbol, equation Value Uncertainty (ppb) speed of light in vacuum c 299 792 458 m s−1 exact∗ Planck constant h 6.626 068 96(33)×10−34 Js 50 Planck constant, reduced ≡ h/2π 1.054 571 628(53)×10−34 Js 50 = 6.582 118 99(16)×10−22 MeV s 25 electron charge magnitude e 1.602 176 487(40)×10−19 C = 4.803 204 27(12)×10−10 esu 25, 25 conversion constant c 197.326 9631(49) MeV fm 25 conversion constant (c)2 0.389 379 304(19) GeV2 mbarn 50 2 −31 electron mass me 0.510 998 910(13) MeV/c = 9.109 382 15(45)×10 kg 25, 50 2 −27 proton mass mp 938.272 013(23) MeV/c = 1.672 621 637(83)×10 kg 25, 50 = 1.007 276 466 77(10) u = 1836.152 672 47(80) me 0.10, 0.43 2 deuteron mass md 1875.612 793(47) MeV/c 25 12 2 −27 unified atomic mass unit (u) (mass C atom)/12 = (1 g)/(NA mol) 931.494 028(23) MeV/c = 1.660 538 782(83)×10 kg 25, 50 2 −12 −1 permittivity of free space 0 =1/μ0c 8.854 187 817 ..
    [Show full text]
  • CODATA RECOMMENDED VALUES of the FUNDAMENTAL PHYSICAL CONSTANTS: 2014 NIST SP 961 (Sept/2015) Values From: P
    CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2014 NIST SP 961 (Sept/2015) Values from: P. J. Mohr, D. B. Newell, and B. N. Taylor, arXiv:1507.07956 Amoreextensivelistingofconstantsisavailableintheabove reference and on the NIST Physics Laboratory Web site physics.nist.gov/constants. The number in parentheses is the one-standard-deviation uncertainty in the last two digits of the given value. Quantity Symbol Numerical value Unit Quantity Symbol Numerical value Unit −1 speed of light in vacuum c, c0 299 792 458 (exact) m s muon g-factor −2(1 + aµ) gµ −2.002 331 8418(13) −7 −2 magnetic constant µ0 4π × 10 (exact) N A muon-proton magnetic moment ratio µµ/µp −3.183 345 142(71) −7 −2 −27 =12.566 370 614... × 10 NA proton mass mp 1.672 621 898(21) × 10 kg 2 −12 −1 electric constant 1/µ0c ϵ0 8.854 187 817... × 10 Fm in u 1.007 276 466 879(91) u −11 3 −1 −2 2 Newtonian constant of gravitation G 6.674 08(31) × 10 m kg s energy equivalent in MeV mpc 938.272 0813(58) MeV −34 Planck constant h 6.626 070 040(81) × 10 Js proton-electron mass ratio mp/me 1836.152 673 89(17) −15 −26 −1 in eV s 4.135 667 662(25) × 10 eV s proton magnetic moment µp 1.410 606 7873(97) × 10 JT −34 h/2π h¯ 1.054 571 800(13) × 10 Js to nuclear magneton ratio µp/µN 2.792 847 3508(85) −16 ′ ′ −6 in eV s 6.582 119 514(40) × 10 eV s proton magnetic shielding correction 1 − µp/µp σp 25.691(11) × 10 −19 ◦ elementary charge e 1.602 176 6208(98) × 10 C (H2O, sphere, 25 C) −15 8 −1 −1 magnetic flux quantum h/2e Φ0 2.067 833 831(13) × 10 Wb proton gyromagnetic ratio
    [Show full text]
  • A Quantitative Determination of the Neutron Moment in Absolute Nuclear Magnetons
    Luis W. Alvarez Phys. Rev. 57, 111 1940 A Quantitative Determination of the Neutron Moment in Absolute Nuclear Magnetons LUIS W. ALVAREZ, Radiation Laboratory, Department of Physics, University of California, Berkeley, California and F. BLOCH, Department of Physics, Stanford University, Polo Alto, California (Received October 30, 1939) Abstract The magnetic resonance method of determining nuclear magnetic moments in molecular beams, recently described by Rabi and his col- laborators, has been extended to allow the determination of the neu- tron moment. In place of deflection by inhomogeneous magnetic fields, magnetic scattering ie used to produce and analyze the polarized beam of neutrons. Partial depolarization of the neutron beam is observed when the Larmor precessional frequency of the neutrons in a strong field is in resonance with a weak oscillating magnetic field normal to the strong field. A knowledge of the frequency and field when the res- onance is observed, plus the assumption that the neutron spin is 1/2 yields the moment directly. The theory of the experiment is developed in some detail, and a description of the apparatus is given. A new method of evaluating magnetic moments in all experiments using the resonance method is described. It is shown that the magnetic moment of any nucleus may be determined directly in absolute nuclear mag- netons merely by a measurement of the ratio of two magnetic fields. These two fields are (a) that at which resonance occurs in a Rabi type experiment for a certain frequency, and (b) that at which protons are accelerated in a cyclotron operated on the nth harmonic of that fre- quency.
    [Show full text]
  • A Parts-Per-Billion Measurement of the Antiproton Magnetic Moment C
    OPEN LETTER doi:10.1038/nature24048 A parts-per-billion measurement of the antiproton magnetic moment C. Smorra1,2, S. Sellner1, M. J. Borchert1,3, J. A. Harrington4, T. Higuchi1,5, H. Nagahama1, T. Tanaka1,5, A. Mooser1, G. Schneider1,6, M. Bohman1,4, K. Blaum4, Y. Matsuda5, C. Ospelkaus3,7, W. Quint8, J. Walz6,9, Y. Yamazaki1 & S. Ulmer1 Precise comparisons of the fundamental properties of matter– of 5.3 MeV. These particles can be captured and cooled in Penning traps antimatter conjugates provide sensitive tests of charge–parity–time by using degrader foils, a well timed high-voltage pulse and electron (CPT) invariance1, which is an important symmetry that rests on cooling17. The core of our experiment is formed by two central devices; basic assumptions of the standard model of particle physics. a superconducting magnet operating at a magnetic field of B0 =​ 1.945 T, Experiments on mesons2, leptons3,4 and baryons5,6 have compared and an assembly of cylindrical Penning-trap electrodes18 (partly shown different properties of matter–antimatter conjugates with fractional in Fig. 1b) that is mounted inside the horizontal bore of the magnet. uncertainties at the parts-per-billion level or better. One specific A part of the electrode assembly forms a spin-state analysis trap with 2 quantity, however, has so far only been known to a fractional an inhomogeneous magnetic field Bz,AT(z) = B0,AT + B2,ATz , 7,8 −2 uncertainty at the parts-per-million level : the magnetic moment at B0,AT =​ 1.23 T and B2,AT =​ 272(12) kT m , and a precision trap 5 of the antiproton, μ p.
    [Show full text]
  • 31295015501306.Pdf (1.378Mb)
    A STUDY OF TK3 MGN3TIC PROPERTIES OF FERROCYAKTDij^S AND FERRICYANIDES by JACK ED7ARD RANDORFF, B. S. A THESIS IN PHYSICS Submitted to the Graduate Faculty of Texas Technological College in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCISIICE Approved Accented June, 1967 f^(A^fjin Cop. a ACKNO/JLEDGS-IENTS I am deeply appreciative of Dr. Billy J. I4arshall for his direction of this thesis; to the Robert A. Welch Foundation of Texas for financial support given to this project; to Dr. V/, 0, Milligan, research director of the forementioned Foundatior^ for the helpful and stimulating discussion with regard to this work and to his research group at Baylor University for the preparation of samples; and to the U. S. Department of Health, Education and V'elfrro for tho presentation of an N,D,E,A. Title IV Fellowship as financial support to pursue this study. ii TABLE OF COirrSxNTS ACKNO'WLEDG&IEOTS ii TABLE OF CONTENTS iii LIST OF TABLES iv LIST OF FIGURES v I, INTRODUCnON 1 II. EXPERIMEOTAL TECHMIQUE 3 Sample Preparation 3 Apparatus 3 Temperature Control and Detection 5 Calibrations and Corrections 6 Set-up Procedure 8 III, RESULTS Aim Discussion l6 IV. FUTURE WORK 33 LIST OF REFERENCES 34 APPENDIX I 35 APPENDIX II 42 APPENDIX III 43 iii LIST OF TABLES Table 1, The values of susceptibility and temperature.,, 19 Table 2, Effective number of Bohr Diagnetons per atom or per molecule, 20 iv LIST OF FIGURES Figure 1, Apparatus Assembly. 9 Figure lA. Internal view of Cahn RM Automatic Electrobalance, 10 Figure 2.
    [Show full text]