Nuclear Magneton Theory of Mass Quantization "Unified Field Theory"
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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. -
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. -
Predicting the Binding Energies of the 1S Nuclides with High Precision, Based on Baryons Which Are Yang-Mills Magnetic Monopoles
Journal of Modern Physics, 2013, 4, 70-93 http://dx.doi.org/10.4236/jmp.2013.44A010 Published Online April 2013 (http://www.scirp.org/journal/jmp) Predicting the Binding Energies of the 1s Nuclides with High Precision, Based on Baryons which Are Yang-Mills Magnetic Monopoles Jay R. Yablon Schenectady, New York, USA Email: [email protected] Received March 22, 2013; revised April 24, 2013; accepted April 29, 2013 Copyright © 2013 Jay R. Yablon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT In an earlier paper, the author employed the thesis that baryons are Yang-Mills magnetic monopoles and that proton and neutron binding energies are determined based on their up and down current quark masses to predict a relationship among the electron and up and down quark masses within experimental errors and to obtain a very accurate relationship for nuclear binding energies generally and for the binding of 56Fe in particular. The free proton and neutron were under- stood to each contain intrinsic binding energies which confine their quarks, wherein some or most (never all) of this energy is released for binding when they are fused into composite nuclides. The purpose of this paper is to further ad- vance this thesis by seeing whether it can explain the specific empirical binding energies of the light 1s nuclides, namely, 2H, 3H, 3He and 4He, with high precision. As the method to achieve this, we show how these 1s binding ener- gies are in fact the components of inner and outer tensor products of Yang-Mills matrices which are implicit in the ex- pressions for these intrinsic binding energies. -
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. -
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. -
Silicon-Burning Process
Silicon-burning process In astrophysics, silicon burning is a very brief[1] sequence of nuclear fusion reactions that occur in massive stars with a minimum of about 8-11 solar masses. Silicon burning is the final stage of fusion for massive stars that have run out of the fuels that power them for their long lives in the main sequence on the Hertzsprung-Russell diagram. It follows the previous stages of hydrogen, helium, carbon, neon and oxygen burning processes. Silicon burning begins when gravitational contraction raises the star's core temperature to 2.7–3.5 billion Kelvin (GK). The exact temperature depends on mass. When a star has completed the silicon-burning phase, no further fusion is possible. The star catastrophically collapses and may explode in what is known as a Type II supernova. Contents Nuclear fusion sequence and silicon photodisintegration Binding energy See also Notes References External links Nuclear fusion sequence and silicon photodisintegration After a star completes the oxygen burning process, its core is composed primarily of silicon and sulfur.[2][3] If it has sufficiently high mass, it further contracts until its core reaches temperatures in the range of 2.7–3.5 GK (230–300 keV). At these temperatures, silicon and other elements can photodisintegrate, emitting a proton or an alpha particle.[2] Silicon burning proceeds by photodisintegration rearrangement,[4] which creates new elements by adding one of these freed alpha particles[2] (the equivalent of a helium nucleus) per capture step in the following sequence (photoejection of alphas not shown): 28 + 4 → 32 14Si 2He 16S 32 + 4 → 36 16S 2He 18Ar 36 + 4 → 40 18Ar 2He 20Ca 40 + 4 → 44 20Ca 2He 22Ti 44 + 4 → 48 22Ti 2He 24Cr 48 + 4 → 52 24Cr 2He 26Fe 52 + 4 → 56 26Fe 2He 28Ni 56 + 4 → 60 [nb 1] 28Ni 2He 30Zn The silicon-burning sequence lasts about one day before being struck by the shock wave that was launched by the core collapse. -
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 .. -
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 -
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. -
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. -
Chapter 1 MAGNETIC NEUTRON SCATTERING
Chapter 1 MAGNETIC NEUTRON SCATTERING. And Recent Developments in the Triple Axis Spectroscopy Igor A . Zaliznyak'" and Seung-Hun Lee(2) (')Department of Physics. Brookhaven National Laboratory. Upton. New York 11973-5000 (')National Institute of Standards and Technology. Gaithersburg. Maryland 20899 1. Introduction..................................................................................... 2 2 . Neutron interaction with matter and scattering cross-section ......... 6 2.1 Basic scattering theory and differential cross-section................. 7 2.2 Neutron interactions and scattering lengths ................................ 9 2.2.1 Nuclear scattering length .................................................. 10 2.2.2 Magnetic scattering length ................................................ 11 2.3 Factorization of the magnetic scattering length and the magnetic form factors ............................................................................................... 16 2.3.1 Magnetic form factors for Hund's ions: vector formalism19 2.3.2 Evaluating the form factors and dipole approximation..... 22 2.3.3 One-electron spin form factor beyond dipole approximation; anisotropic form factors for 3d electrons..................... 27 3 . Magnetic scattering by a crystal ................................................... 31 3.1 Elastic and quasi-elastic magnetic scattering............................ 34 3.2 Dynamical correlation function and dynamical magnetic susceptibility ............................................................................................ -
Neutrons and Magnetism
Collection SFN 13, 01002 (2014) DOI: 10.1051/sfn/20141301002 C Owned by the authors, published by EDP Sciences, 2014 Neutrons and magnetism Mechthild Enderle Institut Laue-Langevin, 6, Rue Jules Horowitz, BP. 156, 38042 Grenoble Cedex, France Abstract. Neutron scattering is a unique technique in magnetism, since it measures directly the Fourier transform of the time-dependent magnetic pair correlations. The neutron interacts only weakly with matter, so that each neutron normally only scatters once in the sample volume. The dynamic pair correlation functions are thus probed in the whole volume of the sample. Here we summarize the relevant formalism and approximations for neutron scattering on magnetic materials, focusing on the investigation of single crystals. The lecture aims to stimulate – not to replace – the study of the relevant literature [1–9]. 1. THERMAL NEUTRON SCATTERING 1.1 Properties of the neutron We recall some important properties of the neutron: – wave (interference, even with itself) – particle (mass m, energy-momentum relation, interactions) – lifetime of free neutron: 15 min (allows to do experiments) p = k = 2 – momentum = p2 = 2 2 = 2 2 – energy E 2m 2m k 2.072 k meV Å – no charge e – spin 1/2 and magnetic moment n =−N ˆ, where = 1.913, N = is the nuclear magneton, 2mp and ˆ is the Pauli spin operator. 1.2 Master equation All interactions of thermal (slow) neutrons with matter are weak, either due to the weakness of the interaction itself (interaction with the unpaired electrons, Foldy, spin-orbit), or, as in the case of the strong interaction with the nucleus, due to the extreme short-range character of the interaction and the extreme “dilution” of the point-like scattering nuclei in the scattering volume.