Optical pumping and the Zeeman Effect
|
|
- Doreen Patterson
- 5 years ago
- Views:
Transcription
1 1. Introduction Optical pumping and the Zeeman Effect The Hamiltonian of an atom with a single electron outside filled shells (as for rubidium) in a magnetic field is HH = HH 0 + ηηii JJ μμ JJ BB JJ μμ II BB II, where II is the spin of the nucleus and JJ is the total spin of all the electrons in the atom. We have JJ = 1, since JJ ssheeeeee = 0 for filled shells, and LL tttttttttt = 0 (figure 1). The term ηηii JJ expresses the interaction between the electron and nuclear magnetic momenta and is called the hyperfine interaction because it splits degenerate energy levels, as does the fine structure interaction. This form resembles the spin-orbit interaction LL SS, but now both operators are acting in abstract spin spaces. It splits levels with JJ = ± 1 and we take it as given, being equal to 3036 MMMMMM and 6835 MMMMMM, for Rb-85 and Rb-87 D 1 lines, respectively (figure ). The contribution of this term is easiest to calculate from II JJ = 1 (FF(FF + 1) II(II + 1) JJ(JJ + 1)) where FF = II + JJ is the total angular momentum. Fig.1: Grotrian diagram for Rb-85 and the D-doublet fine structure (similar to the famous Na D-doublet), with the DD 1 line at 795 nnnn PP1 PP3 SS1, and the DD line at 780 nnnn SS1. We will be using the DD 1 line only and, unlike in the atomic fluorescence experiment, zoom in much more on the line structure. Terms μμ JJ BB JJ, μμ II BB II describe the interaction with the external magnetic field. The μμ II II BB term can be neglected (even though the angular momenta II JJ) because μμ II μμ JJ = μμ BB. The shifts with magnetic field of the energy levels are then due to HH iiiiii = μμ JJ BB JJ only. Page 1
2 The shifts of the Zeeman Effect in the small field limit can be obtained with 1 st order perturbation theory. The dependence is linear for small fields as in our case, with ΔEE = μμ BB gg FF mmmm, where mm = FF, FF, the Lande gyromagnetic factors are gg FF = gg JJ FF(FF+1) II(II+1)+JJ(JJ+1) FF(FF+1) with gg JJ = for the D 1 line, and μμ BB is the Bohr magneton (see Appendix for full calculation). JJ = 1, II = 5, LL = 0 JJ = 1, II = 3, LL = 0 FF = 3 gg FF = 1 3 FF = gg FF = MMMMMM 6835 MMMMMM gg FF = 1 FF = gg FF = 1 3 FF = 1 Fig.: DD 1 line hyperfine structure of Rb-85 (left) and Rb-87 (right) in no magnetic field shows how the lines in figure 1 are split by the hyperfine interaction. The lines are further split into FF + 1 levels when a magnetic field is applied.. Experimental setup The maximum energy shift is 35 MMMMMM for a 50 GG maximum applied field and μμ BB = 1.4 MMMMMM/GG. Even at the highest field we apply, we only slightly move the energies compared to the hyperfine splitting. The Zeeman shift is only ccmm 1 in usual spectroscopy units, too small to measure with grating spectrometers of typical resolution ~0.1 1 ccmm 1. A different, high-resolution spectroscopy, method must be applied..1. Optical pumping A cell containing Rb atomic vapor (with a natural isotope mixture of 7 % Rb-85 and 8 % Rb- 87) is placed between the Rb lamp light source and a detector (Fig. 3). The hot water sleeve keeps the cell at a temperature > 40 0 CC (Rb evaporation point), to maintain the Rb atoms in the gas phase. Exercise: Rubidium is used because it has only two very strong and sharp resonances in the infrared. Estimate the Rb resonance cross section and compare to the sum rule σσ(ωω)dddd = ππ ee mmmm 5 mm = ss Question: why do we go through the trouble of heating with hot water, when heating tapes are available? 0 Page
3 Rb lamp Coil pair for DC and BB(tt) Nulling coils Hot water circulator Rb cell RF coils Photodiode Fig.3: the experimental setup. Polarizing optics is not shown. Optical pumping introduces an inversion between the occupancy of the atomic energy levels, by applying the restrictions of selection rules for transition that occur when the light beam passes through the cell. It is possible to interpret the optical pumping as a classical macro-polarization PP = ii,aaaaaaaaaa from adding the individual atomic polarizations. Optical pumping polarizes the atomic vapor and creates a macroscopic magnetic moment pointing along the horizontal axis... Zeeman Effect Several magnetic fields are applied: A nulling field BB NN along the vertical axis. Since a few GG are important, it is necessary to remove the background contribution of Earth s magnetic field. This is done with a small vertical coil pair that compensates the vertical background component. There is no background transverse (or horizontal across the optical axis) field if the setup is oriented with its optical axis along the horizontal component of the background field. The remaining background longitudinal field (along the optical axis) is compensated with the Zeeman DC field coils (next). A DC and time-dependent field BB ZZ,0 + BB ZZ (tt) oriented along the optical axis. This field splits the state energies with the Zeeman Effect. This requires a large pair, capable of 50 G uniform field across the cell s relatively large volume that sets the DC bias field BB ZZ,0, and a smaller variable field, modulated at a frequency ff 0. In addition, an RF oscillation along the cell axis at frequency ff RRRR is applied to the sample with a coil pair and a function generator. The oscillation can be written as two counter propagating linearly-polarized waves, each of which is a sum of RCP and LCP waves. pp ii Page 3
4 This moment (or alternatively, inverted microscopic distribution) is changed by the RF oscillating magnetic field at a fixed DC bias field. As the total field applied to the cell varies, we are moving sideways on the energy level diagram. When the separation between levels is equal to the applied RF frequency, the optical pumping inversion is disrupted; the cell absorbs more strongly, and transmission changes are detected by the photodiode. This allows inferring the separation between atomic energy levels with a resolution much higher than possible with a spectrometer because the RF oscillation is induced by a current, the frequency of which can be accurately determined. 3. Measurements To observe a resonance, the RF frequency ff RRRR is kept constant and the horizontal variable field BB zz (tt) is applied Connect ff 0 to the oscilloscope reference and the PD to its input Observe the dip in the intensity on the oscilloscope as the resonance condition is met 4. Conclusion Measurements confirm the quantum calculations. The Rb HF structure is applied in atomic clocks on GPS satellites. The Cs HF structure is applied in the even more-precise fountain atomic clock, where the atoms fall back through a region of RF fields. Locking the electronics microwave frequency to the more stable atomic microwave frequency gives a precise time reference. It is also possible to start a precession of the total moment of the cell with changes of applied BB in time (for instance, by turning off the RF field). These transient effects can be detected in the variations of the PD intensity. 5. Appendix Since parts of the Hamiltonian do not commute, no set of eigenkets (of II or JJ ) will diagonalize to total HH. We can choose any basis set we like, obtain the representation of HH in this basis set and then diagonalize the matrix to obtain the exact solution to the energy levels. When choosing the FF, mm FF basis set (eigenkets of FF = II + JJ and its projection along the zz axis), we have to calculate FF, mm FF ηηii JJ μμ JJ BB JJ FF, mm FF. Although the calculation looks similar, we are not doing PT and our matrix elements are not 1 st order energy shifts. To make the matrix small take the simpler case II = 1, JJ = 1 FF = 0,1. The basis set is FF, mm FF = { 1,1, 1,0, 1, 1, 0,0 }. Page 4
5 The result is ΔEE = ηη 4 μμμμ 0 0 ηη 4 ηη μμμμ (exercise: check this). The evolution of the μμμμ 0 0 μμμμ 4 0 3ηη 4 eigenvalues with applied magnetic field is shown in Fig. 4. This is the simplest case. Our Rb cell has a mixture of Rb-85 and Rb-87 isotopes with II = 5 and II = 3, respectively. The size of the matrix (II + 1) (JJ + 1) or 8 and 1, respectively, is the number of states and is unwieldy in these cases. Figure shows the solution for II = 5, JJ = 1 obtained with the Breit Rabi equation 1 EE FF = II ± 1, mm FF = ± Δww 4mmmm II+1 xx where Δww = ηη, xx = gg JJμμ BB BB Δww positive gg JJ in the B-R equation (verified in class)]. [the plus sign and Exercise: obtain and plot the result for the 8 energies for II = 3, JJ = 1 nnnnmm FF nnnnmm FF almost good Is there an exactly0good basis Set for small but finite fields? Analog of nnnnmm jj for the Z Effect? nnmm IImm JJ mm II = 5, mm JJ = 1 mm II = 3, mm JJ = 1 mm II = 1, mm JJ = 1 mm II = 1, mm JJ = 1 mm II = 1, mm JJ = 1 mm II = 1, mm JJ = 1 FF = 3, mm FF = 3,,1,0, 1,, 3 mm II = 3, mm JJ = 1 FF = 1, mm FF = 1,0, 1 mm II = 5, mm JJ = 1 FF = 0, mm FF = 0 mm II = 1, mm JJ = 1 FF =, mm FF =,1,0, 1, mm II = 5, mm JJ = 1 mm II = 3, mm JJ = 1 At low fields, the magnetic interaction is a perturbation on top of the hyperfine splitting. FF and mm FF are almost good quantum numbers It is remarkable that, in this case, there is a closed0from solution over the entire range of the magnetic field, including the middle range, where PT does not apply: this solution is called the Breit Rabi equation mm II = 1, mm JJ = 1 At high fields, the hyperfine splitting is a perturbation of the levels split by the magnetic field. mm II and mm JJ are good quantum numbers JJ = 1 mm JJ = ± 1 and II = 1 mm II = ± 1 mm II = 1, mm JJ = 1 mm II = 1, mm JJ = 1 mm II = 3, mm JJ = 1 mm II = 5, mm JJ = 1 Fig.4: Left panel: eigenvalues for an atom with II = 1, JJ = 1 in an applied external magnetic field. Right panel: the 1 energy levels for an atom with II = 5, JJ = 1 (Rb-85) in a magnetic field. The applied fields are relatively small (only the left-hand-side edge of the plots is measured), where the shifts are approximately linear. It is also possible to fit the curvature of results such as shown and obtain the hyperfine interaction constant ηη, even when relatively small magnetic fields are available. Page 5
6 Name Phys-60 Quantum Mechanics Laboratory Optical pumping and the Zeeman Effect lab report Dates of measurements: Page 6
Elastic light scattering
Elastic light scattering 1. Introduction Elastic light scattering in quantum mechanics Elastic scattering is described in quantum mechanics by the Kramers Heisenberg formula for the differential cross
More informationOptical Pumping in 85 Rb and 87 Rb
Optical Pumping in 85 Rb and 87 Rb John Prior III*, Quinn Pratt, Brennan Campbell, Kjell Hiniker University of San Diego, Department of Physics (Dated: December 14, 2015) Our experiment aimed to determine
More informationAtomic fluorescence. The intensity of a transition line can be described with a transition probability inversely
Atomic fluorescence 1. Introduction Transitions in multi-electron atoms Energy levels of the single-electron hydrogen atom are well-described by EE nn = RR nn2, where RR = 13.6 eeee is the Rydberg constant.
More informationOptical Pumping of Rb 85 & Rb 87
Optical Pumping of Rb 85 & Rb 87 Fleet Admiral Tim Welsh PhD. M.D. J.D. (Dated: February 28, 2013) In this experiment we penetrate the mystery surrounding the hyperfine structure of Rb 85 and Rb 87. We
More informationOptical pumping of rubidium
Optical pumping of rubidium Quinn Pratt, John Prior, Brennan Campbell a) (Dated: 25 October 2015) The effects of a magnetic field incident on a sample of rubidium were examined both in the low-field Zeeman
More informationCompendium of concepts you should know to understand the Optical Pumping experiment. \ CFP Feb. 11, 2009, rev. Ap. 5, 2012, Jan. 1, 2013, Dec.28,2013.
Compendium of concepts you should know to understand the Optical Pumping experiment. \ CFP Feb. 11, 2009, rev. Ap. 5, 2012, Jan. 1, 2013, Dec.28,2013. What follows is specialized to the alkali atoms, of
More informationCalifornia Institute of Technology Physics 77. Optical Pumping. Eric D. Black. September 27, 2004
California Institute of Technology Physics 77 Optical Pumping Eric D. Black September 7, 004 Sometimes you want to magnetize a gas, to align all of the little magnetic moments of the gas atoms in the same
More informationOptical Pumping of Rubidium
Optical Pumping of Rubidium Practical Course M I. Physikalisches Institut Universiät zu Köln February 3, 2014 Abstract The hyperfine levels of Rubidium atoms in a sample cell are split up into their Zeeman
More informationMagnetism of materials
Magnetism of materials 1. Introduction Magnetism and quantum mechanics In the previous experiment, you witnessed a very special case of a diamagnetic material with magnetic susceptibility χχ = 1 (usually
More informationOPTI 511L Fall Objectives:
RJ Jones OPTI 511L Fall 2017 Optical Sciences Experiment: Saturated Absorption Spectroscopy (2 weeks) In this experiment we explore the use of a single mode tunable external cavity diode laser (ECDL) to
More informationAtomic Physics 3 rd year B1
Atomic Physics 3 rd year B1 P. Ewart Lecture notes Lecture slides Problem sets All available on Physics web site: http:www.physics.ox.ac.uk/users/ewart/index.htm Atomic Physics: Astrophysics Plasma Physics
More informationPHY451, Spring /5
PHY451, Spring 2011 Notes on Optical Pumping Procedure & Theory Procedure 1. Turn on the electronics and wait for the cell to warm up: ~ ½ hour. The oven should already e set to 50 C don t change this
More informationPHL424: Nuclear Shell Model. Indian Institute of Technology Ropar
PHL424: Nuclear Shell Model Themes and challenges in modern science Complexity out of simplicity Microscopic How the world, with all its apparent complexity and diversity can be constructed out of a few
More informationOptical Pumping and the Hyperfine Structure of Rubidium 87 Laboratory Manual for Physics 3081
Optical Pumping and the Hyperfine Structure of Rubidium 87 Laboratory Manual for Physics 3081 Thomas Dumitrescu, Solomon Endlich May 2007 Abstract In this experiment you will learn about the powerful experimental
More information(1) Correspondence of the density matrix to traditional method
(1) Correspondence of the density matrix to traditional method New method (with the density matrix) Traditional method (from thermal physics courses) ZZ = TTTT ρρ = EE ρρ EE = dddd xx ρρ xx ii FF = UU
More informationA.1 Alkaline atoms in magnetic fields
164 Appendix the Kohn, virial and Bertrand s theorem, with an original approach. Annex A.4 summarizes elements of the elastic collisions theory required to address scattering problems. Eventually, annex
More informationCharge carrier density in metals and semiconductors
Charge carrier density in metals and semiconductors 1. Introduction The Hall Effect Particles must overlap for the permutation symmetry to be relevant. We saw examples of this in the exchange energy in
More informationQuantum state measurement
Quantum state measurement Introduction The rotation properties of light fields of spin are described by the 3 3 representation of the 0 0 SO(3) group, with the generators JJ ii we found in class, for instance
More informationPart I. Principles and techniques
Part I Principles and techniques 1 General principles and characteristics of optical magnetometers D. F. Jackson Kimball, E. B. Alexandrov, and D. Budker 1.1 Introduction Optical magnetometry encompasses
More informationDoppler-Free Spectroscopy of Hyperfine Zeeman Effects in Rubidium
Doppler-Free Spectroscopy of Hyperfine Zeeman Effects in Rubidium Samuel Bader and Leo Zhou MIT Department of Physics (Dated: May 19, 2013) The hyperfine Zeeman effect is observed via Doppler-free spectroscopy
More informationAlkali metals show splitting of spectral lines in absence of magnetic field. s lines not split p, d lines split
Electron Spin Electron spin hypothesis Solution to H atom problem gave three quantum numbers, n,, m. These apply to all atoms. Experiments show not complete description. Something missing. Alkali metals
More informationSaturation Absorption Spectroscopy of Rubidium Atom
Saturation Absorption Spectroscopy of Rubidium Atom Jayash Panigrahi August 17, 2013 Abstract Saturated absorption spectroscopy has various application in laser cooling which have many relevant uses in
More informationAtomic spectra of one and two-electron systems
Atomic spectra of one and two-electron systems Key Words Term symbol, Selection rule, Fine structure, Atomic spectra, Sodium D-line, Hund s rules, Russell-Saunders coupling, j-j coupling, Spin-orbit coupling,
More informationOBE solutions in the rotating frame
OBE solutions in the rotating frame The light interaction with the 2-level system is VV iiiiii = μμ EE, where μμ is the dipole moment μμ 11 = 0 and μμ 22 = 0 because of parity. Therefore, light does not
More information(b) The wavelength of the radiation that corresponds to this energy is 6
Chapter 7 Problem Solutions 1. A beam of electrons enters a uniform 1.0-T magnetic field. (a) Find the energy difference between electrons whose spins are parallel and antiparallel to the field. (b) Find
More informationATOMIC AND LASER SPECTROSCOPY
ALAN CORNEY ATOMIC AND LASER SPECTROSCOPY CLARENDON PRESS OXFORD 1977 Contents 1. INTRODUCTION 1.1. Planck's radiation law. 1 1.2. The photoelectric effect 4 1.3. Early atomic spectroscopy 5 1.4. The postulates
More informationZeeman Effect - Lab exercises 24
Zeeman Effect - Lab exercises 24 Pieter Zeeman Franziska Beyer August 2010 1 Overview and Introduction The Zeeman effect consists of the splitting of energy levels of atoms if they are situated in a magnetic
More informationFine structure in hydrogen - relativistic effects
LNPhysiqueAtomique016 Fine structure in hydrogen - relativistic effects Electron spin ; relativistic effects In a spectrum from H (or from an alkali), one finds that spectral lines appears in pairs. take
More informationSaturated Absorption Spectroscopy (Based on Teachspin manual)
Saturated Absorption Spectroscopy (Based on Teachspin manual) 1 Background One of the most important scientific applications of lasers is in the area of precision atomic and molecular spectroscopy. Spectroscopy
More information3. Perturbed Angular Correlation Spectroscopy
3. Perturbed Angular Correlation Spectroscopy Dileep Mampallil Augustine K.U.Leuven, Belgium Perturbed Angular Correlation Spectroscopy (PAC) is a gamma ray spectroscopy and can be used to investigate
More informationOptical Pumping in Rubidium
ADVANCED UNDERGRADUATE LABORATORY EXPERIMENT 5, Rb Optical Pumping in Rubidium Revised: March 1990 By: John Pitre 1 Purpose The object of this experiment is to measure the Zeeman splitting of the hyperfine
More informationMore. The Zeeman Effect. Normal Zeeman Effect
More The Zeeman Effect As we mentioned in Chapter, the splitting of spectral lines when an atom is placed in an external magnetic field was looked for by Faraday, predicted on the basis of classical theory
More informationFundamentals of Spectroscopy for Optical Remote Sensing. Course Outline 2009
Fundamentals of Spectroscopy for Optical Remote Sensing Course Outline 2009 Part I. Fundamentals of Quantum Mechanics Chapter 1. Concepts of Quantum and Experimental Facts 1.1. Blackbody Radiation and
More information" = Y(#,$) % R(r) = 1 4& % " = Y(#,$) % R(r) = Recitation Problems: Week 4. a. 5 B, b. 6. , Ne Mg + 15 P 2+ c. 23 V,
Recitation Problems: Week 4 1. Which of the following combinations of quantum numbers are allowed for an electron in a one-electron atom: n l m l m s 2 2 1! 3 1 0 -! 5 1 2! 4-1 0! 3 2 1 0 2 0 0 -! 7 2-2!
More informationAbsorption and Fluorescence Studies on Hyperfine Spectra of Rb and Dressed state picture
Absorption and Fluorescence Studies on Hyperfine Spectra of Rb and Dressed state picture Sabyasachi Barik National Institute of Science Education and Research, Bhubaneswar Project guide- Prof. C.S.Unnikrishnan
More informationPHL424: Nuclear fusion
PHL424: Nuclear fusion Hot Fusion 5 10 15 5 10 8 projectiles on target compound nuclei 1 atom Hot fusion (1961 1974) successful up to element 106 (Seaborgium) Coulomb barrier V C between projectile and
More information(1) Introduction: a new basis set
() Introduction: a new basis set In scattering, we are solving the S eq. for arbitrary VV in integral form We look for solutions to unbound states: certain boundary conditions (EE > 0, plane and spherical
More informationOPTICAL PUMPING OF RUBIDIUM OP1-B. Guide to the Experiment
Instruments Designed for Teaching OPTICAL PUMPING OF RUBIDIUM OP1-B Guide to the Experiment A PRODUCT OF TEACHSPIN, INC. TeachSpin, Inc. 2495 Main Street Suite 409 Buffalo, NY 14214-2153 (716) 885-4701
More informationPhotons in the universe. Indian Institute of Technology Ropar
Photons in the universe Photons in the universe Element production on the sun Spectral lines of hydrogen absorption spectrum absorption hydrogen gas Hydrogen emission spectrum Element production on the
More informationcharges q r p = q 2mc 2mc L (1.4) ptles µ e = g e
APAS 5110. Atomic and Molecular Processes. Fall 2013. 1. Magnetic Moment Classically, the magnetic moment µ of a system of charges q at positions r moving with velocities v is µ = 1 qr v. (1.1) 2c charges
More informationThe Zeeman Effect. Oisin De Conduin /2/2011
The Zeeman Effect Oisin De Conduin 07379510 2/2/2011 Abstract The purpose of this experiment was to study the splitting of a spectral line due to a magnetic field, known as the Zeeman effect. Specifically
More informationLinear relation between Heisenberg exchange and interfacial Dzyaloshinskii Moriya interaction in metal films
Linear relation between Heisenberg exchange and interfacial Dzyaloshinskii Moriya interaction in metal films Hans T. Nembach, Justin M. Shaw, Mathias Weiler*, Emilie Jué and Thomas J. Silva Electromagnetics
More informationLecture 4. Beyound the Dirac equation: QED and nuclear effects
Lecture 4 Beyound the Dirac equation: QED and nuclear effects Plan of the lecture Reminder from the last lecture: Bound-state solutions of Dirac equation Higher-order corrections to Dirac energies: Radiative
More informationPHL424: Feynman diagrams
PHL424: Feynman diagrams In 1940s, R. Feynman developed a diagram technique to describe particle interactions in space-time. Feynman diagram example Richard Feynman time Particles are represented by lines
More informationMore. The Zeeman Effect. Normal Zeeman Effect
More The Zeeman Effect As we mentioned in Chapter 3, the splitting of spectral lines when an atom is placed in an external magnetic field was looked for by Faraday, predicted on the basis of classical
More informationFundamental MRI Principles Module 2 N. Nuclear Magnetic Resonance. X-ray. MRI Hydrogen Protons. Page 1. Electrons
Fundamental MRI Principles Module 2 N S 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons positively charged neutrons no significant charge electrons negatively charged Protons
More informationAtomic and molecular physics Revision lecture
Atomic and molecular physics Revision lecture Answer all questions Angular momentum J`2 ` J z j,m = j j+1 j,m j,m =m j,m Allowed values of mgo from j to +jin integer steps If there is no external field,
More informationSupplementary Information
Supplementary Information I. Sample details In the set of experiments described in the main body, we study an InAs/GaAs QDM in which the QDs are separated by 3 nm of GaAs, 3 nm of Al 0.3 Ga 0.7 As, and
More informationV27: RF Spectroscopy
Martin-Luther-Universität Halle-Wittenberg FB Physik Advanced Lab Course V27: RF Spectroscopy ) Electron spin resonance (ESR) Investigate the resonance behaviour of two coupled LC circuits (an active rf
More informationSecond-order magic radio-frequency dressing for magnetically trapped 87. Rb atoms
DPG-Frühjahrstagung Heidelberg 2015 Second-order magic radio-frequency dressing for magnetically trapped 87 Rb atoms Georgy A. Kazakov, Thorsten Schumm Atominstitut TU Wien PRA 91, 023404 (2015) 21.03.2013
More informationFundamental MRI Principles Module Two
Fundamental MRI Principles Module Two 1 Nuclear Magnetic Resonance There are three main subatomic particles: protons neutrons electrons positively charged no significant charge negatively charged Protons
More informationSpin Dynamics Basics of Nuclear Magnetic Resonance. Malcolm H. Levitt
Spin Dynamics Basics of Nuclear Magnetic Resonance Second edition Malcolm H. Levitt The University of Southampton, UK John Wiley &. Sons, Ltd Preface xxi Preface to the First Edition xxiii Introduction
More informationLecture 0. NC State University
Chemistry 736 Lecture 0 Overview NC State University Overview of Spectroscopy Electronic states and energies Transitions between states Absorption and emission Electronic spectroscopy Instrumentation Concepts
More informationPAPER No. : 8 (PHYSICAL SPECTROSCOPY) MODULE No. : 8 (ALKALI METAL SPECTRA)
Subject Chemistry Paper No and Title Module No and Title Module Tag 8 and Physical Spectroscopy 8: Alkali metal spectra CHE_P8_M8 TABLE OF CONTENTS 1. Learning Outcomes 2. Introduction 3. Multi-electron
More informationZeeman effect - Wikipedia, the free encyclopedia
Zeeman effect From Wikipedia, the free encyclopedia The Zeeman effect (IPA: [ˈzeːmɑn], in English sometimes pronounced /ˈzeɪmən/) is the splitting of a spectral line into several components in the presence
More informationLecture 9 Electronic Spectroscopy
Lecture 9 Electronic Spectroscopy Molecular Orbital Theory: A Review - LCAO approximaton & AO overlap - Variation Principle & Secular Determinant - Homonuclear Diatomic MOs - Energy Levels, Bond Order
More informationMagnetic Resonance Spectroscopy ( )
Magnetic Resonance Spectroscopy In our discussion of spectroscopy, we have shown that absorption of E.M. radiation occurs on resonance: When the frequency of applied E.M. field matches the energy splitting
More informationOPTICAL SPECTROSCOPY AND THE ZEEMAN EFFECT Beyond the First Year workshop Philadelphia, July Greg Elliott, University of Puget Sound
OPTICAL SPECTROSCOPY AND THE ZEEMAN EFFECT Beyond the First Year workshop Philadelphia, July 5-7 Greg Elliott, University of Puget Sound The Zeeman effect offers a striking visual demonstration of a quantum
More informationThe Bose Einstein quantum statistics
Page 1 The Bose Einstein quantum statistics 1. Introduction Quantized lattice vibrations Thermal lattice vibrations in a solid are sorted in classical mechanics in normal modes, special oscillation patterns
More informationSpin resonance. Basic idea. PSC 3151, (301)
Spin Resonance Phys623 Spring 2018 Prof. Ted Jacobson PSC 3151, (301)405-6020 jacobson@physics.umd.edu Spin resonance Spin resonance refers to the enhancement of a spin flipping probability in a magnetic
More informationElectron spins in nonmagnetic semiconductors
Electron spins in nonmagnetic semiconductors Yuichiro K. Kato Institute of Engineering Innovation, The University of Tokyo Physics of non-interacting spins Optical spin injection and detection Spin manipulation
More informationCHAPTER 6: AN APPLICATION OF PERTURBATION THEORY THE FINE AND HYPERFINE STRUCTURE OF THE HYDROGEN ATOM. (From Cohen-Tannoudji, Chapter XII)
CHAPTER 6: AN APPLICATION OF PERTURBATION THEORY THE FINE AND HYPERFINE STRUCTURE OF THE HYDROGEN ATOM (From Cohen-Tannoudji, Chapter XII) We will now incorporate a weak relativistic effects as perturbation
More informationELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications
ELECTRON PARAMAGNETIC RESONANCE Elementary Theory and Practical Applications Second Edition JOHN A. WElL Department of Chemistry, University of Saskatchewan, Saskatoon, Saskatchewan, S7N OWO Canada JAMES
More information2m 2 Ze2. , where δ. ) 2 l,n is the quantum defect (of order one but larger
PHYS 402, Atomic and Molecular Physics Spring 2017, final exam, solutions 1. Hydrogenic atom energies: Consider a hydrogenic atom or ion with nuclear charge Z and the usual quantum states φ nlm. (a) (2
More informationF.G. Major. The Quantum Beat. The Physical Principles of Atomic Clocks. With 230 Illustrations. Springer
F.G. Major The Quantum Beat The Physical Principles of Atomic Clocks With 230 Illustrations Springer Contents Preface Chapter 1. Celestial and Mechanical Clocks 1 1.1 Cyclic Events in Nature 1 1.2 The
More informationIt is seen that for heavier atoms, the nuclear charge causes the spin-orbit interactions to be strong enough the force between the individual l and s.
Lecture 9 Title: - coupling Page- It is seen that for heavier atoms, the nuclear charge causes the spin-orbit interactions to be strong enough the force between the individual l and s. For large Z atoms,
More informationPhysics Spring 2010 Lab 1 - Electron Spin Resonance
Physics 24 -- Spring 2010 Lab 1 - Electron Spin Resonance Theory The application of an external magnetic field to an atom will split the atomic energy levels due to an interaction between the magnetic
More information(2) Orbital angular momentum
(2) Orbital angular momentum Consider SS = 0 and LL = rr pp, where pp is the canonical momentum Note: SS and LL are generators for different parts of the wave function. Note: from AA BB ii = εε iiiiii
More informationImproving the search for the electron s electric dipole moment in ThO
Improving the search for the electron s electric dipole moment in ThO ACME collaboration Electron EDM Zack Lasner Advanced Cold Molecule Electron EDM (ACME) collaboration WIDG, Yale University 9/22/15
More information2.4. Quantum Mechanical description of hydrogen atom
2.4. Quantum Mechanical description of hydrogen atom Atomic units Quantity Atomic unit SI Conversion Ang. mom. h [J s] h = 1, 05459 10 34 Js Mass m e [kg] m e = 9, 1094 10 31 kg Charge e [C] e = 1, 6022
More informationLecture 11: Polarized Light. Fundamentals of Polarized Light. Descriptions of Polarized Light. Scattering Polarization. Zeeman Effect.
Lecture 11: Polarized Light Outline 1 Fundamentals of Polarized Light 2 Descriptions of Polarized Light 3 Scattering Polarization 4 Zeeman Effect 5 Hanle Effect Fundamentals of Polarized Light Electromagnetic
More informationIII.4 Nuclear Magnetic Resonance
III.4 Nuclear Magnetic Resonance Radiofrequency (rf) spectroscopy on nuclear spin states in a uniaxial constant magnetic field B = B 0 z (III.4.1) B 0 is on the order of 1-25 T The rf frequencies vary
More informationAngular Momentum, Electromagnetic Waves
Angular Momentum, Electromagnetic Waves Lecture33: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay As before, we keep in view the four Maxwell s equations for all our discussions.
More informationLecture 11: Nucleon-Nucleon Interaction Basic properties The deuteron NN scattering Meson exchange model
Lecture 11: Nucleon-Nucleon Interaction Basic properties The deuteron NN scattering Meson exchange model Lecture 11: Ohio University PHYS7501, Fall 2017, Z. Meisel (meisel@ohio.edu) Zach Weinersmith (SMBC)
More information6.1 Nondegenerate Perturbation Theory
6.1 Nondegenerate Perturbation Theory Analytic solutions to the Schrödinger equation have not been found for many interesting systems. Fortunately, it is often possible to find expressions which are analytic
More informationThe Nuclear Emphasis
The Nuclear Emphasis Atoms are composed of electrons and nuclei we ll focus almost exclusively on the physical properties of the nucleus and the chemicoelectronic attributes of its environment. The nucleus
More information9. Transitions between Magnetic Levels Spin Transitions Between Spin States. Conservation of Spin Angular Momentum
9. Transitions between Magnetic Levels pin Transitions Between pin tates. Conservation of pin Angular Momentum From the magnetic energy diagram derived in the previous sections (Figures 14, 15 and 16),
More informationChemistry 431. Lecture 23
Chemistry 431 Lecture 23 Introduction The Larmor Frequency The Bloch Equations Measuring T 1 : Inversion Recovery Measuring T 2 : the Spin Echo NC State University NMR spectroscopy The Nuclear Magnetic
More informationLise Meitner, Otto Hahn. Nuclear Fission Hans-Jürgen Wollersheim
Lise Meitner, Otto Hahn Nuclear Fission Hans-Jürgen Wollersheim Details of the 252 Cf decay α s: 96.9% SF: 3.1% T 1/2 = 2.647 a Q α = 6.217 MeV E α = 6.118 MeV α α α α α-decay of 252 Cf Mass data: nucleardata.nuclear.lu.se/database/masses/
More informationQUANTUM MECHANICS AND ATOMIC STRUCTURE
5 CHAPTER QUANTUM MECHANICS AND ATOMIC STRUCTURE 5.1 The Hydrogen Atom 5.2 Shell Model for Many-Electron Atoms 5.3 Aufbau Principle and Electron Configurations 5.4 Shells and the Periodic Table: Photoelectron
More informationTutorial Questions. (look this up on NISTs database of atomic energy levels!), what are the units and magnitude
Tutorial Questions Dr. Greg Severn Dept. of Physics, University of San Diego, San Diego CA 92110 (Dated: Spring 2019) The process of experimental research involves integrating a great deal of different
More information1. neopentyl benzene. 4 of 6
I. 1 H NMR spectroscopy A. Theory 1. The protons and neutrons in atomic nuclei spin, as does the nucleus itself 2. The circulation of nuclear charge can generate a nuclear magnetic moment, u, along the
More informationLaser MEOP of 3 He: Basic Concepts, Current Achievements, and Challenging Prospects
Polarization in Noble Gases, October 8-13, 2017 Laser MEOP of 3 He: Basic Concepts, Current Achievements, and Challenging Prospects Pierre-Jean Nacher Geneviève Tastevin Laboratoire Kastler-Brossel ENS
More informationThe electric dipole moment and hyperfine interactions of KOH
The electric dipole moment and hyperfine interactions of KOH J. Cederberg and D. Olson Department of Physics, St. Olaf College, Northfield, Minnesota 55057 D. Rioux Department of Physics, University of
More information(relativistic effects kinetic energy & spin-orbit coupling) 3. Hyperfine structure: ) (spin-spin coupling of e & p + magnetic moments) 4.
4 Time-ind. Perturbation Theory II We said we solved the Hydrogen atom exactly, but we lied. There are a number of physical effects our solution of the Hamiltonian H = p /m e /r left out. We already said
More informationThe Zeeman Effect in Atomic Mercury (Taryl Kirk )
The Zeeman Effect in Atomic Mercury (Taryl Kirk - 2001) Introduction A state with a well defined quantum number breaks up into several sub-states when the atom is in a magnetic field. The final energies
More informationAtomic Structure. Chapter 8
Atomic Structure Chapter 8 Overview To understand atomic structure requires understanding a special aspect of the electron - spin and its related magnetism - and properties of a collection of identical
More information( ). Expanding the square and keeping in mind that
One-electron atom in a Magnetic Field When the atom is in a magnetic field the magnetic moment of the electron due to its orbital motion and its spin interacts with the field and the Schrodinger Hamiltonian
More informationAtomic and nuclear physics
Atomic and nuclear physics Atomic shell Normal Zeeman effect LEYBOLD Physics Leaflets Observing the normal Zeeman effect in transverse and longitudinal Objects of the experiment Observing the line triplet
More informationFine Structure of the metastable a 3 Σ u + state of the helium molecule
Fine Structure of the metastable a 3 Σ u + state of the helium molecule Rui Su and Charles Markus 12/4/2014 Abstract The original article written by Lichten, McCusker, and Vierima reported the measurement
More informationIntroduction to Electron Paramagnetic Resonance Spectroscopy
Introduction to Electron Paramagnetic Resonance Spectroscopy Art van der Est, Department of Chemistry, Brock University St. Catharines, Ontario, Canada 1 EPR Spectroscopy EPR is magnetic resonance on unpaired
More informationSecondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet
Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and
More informationInfluence of Code Size Variation on the Performance of 2D Hybrid ZCC/MD in OCDMA System
MATEC Web of Conferences 5, 68 (8) MUCET 7 https://doiorg/5/matecconf/8568 Influence of Code Size Variation on the Performance of D Hybrid ZCC/MD in OCDMA System Rima Matem,*, S A Aljunid, M N Junita,
More informationLecture 4: Polarimetry 2. Scattering Polarization. Zeeman Effect. Hanle Effect. Outline
Lecture 4: Polarimetry 2 Outline 1 Scattering Polarization 2 Zeeman Effect 3 Hanle Effect Scattering Polarization Single Particle Scattering light is absorbed and re-emitted if light has low enough energy,
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.76 Modern Topics in Physical Chemistry Spring, Problem Set #2
Reading Assignment: Bernath Chapter 5 MASSACHUSETTS INSTITUTE O TECHNOLOGY 5.76 Modern Topics in Physical Chemistry Spring 994 Problem Set # The following handouts also contain useful information: C &
More informationVariations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra
Variations ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Last Time Probability Density Functions Normal Distribution Expectation / Expectation of a function Independence Uncorrelated
More informationP. W. Atkins and R. S. Friedman. Molecular Quantum Mechanics THIRD EDITION
P. W. Atkins and R. S. Friedman Molecular Quantum Mechanics THIRD EDITION Oxford New York Tokyo OXFORD UNIVERSITY PRESS 1997 Introduction and orientation 1 Black-body radiation 1 Heat capacities 2 The
More informationAtomic Spectra in Astrophysics
Atomic Spectra in Astrophysics Potsdam University : Wi 2016-17 : Dr. Lidia Oskinova lida@astro.physik.uni-potsdam.de Complex Atoms Non-relativistic Schrödinger Equation 02 [ N i=1 ( ) 2 2m e 2 i Ze2 4πǫ
More informationNANOSCALE SCIENCE & TECHNOLOGY
. NANOSCALE SCIENCE & TECHNOLOGY V Two-Level Quantum Systems (Qubits) Lecture notes 5 5. Qubit description Quantum bit (qubit) is an elementary unit of a quantum computer. Similar to classical computers,
More informationAtomic and nuclear physics
Atomic and nuclear physics Atomic shell Normal Zeeman effect LEYBOLD Physics Leaflets Observing the normal Zeeman effect in transverse and longitudinal configuration Spectroscopy with a Fabry-Perot etalon
More information