Ab Initio Calculation of the Neutron-Proton Mass Difference
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Neutron Stars
Chandra X-Ray Observatory X-Ray Astronomy Field Guide Neutron Stars Ordinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons. The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% Chandra Image of Vela Pulsar open space! (NASA/PSU/G.Pavlov et al. What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons! Such extreme forces occur in nature when the central part of a massive star collapses to form a neutron star. The atoms are crushed completely, and the electrons are jammed inside the protons to form a star composed almost entirely of neutrons. -
The Five Common Particles
The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2. -
Photons from 252Cf and 241Am-Be Neutron Sources H
Neutronenbestrahlungsraum Calibration Laboratory LB6411 Am-Be Quelle [email protected] Photons from 252Cf and 241Am-Be neutron sources H. Hoedlmoser, M. Boschung, K. Meier and S. Mayer Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland At the accredited PSI calibration laboratory neutron reference fields traceable to the standards of the Physikalisch-Technische Bundesanstalt (PTB) in Germany are available for the calibration of ambient and personal dose equivalent (rate) meters and passive dosimeters. The photon contribution to H*(10) in the neutron fields of the 252Cf and 241Am-Be sources was measured using various photon dose rate meters and active and passive dosimeters. Measuring photons from a neutron source involves considerable uncertainties due to the presence of neutrons, due to a non-zero neutron sensitivity of the photon detector and due to the energy response of the photon detectors. Therefore eight independent detectors and methods were used to obtain a reliable estimate for the photon contribution as an average of the individual methods. For the 241Am-Be source a photon contribution of approximately 4.9% was determined and for the 252Cf source a contribution of 3.6%. 1) Photon detectors 2) Photons from 252Cf and 241Am-Be neutron sources Figure 1 252Cf decays through -emission (~97%) and through spontaneous fission (~3%) with a half-life of 2.65 y. Both processes are accompanied by photon radiation. Furthermore the spectrum of fission products contains radioactive elements that produce additional gamma photons. In the 241Am-Be source 241Am decays through -emission and various low energy emissions: 241Am237Np + + with a half life of 432.6 y. -
Elementary Particles: an Introduction
Elementary Particles: An Introduction By Dr. Mahendra Singh Deptt. of Physics Brahmanand College, Kanpur What is Particle Physics? • Study the fundamental interactions and constituents of matter? • The Big Questions: – Where does mass come from? – Why is the universe made mostly of matter? – What is the missing mass in the Universe? – How did the Universe begin? Fundamental building blocks of which all matter is composed: Elementary Particles *Pre-1930s it was thought there were just four elementary particles electron proton neutron photon 1932 positron or anti-electron discovered, followed by many other particles (muon, pion etc) We will discover that the electron and photon are indeed fundamental, elementary particles, but protons and neutrons are made of even smaller elementary particles called quarks Four Fundamental Interactions Gravitational Electromagnetic Strong Weak Infinite Range Forces Finite Range Forces Exchange theory of forces suggests that to every force there will be a mediating particle(or exchange particle) Force Exchange Particle Gravitational Graviton Not detected so for EM Photon Strong Pi mesons Weak Intermediate vector bosons Range of a Force R = c Δt c: velocity of light Δt: life time of mediating particle Uncertainity relation: ΔE Δt=h/2p mc2 Δt=h/2p R=h/2pmc So R α 1/m If m=0, R→∞ As masses of graviton and photon are zero, range is infinite for gravitational and EM interactions Since pions and vector bosons have finite mass, strong and weak forces have finite range. Properties of Fundamental Interactions Interaction -
Chapter 5 the Relativistic Point Particle
Chapter 5 The Relativistic Point Particle To formulate the dynamics of a system we can write either the equations of motion, or alternatively, an action. In the case of the relativistic point par- ticle, it is rather easy to write the equations of motion. But the action is so physical and geometrical that it is worth pursuing in its own right. More importantly, while it is difficult to guess the equations of motion for the rela- tivistic string, the action is a natural generalization of the relativistic particle action that we will study in this chapter. We conclude with a discussion of the charged relativistic particle. 5.1 Action for a relativistic point particle How can we find the action S that governs the dynamics of a free relativis- tic particle? To get started we first think about units. The action is the Lagrangian integrated over time, so the units of action are just the units of the Lagrangian multiplied by the units of time. The Lagrangian has units of energy, so the units of action are L2 ML2 [S]=M T = . (5.1.1) T 2 T Recall that the action Snr for a free non-relativistic particle is given by the time integral of the kinetic energy: 1 dx S = mv2(t) dt , v2 ≡ v · v, v = . (5.1.2) nr 2 dt 105 106 CHAPTER 5. THE RELATIVISTIC POINT PARTICLE The equation of motion following by Hamilton’s principle is dv =0. (5.1.3) dt The free particle moves with constant velocity and that is the end of the story. -
Theory of More Than Everything1
Universally of Marineland Alimentary Gastronomy Universe of Murray Gell-Mann Elementary My Dear Watson Unified Theory of My Elementary Participles .. ^ n THEORY OF MORE THAN EVERYTHING1 V. Gates, Empty Kangaroo, M. Roachcock, and W.C. Gall 2 Compartment of Physiques and Astrology Universally of Marineland, Alleged kraP, MD ABSTRACT We derive a theory which, after spontaneous, dynamical, and ad hoc symmetry breaking, and after elimination of all fields except a set of zero measure, produces 10-dimensional superstring theory. Since the latter is a theory of only everything, our theory describes much more than everything, and includes also anything, something, and nothing. (More text should go here. So sue me.) 1Work supported by little or no evidence. 2Address after September 1, 1988: ITP, SHIITE, Roc(e)ky Brook, NY Uniformity of Modern Elementary Particle Physics Unintelligibility of Many Elementary Particle Physicists Universal City of Movieland Alimony Parties You Truth is funnier than fiction | A no-name moose1] Publish or parish | J.C. Polkinghorne Gimme that old minimal supergravity. Gimme that old minimal supergravity. It was good enough for superstrings. 1 It's good enough for me. ||||| Christian Physicist hymn1 2 ] 2. CONCLUSIONS The standard model has by now become almost standard. However, there are at least 42 constants which it doesn't explain. As is well known, this requires a 42 theory with at least @0 times more particles in its spectrum. Unfortunately, so far not all of these 42 new levels of complexity have been discovered; those now known are: (1) grandiose unification | SU(5), SO(10), E6,E7,E8,B12, and Niacin; (2) supersummitry2]; (3) supergravy2]; (4) supursestrings3−5]. -
Opportunities for Neutrino Physics at the Spallation Neutron Source (SNS)
Opportunities for Neutrino Physics at the Spallation Neutron Source (SNS) Paper submitted for the 2008 Carolina International Symposium on Neutrino Physics Yu Efremenko1,2 and W R Hix2,1 1University of Tennessee, Knoxville TN 37919, USA 2Oak Ridge National Laboratory, Oak Ridge TN 37981, USA E-mail: [email protected] Abstract. In this paper we discuss opportunities for a neutrino program at the Spallation Neutrons Source (SNS) being commissioning at ORNL. Possible investigations can include study of neutrino-nuclear cross sections in the energy rage important for supernova dynamics and neutrino nucleosynthesis, search for neutrino-nucleus coherent scattering, and various tests of the standard model of electro-weak interactions. 1. Introduction It seems that only yesterday we gathered together here at Columbia for the first Carolina Neutrino Symposium on Neutrino Physics. To my great astonishment I realized it was already eight years ago. However by looking back we can see that enormous progress has been achieved in the field of neutrino science since that first meeting. Eight years ago we did not know which region of mixing parameters (SMA. LMA, LOW, Vac) [1] would explain the solar neutrino deficit. We did not know whether this deficit is due to neutrino oscillations or some other even more exotic phenomena, like neutrinos decay [2], or due to the some other effects [3]. Hints of neutrino oscillation of atmospheric neutrinos had not been confirmed in accelerator experiments. Double beta decay collaborations were just starting to think about experiments with sensitive masses of hundreds of kilograms. Eight years ago, very few considered that neutrinos can be used as a tool to study the Earth interior [4] or for non- proliferation [5]. -
Gravitational Field of Massive Point Particle in General Relativity
Gravitational Field of Massive Point Particle in General Relativity P. P. Fiziev∗ Department of Theoretical Physics, Faculty of Physics, Sofia University, 5 James Bourchier Boulevard, Sofia 1164, Bulgaria. and The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy. Utilizing various gauges of the radial coordinate we give a description of static spherically sym- metric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist a two-parameters family of such solutions to the Einstein equations which are physically distinguishable but only some of them describe the gravitational field of a single massive point particle with nonzero bare mass M0. In particular, we show that the widespread Hilbert’s form of Schwarzschild solution, which depends only on the Keplerian mass M < M0, does not solve the Einstein equations with a massive point particle’s stress-energy tensor as a source. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravi- tational mass defect of a point particle and determine the dependence of the solutions on this mass − defect. The result can be described as a change of the Newton potential ϕN = GN M/r to a modi- M − 2 0 fied one: ϕG = GN M/ r + GN M/c ln M and a corresponding modification of the four-interval. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass. -
Fall 2009 PHYS 172: Modern Mechanics
PHYS 172: Modern Mechanics Fall 2009 Lecture 16 - Multiparticle Systems; Friction in Depth Read 8.6 Exam #2: Multiple Choice: average was 56/70 Handwritten: average was 15/30 Total average was 71/100 Remember, we are using an absolute grading scale where the values for each grade are listed on the syllabus Typically, exam grades (500/820 points) are lower than homework, recitation, clicker, & labs grades Clicker Question #1 You get in a parked car and start driving. Assume that you travel a distance D in 10 seconds, with a constant acceleration a. Define the system to be the car plus the driver (you), whose total mass is M and acceleration a. Choose the correct statement for this system: A. The final total kinetic energy is Ktotal= MaD. B. The final translational kinetic energy is Ktrans= MaD. C. The total energy of the system changes by +MaD. D. The total energy of the system changes by -MaD.. E. The total energy of the system does not change. Clicker Question Discussion You get in a parked car and start driving. Assume that you travel a distance D in 10 seconds, with a constant acceleration a. Define the system to be the car plus the driver (you), whose total mass is M and acceleration a. Choose the correct statement for this system: A. The final total kinetic energy is Ktotal= MaD.No, this is just the translational K. There is also relative K (wheels, etc.) B. The final translational kinetic energy is Ktrans= MaD. Correct, use point particle system; force is friction applied by the road on the tires. -
Improved Algorithms and Coupled Neutron-Photon Transport For
Submitted to ‘Chinese Physics C’ Improved Algorithms and Coupled Neutron-Photon Transport for Auto-Importance Sampling Method * Xin Wang(王鑫)1,2 Zhen Wu(武祯)3 Rui Qiu(邱睿)1,2;1) Chun-Yan Li(李春艳)3 Man-Chun Liang(梁漫春)1 Hui Zhang(张辉) 1,2 Jun-Li Li(李君利)1,2 Zhi Gang(刚直)4 Hong Xu(徐红)4 1 Department of Engineering Physics, Tsinghua University, Beijing 100084, China 2Key Laboratory of Particle & Radiation Imaging, Ministry of Education, Beijing 100084, China 3 Nuctech Company Limited, Beijing 100084, China 4 State Nuclear Hua Qing (Beijing) Nuclear Power Technology R&D Center Co. Ltd., Beijing 102209, China Abstract: The Auto-Importance Sampling (AIS) method is a Monte Carlo variance reduction technique proposed for deep penetration problems, which can significantly improve computational efficiency without pre-calculations for importance distribution. However, the AIS method is only validated with several simple examples, and cannot be used for coupled neutron-photon transport. This paper presents improved algorithms for the AIS method, including particle transport, fictitious particle creation and adjustment, fictitious surface geometry, random number allocation and calculation of the estimated relative error. These improvements allow the AIS method to be applied to complicated deep penetration problems with complex geometry and multiple materials. A Completely coupled Neutron-Photon Auto-Importance Sampling (CNP-AIS) method is proposed to solve the deep penetration problems of coupled neutron-photon transport using the improved algorithms. The NUREG/CR-6115 PWR benchmark was calculated by using the methods of CNP-AIS, geometry splitting with Russian roulette and analog Monte Carlo, respectively. -
8.1 the Neutron-To-Proton Ratio
M. Pettini: Introduction to Cosmology | Lecture 8 PRIMORDIAL NUCLEOSYNTHESIS Our discussion at the end of the previous lecture concentrated on the rela- tivistic components of the Universe, photons and leptons. Baryons (which are non-relativistic) did not figure because they make a trifling contribu- tion to the energy density. However, from t ∼ 1 s a number of nuclear reactions involving baryons took place. The end result of these reactions was to lock up most of the free neutrons into 4He nuclei and to create trace amounts of D, 3He, 7Li and 7Be. This is Primordial Nucleosynthesis, also referred to as Big Bang Nucleosynthesis (BBN). 8.1 The Neutron-to-Proton Ratio Before neutrino decoupling at around 1 MeV, neutrons and protons are kept in mutual thermal equilibrium through charged-current weak interactions: + n + e ! p +ν ¯e − p + e ! n + νe (8.1) − n ! p + e +ν ¯e While equilibrium persists, the relative number densities of neutrons and protons are given by a Boltzmann factor based on their mass difference: n ∆m c2 1:5 = exp − = exp − (8.2) p eq kT T10 where 10 ∆m = (mn − mp) = 1:29 MeV = 1:5 × 10 K (8.3) 10 and T10 is the temperature in units of 10 K. As discussed in Lecture 7.1.2, this equilibrium will be maintained so long as the timescale for the weak interactions is short compared with the timescale of the cosmic expansion (which increases the mean distance between parti- cles). In 7.2.1 we saw that the ratio of the two rates varies approximately as: Γ T 3 ' : (8.4) H 1:6 × 1010 K 1 This steep dependence on temperature can be appreciated as follows. -
“WHAT IS an ELECTRON?” Contents 1. Quantum Mechanics in A
\WHAT IS AN ELECTRON?" OR PARTICLES AS REPRESENTATIONS ROK GREGORIC Abstract. In these informal notes, we attempt to offer some justification for the math- ematical physicist's answer: \A certain kind of representation.". This requires going through some reasonably basic physical ideas, such as the barest basics of quantum mechanics and special relativity. Contents 1. Quantum Mechanics in a Nutshell2 2. Symmetry7 3. Toward Particles 11 4. Special Relativity in a Nutshell 14 5. Spin 21 6. Particles in Relativistic Quantum Mechaniscs 25 0.1. What these notes are. This are higly informal notes on basic physics. Being a mathematician-in-training myself, I am afraid I am incapable of writing for any other audience. Thus these notes must fall into the unfortunate genre of \physics for math- ematicians", an idiosyncracy on the level of \music for the deaf" or \visual art for the blind" - surely possible in some fashion, but only after overcoming substantial technical obstacles, and even then likely to be accussed by the cognoscenti of \missing the point" of the original. And yet we beat on, boats against the current, . 0.2. How they came about. As usual, this write-up began its life in the form of a series of emails to my good friend Tom Gannon. Allow me to recount, only a tinge apocryphally, one major impetus for its existence: the 2020 New Year's party. Hosted at Tom's apartment, it featured a decent contingent of UT math department's grad student compartment. Among others in attendence were Ivan Tulli, a senior UT grad student working on mathematics inperceptably close to theoretical physics, and his wife Anabel, a genuine experimental physicist from another department, in town to visit her husband.