Shape parameterization

Similar documents
Mon. Tues. Wed. Lab Fri Electric and Rest Energy

5.61 Fall 2007 Lecture #2 page 1. The DEMISE of CLASSICAL PHYSICS

STATISTICAL MECHANICS OF DIATOMIC GASES


Solid state physics. Lecture 3: chemical bonding. Prof. Dr. U. Pietsch

6.Optical and electronic properties of Low

Q Q N, V, e, Quantum Statistics for Ideal Gas and Black Body Radiation. The Canonical Ensemble

Physics 202, Lecture 5. Today s Topics. Announcements: Homework #3 on WebAssign by tonight Due (with Homework #2) on 9/24, 10 PM

Free carriers in materials

Formula overview. Halit Eroglu, 04/2014 With the base formula the following fundamental constants and significant physical parameters were derived.

Hydrogen atom. Energy levels and wave functions Orbital momentum, electron spin and nuclear spin Fine and hyperfine interaction Hydrogen orbitals

UGC POINT LEADING INSTITUE FOR CSIR-JRF/NET, GATE & JAM. are the polar coordinates of P, then. 2 sec sec tan. m 2a m m r. f r.

FI 3103 Quantum Physics

Physics 111. Lecture 38 (Walker: ) Phase Change Latent Heat. May 6, The Three Basic Phases of Matter. Solid Liquid Gas

The angle between L and the z-axis is found from

GAUSS PLANETARY EQUATIONS IN A NON-SINGULAR GRAVITATIONAL POTENTIAL

GRAVITATION 4) R. max. 2 ..(1) ...(2)

Molecules and electronic, vibrational and rotational structure

Fourier transforms (Chapter 15) Fourier integrals are generalizations of Fourier series. The series representation

Shor s Algorithm. Motivation. Why build a classical computer? Why build a quantum computer? Quantum Algorithms. Overview. Shor s factoring algorithm

Q Q N, V, e, Quantum Statistics for Ideal Gas. The Canonical Ensemble 10/12/2009. Physics 4362, Lecture #19. Dr. Peter Kroll

Lecture 17. Physics Department Yarmouk University Irbid Jordan. Chapter V: Scattering Theory - Application. This Chapter:

II.3. DETERMINATION OF THE ELECTRON SPECIFIC CHARGE BY MEANS OF THE MAGNETRON METHOD

Mon. Tues. 6.2 Field of a Magnetized Object 6.3, 6.4 Auxiliary Field & Linear Media HW9

E F. and H v. or A r and F r are dual of each other.

GRAVITATION. (d) If a spring balance having frequency f is taken on moon (having g = g / 6) it will have a frequency of (a) 6f (b) f / 6

Van der Waals three-body force shell model (VTSM) for the Lattice dynamical studies of Potassium fluoride

Applications of Lagrange Equations

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

Previous knowlegde required. Spherical harmonics and some of their properties. Angular momentum. References. Angular momentum operators

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field

( ) 4. Jones Matrix Method 4.1 Jones Matrix Formulation A retardation plate with azimuth angle y. V û ë y û. év ù év ù év. ë y û.

PHYSICS 4E FINAL EXAM SPRING QUARTER 2010 PROF. HIRSCH JUNE 11 Formulas and constants: hc =12,400 ev A ; k B. = hf " #, # $ work function.

Nuclear and Particle Physics

4.4 Linear Dielectrics F

ERRATA. ± Lines are calculated before ( ) or after (+) the Anchor. If the Anchor is a page, t and b indicate, respectively, top and bottom.

CHAPTER 5 CIRCULAR MOTION

D-Cluster Dynamics and Fusion Rate by Langevin Equation

Radiation Equilibrium, Inertia Moments, and the Nucleus Radius in the Electron-Proton Atom

NEWTON S THEORY OF GRAVITY

L N O Q F G. XVII Excitons From a many electron state to an electron-hole pair

From Classical to Quantum mechanics

EXAM NMR (8N090) November , am

Aakash. For Class XII Studying / Passed Students. Physics, Chemistry & Mathematics

( )( )( ) ( ) + ( ) ( ) ( )

"Radiation" Electrons Positrons Neutrons Ions... Paolo Fornasini Univ. Trento. Overview. Paolo Fornasini Univ. Trento. 1/ k 2 /

Loss factor for a clamped edge circular plate subjected to an eccentric loading

A GAUGE-INVARIANT RELATIVISTIC THEORY OF THE RUTHERFORD-SANTILLI NEUTRON

Circular Motion & Torque Test Review. The period is the amount of time it takes for an object to travel around a circular path once.

H 2+ : A Model System for Understanding Chemical Bonds

In the name of Allah Proton Electromagnetic Form Factors

Spin Physics (Experimental)

Electron spin resonance

Exam 3: Equation Summary

Derivation of the differential equation of motion

Physics 1114: Unit 5 Hand-out Homework (Answers)

Random Process Part 1

Lecture 28 Title: Diatomic Molecule : Vibrational and Rotational spectra

The pn junction: 2 Current vs Voltage (IV) characteristics

Neutrino Mass and Forbidden Beta Decays

As the matrix of operator B is Hermitian so its eigenvalues must be real. It only remains to diagonalize the minor M 11 of matrix B.

Constants and Conversions:

( ) ( = ) = ( ) ( ) ( )

Escape Velocity. GMm ] B

Department of Chemistry Chapter 4 continued

Circular-Rotational Motion Mock Exam. Instructions: (92 points) Answer the following questions. SHOW ALL OF YOUR WORK.

Nuclear and Particle Physics - Lecture 20 The shell model

b) (5) What is the magnitude of the force on the 6.0-kg block due to the contact with the 12.0-kg block?

School of Aerospace Engineering Origins of Quantum Theory. Measurements of emission of light (EM radiation) from (H) atoms found discrete lines

Differential Kinematics

ESE (Prelims) - Offline Test Series ELECTRICAL ENGINEERING SUBJECT: Electrical Machines & Systems and Signal Processing SOLUTIONS

* Meysam Mohammadnia Department of Nuclear Engineering, East Tehran Branch, Islamic Azad University, Tehran, Iran *Author for Correspondence

PLS-CADD DRAWING N IC TR EC EL L RA IVE ) R U AT H R ER 0. IDT FO P 9-1 W T OO -1 0 D EN C 0 E M ER C 3 FIN SE W SE DE EA PO /4 O 1 AY D E ) (N W AN N

Accretion disks around rotating black holes. (c)2017 van Putten 1

Lecture 4: Entropy. Chapter I. Basic Principles of Stat Mechanics. A.G. Petukhov, PHYS 743. September 7, 2017

( ) Bose-Einstein condensates in fast rotation. Rotating condensates. Landau levels for a rotating gas. An interesting variant: the r 2 +r 4 potential

Hydrogen Atom and One Electron Ions

Curvature singularity

Physics 201 Lecture 18

PS113 Chapter 5 Dynamics of Uniform Circular Motion

SPH4U Electric Charges and Electric Fields Mr. LoRusso

The local orthonormal basis set (r,θ,φ) is related to the Cartesian system by:

Electrostatics. 1. Show does the force between two point charges change if the dielectric constant of the medium in which they are kept increase?

Standard Model of Particle Physics SS 2012

Phys 201A. Homework 6 Solutions. F A and F r. B. According to Newton s second law, ( ) ( )2. j = ( 6.0 m / s 2 )ˆ i ( 10.4m / s 2 )ˆ j.

Experiment 09: Angular momentum

b) (5) What average force magnitude was applied by the students working together?

Bethe-Salpeter Equation Green s Function and the Bethe-Salpeter Equation for Effective Interaction in the Ladder Approximation

2. Finite Impulse Response Filters (FIR)

Stochastic Processes

Chapter Six Free Electron Fermi Gas

ORBITAL TO GEOCENTRIC EQUATORIAL COORDINATE SYSTEM TRANSFORMATION. x y z. x y z GEOCENTRIC EQUTORIAL TO ROTATING COORDINATE SYSTEM TRANSFORMATION

Kondo vs Fano resonances in Quantum Dot

. D CR Nomenclature D 1

/ / MET Day 000 NC1^ INRTL MNVR I E E PRE SLEEP K PRE SLEEP R E

Standard Model of Particle Physics SS 2013

Signal Circuit and Transistor Small-Signal Model

Optics and magneto-optics of graphene. Vladimir Falko

Homework 1: Solutions

Transcription:

Shap paatization λ ( θ, φ) α ( θ ) λµ λµ, φ λ µ λ axially sytic quaupol axially sytic octupol λ α, α ± α ± λ α, α ±,, α, α ±, Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Octupol collctivity coupling Δl Δj (W.u.) 6 88a 8 B 6 9 Z ( E; ) 6.H. Spa At. Data an Nucl. Data Tabls (989), so subshlls intact via th opato.g. in light actini nucli on has an intaction btwn j / an g 9/ nuton obitals i / an f 7/ poton obitals Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Octupol collctivity Octupol colations nhanc at th agic nubs:, 6, 88, Micoscopically Intu obitals of opposit paity an ΔJ, ΔL clos to Fi lvl 6 a clos to Z88 N f i ν g ( ) ( ) 7 / / 9/ j/ Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Octupol collctivity 6 a 6 a - - - - - In an octupol fo nuclus th cnt of ass an cnt of chag tn to spaat, cating a non-zo lctic ipol ont. Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Th oubl oscillato ( ) ψ ψ ψ ψ E a a V B H -a a V V ω ω ω ν ω V vn vn V E ω ω ω ν ω V o o V E Mzbach uantu Mchanics octupol fo octupol vibational

oulob xcitation ipact paat scatting angl σ i f c P i f σ uth c ( E; I I ) f ( η ξ ) [ b] A A σ E.89 EMV B i f E, A Z Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Scatt α-spctu of 6 a H 6 a E α 6 MV θ lab counts - 6 a-tagt ba iction Si-tcto channl nub ( ) [ ] λ / λ λ M Eλ b λ (xp) λ (tho) P i f σ σ i f l θ σ σ i f uth.7 ().6 ().6. (). ().. (7). (8).96 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Scatt α-spctu of 6 a H 6 a E α 6 MV θ lab counts - 6 a-tagt ba iction channl nub Si-tcto θ ( ) [ ] λ / λ λ M Eλ b λ (xp) λ (tho).7 ().6 ().6. (). ().. (7). (8).96 I f I n I i E E E Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Expintal st-up ϕ ϑ PPA ing count Θ L, φ L 6 6 a PPA count Θ L 9, φ L 8 6 ab ( μg/c ) on -backing ( μg/c ) an cov by B ( μg/c ) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

oulob xcitation of 6 a Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

γ-ay spctu of 6 a 8 Pb 6 a E lab.7 AMV counts θ lab φ lab 6 ngy [kv] Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Signatu of an octupol fo nuclus ( ) [ ( θ ) ( θ ) ( θ )] θ : : - 6 88a.6 -.. E E Singl otational ban with spin squnc: I, -,, -, xcitation ngy E ~ I (I) coptition btwn intaban E an intban E tansitions E tansition stngth - W.u. Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Signatu of an octupol fo nuclus Engy isplacnt δe btwn th positiv- an ngativ-paity stats if thy fo a singl otational ban δ E ( I ) E( I ) I E fo ( I ) E( I ) igi oto W. Nazawicz t al.; Nucl. Phys. A (98) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Elctic tansition quaupol onts in 6 a ngativ paity stats positiv paity stats igi oto ol: ( I ) I I M ( E) I I liqui op: Z (.6.6.8. ) [ f ] 967 (xp) 7 f. (tho) 68 f H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 W. Nazawicz t al.; Nucl. Phys. A67 (987) 7 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Static quaupol onts in 6 a ngativ paity stats positiv paity stats igi oto ol: ( I ) I ( I ) ( I ) ( I ) ( I ) ( E) I ( E) S M I M igi tiaxial oto ol: s ( ) 6cos( γ ) 7 9 8sin ( γ ) H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 Davyov an Filippov, Nucl. Phys. 8, 7 (98) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Elctic tansition octupol onts in 6 a liqui op: Z 7 (.8. 769) [ f ].8..6 ω. MV. I 7 -. ω.mv I ( I ) ( I ) ( I ) ( I ) I M ( E) I ( I ) I ( I ) ( I ) ( I ) I M ( E) I. -..6 I I I H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 W. Nazawicz t al.; Nucl. Phys. A67 (987) 7 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Intinsic lctic ipol onts in 6 a liqui-op contibution: with A Z (. ) 8. [ f] igi oto ol: I M ( E) I I H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 G. Lan t al.; Nucl. Phys. A (986) 8 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Intinsic lctic ipol onts in a / Th liqui-op contibution: with A Z (. ) 8. [ f] Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7 G. Lan t al.; Nucl. Phys. A (986) 8

Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa nt of ass consvation τ τ τ τ y x z o Th cooinats (x, y, z) can b xpss by ( ) ( ) ± ±, iy x z φ θ ( ), τ φ θ * * * 6 α α α ( ) ( ) / * * * 6 α α α ( ) ( ) / * * * α α α Th ipol cooinat is not an inpnnt quantity. It is non-zo fo nucla shaps with both quaupol an octupol gs of fo. { } / 7 9

Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont ( ) z p poton φ θ τ, Th local volu polaization of lctic chag can b iv fo th quint of a iniu in th ngy functional. (Mys Ann. of Phys. (97)) ( ) V nuton poton nuton poton wh p an n a th poton an nuton nsitis, is th volu syty ngy cofficint of th liqui op ol an V is th oulob potntial gnat by p insi th nuclus ( < ) ( ) Z V ( ) n p V p n ( ) V p Kping th cnt of gavity fix, th intgal 9 ( ) 7 Z V

Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont ( ) ( ) V φ θ, Z A 7 8 ( ) ( ) [ ] ( ) ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] Z A 7 7 7 6 6 6 6 6 8 ( ) [ ] ( ) [ ] [ ] ( ) [ ] [ ] Z A 7 7 7 6 6 6 6 6 8

Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont 7 9 Z A 7 6 Z A [ ] f Z A. MV

Suay singl otational ban fo I > no backbning obsv,, foation paats a in xcllnt agnt with calculat valus octupol foation is th tis lag than in octupolvibational nucli qual tansition quaupol onts fo positiv- an ngativpaity stats static quaupol onts a in xcllnt agnt with an axially sytic shap lctic ipol onts a clos to liqui-op valu ( I > ) octupol foation ss to b stabiliz with incasing otational fquncy Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

oulob xcitation of 6 a 6 a tagt bokn aft 8 hous histoph Flischann Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7