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The Impact of Special Relativity in Nuclear Physics: It’s not just E = Mc 2

The Impact of Special Relativity in Nuclear Physics: It’s not just E = Mc 2. Of the 286,00 people living in Nagasaki at the time of the blast, 74,000 were killed and another 75,000 sustained severe injuries. . E = Mc 2. On August 9, 1945.

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The Impact of Special Relativity in Nuclear Physics: It’s not just E = Mc 2

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  1. The Impact of Special Relativity in Nuclear Physics: It’s not just E = Mc2

  2. Of the 286,00 people living in Nagasaki at the time of the blast, 74,000 were killed and another 75,000 sustained severe injuries. E = Mc2 On August 9, 1945

  3. San Onofre Nuclear Power Plant E = Mc2

  4. Nuclear Generation in California, 1960 through 2003Million Kilowatt Hours About 13% of California’s electrical consumption came from nuclear power E = Mc2 http://www.eia.doe.gov/cneaf/nuclear/page/at_a_glance/states/statesca.html

  5. Radioactive decay supplies a significant fraction of the internal heat of the Earth’s mantle. Convection currents driven by this heat cause active plate tectonics. E = Mc2 http://news.bbc.co.uk/1/shared/spl/hi/pop_ups/05/ south_asia_pakistan_and_india_earthquake/html/6.stm

  6. It would be difficult to find an area of physics which has not been profoundly influenced by Special Relativity. Guiding Principles of Special Relativity 1) The speed of light c, is a constant for all observers in inertial reference frames. 2) The laws of physics must remain invariant in form in all inertial reference frames.

  7. These two principles lead us to the Lorentz transformation, which gives us the translation table between two inertial reference frames O and O’. Both O and O’ see the event but they give different coordinates. x’ x O O’

  8. The Lorentz transformation shows that there are conserved quantities which have the same value measured in any inertial reference frame. These quantities are calculated from their respective 4-vectors.

  9. Another extremely important 4-vector is the 4 momentum.

  10. Since we want to describe microscopic systems we know we need to use quantum mechanics. The equation for E gives us two possible approaches to make a relativistic quantum mechanics. Call Y the wave function: The first equation is the Klein-Gordon equation. The second is the Dirac equation.

  11. Under what circumstances should we expect relativity to be important in quantum systems? An approach that focuses on the condition v/c <<1 is too limited. Q. Relativity gives us fermions and Fermi-Dirac statistics and the whole structure of matter relies on the nature of the fermions. Q. Relativity explains low energy aspects of the microscopic structure of matter, such as atomic spectra.

  12. Sodium D lines from the spin-orbit splitting of the 3p atomic state to the 3s1/2 state. Relativistic Q.M. gives the right size of the spin-orbit splitting in atoms. Relativity is essential in understanding atomic spectra, even when the energy of the state is a small fraction of the electron mass. E(3p-splitting)/mec2 = 4 x 10-9 . http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html

  13. The Spin-Orbit Interaction In the atom the S. O. interaction is generally attributed to the interaction of the electron’s magnetic moment and an induced magnetic field from the electron’s motion in the field of the nucleus. However, it is a general property for any interacting fermion to show spin-orbit behavior. This is a consequence of Lorentz invariance (G. Breit, 1937).

  14. How to make interacting fermions. Dirac equation for a free particle. Introduce a 4-potential, Vm and a scalar S. Dirac equation for an interacting particle.

  15. For nuclei modern calculations generate a potential averaged over a scalar meson field and a vector meson field plus some smaller scalar and vector fields.

  16. Relativity and Nuclear Structure DESO L = 1, p state in 11C, E(1p-splitting)/mpc2=2 x 10-3. Strong spin-orbit forces are seen in nuclei.

  17. The magnitude of the nuclear spin-orbit potential is correctly given by a relativistic Q. Field theory using scalar and vector mesons. Velocity dependent forces are required in nuclear structure and are natural outcomes of a relativistic treatment using scalar and vector mesons Radioactive decay and anti-particles

  18. CSULA Proposal to search for other predicted relativistic effects in nuclei 1) Look for true nucleon-nucleon correlations as distinct from apparent correlations due to nonlocalities induced by relativistic effects. 2) Look for explicit evidence of the negative energy states in 208Pb. 3) Exploit the (e,e’p) asymmetry predicted by relativistic theories as a new observable for nuclear states.

  19. THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY Impulse Approximation limitations to the (e,e’p) reaction on 208Pb - Identifying correlations and relativistic effects in the nuclear medium K. Aniol , B. Reitz, A. Saha, J. M. Udias Spokespersons Hall A Collaboration Meeting June 23, 2005 K.Aniol, Hall A Collaboration Mtg., June 23, 2005

  20. THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY (ii) Momentum distributions > 300 MeV/c Excess strength at high pmiss xB≠ 1 E. Quint, thesis, 1988, NIKHEF I. Bobeldijk et al.,PRL 73 (2684)1994 J. M. Udias et al. PRC 48(2731) 1994 J.M. Udias et al. PRC 51(3246) 1996 This was explained via long-range correlations in a nonrelativistic formalism [Bobeldijk,6], but also by relativistic effects in the mean field model [Udias,7]. K.Aniol, Hall A Collaboration Mtg., June 23, 2005

  21. Negative Energy States- Complete Basis The particle is in an orbit of radius R0 and constant angular velocity w in 3 dimensions. If we ignore the Z dimension and use a truncated basis of two dimensions in X and Y, we would interpret the particle’s projected motion in the XY plane as that of a harmonic oscillator.

  22. Asymmetry in the (e,e’p) reaction q is the momentum transferred by the scattered electron. We detect protons knocked out forward and backward of q to determine the asymmetry A.

  23. ATL in 3He, 4He and 16O If relativistic dynamical effects are the main cause responsible for the extra strength, a strong effect on ATL would be seen. There is a notable difference in ATL between 3He and 4He due to the density difference and in 16O. 16O: ATL p1/2 p3/2 M. Rvachev et al. PRL 94:12320,2005 J. Gao et al. PRL84:3265, 2000 E04-107,2004

  24. THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY ATL in 208Pb K.Aniol, Hall A Collaboration Mtg., June 23, 2005

  25. THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY ATL in 208Pb K.Aniol, Hall A Collaboration Mtg., June 23, 2005

  26. Heavy Metal Collaboration

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