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

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

3. San Onofre Nuclear Power Plant E = Mc 2

4. Nuclear Generation in California, 1960 through 2003 Million Kilowatt Hours http://www.eia.doe.gov/cneaf/nuclear/page/at_a_glance/states/statesca.html About 13% of California’s electrical consumption came from nuclear power E = Mc 2

5. http://news.bbc.co.uk/1/shared/spl/hi/pop_ups/05/ south_asia_pakistan_and_india_earthquake/html/6.stm 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 = Mc 2

7. 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.

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

9. 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.

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

11. 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  the wave function: The first equation is the Klein-Gordon equation. The second is the Dirac equation.

12. K-G equation Dirac equation ParticlesBosonsFermions Negative energy states? Yes antiparticles Basis states+E and –E if interactions are present

13. 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.

14. http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/sodzee.html Sodium D lines from the spin- orbit splitting of the 3p atomic state to the 3s 1/2 state. 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)/m e c 2 = 4 x 10 -9. Relativistic Q.M. gives the right size of the spin-orbit splitting in atoms.

15. 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).

16. How to make interacting fermions. Dirac equation for a free particle. Introduce a 4-potential, V  and a scalar S. Dirac equation for an interacting particle.

17. 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.

18. Relativity and Nuclear Structure L = 1, p state in 11 C,  E SO Strong spin-orbit forces are seen in nuclei. E(1p-splitting)/m p c 2 =2 x 10 -3.

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

20. 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. 3) Exploit the (e,e’p) asymmetry predicted by relativistic theories as a new observable for nuclear states. 2) Look for explicit evidence of the negative energy states in 208 Pb.

21. Impulse Approximation limitations to the (e,e’p) reaction on 208 Pb - Identifying correlations and relativistic effects in the nuclear medium THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY 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

22. THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY K.Aniol, Hall A Collaboration Mtg., June 23, 2005 (ii) Momentum distributions > 300 MeV/c 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]. I. Bobeldijk et al., PRL 73 (2684)1994 x B ≠ 1 E. Quint, thesis, 1988, NIKHEF J. M. Udias et al. PRC 48(2731) 1994 J.M. Udias et al. PRC 51(3246) 1996 Excess strength at high p miss

23. Negative Energy States- Complete Basis The particle is in an orbit of radius R 0 and constant angular velocity  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.

24. 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.

25. A TL in 3 He, 4 He and 16 O If relativistic dynamical effects are the main cause responsible for the extra strength, a strong effect on A TL would be seen. There is a notable difference in A TL between 3 He and 4 He due to the density difference and in 16 O. 16 O: A TL p 1/2 p 3/2 M. Rvachev et al. PRL 94:12320,2005 E04-107,2004 J. Gao et al. PRL84:3265, 2000

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

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

28. Heavy Metal Collaboration