Download 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 = Mc2
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.
On August 9, 1945
E = Mc2
San Onofre Nuclear Power Plant
E = Mc2
Nuclear Generation in
California, 1960 through
2003
Million 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
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
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.
These two principles lead us to the Lorentz
transformation, which gives us the
translation table between two inertial
reference frames O and O’.
  v/c
 ct '     
  
 x'     

 y'   0
0
  
 z'   0
0
  
x
O
0
0
1
0
v
O’
0  ct 
 
2
0  x    1 / 1  
0  y 
  Both O and O’ see



1  z  the event but they
x’
give different
coordinates.
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.
x   (ct , x, y, z )
and the conserved quantity
(ct ) 2  x 2  y 2  z 2  (ct ' ) 2  x'2  y '2  z '2
Another extremely important 4-vector is the
4 momentum.

p  ( E , cp x , cp y , cp z )  ( E , cp)

and
E  ( pc)  E ' ( p' c)
2
2
2
2
and in the particle' s rest frame p'  0,
E  ( pc)  E '  (mc ) .
2
2
2
2 2
E  ( pc)  (mc ) .
2
2
2 2
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:
( pc)  (mc ) Y  E Y
 
c  p  mc Y  EY
2
2 2
2
2
The first equation is the Klein-Gordon
equation. The second is the Dirac equation.
Particles
K-G
equation
Dirac
equation
Bosons
Fermions
0,1,
 / 2,3 / 2, 
Negative
energy
states?
Yes
antiparticles
Yes
antiparticles
Basis states
+E and –E if
interactions
are present
+E and –E if
interactions are
present
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.
Sodium D lines from the spinorbit 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
The Spin-Orbit Interaction


L
S

L

S
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).
How to make interacting fermions.
Dirac equation for a free particle.


 
2
c  p  mc Y  EY
Introduce a 4-potential, V and a scalar S.

1

V  (V0 , V )
c
Dirac equation for an interacting particle.
   1 

2
c


(
p

V
)


(
mc

S
)

V
Y

E
Y
o


c
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.
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.
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
A( Z , N )  A( Z  1, N  1)  e  e

A( Z , N )  A( Z  1, N  1)  e  e

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.
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
THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY
K.Aniol, Hall A Collaboration Mtg., June 23, 2005
(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].
THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY
K.Aniol, Hall A Collaboration Mtg., June 23, 2005
Negative Energy States- Complete Basis

R(t )  R0 (sin( t ) cos( ) xˆ  sin( t ) sin(  ) yˆ  cos(t ) zˆ)
The particle is in an orbit of radius R0 and
constant angular velocity  in 3 dimensions.
d 2r
2



r
2
dt
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.
Asymmetry in the (e,e’p) reaction


A1  e  A2  e'  p
   
e  e ' q
NF  NB
A
NF  NB
q is the momentum
transferred by the
scattered electron.
We detect protons knocked out forward and
backward of q to determine the asymmetry A.
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
E04-107,2004
J. Gao et al.
PRL84:3265, 2000
ATL in 208Pb
THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY
K.Aniol, Hall A Collaboration Mtg., June 23, 2005
ATL in 208Pb
THOMAS JEFFERSON NATIONAL ACCELERATOR LABORATORY
K.Aniol, Hall A Collaboration Mtg., June 23, 2005
Heavy Metal
Collaboration