Download LECTURE 6 NUCLEAR PHENOMENOLOGY, MASS SPECTROSCOPY PHY492 Nuclear and Elementary Particle Physics

LECTURE 6
NUCLEAR PHENOMENOLOGY,
MASS SPECTROSCOPY
PHY492 Nuclear and Elementary Particle Physics
Nuclei
A – mass number (= Z+N)
(number of nucleons) A
Z Y N N – neutron number
(number of neutrons) Z – atomic number
(number of protons) Z Isotope (same Z) Nuclear chart Isobar (same A) Isotone (same N) Stable nuclei January 22, 2014 N Unstable nuclei (Exotic Nuclei) PHY492, Lecture 6 2 Nuclear Mass key observable for nuclear structure d n p Mass (proton) = 938 (MeV/c2) ( 3.7x10-­‐27 lb ) Mass (neutron) = 939 (MeV/c2) SUM 938 + 939 = 1877 (MeV/c2) Mass (deuton) = 1875 (MeV/c2) > Magic Numbers Magic numbers explain (without reasons at the beginning) how combined system can gain energies ( can be lighter ). α
n p n p p 2 n 2 Sunlight (energies) Magic numbers : 2 , 8, 20, 28, 50, 82, 126, …. Mass Spectroscopy
The mass of a nucleus is a fundamental quantity that
uniquely defines the nuclide.
J Test nuclear models (magic numbers)
J Test the standard model of particle physics
J Test astrophysical models
Mass systematics Natural abundances of nuclei Data Prediction with
advanced theory
(magic numbers change
for exotic nuclei ) magic
numbers
Prediction with
“text book”
magic numbers 28
January 22, 2014 50
82
PHY492, Lecture 6 126
5 Mass Spectroscopy
How to measure masses of nuclei ?
January 22, 2014 PHY492, Lecture 6 6 Deflection Spectrometers
Mass of nuclei are measured by passing
Ion beams through magnetic and electric fields.
[ 2 steps ]
(1)  Select a constant velocity with
a velocity (Wien) filter
(1) E and B1 fields are at right angles
qE = qvB1
v = E/B1
(2)  Measure a trajectory of ions in a uniform magnetic B2 field
(2) mv2
= qvB2
r
If B1 = B2 = B ,
q
m
=
v
Br
=
E
B 2r
Application : device to measure mass difference (12,13,14C ) January 22, 2014 PHY492, Lecture 6 7 Kinematic Analysis
Kinematic analysis of nuclear reactions allows one to measure the masses of very short-lived nuclei
(missing mass spectroscopy)
c2)
a (Ei, pi) + A(mA
a
→ a (Ef, pf) + A*(E,p)
E tot (initial) = Ei +
E tot (final)
mac2 +
pf
A
a
θ
pi
c2
mA
p
A*
= Ef + E + mac2 + mc2
ΔE = (m-mA)c2 = Ei – Ef – E = pi2/2ma – pf2/2ma – p2/2m
px = pi – pf cosθ , py = pf sinθ
ΔE = Ei ( 1 – ma/m) - Ef ( 1 + ma/m ) + 2ma/m (EiEf)1/2 cosθ
January 22, 2014 PHY492, Lecture 6 8 Penning Trap Measurement
The most precise measurements come from storage devices that
confine ions in three dimensions by means of well-controlled
electromagnetic fields.
Examples: storage rings, Penning Trap , Paul Trap
In a Penning Trap,
(1)  Ions are confined in 2D with
a strong magnetic field (B)
(2) A weak electrostatic field is used to
trap ions in 3D ( along the Z axis)
(1) Cyclotron oscillations (
B v q January 22, 2014 ωc ) mv2
= qvB
r
qBr
v = m
2πm
t = 2πr/v = qB
PHY492, Lecture 6 ωc
= 2πf
= 2π/T
qB
= m
9 Penning Trap Measurement (2)
(2) A weak axially symmetric electrostatic
potential is superimposed to produce
a saddle point at the center
This requires the quadrupole potential;
U
Φ (z,r) = 4d2 (2z2-r2)
1
d=
(2Z02+r02)1/2
2
end caps ring ( so that U is the potential difference
between the endcap and the ring electrodes )
January 22, 2014 PHY492, Lecture 6 10 Penning Trap Measurement (3)
Solving the equations of motions results in
three independent motional modes with frequencies;
ωz = qU/md2 (axial motion)
ω+ = ωc/2 + ωc2/4 – ωz2/2
  ω- = ωc/2 - ωc2/4 – ωz2/2
(cyclotron motion)
(magnetron motion)
The condition on the magnetic field, 2/4 – ω 2/2 > 0
ω
c
z
B2 > 2mU/qd2
In the experiment,
one needs to measure the sum
ω ± = ωc/2 [ 1 ± (1 – 2ω ωc ]
= ωc/2 [ 1 ± (1 – ωz2/ωc2) ]
ω+ + ωω - = ωz2/2ωc = U/2Bd2
(not cyclotron freq. from ω+ only) ω + = ωc - U/2Bd2
ωc = ω+ + ω-, ωc2 = ω+2 + ω-2 + ωz2 (ω+ω- = ωz2/2)
2
z /
January 22, 2014 2)1/2
PHY492, Lecture 6 11