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B-fieldpoints
into page
1900-01 Studying the deflection of these rays in magnetic fields, Becquerel and the Curies establish rays to be charged particles
pi = 0 = pf = prifle + pbullet prifle = – pbullet
-decay
-decay
Some Alpha Decay Energies and Half-lives
Isotope KE(MeV) 1/2 (sec-1)
232Th 4.01 1.41010 y 1.61018
238U 4.19 4.5109 y 4.91018
230Th 4.69 8.0104 y 2.81013
238Pu 5.50 88 years 2.51010
230U 5.89 20.8 days 3.9107
220Rn 6.29 56 seconds 1.2102
222Ac 7.01 5 seconds 0.14216Rn 8.05 45.0 sec 1.510
212Po 8.78 0.30 sec 2.310
216Rn 8.78 0.10 sec 6.910
B
Before decay:
After decay:
Which fragment has a greater momentum?
Potassium nucleus
energy?
A)B) C) both the same
A
1930 Series of studies of nuclear beta decay, e.g.,
Potassium goes to calcium 19K40 20Ca40
Copper goes to zinc 29Cu64 30Zn64 Boron goes to carbon 5B12 6C12 Tritium goes to helium 1H3 2He3
1932 Once the neutron was discovered, included the more fundamental
n p + e
but this only seems to match the maximum value
observed on a spectrum of beta ray energies!
Ee = (mA2 - mB
2 + me2)c2/2mA
For simple 2-body decay, conservation of energy and momentum demand both the recoil of the nucleus and energy of the emitted electron be fixed (by the energy released through the loss of mass) to a single precise value.
No.
of
cou
nts
per
un
it e
ner
gy r
ange
Electron kinetic energy in KeV5 10 15 200
The beta decay spectrum of tritium ( H He). Source: G.M.Lewis, Neutrinos (London: Wykeham, 1970), p.30)
-decay spectrum for neutrons
Electron kinetic energy in MeV
dE
d
1932 n p + e +
charge 0 +1 1 ?mass 939.56563 938.27231 0.51099906 MeV MeV MeV
neutrino mass < 5.1 eV < me /100000 0
???neutrino
0?
the Fermi-Kurie plot.
The Fermi-Kurie plotlooks for any gap between
the observed spectrumand the calculated Tmax
Niels Bohr hypothesized the existence of quantum mechanical restrictions on the principle of energy conservation, but Pauli couldn’t buy that:
Wolfgang Pauli1900-1958
Dear Radioactive Ladies and Gentlemen, as the bearer of these lines, to whom I graciously ask you to listen, will explain to you in more detail, how because of the "wrong" statistics of the N and Li6 nuclei and the continuous beta spectrum, I have hit upon a desperate remedy to save the "exchange theorem" of statistics and the law of conservation of energy. Namely, the possibility that there could exist in the nuclei electrically neutral particles, that I wish to call neutrons, which have spin 1/2 and obey the exclusion principle and which further differ from light quanta in that they do not travel with the velocity of light. The mass of the neutrons should be of the same order of magnitude as the electron mass and in any event not larger than 0.01 proton masses. The continuous beta spectrum would then become understandable by the assumption that in beta decay a neutron is emitted in addition to the electron such that the sum of the energies of the neutron and the electron is constant...
I agree that my remedy could seem incredible because one should have seen those neutrons much earlier if they really exist. But only the one who dare can win and the difficult situation, due to the continuous structure of the beta spectrum, is lighted by a remark of my honoured predecessor, Mr Debye, who told me recently in Bruxelles: "Oh, It's well better not to think to this at all, like new taxes". From now on, every solution to the issue must be discussed. Thus, dear radioactive people, look and judge. Unfortunately, I cannot appear in Tubingen personally since I am indispensable here in Zurich because of a ball on the night of 6/7 December. With my best regards to you, and also to Mr Back. Your humble servant . W. Pauli, December 1930
"I have done a terrible thing. I have postulated a particle that cannot be detected."
1936 Millikan’s group shows at earth’s surface cosmic ray showers are dominated by electrons, gammas, and
X-particles capable of penetrating deep underground (to lake bottom and deep tunnel experiments) and yielding isolated single cloud chamber tracks
Primary proton
1937 Street and Stevenson1938 Anderson and Neddermeyer determine X-particles
•are charged•have 206× the electron’s mass•decay to electrons with a mean lifetime of 2sec
0.000002 sec
1947 Lattes, Muirhead, Occhialini and Powell observe pion decay
Cecil Powell (1947)Bristol University
Nature 163, 82 (1949)
C.F.Powell, P.H. Fowler, D.H.PerkinsNature 159, 694 (1947)
Consistently ~600 microns (0.6 mm)
+ energy always
predictably fixedby E
Under the influence of a magnetic field
simple 2-body decay!
+ + + neutrino?charge +1 +1 ?spin 0 ½ ?
0½
n p + e + neutrino?
+ + + neutrino?Then
- e- + neutrino????
As in the case of decaying radioactive isotopes, the electrons’s energy varied, with a maximum cutoff (whose value was the 2-body prediction)
3 body decay!
p
e
e
2 neutrinos
1953, 1956, 1959Savannah River (1000-MWatt) Nuclear Reactor in South Carolinalooked for the inverse of the process
n p + e + neutrino
Cowan & Reines
also looked forn + neutrino p + e
but never observed!
observed2-3 p + neutrino events/hour
with estimate flux of 51013 neutrinos/cm2-sec
p + neutrino n + e+?
1967 •built at Brookhaven labs•615 tons of tetrachloroethylene•Neutrino interaction 37Cl37Ar(radioactive isotope, ½ = 35 days)Chemically extracting the 37Ar, its radioactivity gives the number of neutrino interactions in the vat(thus the solar neutrino flux). Results: Collected data 1969-1993 (24 years!!) gives a mean of 2.5±0.2 SNU while theory predicts 8 SNU (1 SNU = 1 neutrino interaction per second for 10E+36 target atoms). This is a neutrino deficit of 69%.
Homestake MineExperiment
Underground Neutrino Observatory
The proposed next-generation underground water Čerenkov detector
to probe physics beyond the sensitivity of the highly successful Super-Kamiokande detector in Japan
The SuperK detector is a
water Čerenkov detector
40 m tall40 m diameter
stainless steel cylinder
containing 50,000 metric tons of ultra pure water
The detector is located 1 kilometer below Mt. Ikenoyama inside the Kamioka zinc mine.
The main sensitive region is 36 m high, 34 m in dia viewed by 11,146 inward facing Hamamatsu photomultiplier tubes surrounding 32.5 ktons of water
Underground Neutrino Observatory
• 650 kilotons
• active volume: 440 kilotons
20 times larger than Super-Kamiokande
major components: photomultiplier tubes, excavation, water purification system.
$500M The optimal detector depth to perform the full proposed scientific program ofUNO 4000 meters-water-equivalent
or deeper
1953 Konopinski & Mahmoudintroduce LEPTON NUMBER to account for which decays/reactions are possible,which not
e, ( ) assigned L = +1e+, + ( +) assigned L =1
n p + e + neutrino
_
p + neutrino n + e+
_
n + e+ _
n + p + e?? ??
1962 Lederman,Schwartz,Steinberger Brookhaven National Laboratory
using a as a source of antineutrinos
and a 44-foot thick stack of steel (from a dismantled warship hull) to shield everything but the ’s
found 29 instances of
+ p + + n
but none of
+ p e+ + n
1988 Nobel Prize in Physics
"for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino"
So not just ONE KIND of neutrino, the leptons are associated into “families”
ee
n
p
e
e
e
e
For spin½S =
·p=H
Helicity “handedness” For a moving particle state, its lab frame velocity defines an obvious
direction for quantizationms
sfraction of spin “aligned” in this direction
|Sz|
|S|=
mSħ
s(s+1)ħ=
mS
s(s+1)
spin
s
spin
sv v
though12
^
Notice individual spin-½ particles haveHELICITY +1 (ms = +½) RIGHT-HANDEDHELICITY +1 (ms = ½) LEFT-HANDED
spin
sv
However:
HELICITY +1 (ms = +½) RIGHT-HANDEDHELICITY +1 (ms = ½) LEFT-HANDED
not “aligned”just mostly so
57735.03
1
)2/3)(2/1(
2/1
)1(
ss
ms
But helicity (say of an electron) is not some LORENTZ-INVARIANT quantity! Its value depends upon the frame of reference: Imagine a right-handed electron traveling to the right when observed in a frame itself moving right with a speed > v.
It will be left-handed!
So HELICITY must NOT appear in the Lagrangian for any QED or QCD process (well, it hasn’t yet, anyway!).
HELICITY is NOT like some QUANTUM NUMBER.It is NOT unambiguously defined.
But what about a massless particle (like the or…the neutrino?)
m < 5.1 eV << me = 0.511003 MeV e
m < 160 keV
m < 24 MeVRecall for a massless particle: v = c
Which means it is impossible (by any change of reference frame)to reverse the handedness of a massless particle.
HELICITY is an INVARIANT
a fundamental, FIXED property of a neutrino or photon.
Experimentally what is generally measured is a ratio comparing the number of a particles in a beam, or from a source,
that are parallel or anti-parallel to the beams direction.
Helicity =
NN
NN
Longitudinal polarization turns out to be hard to measure; Transverse polarization is much easier to detect.
There are several schemes for rotating the polarization of massive particles.
decay source
aluminum
analyzer
light element(metallic)reflector
++++++
+ + ++
++
e
to analyzer
Electro-static bending magnetic bending precesses spin
Coulomb scatteringdoesn’t alter
spin direction!
EE E
BB
B
Crossed magnetic/electric fields: E B selects the velocity v= cEB
but the spin precesses about the B-filed direction
Can be built/designed to rotate the spin by a pre-calculated amount(say 90O)
Following any scheme for rotating spins, beams of particles can beSpin analyzed by punching through a thin foil of some heavy element!
Head-on view of approaching nuclei
+ +
mc
eh
, oppositely aligned!
electron passing nuclei on the right
+ +
pr, oppositely aligned!
“orbital” angular momentum of nuclei
( up!)
0|||| BB
positive!
The interaction makes the potential energy increase with r BU
Sees B of approaching nuclei UP
BU
positive
negative
The interaction makes the potential energy increase with r
Ur
Fr
So gives a positive (repulsive) force
which knocks electrons to the RIGHT!
electron passing nuclei on the left
+ +
pr
“orbital” angular momentum of nuclei
( down!)
0|||| BB
negative!
Sees B of approaching nuclei DOWN
Ur
Fr
So gives an attractive force knocks electrons to the LEFT!
When positivemore electronsscatter LEFTthan RIGHT
When negativemore RIGHT than LEFT
EXPERIMENTALLYThe weak decay products , e
H = + for e, vc
H = for e, vc
predominantlyright-handed
predominantlyleft-handed
Until 1960s
assumed, like s neutrinos come in both helicities: +1 and -1…created in ~equal numbers (half polarized +1, half 1)
1961 1st observed PION DECAYS at REST(where , come out back-to-back)
_
_
spin-0
spins ,
(each spin-½)oppositely
aligned!Were these half +1, half -1?
No! Always polarized RIGHT-HANDED! So these must be also!
++
Each ALWAYS left-handed!
ALL NEUTRINOS ARE LEFT-HANDED
ALL NEUTRINOS ARE RIGHT-HANDED
Helicity = ms/s = 1
Helicity = ms/s = 1
Dirac Equation (spin-½ particles)
( p m 0
j 0 j
j 0
p • ( ) = ( ) 0 0
0 p • p • 0
where p • pxpypz0 11 0
0 -ii 0
1 00 -1
pz pxipy
px+ipy pz
( 0 p0 • p m
Our “Plane wave” solutions (for FREE Dirac particles)
r,t) = a exp[i/h(Et-p • r)]u(E,p) a e(i/h)xpu(E,p)
which gave
( p mu = ( )( )E/cmc p•uA
p•E/cmc uB
from which we note:
uA = ( p • uB uB = ( p • uA cmc
cmc
Dirac Equation (spin-½ particles)Ec
multiply from left by (-i1 recall i0123
-i31 = -i1)223 = +i23
= +i23)( )( ) = +ii1)( ) = 1
p • )I )= im3
E
c
since =
since (i)
0 1-1 0
0 1-1 0
-1 0 0 -1
so px 1 px 1I
px1py 2pz 3 = m
-i30 = +i0123= 5
-i32 = 2-i33 = 3
p • )I )= im3
E
c
This gives an equation that looks MORE complicated! How can this form be useful?
For a ~massless particle (like the or any a relativistic Dirac particle E >> moc2)
E=|p|c as mo0 (or at least mo<<E)
p|p • )I )=
Which then gives:
or:
p • I )=
^
What do you think this looks like?
p • I
^ is a HELICITY OPERATOR!
I = 2
00
2
2
In Problem Set #5 we saw that if the z-axis was chosen to be the direction of a particle’s momentum
2122
2
1 , , ,
0
(0
(
vvu
c
mcE
c
mcE
u
were all well-definedeigenspinors
of Sz
i.e. p • I )u(p)= u(p)
^ “helicity states”
p • I )=
^
p • I )
^5 “measures”the helicity of
So
2122
2
1 , , ,
0
(0
(
vvu
c
mcE
c
mcE
u
Looking specifically at
5u(p) = =
01
10 uA
uB
uB
uA
B
A
upmcE
c
upmcE
c
)(
)(
2
2
)()(
0
0)(
2
2pu
mcE
pcmcE
pc
For massless Dirac particles (or in the relativistic limit)
5u(p)=
)(
)(0
0)(pu
pE
c
pE
c
p • I)u(p)
^
We’ll find a useful definition in the “left-handed spinor”
uL(p)= u(p)(1 5)
2
Think:“Helicity=1”
In general NOT an exact helicity state (if not massless!)
Since 5u(p) = ±u(p) for massless or relativistic Dirac particles
)()1( 521 pu 0 if u(p) carries helicity +1
u(p) if u(p) carries helicity 1if neither it still measures how close this state is to being pure left-handed
separates out the “helicity 1 component”
Think of it as a “projection operator” that picks out the helicity 1 component of u(p)
Similarly, since for ANTI-particles: 5 v(p) = (p· I)v(p)
again for m 0
we also define: vL(p)= v(p)(1 5)
2
with corresponding “RIGHT-HANDED” spinors:
uR(p) = u(p)(1 5)
2 vR(p)= v(p)(1 5)
2
and adjoint spinors like0†
LLuu 0
2)51(0
2
51 )( †† uu
since
5†= 5
2)51(0 †u
since 5 = - 5
2)51( u
Chiral Spinors Particles
uL = ½(1 5)u
uR = ½(1+ 5)u
uL = u ½(1 5)
uR = u ½(1 5)
Anti-particles
vL = ½(1 5)v
vR = ½(1 5)v
vL = v ½(1 5)
vR = v ½(1 5)
Note: uL+ uR = ( )u + ( )u = u
as well as ( ) ( ) u = ( ) u
=( ) u =( ) u = uL
as well as ( ) ( ) u = uR = uR
1 5
21 5
2
1 5
21 5
2 5+( 5)2
4
1 5
21 5
21 5
2
5
41 5
2
Truly PROJECTION OPERATORS!
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