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!