Short-Lived Resonance States - PowerPoint Presentation

Slide1

Short-Lived Resonance States Slide2

Forces and Fields

Since 1932,

the number

of fundamental particles has increased enormously,

and

the

description of

these new particles and their interactions was soon

found to

be inadequate in terms of the two

fields.

Since the diameter of a

nucleus is

measured in femtometres (

10

-15

m) while an atomic diameter is about

0·1 nanometer

(

10

-10

m

) the repulsive force between two nuclear protons will

be times

larger than the electrostatic force between a nuclear proton and

an orbital

electron

in an

atom. Slide3

But nuclear protons do

not repel each other

and so we conclude that there must be an even stronger attractive force within the nucleus, between

protons, which overcomes the strong

Coulomb repulsive force. This force, which is associated with the production of mesons, is the third field of force and is involved in the so-called strong interactions. Slide4

It

occurs between nucleons and is a short-range force acting at distances appreciably less than a nuclear diameter. Theory shows that the strong interaction is about 137 times as great as the electromagnetic interaction within the nucleus. It

is the interaction considered by Yukawa in his original theory of meson production. The fourth and

last type of force, known as the weak interaction, is also a

nuclear

force which governs the radioactive meson decay

processes .

It

is

involved in

lepton changes and is only about

10

-10

times the strength of the

electromagnetic

field.Slide5

Thus there are four basic force fields in physics, each of which has

a 'source', such

as charge for the electromagnetic field or mass for the gravitational field, and

a

field particle associated with the energy changes of the system. These are

shown in

Table 27.1, which includes a rough

guide to

the relative interaction strengths.

Just

as the photon is the quantum of the electromagnetic field the meson is

the quantum

of the nuclear field. The 'graviton' and the 'intermediate boson'

. Slide6

Associated with each of these fields is a characteristic time. The range of

the strong interactions

10

-15

m

or 1 fm corresponds to about

10

-23

s

, which is

the minimum

time for a signal to travel across a

nucleus of

diameter 3 fm.

This

is the basic nuclear time for comparison purposes, so that an

event taking place

in a shorter time

interval than

this has no meaning. The strength of

the electromagnetic field is

10

- 3

of the

strong field so that the associated time will be

correspondingly greater, viz

.

10

3

x

10

-23

=

10

-20

s

. Most

electromagnetic interactions

have lifetimes of the

order of 10

-15

10

-20

s

, which

corresponds roughly

to the time taken for

a photon

to pass across an atom, i.e

., 1/3x

10

- 18

s. Slide7
Slide8

Table 27.1 also shows that the strength of the weak interaction as

10

-13

times that

of the strong interaction, so that the corresponding weak interaction time

will

be

10

13

x 10

-

23

s=10

-10

. Most

weak decay processes have a mean lifetime

10

-8 _

10

-13

s

, which is very long compared with the time associated

with strong interactions. The

word 'stable' is used to describe all particles except the

strong

interaction

particles, i.e

. all particles immune to strong decay.Slide9

Physical phenomena are ultimately measured in

terms of

energy changes

arising

from four basic

types of

physical force. All atomic and nuclear

interactions can

be described in

terms of

electromagnetic, strong and weak interactions

or forces

. Strong interactions involve particles of high energy whereas lepton

decay processes

are the

result of

weak interactions. The electromagnetic interaction

is proportional

to the charges involved. The name 'hadron' is used for particles

that interact

with each other through the strong interaction. Slide10

What is an Elementary Particle?

Fifty years ago it was

easy to

build a system of atoms and nuclei using

only Protons and

electrons and even with the advent of the neutron there was

little difficulty

in

setting up

models in terms of three elementary particles as units.

With the discovery of

the first antiparticle, the positron, and the emergence of

the

neutrinos

and mesons; it became clear that use of the word elementary

as referring

to the permanent

units of

an atom was obsolete.Slide11

The words 'elementary'

and 'fundamental’,

became

meaningless. Of

these particles only the electrons,

proton

and neutrinos are infinitely stable. The others have comparatively

short lifetimes

, so that it is impossible to recognize them all as fundamental or

elementary

. However, as these particles have discrete masses it is not

impossible to

regard them as

higher quantum

states of a basic state or states. Slide12

We shall return to this point in our discussion of resonance particles and quarks. Thus the lifetime of 10

-10

S may be regarded as long compared with the strong interaction characteristic time, and in this chapter all particles with this lifetime are regarded as stable.Slide13

Short-Lived or Resonance Particles

The neutral

pion

p

0

- the lightest of all

the

strongly

interacting particles with a mean

lifetime of

about 10

- 16

s

characteristic of

electromagnetic

decay is the one

of the

shortest-lived

of

pions.

During the last few years there has been a profusion

of new

particles which have increased the number already known to more

than 100

. These are the new resonance particles which are extremely

unstable with

lifetimes

of about 10

-23

s

showing that they are strongly

interacting particles

. They are called resonance particles because they are recognized by

the resonance

peaks in a normal energy

spectrum of

an event.Slide14

Thus if protons

were collected

at various energies in

a

p

+

+ P

+

collision, the energy distribution

curve

Could be

as shown in Fig. 27.1, which is purely schematic.

Peak I is

the main peak of the proton beam and peaks II, III and IV are

inelastic (high-absorption

) scattering peaks coinciding with resonance states between

the two

particles.

This curve

shows that the system,

can

exist in a set of

intermediate

short-lived excited states. Slide15
Slide16

These new enhanced

probability, Or resonant

states, can be assigned mass, charge and spin consistent with

the conservation

laws. Their

independence is

momentary, as decay times are

only 10

- 7

times the previous shortest lived particle, namely the

p

o

-meson. Although

too

short to measure,

this

time is

sufficient for the excess energy to reassemble

in the

form of mesons and other particles

. Resonances can therefore only be

inferred by

their decay products and this is how such particles have been found.Slide17

The first resonant particle to be discovered was the N* particle, in 1951, by

Fermi

, but it remained

unnamed. In

1960 the

reaction

was

being studied by Alvarez and his group at the Lawrence

Radiation Laboratory

and many hundreds of plates

were analyzed

by a computer. Some of the results suggested that the conservation

of linear

momentum law was being violated

and

two

resulting particles

were

indicated

rather than three. Possibilities were Slide18

where y* is a suggested new resonance particle (or an excited baryon state)

showing

strong nuclear decay

in 10

-23

S into

The

analysis of a large number K

-

+ p

+

events gave a most probable y* mass of

1385

MeV and a decay time of

10

-23

s,

showing the y* particle to be a strong

interaction

particle. This is now designated as an excited

L state. (See Table 27.2C.) The Fermi particle of 1951 was eventually named the N*

particle.Slide19

The scattering cross-section in pion-proton collisions gave a resonance peak at about

200

MeV corresponding to a rest mass of the 'particle' of 1236 MeV. Again

the estimated

lifetime was

about

10

-23

s

, showing strong nuclear decay.

Originally called

a N* resonance, indicating a nucleon excited state,

it is

now designated as

D

baryon

resonance.Slide20

Other resonances have since been discovered, and although the recognition of

such states is

difficult their masses and spin characteristics have been

measured. They

all show strong nuclear decay yielding baryons (often nucleons) and

mesons which

are easily observed. Including these resonances there are now nearly a

hundred

'particles' which are listed as in

Tables 27.2

A, Band C. These show

the long-lived

'stable' particles together with the mass spectrum of leptons,

mesons and

baryons without their antiparticles. The resonant particles can be

looked Upon as

the excited states of some of the stable particles with

correspondingly greater

masses and higher (real)

spins

J

. Slide21

Mesons are then regarded as mass

energy emission when transitions take place between the resonant particles, and to the (relatively) stable ground states corresponding to the old particles. The production of mesons therefore follows the transitions permitted by the appropriate conservation laws. A simple example is the production of excited Pions of spin one from the transitions shown in Fig. 27.3. This is only part of many quantum exchange possibilities between resonance and long-lived states

.Slide22
Slide23
Slide24
Slide25
Slide26

Conservation Laws: Baryon and Lepton Conservation

We are already familiar

with many

conservation laws in atomic and nuclear

systems

, such as the

conservation of

1.

charge

,

2.

mass/energy

,

3.

linear

momentum

4.

and

angular

momentum

.

In atomic physics we know that the application

of these laws leads

to selection rules for allowed

spectra and

in nuclear physics to

the prediction

of new particles, e.g.

neutrinos. In

the field of

sub nuclear

physics we

are now

presented with a whole new

list of

particles which are observed in

collision Experiments and

in different modes of decay. Some modes of decay are

never observed, and

it is natural to suppose that these are prevented by some

unknown law

of conservation. Thus new laws of conservation have been deduced from

a study

of all possible types of particle

reaction and

decay, as well

as mathematically

.Slide27

One of the great

mysteries of

nuclear physics is the stability of the proton.

We know

that the

free neutron

is unstable to

b

-

decay by,

“

so

why not

since

spins would still be conserved? Some

laws

must

prevent

this. This is the law of conservation of baryon number in which all baryons are assigned a

baryon number

B= 1, all anti baryons have B= -1,

and

all

mesons and leptons have

B = O. Thus for

we

have

so

that this reaction 'goes'; but

for

we have . This decay does not occur as the baryon number is not conserved. 4Slide28

similarly

it can be shown that lepton numbers must also be conserved if

we assign

a

lepton number

l

= 1 or -1 as follows to the leptons, remembering that

l

= 0 for mesons and baryons, and treating muons and electrons differently,

The

equation

then

hasSlide29
Slide30

Proton decay is really

f

orbidden because it is the lightest baryon in the mass spectrum. See Table 27.2C. The muon decays we discussed in the last chapter,

vizSlide31

are seen also to conserve the lepton numbers and therefore 'go'. Since muon and electron decays are all weak interactions, i.e. strong interactions do not produce leptons, it follows that lepton conservation does not apply to decay by strong interactions.