VOLUME

16,

NUMBER

17

PHYSICAL REVIEW LETTERS

25

APRIL

1966

give

strong

assurance

that the radiation is

in-

deed universal.

The

equivalent black-body

temperature has been

reported as

3.

1+

1'K'

and

3.

0+0.

5'K.

'

For our

discussion, we shall

consider

T

=3.

0,

at

which

temperature the

photon density

is 548

cm

'

and

the

mean

pho-

ton

energy

7.

0x10

4

eV.

Although

at

this

tem-

perature

the

number of

photons

in

the

spectral

range

of the measurements

(A

=-

3.

2

cm)

is

only

5

&10

'

of the

total,

the

slope

of

the

spec-

trum is such

that

any

reasonable

extrapola-

tion to

shorter

wavelengths

would

yield

at least

a

substantial

part

of

the

3'

black-body

photon

density. Moreover,

two

indirect

confirma-

tions of the existence

of the radiation

have been

reported:

One

lies in the

slope

of the

isotropic

part

of

the

x-

and

gamma-ray

spectrum'

and

the

other in the

absence

of muon-poor air

show-

ers

above

10"

eV.

'

As the last

statement

implies,

severa, l

con-

sequences

of the existence

of the

thermal

ra-

diation

have

quickly

been

noted. One is to pro-

vide

a

source

of

x

rays

and

gamma

rays

by

inverse

Compton

interactions with

cosmic-

ray

electrons.

'»

Another is

to make the

universe

opaque

to

high-energy

photons,

above

2

x10'4

eV,

because of positron-electron

pair

creation

by

photon-photon

interactions.

'~"

A

third effect is

to

deplete

the

density

of

en-

ergetic

electrons

by

the

energy

losses

in the

inverse

Compton

interactions.

'~'

Hoyle'

also

considered the effect of the

thermal radiation

on cosmic-ray

protons,

but concluded

that the

time scale

for

energy

degradation

is

greater

than

the

expansion

time

of the universe

for all

protons

up

to

10

'

eV. This

conclusion

is

wrong

because he

only

considered

the

proton

Comp-

ton

effect

and

neglected

two

stronger

proces-

ses, namely

pair

creation and

photopion

pro-

duction,

which we now wish

to examine.

The

threshold

energy

for

pion

production

by

protons

on

photons

of

energy

7

x10

~

eV

(the

mean

energy

of black-body radiation

at

3'K)

is

10'

eV,

and some

pion

production

occurs

at

lesser

proton

energies

because

of the

high-

frequency

tail

of the

photon

spectrum.

The

cross section rises

rapidly

above the

thresh-

old

p

going

through

a

peak

exc

ceding

400

p,

b

at

the

~„~

resonance

(2.

3

x10'0-eV

proton

en-

ergy

on

7

x10

'-eV

photon),

and descending

thereafter

to about

200

p.

b,

about which

mi-

nor

wiggles

occur

owing

to the

superposition

of

higher

resonances.

With

a

mean

cross

sec-

tion

of

200

pb

and

a

photon

density

of

550

cm

the

mean

path

for

interaction

is

(nv)

'

=9

x10'4

cm.

However,

the

distance

scale for

loss

of

energy

is

L

=(E/AE)(nv)

',

E

being

the initial

proton

energy

and AE

the

energy

loss

per

in-

teraction.

At the

threshold for

single-pion

production,

~/E

is

only

0.

13,

but

it

rises

to

an

average

value of 0.

22

at

the

-,

',

-,

reso-

nance,

and continues

to rise

thereafter

as

multiple

pions

are

produced

or more

kinetic

energy

is

given

to

a,

single

pion.

L

is

there-

fore on

the

order

of

4x10"

cm,

and the

time

sca.

le for

energy

loss is

10"

sec,

which

is

several

hundred times less

than

the

expansion

time

of

the universe.

L is also more

than

an

order

of

magnitude

less

than

the

distance to

the

nearest

quasar.

There

is

abundant

evidence

that

above

10"

eV,

the

cosmic

rays

are not confined

to

the

galaxy;

the

local

intensity

is

a

sample

of the

flux in

a

much

larger

sphere.

If

the sources

of

very

high-energy

particles

are

uniformly

distributed in

space

and

time,

the

effect of

interactions like those

described here is to

deplete

the

spectrum

by

a

factor

equal

to the

ratio of

the time

scale

for

energy

loss to

one-

third the expansion

time.

If,

on the other

hand,

the sources of such

particles

exist

only

far

back in time

or

at

great

distances,

the deple-

tion

is

much

stronger.

It

may

also be

noted

that

if

the

primeval-fireball model is

correct,

going

back

in

time

raises the mean

photon

en-

ergy

as

(1-t/T)

'

and

the

photon

density

as

(1

t/T),

T

bein—

g

the expansion

time;

thus

the effect

may

be

somewhat

larger

than

our

computations

on

a

static model

indicate.

It

should be noted that the cut in the

spectrum

due to

photopion

processes

is

rather

sharp,

because

of

the

steepness

of

the

high-frequency

tail

of

the

Planck distribution.

Only

1%

of

the

photons

have

energies

exceeding

3 times

the mean

value; also,

close to the

threshold

the cross section

is smaller than

200

p,

b and

the fractional

energy

loss

per

interaction

is

a

minimum. Therefore,

below

3

&10"

eV the

process

should have

a completely negligible

effect on the

proton

spectrum.

As

10'

eV is

approached,

the

effect should rise

rapidly',

and above

2

x

1

0

eVp

it

should be a, factor

of several hundred. At

present

the data

above

10'9

eV are rather

sparse,

and the

highest

energy

recorded is

represented

by

a single

event

at

10'0

eV.

'

A

smooth representation

and extrapolation

of

the spectrum

gives

an

integra,

l

frequency

of

about

one event on

100