REFERENCEIC/73/110

INTERNAL REPORT(Limited distribution)

International Atomic Energy Agency

and

United Nations Educational Scientific and Cultural Organization

INTERNATIONAL CENTRE FOE THEORETICAL PHYSICS

ANTIMATTER IN THE UNIVERSE 7 *

G. Steigman **

International Centre for Theoretical Physics, Trieste, Italy.

ABSTRACT

The evidence which might indicate the presence of astrophysically

interesting amounts of antimatter in the Universe is reviewed. It appears

that the Galaxy is made entirely of ordinary matter and if antimatter exists

at all in the Universe it must "be well separated from ordinary matter. An

investigation of symmetric cosmological models further strengthens the

indication that there is no antimatter in the Universe.

MIRAMARE - TRIESTE

August 1973

Not to be submitted for publication.

Based on a seminar presented at the Summer Session on Theoretical

Astrophysics held at the ICTP, Trieste, 3 July - 31 August 1973.

Permanent address: Department of Astronomy, Yale University, Nev Kaven,

Conn. , USA.

— - . - - . .P~ - , r t i * - . j» :ti' *"••

• * . •

Introduction

It is by now well known that particles come in pairs - for every

particle there is an antiparticle, A particle and its antiparticle have

the same mass and (if the particle is charged) opposite electric charge

(and so too for "baryon charge, lepton charge, etc.). We understand this

particle-antiparticle symmetry as a necessary consequence of any causal

quantum theory which is consistent with special relativity. These theoretical

predictions have been amply verified in laboratory experiments. It is

natural then to inquire if this symmetry in the laws of microphysics manifests

itself on the macroscopic scale in the Universe. That is, should the Universe

be symmetric between particles and antiparticles and, more important, is there

any evidence to indicate that the Universe contains equal numbers of particles

and antiparticles?

It is useful to recall that there are many cases where the symmetry of

'the laws of the physics at a microscopic level are strongly violated for

macroscopic situations'. As an example, recall that Maxwell's equations are

time symmetric but the interesting physical solutions are outgoing spherical

waves, not incoming spherical waves or some 50-50 mixture of the two. Similarly,

we must search very hard and "be quite ingenious to find evidence for a small

amount of parity violation at the microscopic level. However, we need only

look around us to find that real,macroscopic,physical systems strongly violate

mirror symmetry. Perhaps it is a requirement that, in order for a large scale

physical system to be "interesting", the symmetries of the microphysics must

be strongly violated. If so, then perhaps to have an "interesting" Universe

the symmetry between particles and antiparticles must be broken on the large

scale. We understand that the breaking of the time symmetry in Maxwell's

equations is achieved through the appropriate choice of boundary conditions.

Similarly, "boundary conditions (say, at the origin of a "big bang" cosmological

model) may play the crucial role in fixing the content (e.g., baryon number,

lepton number, etc.) of the Universe. It may be that all boundary conditions

are possible but that "interesting" Universes only develop when the baryon

number is non-rzero. We shall return to this possibility later.

There is, in addition, another reason why we may not expect exact

particle-antiparticle symmetry in astrophysics! systems. It is related to

the fact that, whereas electric charge is transmitted via a long-range

interaction, baryon charge is transmitted via the short-range strong inter-

actions. Similarly, lepton charge is carried via the short-range weak

— 2 —

interaction. The point is the following. Most theories of relativistic

gravity (including, of course, general relativity) predict tile existence of

collapsed bodies in the Universe: "black holes (and, perhaps, their time-

reversed counterparts, white holes). The probability that such objects exist

seems large and, indeed, there have already been claims that such objects

have been discovered. Now, because of the long range of the gravitational

and electromagnetic interactions, it is in principle possible to measure the

gravitational mass and the electric charge (as well as the angular momentum)

of such a collapsed body. However, because of the short range of the strong

and weak interactions, it is in principle impossible to learn the baryon

number or lepton number of a black hole. Indeed, we may throw baryons down

a black hole and watch them disappear, in apparent violation of the conservation

law which requiresAparticles and antiparticles only be created or destroyed in

pairs. Similarly, if We ever atumble upon a white hole we may find the

material issuing forth to have a non-zero baryon number - again in apparent

, contradiction with the law requiring that baryon number be exactly and locally

conserved.

The previous examples perhaps render less certain the notion that the

Universe is required to have exactly zero baryon number. But such arguments,

about what the Universe should or should not be, can never be conclusive. To

determine whether or not the Universe has equally many particles as anti-

particles, we must turn to observational astronomy and consider the evidence.

The evidence relating to the possible existence of large (astrophysically

significant) amounts of antimatter" in Jhe Universe has been reviewed in some

.detail quite recently . As a result, we shall present in the following

sections a summary of that evidence. Those interested in a somewhat more

detailed discussion are referred to the above references.

Direct evidence

In principle, the detection of antimatter is quite straightforward and

extremely simple. You take your detector - the most rudimentary device will

do - to a region you expect to contain antimatter and you place it down and

wait. If your detector starts disappearing you clear out quickly - you

have discovered antimatterI Just such experiments have, in fact, already

been performed. The manned landings on the Moon, as well as the unmanned

probes which have landed on Venus, give us convincing evidence that at least

- 3"-

those two astronomical bodies are made of ordinary matter. Of course, it

was not to be expected that our Solar System would be a mixture of regions

of matter with regions of antimatter. And, indeed, evidence that the Solar

System contains very little, if any, antimatter has been available to us for

some time from the solar wind which sweeps out from the Sun and past the

planets.

Since our ability to travel around the Universe or even our own Galaxy

performing the above sort of experiment is severely limited, we are indeed

fortunate"that we receive a flux of particles, from outside the Solar System,

vhose properties we can study. These are the cosmic rays - basically,

.atomic nuclei (mostly protons) travelling at relativistic velocities. In

the search for indications of the presence of antimatter in the Universe, the

cosmic rays are something of a mixed blessing. On the one hand, it is

relatively easy to identify an antinucleus in the cosmic rays. On the other

hand, since the cosmic rays are charged particles moving in magnetic fields,

we cannot trace their trajectories back to their regions of origin. As a

result, we know very well what the cosmic rays are made of, but almost nothing

of where they come from.

Despite intensive searches, no antinucleus has ever been found in the

cosmic rays. The results are summarized in Table I, where the 95% confidence

level limits to antinuclei with charge Z are presented.

In collisions between cosmic ray nuclei and the nuclei present in the

interstellar gas, some antinuclei will be produced as secondaries. These

will, for the most part, be antiprotons; the probability of producing heavier2

antinuclei being vanishingly small. In passing through a few grams per cm

of interstellar gas, the cosmic rays should produce a secondary antiproton-k

flux whose magnitude is £, 10 of the primary flux. Thus, it is clear from

Table I that, with a modest increase in sensitivity, antiprotons should be

found in the cosmic rays. But, of course, if and when they are found, it will

be difficult, if not impossible, to determine if they are the predicted

secondary component or if they perhaps represent a truly primary component.

The discovery of antiprotons in the cosmic rays will be of great importance

but will not provide us with unambiguous evidence for the existence of large

(in the astrophysical sense) regions made of antimatter. Bather, of greater

significance would be the discovery of a heavier antinucleus, say, He or C

or, better yet» Fe. Then we would have convincing evidence that somewhere

there exist large quantities of antimatter.

- h -

But, so far, all the evidence suggests.that no such, regions exist.

. To rather good accuracy, we knov that the' regions which.' supply us with cosmic

rays have very little, if any, antimatter. What we do not know is what

regions we have surveyed through the cosmic rays.

The cosmic rays spend no more that a few million years in the disc of

the Galaxy, so they must be able to travel a't least the thickness of the disc

in that time. Therefore, it is likely that the volume in which the observed

cosmic rays originate has a typical dimension of the order of a few thousand

light years. Some theories of the propagation of cosmic rays, coupled with

the high isotropy of the cosmic rays and the uniformity of the non-thermal

radio background,and the lack of time dependence over long time scales of the

cosmic ray flux at Earth, suggest that, in fact, the observed cosmic rays

provide us with a sample of our entire Galaxy. Finally, it is often suggested

that, to explain the high isotropy of the cosmic rays, it might be necessary

to assume that most of their sources are extragalactic in origin. It is

-clear from Table I that, even if one part in a thousand of the observed cosmic

rays were extragalactic, then we would already have learned that antimatter

in the Universe, if it exists at all, is by no means common. What we have

learned, given our limited knowledge of the propagation of cosmic rays, is

that a large.part of our own Galaxy, and perhaps all of our Galaxy, contains

virtually no antimatter.

Indirect evidence

Short- of travelling around the Universe, the cosmic rays provide us

with the only direct evidence of the antimatter content of the Galaxy and,

perhaps, the Universe. However, if antimatter were indeed present in large

amounts, we would have indirect evidence indicating its presence.

The first such piece of indirect evidence arises from the effect of

Faraday rotation. A polarized wave propagating through a magnetized plasma

will have its plane of polarization rotated. The amount of rotation is

wavelength dependent and the magnitude of the effect is proportional to the

integral along the line of sight of the product of the electron (positron)

density and the magnetic field (AQ i* n B d£) . The sense of rotation forJ e

positrons is different to that for electron6,s° that if along a given line of

sight there were (on the average) equally many positrons as electrons, there

would be (on the average) no net Faraday rotation (A9 ^ (n - n +}Bdi ^ 0).j e- e

. - 5 -

Observations of Faraday rotation coupled with observations of pulsar

dispersion , (D y (n _ + n .)dH) indicate that along a typical line of

sight in the Galaxy there axe not equally many positrons as electrons. We thus

have an important piece of indirect evidence about the composition of the

Galaxy which complements the previously discussed direct evidence from the

cosmic rays. The Galaxy almost certainly contains no (astrophysically

significant amounts of) antimatter.

Further indirect evidence of the presence of antimatter can only be

obtained when matter and antimatter meet and annihilate. Then we might

expect to detect the annihilation products. It should be remembered that

antinuclei made of antiprotons and antineutrons will have the same gamma ray

lines as ordinary nuclei.. Similarly, antiatoms and antimolecules will have

the same infrared, optical and ultraviolet emission (and absorption) spectra

as ordinary atoms and molecules.

2For annihilations at rest (E £ Me ) the primary annihilation products

-are pions; roughly 5 - 6 pions are produced with roughly equal numbers of

TT , TT~ , 7T (of course, by charge conservation, n(ir ) = n(Tr~)) in a

typical annihilation. The charged pions decay into muons with the emission

of a muon neutrino. The muons decay into electrons (and positrons) with the

further emission of a muon neutrino and an electron neutrino. The TT 'S

decay into two gamma rays. The neutrinos "are very difficult to detect and

probably do not provide us with any significant indirect evidence of the

absence of antimatter in the Universe (see Ref.3)- The electron-positron

pairs produced in annihilation will not travel very far from where they are

created. • They will either be tied to local magnetic fields or will Compton-

scatter with any photons present (e.g., starlight, black-body, etc.) and

rapidly lose energy. Furthermore, since there exist mechanisms for acceler-

ating electrons and positrons to high energy (pulsars), the electron-positron

component of annihilation is not likely to provide any unambiguous indication

(even of an indirect nature) of the presence of antimatter.

If there is antimatter in the Universe and if significant amounts of

antimatter are mixed with ordinary matter so that annihilation is occurring

on a large scale, then the annihilation gamma rays would provide us with

the best indirect evidence for the existence of antimatter on a large scale

in the Universe. In a typical annihilation, a spectrum of gamma rays is

produced extending from several tens of MeV to several hundred MeV. On

average, 3 - ^ gammas are produced per annihilation, most with energy >. TO MeV.

There are, of course, many ways to produce energetic gamma rays so that

observations of such gamma rays enable us only to place limits on the amount

- 6 -

of annihilation which, may "be occurring. On the other hand, unlike the

cosmic rays, photons travel'in straight lines and so we do have information

about their regions of origin. The OSO-3 observations- indicate the

existence of a gamma ray background (E £, 70 MeV) with three distinct

components. There is an isotropic component •which presumably comes from

large distances in the Universe (perhaps from an intergalactic gas or from

clusters of galaxies, etc.) There is a galactic component which correlates

well with the distribution of hydrogen in the Galaxy. And, finally, there

is a component in the galactic centre;which may or may not arise from the

integrated effect of individual sources.

If we know the size of the region from which the gamma rays come, we

may from the observed flux ffi ) derive the annihilation rate per unit

volume (S) under the assumption that all the observed gamma rays originate in

annihilations. Clearly this gives us an upper limit to S :

'v gy SR . (1)

' In the above, g is the number of gammas in a typical annihilation (̂ 3 - M

and E is a typical dimension of the emitting volume. The annihilation rate

per unit volume may be written as

S = fn2(ov) . • (2)

The overall density is n , the annihilation cross-section is 0" , the

relative velocity is v . f is either the fraction of all matter that is

antimatter or, if one assumes equal amounts of matter and antimatter which

are incompletely mixed, then f is a fraction of all matter that is mixed.

The status of the gamma ray observations as they relate to the question of

antimatter has been reviewed many times (see Refs.l and 2 and, for the most

recent review, see Ref.l6). The results are summarized in Table II.

From the above results, derived from the observations of the galactic

and extragalactic gamma ray backgrounds, we see little evidence for the

existence of antimatter in the Universe at all. Clearly, if antimatter

exists it either does so in very small amounts or manages to be well separated

from regions made of ordinary matter. On how large a scale might antimatter

exist separated from ordinary matter? In this context it is of interest toIT)

consider the observations -of clusters of galaxies as x-ray sources. InIT)

particular, the Coma cluster of galaxies has been detected • as an x-ray

source whose spectrum is interpreted as thermal bremsstrahlung radiation from

• • ' - 7 -

a hot intracluster gas. If this interpretation is correct, then from the

lack of gamma rays from Coma, less-that one part in 10 . of that gas could

be antimatter. It thus appears that if antimatter exists at all it must "be

separated from ordinary matter on scales larger than clusters of galaxies.

Symmetric cosmologies

In the preceding sections it has emerged that there is no evidence

whatever in support of the notion that the Universe contains equal amounts

of antimatter and matter. Indeed, if antimatter were to exist in comparable

amounts to ordinary matter, then it must be very veil hidden; it would haveat least

to be separated from ordinary matter on scales^as large as clusters of galaxies,

Since there is little evidence, at present, which could exclude the existence

of antimatter, on such a large scale, it is of interest to enquire into the

evolution of such a symmetric Universe. By investigating symmetric

cosmologies, we may learn how such a Universe might have evolved and, in

particular, discover if antimatter will survive annihilation and contrive to

separate itself from matter on scales as large1 as clusters of galaxies.

We shall discover that all symmetric cosmologies thus far proposed

encounter severe,and perhaps fatal,difficulties. This may either be taken

as another indication that our Universe is not symmetric between particles

and antiparticles. On the other hand, it may simply mean that we have not

yet been clever enough to discover the "correct" cosmological model. Should

we, at some future date, find unambiguous evidence (say, the discovery of an

anti-carbon nucleus in the cosmic rays) for the existence of large amounts of

antimatter in the Universe, then a re-investigation of symmetric cosmological

models would certainly be called for.

Below we briefly review the status of three cosmological models: the

symmetric hot big-bang model, the symmetric steady-state model, and the

Alfven-Klein model. For a more detailed discussion of these matters, see

Refs.l, 2, 3 and 18.

The symmetric hot big-bang model

The cosmological model which has met with most observational success is

the "standard" hot big-bang model, which predicts the existence of the 3°K

black-body background radiation as well as the existence of primordial helium

(Y # 0.25)-. In the "standard" model it is implicitly assumed that there is

" . ' - 8 -

an excess of baryons over antibaryons in the Universe and, indeed, that there

is at present no astrophysically interesting amount of antimatter in the

Universe. In order to understand why this unsymmetrlc assumption has been

required, it is necessary to examine the early stages in the evolution of the

Universe.

For very early times, the temperature and density vill be very high.

When the temperature is comparable with the nucleon rest mass (i.e. kT & Me ),

nucleon-antinucleon pairs are prolifically produced and the number of nucleons

(and antinucleons) is comparable to the number of photons. When the temperature2

drops much below Me , pairs are no longer produced but can still annihilate.As a result, the ratio of nucleon pairs to photons rapidly decreases;

^ ^ exp(-|-] for kT<Mc2 . ' (3)

Since the density of nucleon pairs is now rapidly decreasing, the lifetime

of a given nucleon (or antinucleon) against annihilation increases rapidly.

In an evolving Universe, that annihilation lifetime rapidly exceeds the age

of the Universe. Thereafter, virtually no annihilation occurs and the ratio

of nucleons to photons will remain constant for all subsequent times. The

temperature at which the age of the Universe and the annihilation lifetime are

the same is: T « 20 MeV. • LAt this stage the nucleon to photon ratio is:

n /n « .10" . The nucleon to photon ratio, therefore, must have roughly

this value at present. We know the density of black-body photons:

n -x. 1+00 cm" and we know a lower limit to the density of nucleons (those

in observed galaxies): n 5; 10 cm . Thus the present value of the

nucleon to photon ratio (nN/nY X 10 ) is roughly nine orders of magnitude

larger than that predicted by the "standard" hot big-bang model. Either the

Universe is not symmetric (e.g., in the early stages when kT >; Me there9

would have had to be one extra baryon for every 10 baryon-antibaryon pairs)

or the "standard" hot big-bang model is wrong.

It is clear that, within the context of a hot big-bang model, a

symmetric Universe would require that nucleons be segregated from antinucleons

at very early times, so that annihilation could be avoided. Since the

nucleon to photon ratio drops to the observed value when kT. s; 30 MeV, it

is clear that any such separation must occur at earlier times when the

temperature and density are higher. Statistical fluctuations in the distrib-

ution of nucleons and antinucleons are wholly inadequate. It is clear that,

in a symmetric hot big-bang model, some physical mechanism would be required

- 9 _

which pushes, nucleons one way and antinucleons the.other, .At .such. high.

temperatures • (k.T ^ Me ) and densities' C >, nuclear density} the' onlypossibility is that the' strong interactions among the hadrons might play an

important role.

The strong interaction is so imperfectly understood that it is perhaps

premature to expect to undertand the thermodynamics of a gas of strongly inter-191-21)acting particles at high temperatures and densities. Nevertheless, Omnes

has suggested that, due to the effects of the strong interaction on a gas in

statistical equilibrium, a phase transition occurs at high temperatures which

separates nucleons from antinucleons. Since the calculations in support of

this suggestion do not satisfy time reversal invariance (or detailed balancing)

it is not at all clear, at least to me, that a phase transition is actually

inevitable. On the other hand, one can simply in an ad hoc manner postulate

that some physical mechanism •will separate nucleons from antinucleons early on

in a hot big-bang model. It is then important to inquire into the effects

of the subsequent re-mixing. Omnes has argued that the re-mixing is controlled

(at least in the early stages where annihilation is important) by diffusion.

He claimed that, since the proton (and'antiproton) is tied to the high-density

gas of electrons and positrons present, the re-mixing and subsequent annihilation

are inhibited. However, for temperatures % 1 MeV, the nucleon in the

early Universe spends half its life as a neutron. The neutron diffuses much

further than the proton and, as a result, the re-mixing is much more efficientlfti

than Omnes estimated. Hence, there will also be much more annihilation1 Q\

For T i l MeV, we have found the surviving nucleon to photon ratio to be

< 10~ - still seven orders of magnitude below its observed value. Further,

we have also found that the re-mixing would continue much longer than previously

estimated so that the situation is even worse. In conclusion, it seems that,

even if nucleons and antinucleons were separated by some mechanism in the

early stages of evolution of a symmetric hot big-bang Universe, the subsequent

re-mixing and annihilation would still be catastrophic. It appears that such

a symmetric model would contain, at present, at least nine orders of magnitude

less matter than our Universe is observed to contain. This seems to offer the

strong suggestion that the Universe is not, in fact, symmetric.

The symmetric steady-state model

22)The steady-state model requires the continuous creation of matter

t

to compensate for the diluting effect of the expansion of the Universe. If

we accept that all such creation must be in particle-antiparticle pairs, then

the Universe should be symmetric. Now, if creation is uniform in space and

- 10 -

time, all of intergalactic apace should he filled with., a particle-antiparticle

symmetric gas at the critical density. Cn « 10 cm" ). In such, a gaa,

annihilations are always occurring, which, of course produce gamma rays. The

flux of gamma rays from such, a gas would be at least five orders of magnitude23}

' higher than the observed flux. When Hoyle realized this, he suggested

that creation occurs non-unifonnly, perhaps in active regions such as galactic

nuclei, QSO's, Seyfert galaxies, etc. In such regions, the annihilation-

produced gamma.rays could be absorbed, accounting for their non-observation.

However, in such regions, annihilation will be more rapid than in diffuse

intergalactic space. As a result, the flux of neutrinos (rauon neutrinos which

will not be absorbed at their source) would be several orders of magnitude

above present limits . A symmetric steady-state (or continuous-creation)

model thus seriously violates observational constraints.

The Alfven-Klein model2I4.) 25)

In this cosmological model, the observed Universe (called the

Metagalaxy) is to have once been a more dilute symmetric gas which initially

began contracting under the influence of gravity. When the density increases,

so does the annihilation' rate. It is then suggested that the pressure exerted

by the annihilation products (high-energy electrons, positrons and gamma rays)

on .the infalling gas is sufficient to halt the collapse and turn the contraction

into the observed expansion of. the Universe. There are a large number of

serious problems with this model.

2U) 25)The first such model Universes * were inside their Schwarzschild

26)radii before the contraction was to have been halted. But, it is well known

that, in that case, the contraction will never be halted. This may be avoided

by arranging the present epoch to be close to the "bounce" epoch. However,

even that may not work since the initial model would have had a larger mass

(and, hence, a larger Schwarzschild radius) than the present Universe because

there has been annihilation. Furthermore, if we are close to the "bounce",

then the uniformity of expansion is difficult to understand since in such a

model the outside begins expanding before the inside.

In addition, there are some serious quantitative problems. The major

one is that the Universe (or Metagalaxy) is very optically thin io the products

of annihilation. How, then, are they effective in halting the collapse and

turning it into expansion? The only possibility is that magnetic fields play a

role in transmitting the pressure. But in that case the isotropy and homo-

geneity of the Universe and the uniformity of the expansion are difficult to

reconcile. Furthermore, since the Universe is optically thin to the 3°K

- 11 -

a

radiation, it would have to be produced in sources. The Isotropy of the 3°K

"background, as well as the x-ray "background Cto vhieh trie' Universe is also

optically thin) would have to be explained in this model "by claiming we were

located, very precisely, at the centre of the Universe,

The observational and theoretical difficulties generated by this

model, only- some of which, have "been discussed above (see Eefs.l and 2 for

more, details) rule it out as a tenable cosmological model.

Conclusions

We have reviewed the evidence which might potentially indicate the

presence of antimatter in the Universe. The direct evidence is somewhat

limited. We know that the Solar System and the cosmic rays contain no anti-

matter. We are not sure where the cosmic rays come from, but probably they

are telling us that at least the Galaxy contains no antimatter. Faraday

rotation and the gamma-ray observations give further support that the Galaxy

probably contains no antimatter. The gamma-ray observations also indicate

that either there is no antimatter in intergalactic space or that, if anti-

matter is present, it must be well separated from ordinary matter. Finally,

we have seen that all symmetric cosmological models so far constructed encounter

severe observational and theoretical difficulties. Taken together, the

evidence seems to indicate overwhelmingly that our Universe is not symmetric.

Perhaps we can reconcile this result with our notions of symmetry as follows.

Imagine a collection (an ense'mble) of very many possible Universes. Suppose

most of them contain exactly equal numbers of baryons and antibaryons. Those

Universes will have a. drastic annihilation catastrophe: they will be left-9

with ^ 10 as much matter as our Universe contains. It is unlikely that

these symmetric Universes will evolve into interesting Universes in the sense

that, with such little matter, probably neither galaxies nor stars nor planets,

etc. will form. On the other hand, in the ensemble of initial Universes,

some small number of them may have a slight excess of baryons or antibaryons.

Because of this small excess (AB/B ^ 10 ) these Universes will avoid the

annihilation catastrophe and may evolve into interesting Universes. A

requirement for an "interesting" Universe may well be a non-zero baryon number.

ACKNOWLEDGMENTS

I wish to thank Prof. Abdus Salam, the International Atomic Energy Agency and UNESCO for hospitality

at the International Centre for Theoretical Physics, Trieste.

- 12 -

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- 1U -

TABLE I

95% confidence level limits to antinuclei in the cosmic rays

Nuclear charge

1

2

£ 2

£ 3

2: 6

Rigidity ^ (GV)

< 0.6

< l . U

1 - 6

^ 1 0 3

< i.k

1 - 1 0

10 - 25

lU - 100

< 3

1+ - 125

< 33

33 - 100

< 1.1+

10 - 18

8

3

1

5

61

8

9

3

3

52

2

!

8

x 10"

x 10~3

x 1 0 " 2

xlO-2

xlO-3

xlO- 3

x 10"2

x 10~3

x 10-2

xlO"3

xio"3

xiO-11

x 10"2

xlO-2

xlO-2

Reference

1+

5

6i

T ;

i8 |8 |

910

1 1

12

13

13

5Ik

Ca) Rigidity iB the momentum per unit charge; for relativistic particles it

is proportional to the kinetic energy per nucleon.

- 15 -

TABLE II

Gamma-ray limits to matter-antimatter annihilation

Component ofY rays

Is.otropic

Galactic

Possible source

Cool intergalactic gas

Hot intergalactic gas

Cool interstellar clouds

Hot intereloud medium

Comments

If f - 1 , then n £ 10"11 cm"3

If f = 1 , then n £ 10"9 cm"3

or, if n = nQ , then f £ 10"

fSi<r16

f < ID"12

•) n is the density necessary to close the Universe .

CURRENT ICTP PREPRINTS AND INTERNAL REPORTS

IC/73/72* M. KUPCZYNSKI: Uniurity without theINT.REP. optical theorem.

IC/73/73 C.J. ISHAM, ABDUS SALAM and J.STRATHDEE:Is quantum gravity ambiguity-free?

IC/73/74* S. SHAFEEand A. SHAFEE: Exoticity andINT.REP. phase consistency.

IC/73/75 M.A.AHMED: Causality and null-planecommutators.

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IC/73/77 S.J. HAKIM and W.L. KENNEDY: Breakingscale symmetry: mesons.

IC/73/87 * S.KITAKADO And WINC-YTN YU; A rINT. REP. for early scaling of inclusive reactions.

IC/73/88

IC/73/89 *INT. REP.

1C/73/91

IC/73/94

1C/73/95

J. CHELA-FLORES : Physical quantities in aclassical two-tensor theory of gravitation.

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IC/73/78 A-M. ABDEL-RAHMAN: On modificationsof the Fubini-Dashen-Gell-Mann sum rulefor Compton scattering.

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' IC/73/80 * M.A.AHMED: Two-particle inclusiveINT. REP. electroproduction.

IC/73/81 * J.C. PATI and ABDUS SALAM: InconsistencyINT.REP. of a class of gauge theories based on Han-Nambu-

like quarks.

IC/73/82 * A.O. BARUT: Spin-statistics connection forINT.REP. dyonium.

IC/73/83 * A.O. BARUT: Gauge co-ordinates.INT. REP.

IC/73/84 * A.O. BARUT: External (kinematical) andINT.REP. internal (dynamical) conformal symmetry and

discrete mass spectrum.

IC/73/85 J.C. PATI and ABDUS SALAM : Is baryonnumber conserving)

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(Preliminary version.)

IC/73/96.* B. PACZYNSKI : Linear series of stellarINT. REP. models and thermal stability of stars.

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duction electrons in small gap semiconductors.

IC/73/99 * S.A. BONOMETTO : Induced pair productionINT. REP. and the transparency of the Universe.

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group of asymptotic symmetry in generalrelativity.

IC/73/107* N.KUMAR and R.R. SUBRAMANIAN :INT.REP. A probabilistic approach to the problem of

electron localization in disordered systemsand sharpness of the mobility edge.

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