ANNUAL REPORTSON THEPROGRESS OF CHEMISTRY.RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.I&-oduction and Summary.AMONG the advances made in nuclear physics during the currentyear, the oustanding feature is the discovery and investigationof a new type of nuclear reaction for which the name ‘(nuclearfission ” has been fairly generally adopted ((‘ nuclear cleavage ”is used sometimes). In this reaction the nucleus does not merelyemit light particles (like protons, neutrons, or a-particles) butbreaks up into two fragments of roughly half the original mass,with the liberation of an energy of about 200 m.v., which is verymuch larger than the energies (up to 27 m.v.) liberated in ordinarynuclear reactions. Both fission fragments contain too large anumber of neutrons to be stable and readjust themselves by theemission of one or several electrons (p-particles), giving rise toradioactive chains similar to the well-known natural radioactivefamilies.A large number of different radioactive substances thusoriginating from nuclear fission have been identified and the listis probably still far from complete. Special interest has beenfocused on the observation that neutrons are emitted in the actof fission. These neutrons can, under suitable conditions, causefurther fission processes, and consequently the possibility seemsto exist that one neutron should start an ever-increasing avalancheof neutrons, a “nuclear chain reaction,” with the consequentliberation of nuclear energy on a large scale.Another important achievement is the discovery of a methodfor the chemical separation of isomeric nuclei.This method hasproved very helpful in clarifying nuclear isomerism in bromine andtellurium. An excited, metastable (isomeric) state of the stablenucleus 1I5In has been found to be the explanation of a long-known4-hours activity of indium, produced by neutron bombardment,and several other ways of exciting this level have been discovered.Further items dealt with in this Report are : nuclear reactionsin the interior of stars; a new radioactive element (2 = 87) in th8 EADIOACTIVITY AND SUB-ATOMIC PHENOMENA.actinium family; and the discovery of stable 3He. I n addition, adetailed account is given of the present state of the theory ofnuclear forces.Nuclear Fission.HistoricaL-Although the discovery of nuclear fission was brieflyannounced in last year’s Report, the events leading up t o it areworthy of record. Ever since the discovery of the production ofartificial radioactivity by neutrons,l the case of the two heaviestelements thorium and uranium has aroused special interest.2 Inthe case of uranium some of the active bodies produced werebelieved to have atomic numbers greater than 92, and attemptswere made to assign definite atomic numbers to them by comparingtheir chemical properties with those to be expected from an extrapol-ation of the Periodic Table, combined with EL study of their geneticrelations and of the particles emitted in their transformations.The investigation of these products was rendered extremely difficultby their surprisingly large number.In the beginning of 1938, tendifferent active bodies with half-lives ranging from 10 secondsto 60 days had been ascertained, mainly through the efforts of0. Hahn, L. Meitner, and F. Stras~rnann.~ Seven of them showedproperties compatible with ‘‘ transuranic ” elements but not withany element between uranium (2 = 92) and polonium (2 = 84).The production of still lower elements seemed t o be excluded byall experimental evidence of nuclear physics, since no reactionwas known in which more than two elementary charges (the chargeof an a-particle) were given off.It was therefore a great surprise to ( f i e . ) I. Curie and P.Savitch when they discovered yet another disintegration productof uranium (of 3.5 hours half-life) which behaved chemically likea rare-earth element, for none of the transuranic elements could beexpected to show such a behaviour.The authors suggested anumber of alternative explanations for their curious observationbut their publications did not mention the possibility of theproduction of nuclei much lighter than uranium. Also 0. Hahnand F. Stra~srnann,~ who found two more rare-earth activities andthree alkaline-earth activities, thought at first that they weredealing with isotopes of actinium and radium, respectively. How-ever, when they used fractional crystallisation they found that1 E. Fermi, F. Amsldi, 0. d’Agostino, F. Rasetti, and E. S e e , Proo. Roy.SOC., 1934, A , 146, 483.2 E.Fermi, Nature, 1934, 133, 898.3 Ber., 1937, 70, 1374; Naturwks., 1938, 26, 475.4 Compt. rend., 1938, 206, 906, 1643; J . Phys. Radium, 1938, 9, 355.Ibid., 1939, 27, 11. Natum*s8., 1938, 26, 755FRISCH : NUCLEAR FISSION. 9their " radium " could not be separated from barium but was easilyseparated from radio-thorium (a radium isotope) in the samecrystallisation experiment. With some hesitation they suggestedthat the uranium nucleus breaks up into two parts of comparablesize, a barium nucleus (2 = 56) and a krypton nucleus (2 = 36)(36 + 56 = 92).The physical interpretation of these findings was given by L.Meitner and 0. R. Frisch,' who pointed out that the mutualrepulsion of charges in a heavy nucleus reduces the form stabilityof the nucleus, in the same way as the stability of a liquid drop(due to its surface tension) is decreased when the drop is given ahigh electric charge.A relatively small disturbance such as theaddition of a neutron may then cause so large a deformation that thenucleus does not recover its spherical shape but breaks up into twosmaller nuclei. After this the electrical repulsion of the two frag-ments makes them fly apart with considerable speed; it wasestimated that they must get a kinetic energy of about 100 m.v.each. On the other hand, it was shown that an energy liberation ofabout 208 m.v. must, in fact, be expected, on account of the estimatedmass defects (packing fractions) of the fission fragments and theuranium nucleus.Physical evidence (as opposed to the chemical evidence of Hahnand Strassmann) for the existence of this new reaction was obtainedvery soon and almost simultaneously in a number of laboratories.I n one type of experiment * the heavily ionising fission fragmentswere discovered by means of an ionisation chamber connected to alinear amplifier.Another type of experiment9 was based on thecollection of the fission fragments, which are able, on account oftheir large velocity, to emerge from a uranium layer and even topenetrate additional layers of material ; the successful collection offission fragments was demonstrated by their radioactivity. Tracksof the fission fragments, recognisable through their dense ionisation,were made visible by means of the cloud chamber lo and in theemulsion of photographic plates l1 covered with uranium andexposed to neutrons.The number of ions Energy and range of the Jission fragments.Nature, 1939, 143, 239.0.R. Frisch, Nature, 1939, 143, 276; G. K. Green and L. W. Alvarez,Physical Rev., 1939, 55, 417; R. D. Fowler and R. W. Dodson, ibid., p. 417;R. B. Roberts, R. C. Meyers, and L. R. Hafstad, ibid., p. 416.F. Joliot, Cornpt. rend., 1939, 208, 341 ; E. McMillan, Physical Rev., 1939,55, 510; L. Meitner and 0. R. Frisch, Nature, 1939, 143, 471.lo D. R. Corson and R. L. Thornton, Physical Rev., 1939,55, 609; F. Joliot,Cornpt. rend., 1939, 208, 647.l1 L. Myssowsky and A. Idanoff, Nuture, 1939, 143, 79410 RADIOACTIVITY AND SUB-ATOIEIC PHENOMENA.formed by one fission fragment is a convenient measure of its energy.By using a very thin uranium layer and an ionisation chamberdesigned to allow nearly complete collection of the ions formed,W.Jentschke and F. Prank1 l2 showed that the energy distributionof the fission fragments was not uniform but consisted of two well-separated energy groups of about equal intensity. The ratio of thetwo energies was given as 1.6, and the phenomenon was interpretedas indicating that the uranium nucleus undergoes fission in anunsymmetrical way such that the two fragments have a mass ratioof 1.6. (on account of the conservation of momentum, the energiesof the two fragments must be in the inverse ratio of their masses).G. von Droste l3 believed that he had found indications of a sub-division of these groups, but this was not confirmed in the experi-ments of E.T. Booth, J. R. Dunning, and F. G. Slack l4 and ofL. Simons (not yet published), who find two energy groups of about72 and 100 m.v. respectively, corresponding to a mass ratio of 1.4.The total energy of the fission fragments has recently beenchecked by an entirely independent method,l5 'uix., the measure-ment of the heat produced in a sample of uranium exposed to anintense beam of neutrons. The result, 175 m.v. with a probableerror of lo%, is seen to agree well with the sum of the two energiesfound in the ionisation experiments, but it must be rememberedthat an appreciable fraction of the heat produced was due to thesubsequent p-disintegrations of the fission fragments rather thanto their kinetic energy.The accuracy of both types of experimentsis, however, not sufficient for any definite conclusions to be drawnfrom them.For the maximum range of the fission fragments in air, figuresbetween 1 and 3 cm. have been published. The most reliableexperiments l6 indicate that the two energy groups have ranges of1.5 and 2.2 cm. respectively. I n these experiments the particleswere detected by means of their ionisation. It was suggested l7 thatthe higher value of 3 cm. found by J ~ l i o t , ~ who detected the fissionfragments by their radioactivity, might be explained by assumingthat the fragments can travel a short way after losing their chargeand thereby their ionising power. The value of 2-2 cm. for themaximum range was, however, also found by McMillan9 who, likeJoliot, used the radioactivity of the fragments to detect theirpresence.12 Naturwiss., 1939, 27, 134.1 4 Physical Rev., 1939, 55, 981.1 5 M.C. Henderson, ibid., 56, 703.l6 E. T. Booth, J. R. Dunning, and F. G. Slack, ibid., 55, 982.l7 G. Beck and P. Havas, Cornpt. rend., 1939, 208, 1643.l3 Ibid., p. 198FRISCH : NUCLEaR FISSION. 11“ Transuranic Elements.”-When nuclear fission was discoveredit was immediately realised that the arguments for the formation ofelements beyond uranium were no longer conclusive. Some ofthem were identified very soon as isotopes of tellurium and iodine,18but others have not so far been identified. It was shown, however,by L. Meitner and 0. R.Frisch that they certainly originate froma fission of the uranium nucleus, so they cannot be “ transuranic ”elements. The authors collected the fission fragments emergingfrom a uranium layer, by placing a dish of water 1 mm. below theuranium layer. The water was then subjegted to the chemicalprocedure which had been developed3 for the isolation of thetransuranic substances, i.e., precipitation of platinum sulphide fromthe 2~-hydrochloric solution. All the “ transuranic ” ‘periods werefound to be present (except the longest one, of 60 days, for whichthe time of irradiation was far too short). Since then, one more ofthese substances has been identified as m01ybdenum.l~ The wholeof the chemical evidence is discussed in the next section.Capture of neutrons in uranium without subsequent fission does,however, occur, and results in the formation of a uranium isotopeof 25 minutes half-life.Since this isotope emits negative electrons,it must transform itself into an element of atomic number 93. Thesearch for any radiations which might be emitted from this elementhas, however, been so far unsuccessful,2o which points to either a veryshort or, more likely, a very long period. A method of concentratingthe 25-minutes uranium, based on a change of valency causedby the energy liberation due to the neutron capture, has beenreported by J. W. Irvine.21The production of this isotope is a typical case of “resonancecapture,” 22 i.e., of the selective capture of neutrons within a narrowenergy region.On account of the high value (about 10-21 cm.2)of the capture cross-section, the process must be attributed to theabundant isotope 23*U. On the other hand, the resonance neutronsdo not seem to cause fission to a measurable extent, although fissionis observed with the still slower neutrons of thermal energy, as wellas with fast ones. It was pointed out by N. Bohr23 that thisapparently erratic behaviour of the fission probability can beexplained by ascribing the fission observed with slow neutrons tothe rare isotope 236U (actino-uranium, abundance 007%). Thel8 P. Abelson, PhyeiccsZ Rev., 1939, 55, 418; N. Feather and E. Bretscher,Nature, 1939, 143, 516.l9 0. Hahn and F. Strassmann, Naturwk., 1939, 27, 451.2o E. SegrB, Physical Rem, 1939, 55, 1104.21 Ibid., p.1105.22 L. Meitner, 0. Hahn, and F. Stragsmann, 2. Physik, 1937, 106, 249.23 Physical Rev,, 1939, 65, 41812 RADIOACTIVITY AND SUB- ATOMIC PHENOMENA.main isotope =SU is assumed to undergo fission with fast neutronsonly, the fission probability decreasing rapidly 24 for neutron energiesbelow 1 m.v. The arguments for this view are strong, but directproof will have to wait for at least a partial separation of the uraniumisotopes.Identification of Fission Products.-Of the substances originallybelieved to be “ transuranic elements,” the first to be identifiedwere a 3 days activity and its 2.4-hours daughter substance,which were found to be tellurium and iodine respectively. It wasfound by Abelson and independently by Feather and Bretscher 18that these bodies emitted a soft y-radiation which, by absorptionexperiments with suitable elements, could be identified as thecharacteristic X-rays of iodine and xenon, respectively.(TheX-rays are emitted after the P-disintegration and must thereforebe characteristic of the daughter element.) This “ physical ”identihation was supported by chemical tests. Hahn andStrassmann19 confirmed the iodine but found that the 3-daysactivity is a mixture of two substances with nearly identicalperiods but different chemical properties, one being tellurium(which transforms itself into the 2.4-hours iodine) and the othermolybdenum. The latter is perhaps the same isotope as the onestudied by G. T. Seaborg and E. Segr8,25 who obtained it bybombarding molybdenum with deuterons or neutrons.In three further publications P.Abelson26 reported a numberof new activities. Three had the chemical properties of iodine,six of tellurium, and three of antimony. Their periods, geneticrelations, and supposed atomic weights are given in the table onp. 14.Little is known about the formation of active bromine isotopesfrom uranium. Various periods have been observed27 but onlyone of them28 (of about 40 mins.) by more than one author.Bromine isotopes with periods of 2.5 hours and 22 hours have beenreported 29 to be formed by the fission of thorium.An interesting line of attack has been opened by 0. Hahn andF. Strassmann.30 It is based upon the fact that any noble gasesformed (either as primary products or by subsequent P-decay) canbe continuously removed by bubbling air through a uranium (orthorium) solution during the irradiation.The air is then passed34 R. B. Roberts, R. C. Meyers, and L. R. Hafstad, ibid., p. 416.2 K Ibid., p. 808. Ibid., pp. 670, 876; 56, 1.27 J. Thibaud and A. Moussa, Cornpt. rend., 1939, 208, 652, 744.28 R. W. Dodson and R. D. Fowler, PhyahZ Rev., 1939, 55, 880.29 E. Bretscher and L. G. Cook, Nature, 1939, 143, 559.30 Natuwbs., 1939, 27, 89, 163FRISCH : NUCLEAR FISSION. 13through a wash-bottle or (better) absorption coal ; the productscollected can be subjected to various chemical separations. Severalisotopes of cesium, barium, lanthanum, rubidium, and strontiumhave been found by F. A. Heyn, A.H. W. Aten, jun., and C. J.Bakker,31 and by 0. Hahn and 3’. Stra~smann,~~ and their periodsand genetic relations have been determined. By varying the speedof the air, estimates of the periods of the corresponding noble-gasisotopes have been obtained. The same cesium, etc., isotopes, anda few more, have also been obtained from the irradiated uraniumsolution directly ;6* 33 the absence of some of these periods amongthe substances collected by the “ bubbling ” method indicates eitherthat they are primary fragments of the fission or, more probably,that they originate from a noble gas with a period less than a fewseconds (the time required for the gas to reach the collecting bottle).A rubidium isotope of 17 minutes half-life 34 is probably identicalwith s*Rb which can be obtained from rubidium by slow-neutronb~mbardment.~~ The same isotope was found to grow from akrypton of 3 hours half-life, which is formed, together with severalother noble-gas activities of longer period, in the fission of th0rium.3~Some investigators have carried out chemical tests on the activeproducts collected by the “ recoil method,” that is, on a surface(filter-paper, glass, or water) placed a t a small distance from auranium (or thorium) layer irradiated with neutrons.L. Meitner 36found periods of about 40 minutes and 13.5 hours, with the chemicalproperties of “ transuranics,” among the fission products fromthorium. G. N. Glasoe and J. Steigman3’ attempted to dis-criminate between lighter and heavier fission products by placinga screen of cellophane, of thickness equivalent to the range (1.5 cm.)of the less penetrating fragments, between the uranium layer andthe collecting surface.Unfortunately, in this kind of experimentthe activities obtainable are very weak.It has been possible to assign definite atomic weights to some ofthe periods. For example,31 the barium activity of 86 minuteshalf-life obtained from uranium or thorium agrees with respect toboth the period and the hardness of the P-rays with a barium isotopewhich is obtained from ordinary barium by bombardment withslow neutrons and must therefore be 139Ba (all the barium isotopesfrom 134 to 138 are stable, and the isotopes 130 and 132, whichmight form active isotopes by capturing a neutron, are very rare).31 Nature, 1939, 143, 516, 679.33 C.Lieber, Naturwiss., 1939, 27, 421.3* (Mme.) I. Curie and P. Savitch, Compt. rend., 1939, 208, 343.35 A. Langsdorf, jun., Physical Rem., 1939, 56, 205.36 Nature, 1939, 143, 637.3a Naturwiss., 1939, 27, 529,37 Physical Rev., 1939, 55, 98214 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.The following table includes only those activities, resulting fromthe fission of uranium, which the Reporter believes to be fairly wellestablished. A number of them have also been observed among thefission products of thorium; they are marked with an asterisk.Papers dealing with thorium fission products are given in refs. (28),(291, (31), (34), (35), and (38).Table of chemically identi3ed products of the Jission of uranium andt hori urn.Ref., no.28, 3231, 32, 34, 3530, 3319, 3818, 19, 26, 32, 38262626, 3226, 3226, 326, 29, 31, 32, 386, 29, 31, 32, 386, 34Atomicweight.88{ (89)(99 or 101)131139(140)Br, 35-40 mins.Kr,* 3 hours+Rb,* 17 mins.Sr, 7 mins.Sr, 6 hours --+ Y, 3.5 hours.Sr, 54 days.Mo,* 67 hours.Sb, 5 mins.(+) Te,* 77 hours--+ I,* 2.4hours.Sb, 80 hours-Te, 10 hours.Sb, 4.2 hours-Te, 70 mins.Te, 43 rnins. -+- I, 54 mins.Te. 60 mins. _I, I. 22 hours. . ,Te; 30 hours (isomers) --+ I, 8 days. Te, 25 mins.}Xe,* few sees. --+ Cs,* 33 mins. --+- Ba,* 86m i n S .12 days.40 hours.Xe,* ca. 15 mins. --+ Cs,* 33 mins. + Ba,*Ba, 14 mins. -+ La,* 2-5-3.5 hours --+- La,** Results also from the fission of thorium.It is seen that the active isotopes identified so far form, roughlyspeaking, two groups, one around krypton and with atomic weightsof about 90 or 100, and one around xenon and with atomic weightsin the neighbourhood of 140.This supports the conclusion drawnfrom the presence of two energy groups among the fission fragmentsthat for some (probably energetic) reason 39 the fission into two partsof equal size does not occur or is, a t least, much less probable thanthe fission into two parts with a mass ratio of about 5 : 7.The Emission of Neutrons in the Fission Process.-On account ofthe large energy liberation in nuclear fission (about 170 m.v.) it wasto be expected that a fraction of this energy might be used up in" evaporating " one or several neutrons from the nascent nuclei(the energy required to remove a neutron from such a nucleus isprobably only about 4 m.v.).The problem of discovering andcounting the neutrons emitted on top of the background of the38 0. Hahn, F. Strassmann, and S. Flugge, Naturwiss., 1939, 27, 544.39 G. Beck and P. Havas, Compt. rend., 1939, 208, 1084&RlSCH : NUCLEAR FISSION. 15'neutron bombardment required to produce a sufficient number offissions is by no means simple. H. von Halban, jun., F. Joliot, andL. Kowarski 4O used a large container filled with a solution of uranylnitrate, with a neutron source at the centre. Neutron detectorsplaced at various distances from the source served to determine thedensity distribution of neutrons within the tank.The experimentwas then repeated, a solution of ammonium nitrate of the samemolar concentration being used (this amounts very nearly toremoving the uranium nuclei while leaving the concentrations of allthe other nuclei unchanged). I n spite of the fact that the uraniumabsorbs neutrons, the average neutron density within the tankwas found to be even slightly larger in the presence of the uraniumnuclei. From a quantitative consideration of all the nuclearprocesses taking place in the two solutions, the authors concludedthat between three and four neutrons, on an average, are emittedin every fission process. A somewhat smaller figure, 2.3, wasobtained by L. Szilard and W. H. Zinn,41 who avoided the " back-ground" of primary neutrons by using a neutron source whichemits fairly slow neutrons, and a neutron detector which does notrespond t o neutrons of such a low energy.The interpretationof this experiment is on the whole more complicated and impliesa number of corrections but their result is confirmed by some recentexperiments by H. von Halban, jun., F. Joliot, L. Kowarski, and F.Perrin,42 from which the same figure of 2.3 can be deduced. Otherinvestigators43 have found figures between 1.5 and 6 neutrons perfission, but their experimental arrangements were such that it isdifficult to compare their results.Nuclear Fission as a Possible Basis for a Chain Reaction.-Theemission of more than one neutron, on an average, in the fissionprocess is a very important fact in so far as it suggests, for thefirst time, the possibility of a nuclear chain reaction.A neutron,placed within a large mass of uranium, would hit a uranium nucleusand cause fission, thereby liberating, let us say, two neutrons;these in turn would cause fission of two further uranium nuclei andliberate four neutrons, and so on. Since the energy release in thisreaction would be about lo* times larger than in ordinary chemicalreactions there has been considerable concern about the catastrophicconsequences of such an experiment, and it has been feared that it40 Nature, 1939, 143, 471, 680.41 Physical Rev., 1939, 55, 799.42 J . Phys. Radium, 1939, 10, 428.43 H. L. Anderson, E. Fermi, and H. B. Hanstein, Physical Rev., 1939, 55,707; J.L. Michiels, G. Parry, and G. P. Thomson, Nature, 1939, 143, 760;G. von Droste and H. Reddemann, Naturwiss., 1939,27,371; H. L. Anderson,E. Fermi, and L. Szilard, Physical Rev., 1939, 56, 28416 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.might form the basis for the construction of a super-bomb exceedingthe action of ordinary bombs by a factor of lo6 or more.Fortunately, our progressing knowledge of the fission process hastended to dissipate these fears, and there are now a number of strongarguments to the effect that the construction of such a super-bombwould be, if not impossible, then at least prohibitively expensive,and that furthermore the bomb would not be so effective as wasthought at first.Let us begin with the simplest arrangement : a solid sphere ofuranium or uranium oxide.The mean free path of a fast neutronin U,O, is about 10 cm., but the mean path covered by a neutronbefore causing a fission is much longer, since only one collision inabout 100 causes fission of the uranium nucleus hit. I n con-sequence, the sphere must be fairly large, otherwise too manyneutrons would escape from it without causing fission. Accordingto a calculation by F. P e ~ ~ i n , ~ ~ the sphere must have a diameter ofabout 9 feet and contain 40 tons of U,O,.I n this calculation it is implicitly assumed that those collisionswhich do not lead to fission are ‘‘ elastic,” leaving the energy of theneutron nearly unchanged. It is however known, fiom experimentswith other heavy nuclei, that most collisions are inelastic ; thereforethe energy of a neutron will be reduced, after a few collisions, tosomething like 0.1 m.v., which is too small to cause fission.Onemight think of using a still larger block of uranium which wouldallow the neutrons to undergo a very large number of collisions andultimately to get down to thermal energy when they can causefission again (this time of the 235U nuclei), but then practicallyall the neutrons would be captured in one of the resonance levelson the way down, without causing fission.If one wants to utilise the fission caused by slow neutrons, theobvious thing to do is to mix the uranium with a hydrogenoussubstance, such as water. Collisions with hydrogen nuclei rapidlycarry the neutrons down to thermal energy, and the number ofneutrons captured by the uranium on the way down will becomesmaller with increasing hydrogen concentration. At the same time,however, the number captured by the hydrogen itself will increase.Experiments by the Paris group42 indicate that the optimummixture contains about four atoms of hydrogen to one atom ofuranium, but even in this mixture the production of neutrons is toosmall to replace those which are absorbed.The possibility of producing a nuclear chain reaction seems todepend upon the separation of the uranium isotopes.No completeseparation is required; if several kg. of uranium with about ten4 4 Compt. rend., 1939, 208, 1394PRISCH : NUCLEAR FISSION. 17times the normal concentration of 235U could be produced, thecapture of neutrons in the uranium would probably be sufficientlyreduced to permit a chain reaction to develop.Methods for theseparation of isotopes have recently been greatly improved and itdoes not seem unlikely that such an experiment may be carriedout before long. It would not, however, form an effective basis forthe construction of a super-bomb, a t any rate according to presentknowledge, because the reaction is not fast enough. The timerequired for a neutron to become thermal is about see. ; EL furtherlo* sec. is lost, on an average, before the neutron hits a uraniumnucleus. So the ‘‘ reproduction cycle ” takes about loA sec., andthe time required to double the “ population ” of neutrons is probablyseveral times longer.As soon as the temperature has reachedseveral thousand degrees the container will be broken, and in a timeof lo4 sec. the parts of the bomb will be well separated. Theneutrons will then be able to escape and the reaction will stop.Consequently, the energy liberated will only be about sufficient tobreak the container or, in other words, of the same order as withordinary explosives.The question then arises whether it would be possible to controlthe reaction in such a way that it does not result in an explosion butproceeds a t a moderate speed so as to permit the utilisation of theenergy liberated. It was pointed out by F. Adler and H. von Halban,j ~ n . , ~ ~ and independently by F. Perri11,~6 that this can be achievedby simply adding a suitable amount of a cadmium compound to theabove-mentioned mixture of uranium and water.The effect of thecadmium would be to make the reaction strongly temperature-dependent with a negative temperature coefficient. The captureprobability of neutrons in cadmium increases with increasing neutronvelocity and, therefore, with increasing temperature, whereas foruranium and hydrogen it remains constant. Consequently, withincreasing temperature an increasing fraction of neutrons iscaptured by the cadmium rather than causing fission of the uranium,and above a certain temperature the chain reaction will no longer beself-sustained. The reaction vessel will adjust itself at a temper-ature just below the critical value; any attempt to cool it will causeonly a temporary drop in temperature with consequent increase ofthe reaction rate and return to the critical temperature.Thereaction can be interrupted by simply heating the reaction vessel.It is seen that the behaviour of this reaction, surprising as it mayseem, would be very convenient indeed. On account of the highcost of isotopically separated uranium it would probably not bea serious competitor with other sources of energy, but it might45 Nature, 1939, 143, 793. 4 6 Compt. rend., 1939, 208, 157318 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.gain great importance for large-scale production of artificial radio.activity .Delayed Neutron Emission.-Even before the discovery of neutronemission in the fission process itself, it was found4' that uraniumand thorium emit neutrons for a short time after bombardmentwith neutrons. The decay of this radiation was analysed48 intotwo components of 10-15 secs. and 45 secs., and later a further twocomponent^,^^ of about 3 and 0.3 sec., were found, attempts to findstill shorter components 50 being unsuccessful. These neutronsare obviously not connected with the fission process itself but areemitted from some of the fission products.The emission of hardp-particles, with a decay similar to that of the " delayed neutrons,"has been observed,50a and the simultaneous emission of a P-particleand a neutron must be expected to happen occasionally if the@-disintegration energy is sufficient for such a process. The theoryof this phenomenon was given by N.Bohr and J. A. Wheeler,51together with that of many other aspects of nuclear fission.In the fission process itself there is no appreciable delay. G. K.Green and L. W. Alvarez 52 bombarded uranium with a periodicallyinterrupted beam of neutrons; no fissions were observed duringthe intervals, and the authors concluded that the delay, if any,must be less than 0.003 sec. A still more sensitive test was madeby N. Feather.53 It is based on the fact that by the impact of afast neutron a uranium nucleus is given a certain velocity, whichit loses again within about 10-13 sec., on account of collisions withsurrounding atoms. Feather collected fission fragments from athin uranium layer and found that the number and penetratingpower of those emerging in a forward direction (with respect to theincoming neutrons) was slightly greater than of those emerging in abackward direction.This difference can only be explained if thenucleus undergoes fission while still in motion, i e . , within about10-13 sec.Other Cases of Nuclear Fission.-Fission of protoactinium (2 =91) under neutron bombardment has been reported by A. von Grosse,E. T. Booth, and J. R. Dunning.54 The typical bursts of ionisationdue to the fission fragments were observed by means of a linear47 R. B. Roberts, L. R. Hafstad, R. C. Meyers, and P. Wang, Physical Rev.,1939, 55, 510, 664.4 8 E. T. Booth, J. R. Dunning, and F. G. Slack, ibid., p. 876.49 K. J. Brostram, J. Koch, and T. Lauritsen, Nature, 1939, 144, 830.50 D.F. Gibbs and G. P. Thomson, ibid., p. 202.50a H. H. Barschall, W. T. Harris, M. H. Kanner, and L. A. Turner,Physical Rev., 1939, 55, 989; see also refs. (2) and (22).51 Physical Rev., 1939, 56, 426.63 Nature, 1939, 143, 597.52 Ibid., 55, 417.54 Physical Rev., 1939, 56, 382. FRIYCH : NUCLEAR ISOMERISM. 19amplifier, and fission products were collected by the recoil method.Chemical separations showed the presence of a rubidium with 17mins. and a caesium with about 30 mins. period, which are probablyidentical with those resulting from uranium and thorium fission.Slow neutrons do not cause fission of protoactinium, and the energythreshold seems to be about 1 m.v.A few cases of fission. of elements below thorium have beenrep0rted,5~ but other investigators have not confirmed these results.Fission of uranium under bombardment with 9-m.v.deuteronsfrom the Cambridge cyclotron has been reported by D. H. T. GanL5(jThe yield of this process is small and falls of3 rapidly with decreasingdeuteron energy.No fission of either thorium or uranium was observed2* underirradiation with y-rays of 17 m.v. energy, obtained by the bombard-ment of lithium with protons. This result is in agreement withtheory 51 which predicts a very small yield for this reaction.The spontaneous fission of uranium or thorium is energeticallypossible but, according to theory,51 exceedingly improbable. W. F.Libby,57 using several very sensitive tests, found no indication of it,and concluded that the average life of a uranium or thorium nucleuswould be a t least 1014 years if it were limited only by the spontaneousfission.Nuclear Isomerism.An interesting case of isomerism, exhibited by the nucleus l151n,has been the subject of considerable study.It has been known for along time that a period of 4.1 hours is produced in indium by neutronbombardment, and that this period follows the chemical reactionsof indium. This activity has been thoroughly investigated byM. Goldhaber, R. D. Hill, and L. S~ilard,~* who found that itcan be produced by neutrons of 2-5 m.v. but not by slow neutrons.The latter fhding shows that it is not the result of neutron capture(which occurs always most easily with slow neutrons). On theother hand, it cannot be produced by a neutron-loss reactioneither, for 2-5 m.v.is far too small an energy to knock off aneutron from the nucleus. In view of the chemical evidence whichexcludes the emission of charged particles, the only remainingexplanation seems to be that the activity is due to an excited stateof the stable nucleus 1151n (the other stable isotope 1131n is too rareto account for the observed yield). This state, for which the symboll151n* has been used, is metastable ; Le., the return, by emission ofradiation, into the ground state (which in general takes place within5 5 C. Magnan, Cornpt. rend., 1939, 205, 742. 56 Nature, 1939, 144, 707.5 7 Physical Rev., 1939, 55, 1269. 5 8 Ibid., p. 4720 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.a very small fraction of a second) is greatly delayed, so that the half-life of the state has the observed value of 4-1 hours.The correctiiess of this explanation has been proved in the mostdirect way, by showing 59 that l151n* nuclei can be produced byirradiating indium with X-rays.By varying the voltage of theX-ray tube, the energy threshold was found 60 to be about 1.3 m.v.This is considerably more than the excitation energy of 115In* (theenergy difference between l151n* and 1I5In), which is probablyabout 0.6 m.v., to judge from the energy of the electrons which areemitted when l151n* returns into the ground state. The mechanismof the excitation process is obviously such that the indium nucleiare first raised into a level at about 1.3 m.v. ; some of them will goback into the ground state but some will be “trapped ” in themetastable level at 0.6 m.v.Direct excitation of this level byX-rays of 0.6 m.v. is not possible, since a “ forbidden ” transitionis always forbidden both ways.The energy necessary for the excitation of the nucleus can alsobe provided by the impact of charged particles. Both protons 61and a-particles 62 have been found to produce the 4-l-hours activityin indium.Chemical Separation of Nuclear Isomers.-The energy liberatedin the transition between two isomeric states of a nucleus doesnot, in general, appear as radiation but is used to eject one of theelectrons of the K or L shell (“ internal conversion ”). I n thesubsequent re-establishment of the shell, the characteristic X-raysare emitted.By investigating these X-rays, it has in some casesbeen possible to check the atomic number of the resulting nucleus.For example, L. I. Roussinow and A. A. Yusephovich 63 placedradioactive bromine ( 80Br, periods of 18 mins. and 4.4 hours) betweenthe pole pieces of a magnet in order to prevent the p-particles fromreaching the counter. The radiation then recorded by the counterwas found to contain a soft component which, from its absorptionin selenium, arsenic, mercury, and lead, was identified with thecharacteristic X-rays of bromine. The radiation showed a simpledecay with 4.4 hours period and must therefore be emitted in thetransition from the 4-4-hours state of 80Br into a lower state of thesame nucleus.That this lower state is identical with the isomer of 18 mins.periodwas shown conclusively by E. Segrb, R. S. Halford, and G. T. Seaborg 64L 9 B. Pontecorvo and A. Lazard, Compt. Tend., 1939, 208, 99.G. B. Collins, B. Waldman, E. M. Stubblefield, and M. Goldhaber,Ph,ysical Rev., 1939, 55, 507.61 S. W. Barnes and P. W. Aradine, ibid., p. 50.E2 K. Lark-Horovitz, J. R. Risser, and R. N. Smith, ibid:, p. 878.c3 md., p. 979. Ibid., p. 321FRISCH : NUCLEAR ISOMERISM. 21who succeeded in isolating, by a chemical method, the nucleiwhich result from the isomeric transition, and found that theydecayed with a period of 18 mins. The separation method isin principle the same as in the classical experiment of L. Szilardand T. A. Chalmer~,~~ and is based on the recoil of the brominenuclei which is caused by the ejection of an electron in the isomerictransition. The recoil energy is sufficient to remove the bromineatom from the molecule to which it belongs, or at least to activatethe molecule so that it can undergo some chemical reaction.Segri:et al. prepared tert.-butyl bromide containing S%r and introducedit into aqueous methyl alcohol at O", where it underwent chemicalreaction resulting in the liberation of hydrogen bromide. Thisreaction requires an activation energy which may be supplied by theisomeric transition. After the reaction had gone on for some time,silver bromide was precipitated from the solution (after extractionof the butyl bromide with benzene). The precipitate was found todecay with a period of 1s mins., even if the separation was carriedout many hours after the preparation of the 8oBr when the 18-mins.period had apparently died off.If the precipitation was repeatedwith intervals of several hours, the same lot of butyl bromide beingused, the initial activity of the precipitate decreased with a periodof 4.4 hours, the period of the upper state of 80Br, as expected.Don C. DeVault and W. F. Libby 66 also separated the bromineisomers, by preparing a bromate solution containing soBr andprecipitating silver bromide from it. Immediately after precipit-ation the solution was found to be nearly inactive, and the authorsthink it probable that the upper state does not emit p-rays a t allbut that the apparent 4.4-hours P-decay of aoBr is due to the equi-librium between the upper state and its shorter-lived p-activedaughter substance.Three pairs of isomers of tellurium isotopes have been recognisedthrough the work of G.T. Seaborg, J. J. Livingood, and J. W.Kennedy,G7 and separation experiments showed that in all threecases the shorter period grows from the longer one. The isotopesare : 12'Te (90 days-10 hours), 129Te (30 days-70 mins.), and131Te (30 hours-25 mins.).It is becoming increasingly clear that nuclear isomerism, whichwas at first believed to be a peculiarity of a few nuclei only, is infact a very common phenomenon, the possibility of which must beconstantly kept in mind when assignments of radioactive periodsto definite isotopes are attempted. In particular, the occurrence66 Nature, 1934, 134, 462.6 6 Physical Rev., 1939, 55, 322.6 7 Ibid., pp.410, 79422 RADIOACTIVITY AND SUB- ATOMIC PHENOMENA.of active isomers of stable nuclei (as in the case of indium) increasesthe number of possible assignments in a disturbing manner.There are fortunately several ways in which the transition betweenisomeric states can be distinguished from a true p-transition(emission of an electron from the nucleus itself). Two have alreadybeen mentioned, vix., the study of the characteristic X-rays and therecoil separation. A further important criterion is the energydistribution of the electrons emitted in the transformation. Theinternal-conversion electrons, ejected from the K or the L shell as aconsequence of the transition between two states of the samenucleus, have a line spectrum, i.e., they are concentrated in one or afew narrow energy bands, whereas the electrons emitted from thenucleus itself in a p-transformation have the well-known continuous(bell-shaped) distribution. The use of a p-spectrograph permitsimmediate decision, but is not essential since even simple absorptionexperiments will show the difference: the absorption of a true,continuous p-spectrum is approximately exponential or, in otherwords, the logarithm of the transmitted intensity plotted againstthe thickness of the absorber gives nearly a straight line, but in thecase of an isomeric transition the plot bends downwards [see, e.g.,ref.(25)l.Nuclear Reactions in the Interior of Xtars.An important contribution to the problem of energy productionin stars has been given in a paper by H.A. Bethe.68 His conclusionsare based on a very careful and exhaustive discussion of all thosenuclear reactions which may be expected to occur in stars. Thetemperature in the interior of a star can be calculated, accordingto Sir A. Eddington, without making special assumptions as to thenature of the energy source, and is, e.g., a t the centre of the sun1-9 x lU7". On account of the presence of large amounts of hydrogenand helium, any nucleus present will be subjected to an intensebombardment by protons and a-particles possessing a Maxwellianenergy distribution, with energies of the order of 20,000 volts.Bethe shows that under these conditions most light nuclei arequickly broken up into protons and a-particles, so they cannot forma permanent energy source.This does not hold, however, for thefollowing cycle of reactions :E2C + H --+ 13N 13C + H --+ 14N1*N + H -+ l5O 15N + M + 12C + HeDuring the cycle, four protons are absorbed and two positronsemitted and the end result is a helium nucleus and the original 12C68 Physical Rev., 1939, 55, 434.13N --+ 13C + e+150 --+ l5N + eFRISCH : NATURAL RADIOACTIVITY. 23nucleus. I n other words, the carbon acts as a catalyst for thereaction 4H+ He + 2e+, which is accompanied by an energyevolution of about 30 m.v. Possible side reactions are discussed,and it is found that they are too weak to destroy the catalyst, evenin the course of astronomical times.From the nuclear reactions discussed, no other cycle can beconstructed which does not result in the quick destruction of thecatalyst.Elements below carbon do not permit the accumulationof four protons, but break up with emission of an a-particle beforethe last proton can be added. Elements higher than 15N have tooslow a reaction rate (because of their high charge which repels theprotons) to be of any importance in the energy production. Actually,the C-N cycle gives just the right amount of energy, in the sunand several other stars for which it was checked, to replace theenergy lost by radiation.One important conclusion drawn by Bethe is that a t presentheavy elements are not being built up to any appreciable extent,in the sun or other stable stars.It is probable that the buildingup of the heavy elements has taken place in the remote past, underextreme conditions of pressure and temperature (stellar or cosmicexplosions). Some stimulating speculations on this subject arecontained in a paper by C. F. von Weiz~acker.~~Natural Radioactivity.The discovery of a new natural radio-element has been announcedby M. Perey.'O The element-which has been given the nameactinium-K-originates from actinium by the emission of an a-particle. These a-particles had been known for a long time but hadbeen ascribed to impurities; Perey showed that they are presenteven if all the relevant impurities are removed. If measured on ap-ray electroscope, freshly purified actinium is practically inactiveand it takes days before the activity due to actinium-B and -Gbegins to develop.Perey found that a sniall fraction (0.5%) of thefinal activity develops within the first hour after purification, beingapparently due to a body of 21 minutes half-life growing directlyfrom the actinium. This active body was separated chemically andfound to follow the reactions of an alkaline element. On account ofthis chemical evidence, and on the assumption that it originatesfrom actinium through the emission of an a-particle, the newelement must have the atomic number 87. This seemsto be thefirst definite proof of the existence of an element with this atomicnumber.69 Physikal. Z., 1938, 39, 633.70 Compt. rend., 1939, 208, 97; J .Phys. Radium, 1939, 10, 43524 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.It is also noteworthy that, according to these observations, thedecay of actinium is a branching reaction similar to the decay ofradium-C, thorium-C, and actinium-C. The ct-p branching ratiois about 1 : 100, i.e., about one out of a hundred actinium nucleidecays with the emission of an a-particle.The Existence of Stable 3He.Using the Berkeley cyclotron as a mass spectrograph of very highintensity, L. W. Alvarez and R. Cornog 71 discovered the presenceof small quantities of 3He in ordinary helium. On adjusting themagnetic field so as to give resonance for doubly charged ions of mass3, they observed a weak beam with a range of 54 cm. in air, the rangeexpected for 3He nuclei of the energy determined by the field.Atmospheric helium was found to contain about ten times more3He than helium from gas wells.3He is by far the rarest stableisotope yet discovered ; a its " abundance " in atmospheric heliumis only about lo-'. The authors looked also for a possible beam of5PIe nuclei but without result.If 3He is stable, 3H should be unstable, decaying into 3He with theemission of P-particles. Alvarez and Cornog found that a long-lived activity which can be passed through hot palladium is producedon bombarding deuterium with deuterons and believe that thisactivity is due to the 3H which is known to be formed in the reaction2D + 'D -+ 3H + 'H.0. R. F.The Theory of Nuclear Forces.I n the year under review, progress of our knowledge of the nuclearforces has largely been negative, in that the discovery of the quadripolemoment of the deuteron by Rabi and his collaborators 1 has provedthe inadequacy of certain assumptions which had so far been thebasis of most discussions.The meson * theory of nuclear forceshas made further progress, but important diiEculties remain.Since the subject has not been specifically discussed in theseReports, it seems advisable not to limit the discussion to the currentyear, but to include a summary of the earlier development.It is now practically certain that nuclei consist of protons andneutrons. The Coulomb forces between the protons are repulsiveand do not affect the neutrons a t all. Magnetic forces (due to spin)7 1 Physical Rev., 1939, 56, 379, 613.1 J.H. B. Kellogg, I. I. Rabi, N. F. Ramsay, and J. R. Zacharias, PhysicalRev., 1939, 55, 318. * This term is now used instead of " mesotron.PEIERLS : THE THEORY OF NUCLEAR FORCES. 25between these particles might in certain circumstances produceattraction, but would be too weak to account for the observedstability of nuclei. It is therefore necessary to postulate forces ofa new type, “nuclear forces,” which hold the parts of a nucleustogether .However, if they were alwaysattractive, and acted between any two particles in the nucleus, thebinding energy of a nucleus would increase roughly as the numberof pairs of particles in the nucleus, Le., roughly proportionally tothe square of the mass number; the size of the nucleus would beindependent of the number of particles in it, since they would allcluster closely together.2 I n fact, however, both the bindingenergy and the volume (as estimated from scattering experiments,or from the Gamow barrier of radioactive nuclei,2 or from theenergy differences of light isobars 3, are roughly proportionalto the mass number.The reason for this might be that, as in aliquefied gas, the forces between the particles become repulsive atvery close approach. However, we are here dealing with shortdistances in which the quantum effect of penetration throughpotential barriers is of importance, and a repulsive force will not beable to keep the particles away from each other unless it is ofenormous strength. For this reason the explanation has notfound much favour.An alternative is to assume that the forces are attractive betweensome pairs of particles and repulsive between others.This wouldbe in analogy with the forces acting in homopolar molecules, whichmay be attractive or repulsive according to whether there is avalency bond between the atoms in question or not. Whether thisis the case depends in quantum theory on the symmetry of the wavefunction of the molecule with respect to the interchange of anelectron between the two atoms. Similarly W. Heisenberg4 andE. Majorana suggested that the nuclear forces between twoparticles might be exchange forces, i.e., that they might depend onthe symmetry of the wave function with respect to the two particles.A symmetric state would then give a different interaction from anantisymmetric state.Such forces are known as “ exchange forces.”This would give the required saturation of the forces sinceaccording to Pauli’s principle the wave function of a large nucleuscannot be symmetric in too many particles. I n fact, accordingThese forces must be attractive.H. A. Bethe and R. F. Bachor, Rev. illod. Physics, 1936, 8, 82.H. A. Bethe, Physical Rev., 1938, 54, 436; J. G. Fox, E. C. Creutz, M. G.White, and L. A. Ddsasso, ibid., 1939, 55, 1106; H. Brown and D. R. Inglis,ihid., p. 1182.2. Physik, 1932, 77, 1. Ibid., 1933, 82, 13726 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.to Heisenberg’s original scheme a neutron in the nucleus would beunivalent, forming a bond only with one proton, whereas onMajorana’s scheme it would be tervalent, forming bonds with twoprotons and a second neutron. (When considering this analogybetween nuclei and molecules it should, however, be realised that,owing to the high zero-point energy of the particles inside a nucleus,no definite positions can be allocated to them, and hence a geo-metrical localisation of the bonds or the use of structural formulzeis impossible.Nevertheless, it will still be true that each particlewill, on the average, be closer to those to which it is linked by“ bonds ” than to the others.)We may therefore expect that the force between two particlesdepends (a) on whether the wave function is symmetric or anti-symmetric (abbreviated to + and -), ( b ) on whether the spinsof the particles are parallel ( f f ) or opposite (J.+), ( c ) on the natureof the particles, i.e., whether neutron-neutron, proton-proton, orneutron-proton, ( d ) on the distance between the particles, and ( e )on their orientation, i.e., on the direction of the line joining themrelative to the direction of their resultant spin.Factors (a) and (b) give rise to four different arrangements :of which, however, in the case 6f like particles the last two are ruledout by Pauli’s principle.6 As regards ( c ) , it seems highly probablefrom the symmetry of the table of stable and radioactive isotopesthat the force between two protons is the same as that between twoneutrons, except for the electrostatic repulsion between the protons,which is responsible for the excess of neutrons over protons in allheavier nuclei.This leaves four possible cases of interactionbetween unlike particles and two between like particles.As regards (d), the force must in the main represent attractionand, if one introduces the exchange forces in order to account forthe saturation, there is no need to assume that attraction changesinto repulsion a t close approach. The potential is then of the typeof a potential well, which is characterised by its width ( i e . , therange of the force) and its depth (Le., the mean potential energy forclose approach). Lastly, as regards the dependence on direction( e ) , this possibility was not taken into account until experimentalevidence made it unavoidable, and so it has been considered incomparatively little work.6 The forces are customarily represented as a combination of four terms,of which the “ Wigner force ” is the same in all four cases, “ Majorana’s ” isattractive for the symmetric states and repulsive for the others, “Heisen-berg’s ” attractive for (+++) and (-J.-f) and “ Bartlett’s ” for parallel spin.We shall return to this point laterPEIERLS THE THEORY OF NUCLEAR FORCES. 27The most reliable evidence on the interaction potentials comesfrom the direct observation of the interaction between two particles.The angular momentum about the common centre of gravity is thena constant, and in quantum theory equal to a multiple of h / 2 x . Ifthe angular momentum is 1 units, centrifugal force makes it unlikelythat the particles approach more closely than to about 1 timesthe wave-length.Hence if the wave-length is much larger than therange of the interaction forces, only pairs of particles without orbitalangular momentum (1 = 0) are able to interact. From the angulardistribution of the neutrons and protons scattered by hydrogen, it isindeed possible t o verify that, up to energies of several m.v. (ie.,wave-lengths down to 3 x 10-13 cm.) only particles with zeroangular momentum are scattered '), so that the range of the forces iscertainly less than about 3 x 10J3 cm. Further, in the case of theneutron-proton interaction, the amount of scattering is theoreticallygiven by a constant which, for a given shape of the potential well,depends on its depth B and width a only in the combination Ba2,although it depends, of course, to a certain extent on the detailedshape of the well. It is found that by a suitable choice of thisconstant one can represent the data on the scattering, provided oneadmits two different values of the constant for pairs with paralleland with opposite spin.2 The bound state of the deuteron must alsobe expected to have no orbital angular momentum.Moreover, thebinding energy can again be shown to depend only on the combin-ation Ba2, and can therefore be compared with one of the twoconstants from scattering. The agreement seems satisfactoryY2- *The one unit of angular momentum which the deuteron is knownto possess must then be due to the spin of the particles, and thenormal state has therefore parallel spins.Moreover, a generaltheorem of wave mechanics states that even orbital momentumalways belongs to a symmetric state.We have thus obtained some information about the forces betweenunlike particles in a symmetric state with parallel spin. The secondconstant which is derived from the scattering law, together withcertain experiments on the phase of the scattered waveYg gives thesame information about the case of opposite spin, in which theinteraction is much weaker.I n the case of the proton-proton scattering, the situation is' P. I. Dee and C. W. Gilbert, Proc. Roy. SOC., 1937, A , 163,265.* M. A. Tuve and L. R. Hafstad, Physical Rev., 1936, 50, 308; cf., how-ever, M.Goldhaber, Nature, 1936, 137, 824; E. Amaldi, D. Bocciarelli, F.Rasetti, and G. C. Trabacchi, Physical Rev., 1939, 56, 881 ; T. Goloborodkoand A. Leipunski, ibid., p. 891.F. G. Brickwedde, J. R. Dunning, H. J. Hoge, and J. H. Manley, ibid.,1938, 54, 266; E. Teller, ibid., 1936, 49, 42028 RADIOACTMTY AND SUB-ATOMIC PHENOMENA.similar in that we have again a case in which the wave-lengthgreatly exceeds the range of the force, and in which therefore onlycollisions with no orbital angular momentum are affected by thenuclear forces. The mathematical treatment of the collision processis more complicated than for neutron-proton scattering, owing tothe simultaneous presence of the Coulomb repulsion.l0 As a resultof the higher experimental accuracy obtainable with protons,measurements of the scattering at a number of angles and energiesmake it possible to determine not only a combination of width anddepth of the potential well, but both the width and the depthseparately.In principle, such data would be suflicient to determinethe whole potential function (i.e., the shape of the well), and evenwith the data at present available, some shapes give a better fit thanothers. Amongst the functions that have so far been tried, the bestfit is obtained with the potential functionVfr) = B.e-r’a/(r/a) . . . . . (2)which suggests itself from the meson theory of nuclear forces,the constants having the values B = 46.8 m.v. and a = 1.2 xcm.11These values for a and B give the same value of Ba2 as that foundfor the symmetric state with opposite spin of the neutron-protoninteraction.12 This has given rise to the “ charge-independence ”hypothesis, which claims that the nuclear force between two particlesis independent of whether either of them is a neutron or a proton.13It is clear that this hypothesis is a generalisation which goes beyondthe direct experimental evidence in so far as very little is knownfrom this source about the interaction in an antisymmetric stateeither for like or for unlike particles.Similar results have been obtained by considering the bindingenergies of light nuclei containing more than two particles.Thisis usually done on the assumption that the interaction energybetween two particles is not affected by the presence of otherparticles, so that the potential energy of the nucleus is the sum ofthe interaction energies of all possible pairs of particles.Thisassumption is plausible enough; it is very exactly satisfied in the10 G. Breit, H. M. Thaxton, and L. Eisenbud, Physical Rev., 1939, 55,1018 ;L. E. Hoisington, S. S. Share, and G. Breit, ibid., 56, 884.l1 M. A. Tuve, N. P. Heydenburg, and L. R. Hafstad, ibid., 1936, 49,402;L. R. Hafstad, N. P. Heydenburg, and M. A. Tuve, ibid., 1937, 51, 1023;1938, 53, 239; R. G. Herb, D. W. Kerst, D. B. Parkinson, and G. J. Plain,ibid., 1939, 55, 998; N. P. Heydenburg, L. R. Hafstad, andM. A. TUVB, ibid.,p. 603.l2 G. Breit, L. E. Hoisington, S. 5. Share, and H. M. Thaxton, ibid.,p. 1103; cf., however, F. E.Brown and M. S. Plesset, ibid., 56, 84.13 G. Breit, E. U. Condon, and R. D. Present, ibid., 1936, 50, 825PEIERLS : THE THEORY OF NUCLEAR PORCES. 29atom, but reasons have been given why it might not hold in thenucleus . l4Once this assumption is made, the binding energy of any nucleusis known in principle, provided one knows the interaction betweentwo elementary particles for the six cases enumerated above. Theactual determination, however, requires the solution of a wave-mechanical many-body problem, which involves very lengthycalculations and cannot be reliably carried out except in the caseof the lightest nuclei.The nuclei up to mass number 4 (2H, 3H, 3He, 4He) all have wavefunctions which are very nearly symmetric in all particles, andtherefore involve only three of the six possible interaction functions.About these it is usually assumed that their dependence on distanceis the same, so that they differ merely by multiplicative factors.If, moreover, a specific assumption is made as to the shape of thepotential well, we are left with the three depth constants and thewidth (which is assumed the same for all three) as parameters.One can then, for example, determine these four parameters fromthe binding energy of the deuteron, together with the data onneutron-proton and proton-proton scattering, and can then workout the mass defects of the other light n~c1ei.l~ This leads to fairagreement, considering the simplifying assumptions on which thetheoretical values are based. It is satisfactory, in particular, thatfor the range, to which the mass defects are very sensitive, oneobtains the same order of magnitude whether one starts from themass defects or from the proton-proton scattering.A number ofdifficulties remain, but the impression is, on the whole, that the theoryis along the right lines.The position is less clear for nuclei of mass number greater than4. In these the wave function cannot be symmetric because ofPauli's principle, and the interaction functions of antisymmetricstates will come in. The calculations become progressively moredifficult as the number of particles increases. It is possible toobtain some inequalities limiting the ratio of the force constantsin the antisymmetric case to the others,16 and some more detailedwork has been d0ne.l'l4 H.Primakoff and T. Holstein, Physical Rev., 1939, 55, 1218.l6 W. Rarita and R. D. Present, ibid., 1937, 51, 788; H. Margenau andD. T. Warren, ibid., 52,790; 52, 1027; H. Margenau and W. A. Tyrrell, ibid.,1938,54, 422 ; W. Rarita and Z. I. Slawsky, ibid., p. 1053, and others.l6 G. Breit and E. Feenberg, ibid., 1936, 50, 850; H. Volz, 2. Physik,1937, 105, 537; D. R. Inglis, Physical Rev., 1937, 51, 531; N. I<emmer,Nature, 1937, 140, 192.l7 E.g., G. Breit and J. R. Stern, Physical Rev., 1938, 53, 459; E. Wigner,ibid., 1937, 51, 106; E. Wigner and E. Feenberg, ibid., p. 95; D. R. Inglis,ibid., p. 525 ; H. Margeneu, ibid., 1939, 55, 117330 RADIOACTIVITY AND SUB- ATOMIC PHENOMENA.The situation was, however, completely changed by the discovery 1that the deuteron has an electric quadripole moment.The signof this shows that the line joining the proton and the neutron ismore likely to be parallel to the direction of the resultant spin thana t right angles to it. This proves that the forces between theparticles cannot be strictly central forces. Moreover, the magnitudeof the quadripole moment suggests that the forces are not evenapproximately central, but that the directional dependence of theforce is an effect of the same order of magnitude as the wholeattractive force.18This new fact therefore throws doubt on the validity of all theprevious work. No doubt the agreement obtained in determiningthe range of the forces and other constants in different ways is notfortuitous, and some of the old calculations can certainly be justifiedwith the new, more generalised, type of force, but it will be necessaryto reconsider some of the old work from this point of view.Moreover, there may not now be any need for assuming exchangeforces, since the directional dependence will, on its own, alreadyensure saturation of the forces in heavy nuclei.In a heavy nucleus,each particle must have neighbours which adjoin it in every direction,and if the force is attractive in some directions and repulsive inothers, it is never possible to make it attractive between all particlesin the nucleus.19One particular type of directional dependence is supplied bya law of force that may be obtained from the meson theory ofnuclear forces (see below).In this, the interaction of a proton anda neutron depends on direction in the same way as that betweentwo magnetic dipoles. This law cannot be completely correct,since (just like the interaction between two dipoles) it leads to apotential which a t small distances behaves like the inverse cube,and this would make the binding energy of the deuteron infinitelylarge. One may avoid this difficulty by modifying the law ofinteraction for small distances (“ cutting-off ” 19), but in order to beconvincing this artifice would require support by further comparisonwith experimental data.An independent line of development of the theory is the mesontheory of nuclear forces. A rough outline of this was given in lastyear’s Report on the meson.20 The detailed results of the theorydepend on a number of assumptions about the spin of the mesonand the action of the meson field on the neutron or proton.If themeson has no spin, one would obtain repulsion in the normal state18 R. F. Christy and S. Kusaka, Physical Rev., 1939, 55, 665.lS H. A. Bethe, ibid., p. 1261.2o Ann. Reportu, 1938, 35, 20PEIERLS : THE THEORY OF NUCLEAR FORCES. 31of the deuteron. If the spin is one unit, the field is more closelyanalogous to the electromagnetic field, and its action on the heavyparticles may be similar either to the action of a field on a charge,or to that of a dipole, or to both. If we take the analogy of a chargeonly, it is impossible to obtain the right answer for both the (+ tf)and the (+J.f) interaction of the deuteron.If a dipole term isincluded, this produces a force similar to the force between twodipoles. I n view of what was said above about the directionaldependence of the force, this may be desirable, but it leads to aninfinite binding energy of the deuteron, unless the force is arbitrarily“ cut off ” at close approach. I f one uses the artifice of cuttingoff, it is apparently possible to obtain the right results for bothsymmetric states of the deuteron and its quadripole moment withoutusing the “ charge ” type of interaction a t all, which makes forsimplicity.19Alternatively, it has been suggested21 that one can avoid thediverging term by postulating two *kinds of mesons of different spin,and adjusting the “ charge” and “dipole” constants for bothin such a manner as to cancel the diverging terms in the nuclearforce.The theory then gives rise to a central force between neutronand proton which can be so adjusted as to yield the correct resultsfor both the (+ .ff) and the (+ J. +) interaction. The shape of thepotential well is then given by the equation ( Z ) , which has beenfound to give good agreement with the observed proton-protonscattering, but if one uses the relation between the meson mass andthe range of the force as outlined in last year’s ReportFO one wouldobtain a meson mass of 326 electron masses, which does not agreewith cosmic-ray results. This discrepancy may not be very serious,since in any case the interact’ion between like particles would betransmitted by neutral mesons,2o the mass of which is not known;indeed, if the forces are not required to be exchange forces, it iseven possible to assume that aZZ nuclear forces are transmitted byneutral mesons,19 and hence to conserve the “ charge-independencehypothesis.” If this point of view were correct, it would detractfrom the success of Yukawa’s theory in predicting the existence ofthe meson from nuclear forces, since the mesons found in cosmicrays would then have little connection with those responsible for thenuclear forces.If one adopts the artifice of avoiding the infinite terms by meansof two types of mesons,21 the forces become approximately centralforces. It is, however, likely that a more rigorous treatment, whichtakes into account relativistic effects, would again give a directional21 N. Kemmer, Proc. Roy. SOC., 1937, A , 166, 127; C . Maller and L. Rosen-feld, Nature, 1939, 144, 24132 RADIOACTIVITY AND SUB-ATOMIC PHENOMENA.dependence, and might thus account for the quadripole momentof the deuteron.22 These effects are analogous to the magneticinteraction between spin and orbit (multiplet structure) in the atom.Whereas, however, in the atom this is only a minor correction, in thenucleus it would be of greater importance; its smallness in theatom is, in the last resort, due to the smallness of the dimensionlessconstant 2xe2/hc = 1/137 (e = electronic charge, h = Planck’sconstant, c = velocity of light) which measures the interaction of theelectron with the electromagnetic field. If the correspondingconstant of the meson theory is so adjusted as to give the right orderof magnitude for the nuclear forces,23 its value becomes about 1/5.This means that the coupling of a proton or neutron with the mesonfield is very much stronger than that of an electron with the electro-magnetic field. Hence, many approximate calculations whichtreat this coupling as weak, and which are justified in the theoryof radiation, are not justified in the meson theory. The mathe-matical difficulties created by this have not yet been overcome.One of them is reflected in the fact, already mentioned, that in themeson theory the interaction force between two particles may bealtered if a third particle is present to interact with the first t ~ 0 . l ~Owing to these mathematical difficulties, a number of questionsof fact have not been answered, without which the final verdict onthe meson theory of nuclear forces cannot be given, but at presentit represents the most hopeful line of attack. R. P.0. R. FRISCEI.R. PEIERLS.22 Idem, Nature, 1939, 144, 476.23 H. Friihlich, W. Heitler, and N. Kemmor, Proc. Roy. Soc., 1938, A, 166,154