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IX. The Nuclear Constitution and Neutron Captures
IX. THE NUCLEAR CONSTITUTION AND NEUTRON CAPTURES UNPUBLISHED MANUSCRIPT [1935?]
See Introduction, sect. 2, ref. 36
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Neutron Capture and Nuclear Constitution”, [ 1935-19361, contains two typewritten manuscripts, an outline (1 page) in pencil in Kalckar’s handwriting, and 3 pages, numbered 3 to 5, in pencil in Rosenfeld’s handwriting. Except for a few Danish words it is all in English. The first manuscript, reproduced here, is entitled “The nuclear constitution and neutron Captures” and consists of 4 typewritten pages. The numerous errors in typing and spelling have been retained, since the status of this manuscript is uncertain, and poor typographical quality may contain a clue. The second manuscript, entitled “Nuclear constitution and quantum mechanics”, consists of 2 typewritten pages (with a carbon copy and a second typescript of page 1) with corrections in pencil in Rosenfeld’s handwriting. The handwritten pages by Rosenfeld are apparently a sequel to this. The manuscripts are on microfilm Bohr MSS no. 14.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The nuclear constitution and neutron Captures. The problem of nuclear constitution presents as wellknown features which differ essentially from the problem of the electronic constitution of atoms. In accounting for the properties of the atom it is justified to speak of individual electrons and even in first approximation characterize the state of atom in ascribing to each electron separately in definite type of binding expressed by quantum numbers referring to the stationary states of a particle bound in a given field of force, determined by the charge on the nuclear charge and the average electronic dencity distribution. As regards the properties of the nucleus we can surely in forst approximation account for its mass by considering it as built up of separate units of masses equal to that of the neutron, but already as regards the unclear [sic] charge we meet with a new aspect of the atomicity of electricity, which cannot simply be accounted for by saying that the nucleus contains a certain number of positions with properties of the kind we know from ordinary electron theory. Also the attempt to consider the neutron and the proton as ultimate constituents of the nucleus would seem arbitrary in the sense that the behaviour of these particles in the nucleus cannot be predicted from properties ascribed to the single particles. Our only source of Information is indeed the study of the nuclear reactions and transmutations of the nucleus in collision with other nuclei or neutrons. Especially the discoveries of the great effectivity of neutrons in producing nuclear transmutations has brought a number of features to light which can hardly be reconciled with the attempts hithers made of constructing models of the nucleus on similar lines as those which have shown themselves so fruitful in accounting for the properties of atoms. Not only the great protons and aparticles by neutron impacts but above all readiness by which neutrons attack themselves to the nucleus in such impacts cannot be reconciled with the view that the neutrons, which penetrate into the nucleus moves in a seperate arbit in the field of the other nuclear particles in a similar way as is assumed for each of the particles in the shell type of nuclear models. already in the early researches of Fermi and his collaboraters on nuclear transmutations by high speed neutrons, it was found that the effective crossections for captures was in several cases found to be of the same order of magnitude of the crossections by which charged particles are expelled. This is much unexpected since in the former case in contrust to the latter, where energy balance is secured by the kinetic energy of hte expelled particles the binding energy has to be cemitted as electromagnetic radiation which in ordinary twobody collisions is generally most improbable. These captures can therefor hardly be explained unless we assume that the kinetic energy of the penetrating neutron is at once shared amond the individual heavy nuclear particles and that
MS,
2
PART I : PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
CIS, p. 3
no particle, charged or uncharged, has sufficient energy to leave the nucleus before, as a consequence of the continuors energy exchange, it happens that a particle finds itself on the surface of the nucleus with sufficient energy to escape. with the great probability of neutrons captures in comparison with neutron scattering observed in such processes. In this threatment the behaviour of the neutron within the nucleus is namely described by a seperate orbit or more accurately wave function, while it would seem that the great probabilityradiative processes can only be explained if the state of the combined system of nucleus and neutron is treated essentially as a manybody problem on the lines of quantum mecanicscorresponding to an ordinary continualexchange of energy between all the nuclear particles. Such a treatment would of couse be very complicatedin detail, but it should be possible in this case just as in the case of high speed nuclear impacts to draw conclusions as regards the duration of the encounter from the impirical data regarding the transition probabilityfor c-ray emission, which gives the lifeelectrostatic energy liberated by such an expulsion. the essential point however is that from the great output of a-particles by neutron impacts on certain nuclei, we can on this view not draw any conclusion as regarding the existence of a-particles in the normal nuclear state. A problem of exstreme interest is afforded by the more recent discovery exstraordinary pacility with which low speed neutrons in certain cases attack themselves to nuclei. Indeed in several cases crossections for such collisions have been found, which exceed the ordinary nuclear crossections by a factor of several thousands. This must of course be explained by a peculiar quantummachanical resonance effect arising from an approximate coinfidence of the total energy of the nucleus and the neutron before the collision with some stationary state of the system formed by a more or less stable combination of the two particles. The very interesting treatment of such resonance effects, given by Bethe, would, however, not seem reconcilable. This would indeed mean, that such an encounterbetween neutron and nucleus has sufficient duration to permit a competition between mechanical and radiation processes to take place. Of course in the closer account of any such processes it is necessary essentially to take the requirements of quantum mechanics into account, which secure us that the nucleus after an encounter finds itself in same stationary state, just as before. the greater the time till energy of the impringing neutron is the more adequate will a simple mechanical consideration be to describe the essential features of the encounter, and if the picture is essentially correct we shall especially expect that the collision will lead to the expulsion of several particles in sted of one as hitherto observed, because it will from simple mechanical arguments clearly be more likely that the superfluos energy in sted of being concentrated on one particle in such a case will be devided among several. The whole process is of course most complicated and
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the preference for the ejection of charged particles by nuclear impacts must naturally be explained by the potential for excited nuclear states of the order of magnitude of l o - * sec. The object of these remarks is, however, primarily emphasize to the essential difference between the problems of atomic and nuclear constitutions, which, in spite of the great success especilly obtained by Gamow of appliation of quantum mechamnics to the general problems of radioactivity-leaves the latter in a situation where rapidly increasing experimental evidence cannot be comprehended by present simple models of nuclear constitution.
MS, P . 4
See Introduction, sect. 2, ref. 36
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Neutron Capture and Nuclear Constitution”, [ 1935-19361, contains two typewritten manuscripts, an outline (1 page) in pencil in Kalckar’s handwriting, and 3 pages, numbered 3 to 5, in pencil in Rosenfeld’s handwriting. Except for a few Danish words it is all in English. The first manuscript, reproduced here, is entitled “The nuclear constitution and neutron Captures” and consists of 4 typewritten pages. The numerous errors in typing and spelling have been retained, since the status of this manuscript is uncertain, and poor typographical quality may contain a clue. The second manuscript, entitled “Nuclear constitution and quantum mechanics”, consists of 2 typewritten pages (with a carbon copy and a second typescript of page 1) with corrections in pencil in Rosenfeld’s handwriting. The handwritten pages by Rosenfeld are apparently a sequel to this. The manuscripts are on microfilm Bohr MSS no. 14.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The nuclear constitution and neutron Captures. The problem of nuclear constitution presents as wellknown features which differ essentially from the problem of the electronic constitution of atoms. In accounting for the properties of the atom it is justified to speak of individual electrons and even in first approximation characterize the state of atom in ascribing to each electron separately in definite type of binding expressed by quantum numbers referring to the stationary states of a particle bound in a given field of force, determined by the charge on the nuclear charge and the average electronic dencity distribution. As regards the properties of the nucleus we can surely in forst approximation account for its mass by considering it as built up of separate units of masses equal to that of the neutron, but already as regards the unclear [sic] charge we meet with a new aspect of the atomicity of electricity, which cannot simply be accounted for by saying that the nucleus contains a certain number of positions with properties of the kind we know from ordinary electron theory. Also the attempt to consider the neutron and the proton as ultimate constituents of the nucleus would seem arbitrary in the sense that the behaviour of these particles in the nucleus cannot be predicted from properties ascribed to the single particles. Our only source of Information is indeed the study of the nuclear reactions and transmutations of the nucleus in collision with other nuclei or neutrons. Especially the discoveries of the great effectivity of neutrons in producing nuclear transmutations has brought a number of features to light which can hardly be reconciled with the attempts hithers made of constructing models of the nucleus on similar lines as those which have shown themselves so fruitful in accounting for the properties of atoms. Not only the great protons and aparticles by neutron impacts but above all readiness by which neutrons attack themselves to the nucleus in such impacts cannot be reconciled with the view that the neutrons, which penetrate into the nucleus moves in a seperate arbit in the field of the other nuclear particles in a similar way as is assumed for each of the particles in the shell type of nuclear models. already in the early researches of Fermi and his collaboraters on nuclear transmutations by high speed neutrons, it was found that the effective crossections for captures was in several cases found to be of the same order of magnitude of the crossections by which charged particles are expelled. This is much unexpected since in the former case in contrust to the latter, where energy balance is secured by the kinetic energy of hte expelled particles the binding energy has to be cemitted as electromagnetic radiation which in ordinary twobody collisions is generally most improbable. These captures can therefor hardly be explained unless we assume that the kinetic energy of the penetrating neutron is at once shared amond the individual heavy nuclear particles and that
MS,
2
PART I : PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
CIS, p. 3
no particle, charged or uncharged, has sufficient energy to leave the nucleus before, as a consequence of the continuors energy exchange, it happens that a particle finds itself on the surface of the nucleus with sufficient energy to escape. with the great probability of neutrons captures in comparison with neutron scattering observed in such processes. In this threatment the behaviour of the neutron within the nucleus is namely described by a seperate orbit or more accurately wave function, while it would seem that the great probabilityradiative processes can only be explained if the state of the combined system of nucleus and neutron is treated essentially as a manybody problem on the lines of quantum mecanicscorresponding to an ordinary continualexchange of energy between all the nuclear particles. Such a treatment would of couse be very complicatedin detail, but it should be possible in this case just as in the case of high speed nuclear impacts to draw conclusions as regards the duration of the encounter from the impirical data regarding the transition probabilityfor c-ray emission, which gives the lifeelectrostatic energy liberated by such an expulsion. the essential point however is that from the great output of a-particles by neutron impacts on certain nuclei, we can on this view not draw any conclusion as regarding the existence of a-particles in the normal nuclear state. A problem of exstreme interest is afforded by the more recent discovery exstraordinary pacility with which low speed neutrons in certain cases attack themselves to nuclei. Indeed in several cases crossections for such collisions have been found, which exceed the ordinary nuclear crossections by a factor of several thousands. This must of course be explained by a peculiar quantummachanical resonance effect arising from an approximate coinfidence of the total energy of the nucleus and the neutron before the collision with some stationary state of the system formed by a more or less stable combination of the two particles. The very interesting treatment of such resonance effects, given by Bethe, would, however, not seem reconcilable. This would indeed mean, that such an encounterbetween neutron and nucleus has sufficient duration to permit a competition between mechanical and radiation processes to take place. Of course in the closer account of any such processes it is necessary essentially to take the requirements of quantum mechanics into account, which secure us that the nucleus after an encounter finds itself in same stationary state, just as before. the greater the time till energy of the impringing neutron is the more adequate will a simple mechanical consideration be to describe the essential features of the encounter, and if the picture is essentially correct we shall especially expect that the collision will lead to the expulsion of several particles in sted of one as hitherto observed, because it will from simple mechanical arguments clearly be more likely that the superfluos energy in sted of being concentrated on one particle in such a case will be devided among several. The whole process is of course most complicated and
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the preference for the ejection of charged particles by nuclear impacts must naturally be explained by the potential for excited nuclear states of the order of magnitude of l o - * sec. The object of these remarks is, however, primarily emphasize to the essential difference between the problems of atomic and nuclear constitutions, which, in spite of the great success especilly obtained by Gamow of appliation of quantum mechamnics to the general problems of radioactivity-leaves the latter in a situation where rapidly increasing experimental evidence cannot be comprehended by present simple models of nuclear constitution.
MS, P . 4