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Mirror Nuclei, A<= Atomic Energy of Canada Limited MIRROR NUCLEI, A < 100 by J.C. HARDY Presented as an invited talk to the Canadian Association of Physicists meeting held in Montreal, June 18-21, 1973 Chalk River Nuclear Laboratories Chalk River, Ontario August 1973 AECL-4604 Atomic Energy of Canada Limited MIRROR NUCLEI, A <: 100 by J.C. HARDY Presented as an invited talk to the Canadian Association of Physicists meeting held in Montreal, June 18-21, 1973. Chalk River Nuclear Laboratories Chalk River, Ontario August 1973 AECL- Mirror Nuclei, A <, ICC by J.C Hardy ABSTRACT The effects of charge-dependent forces are described, and their dependence on the nuclear mass is discussed, it is proposed that large isospin impurities may occur in heavier nuclei (A <s 10G) with N ~ Z. several classes of p-decay experi- ment are sensitive to these effects, and a detailed description is given of recent chalk River experiments to study the super- allowed decay of 0*, T7 = -1 nuclei. This work has included the first measurement of mirror Fermi decay branches within a T = 1 multiplet. These and other data on superallowed p-decay are analyzed with particular emphasis on the charge dependent corrections to which mirror comparisons are particularly sensitive. The results are discussed in terms of the theory of weak interactions and the question of the existence of a heavy intermediate vector boson. It is suggested that some discrepancies for nuclei with A > 40 may be attributed to the proposed increase in charge dependent mixing. Some other experimental evidence suggesting the same conclusion is also given. Chalk River Nuclear Laboratories Chalk River, Ontario August 1973 *Presented as an invited talk to the Congress of the Canadian Association of Physicists held in Montreal, June 18-21, 1973. AECL-4604 Noyaux ~à miroir, A5 100* J.C. Hardy ^Communication présentée, sur invitation, au Congres de l'Association Canadienne des Physiciens tenu a Montréal du 18 au 21 juin 1973. Résumé On décrit les effets des forces dépendant de la charge ainsi que la mesure dans laquelle ils dépendent aussi de la masse nucléaire. On suggère que de grandes impuretés d'isospin sont susceptibles de se produire dans les noyaux lourds (A^ 100) oxi N ^ Z. Plusieurs catégories d'expériences a décroissance f3 sont sensibles à ces effets. On décrit en détail de récents travaux effectués a Chalk River pour étudier la décroissance supra-permise de noyaux 0 , !„ = -1. Ces travaux ont permis d'effectuer la première mesure des branches de décroissance Fermi "a miroir "à l'intérieur d'un multiplet T = 1. Ces données, ainsi que d'autres obtenues en ce qui concerne la décroissance $ suprapermise, sont analysées cotup te-tenu, particulièrement, des corrections dépendant de la charge auxquelles les comparaisons de miroir sont particulièrement sensibles. Les résultats obtenus sont commentés en fonction de la théorie des faibles interactions et de la question de l'existence d'un boson lourd de vecteur intermédiaire. On suggère que certains désaccords, pour les noyaux où k > 40 peuvent être attribués a l'augmentation proposée pour le mélange dépendant de la charge. Quelques preuves expérimentales, suggérant la même conclusion, sont également données. L'Energie Atomique du Canada, Limitée Laboratoires Nucléaires de Chalk River Chalk River, Ontario Août 1973 AECL-4604 Mirror Nuclei, A <; 100 J.C. Hardy In choosing the title for my talk, I had intended to attract those listeners who believe, as do most nuclear physicists, that for all practical purposes the study of mirror nuclei stops at mass 40. A description of some results with light nuclei, combined with a speculative discussion of the possibilities in extending such studies up to mass 100, seemed to provide the right balance between fact and fiction. I now find that the CAP has taken matters into its own hands and advertised my talk as a description of mirror nuclei with "A 2 100". Since it is problematic whether any nuclei fitting that description are even nucleon stable, let alone accessible, I am afraid that their great leap forward places me_ squarely in the lunatic fringe. However, by retaining my original intentions to discuss light, nucleon stable and reasonably accessible nuclei, I hope to prove a certain degree of sanity. If nucleons experienced the same forces regardless of their charge, then mirror nuclei would be identical in every respect. Simply changing the neutrons in a nucleus into protons and vice versa would leave the nuclear energy levels, transition strengths and so on unaffected. Furthermore, this not only applies to levels in the mirror nuclei but to their analogues in other nuclei with the same A as well. Under these CAP - Canadian Association of Physicists conditions we should say that isobaric spin was a good quantum number since T commutes with a charge-independent nuclear Hamiltonian. In practice of course, the Hamiltonian is not charge independent, certainly the coulomb force plays a significant role in nuclear structure, and very likely charge dependence in the nuclear force itself is also discernible. As a result, in crossing an isobaric multiplet between two mirror nuclei, one observes many differences, the most obvious being the large changes in ground-state energies. However, since the Coulomb force is spin independent and has a long range it is not surprising that it affects the energies of states most strongly, and in a general sense the magnitude of the effect can easily be reproduced by calculations. A much smaller effect - and one that is more challenging theoretically - is the change in the structure of the wave functions caused by charge dependent forces. To what extent does isospin remain a good quantum number? Superficially one might imagine that because the p Coulomb energy is proportional to z while the nuclear energy varies more slowly with A, then charge dependent effects such as isospin impurities would become more significant for heavier nuclei. Actually, the total of all charge-dependent mixing undoubtedly does increase for heavier nuclei but surprisingly the same cannot be said of isospin impurities: it is well known that analogue states are readily identified in all nuclei up to the very heaviest. The explanation is not difficult to understand, and has particular relevance to mirror nuclei, so I shall spend a few minutes discussing it. Figure 1 shows schematically some of the effects of charge-dependent forces on the wave functions of a nucleus with Tz = §(N-z), a ground state isospin of T = | T | , and a variety of excited states with the same and higher isospin. The total effect on the ground state is seen at the top of the figure where all states, including those with the same T, are shown to mix with it. Obviously not all of this mixing contaminates the isospin of the ground state so actual isospin impurities must involve much fewer states, as represented by the diagram at the middle of the figure. Finally, the diagram at the bottom demonstrates an effect that is much more nearly accessible experimentally: the mixing of one specific T+l state with the ground state. Evidently this is the smallest effect of all. Two methods for detecting mixing with p-decay experi- ments are also displayed in the figure. The first illustrates that superallowed (Fermi) p-decay between analogue states, while insensitive to the total charge-dependent mixing, can provide a measure of the difference between such mixing in two members of a multiplet; this is possible, in principle at least, by comparing the measured transition intensity with calculations that assume perfect overlap between initial and final states. I shall return to this problem later. The second method requires measurement of the Fermi matrix element between two states that are not analogues of one another; in the example shown, this yields a value for the mixing between the initial state and the analogue of the final state. To get some idea of how these effects may vary from nucleus to nucleus in the periodic table, let us consider specifically the case of isospin mixing in the ground states of even-even nuclei. Most coulomb mixing will occur with excited states in which a proton has been promoted up one major oscillator shell1), if the ground state is represented by Pig. 2a then these particle-hole states are of the type shown in Pig. 2b and 2c. Since there is no neutron-particle equivalent to Fig. 2b, these states have the same isospin T as the ground state, and cannot therefore cause isospin mixing; clearly the number of such states increases with neutron excess. Similarly only some of the states described by Fig. 2c have different isospin from the ground state, but the proportion of isospin-preserving states increases with the T off the nucleus. •Thus, although the total number of states involved in charge- dependent mixing increases for heavier nuclei, isospin impurities are actually quenched by the large neutron excess. The crucial conclusion must be that to study isospin-breaking effects one should look to heavier nuclei, but to those with a small neutron excess. Figure 3 gives ground state isospin impurities based on this particle-hole scheme ' and on Hartree-Fock calculations 2) by Lee and cusson '. The comparison between nuclei in the valley of p-stability, where impurities level off at 1% or less, and mirror nuclei with N ~ Z is really striking, as is the suggestion that the latter's impurities could possibly reach IO56. With this picture in mind I should now like to discuss some specific experiments that reflect the importance of charge-dependent mixing. These will be studies of super- allowed p-decay. 1 shall begin by outlining the basic con- cepts involved in a description of the physical process.
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