“…These numerical studies show also that the average S-matrix S of the IAR cannot be represented by a single pole term in the case F ~ -,~F +. Thus our basic assumption (2), that this can be done is a rather strong and nontrivial assumption. We would stress that the assumption (2) can be tested however by comparison with the data in each particular experiment and that these tests have shown the validity of assumption (2) in all experiments done on IAR in heavy nuclei 9…”
Section: ~1 =El -5 Rl =Elmentioning
confidence: 99%
“…For the case of an isolated IAR we assume that there is an averaging interval 10 and that the average S-matrix S(E +ilo) can be approximated by the function S(E + ilo) which consists of a symmetrical background matrix SB(E + ilo) and a single pole term. (2) where the parameters are the complex pole el=E~ i 2 F1 and the vector n=(nl, na, ..., nu) of the complex decay amplitudes and where N is the number of open channels.…”
Section: E + Ii-~ Kmentioning
confidence: 99%
“…With the discovery of the fine structure splitting of the isobaric analog resonances (IAR) in 92Mo-l-p [1] and 4~ [2], the problem of the fine structure splitting of isobaric analog resonances in heavy nuclei was posed. This problem was discussed in the various theories of IAR and of doorway-resonances [3][4][5][6][7][8][9][10], Extensive reviews of the fine structure problem were given by Mahaux and Weidenmiiller [1t] and by Lane [12].…”
It is shown that the position of the pole of the inverse average S-matrix of an isolated isobaric analog resonance (IAR) is a very useful parameter, which allows one to distinguish between the weak and the strong coupling case of the finestructure distribution of the resonance. It gives also a direct measure of the purity of analog spin of the resonance. As an example the lowest IAR in 2~ is discussed.
“…These numerical studies show also that the average S-matrix S of the IAR cannot be represented by a single pole term in the case F ~ -,~F +. Thus our basic assumption (2), that this can be done is a rather strong and nontrivial assumption. We would stress that the assumption (2) can be tested however by comparison with the data in each particular experiment and that these tests have shown the validity of assumption (2) in all experiments done on IAR in heavy nuclei 9…”
Section: ~1 =El -5 Rl =Elmentioning
confidence: 99%
“…For the case of an isolated IAR we assume that there is an averaging interval 10 and that the average S-matrix S(E +ilo) can be approximated by the function S(E + ilo) which consists of a symmetrical background matrix SB(E + ilo) and a single pole term. (2) where the parameters are the complex pole el=E~ i 2 F1 and the vector n=(nl, na, ..., nu) of the complex decay amplitudes and where N is the number of open channels.…”
Section: E + Ii-~ Kmentioning
confidence: 99%
“…With the discovery of the fine structure splitting of the isobaric analog resonances (IAR) in 92Mo-l-p [1] and 4~ [2], the problem of the fine structure splitting of isobaric analog resonances in heavy nuclei was posed. This problem was discussed in the various theories of IAR and of doorway-resonances [3][4][5][6][7][8][9][10], Extensive reviews of the fine structure problem were given by Mahaux and Weidenmiiller [1t] and by Lane [12].…”
It is shown that the position of the pole of the inverse average S-matrix of an isolated isobaric analog resonance (IAR) is a very useful parameter, which allows one to distinguish between the weak and the strong coupling case of the finestructure distribution of the resonance. It gives also a direct measure of the purity of analog spin of the resonance. As an example the lowest IAR in 2~ is discussed.
“…A particularly interesting series of experiments are those being performed (15) at Duke University with high-resolution proton beams. This work shows the highly detailed nature of analogue resonances, that is, as coherent superpositions of many complicated compound states yielding a beautifully modulated wave train, the modulation being observed only in conventional experiments with poor-resolution proton beams.…”
The major feature of isospin in nuclei that I have discussed here is its application to all nuclei. The rebirth of this quantum number in nuclear physics occurred in the early 1960's and was initiated almost entirely by the important work of Anderson et al. (4) and Fox et al. (5). There is still great interest in the use of isospin in its fullest sense as predicted by Wigner (3), and indeed isospin concepts have been largely responsible for demonstrating that nuclei in the doubly "magic number" region of (208)Pb are remarkably in agreement with shell model theory. The early experiments have also initiated a whole new set of more sophisticated experiments (some of which I have briefly alluded to above) which promise to keep many physicists busy for a long time to come. A particularly interesting series of experiments are those being performed (15) at Duke University with high-resolution proton beams. This work shows the highly detailed nature of analogue resonances, that is, as coherent superpositions of many complicated compound states yielding a beautifully modulated wave train, the modulation being observed only in conventional experiments with poor-resolution proton beams. Similarly, nuclear theorists have been led to vastly improve their interpretation of, and computational techniques for, both nuclear reactions and nuclear structure in order to meet the more stringent tests provided by such experiments. Perhaps a lesson can be learned from the historical development of the isospin concept. In the past the belief that T . T would not significantly commute with the dynamical Hamiltonian so that isospin would not be conserved sufficiently well enough certainly delayed the nuclear travels of isospin into the realm of heavy nuclei. Hopefully the same mistake will not occur in the future for other approximate symmetries of nature.
“…E p , keV (p,γ) E*, keV (p,γ) S, eV E p , keV [6] (p,γ) E p , keV [8] (p,γ) S, eV [8] E p , keV [7] (p,γ) - No. E p , keV (p,γ) E*, keV (p,γ) S, eV E p , keV [6] (p,γ) E p , keV [8] (p,γ) S, eV [8] E p , keV [7] (p,γ) …”
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