Isospin splitting of the giant resonance. I. Isodoublets
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We study the isospin splitting of the giant resonance of $T=\frac{1}{2}$ nuclei with sum rules. The particular isospin geometry involved in this case permits a number of simplifications in the isospin sum rules and several largely model independent relations are obtained and discussed. It turns out that for several light isodoublets the "symmetry" energy $U$ tends to be smaller that $60(T+1){A}^{\ensuremath{-}1}$ MeV.NUCLEAR STRUCTURE $T=\frac{1}{2}$ nuclei; calculated isospin splitting of $E1$ resonance with sum rules, model independent results discussed.Cite
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We obtain two isospin amplitude decompositions of the B→Kππ decays. We use the method of addition of three isospin vectors, and prove the equivalency of the two isospin amplitude decompositions obtained. We only have considered contributions of the Hamiltonian to the transitions with change of isospin ΔI=0 and ΔI=1. The symmetry of isospin allows to relate the charged B+→K+π+π−, B+→K+π0π0, and B+→K0π0π+ channels with the neutral B0→K0π+π−, B0→K0π0π0, and B0→K+π0π− channels. Additionally, we obtain equivalent triangular relations in the charged and neutral channels.
Hamiltonian (control theory)
Weak isospin
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The relation between strong isospin I and weak isospin i is discussed. In particular an equation between the third components I 3 and i 3 is given. This relation indicates that the strong isospin and weak isospin symmetries are both SU (2) subgroups of a new SU (3) symmetry underlying the structure of leptons and quarks.
Weak isospin
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Weak isospin
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Weak isospin
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We study the isospin splitting of the giant resonance of $T=\frac{1}{2}$ nuclei with sum rules. The particular isospin geometry involved in this case permits a number of simplifications in the isospin sum rules and several largely model independent relations are obtained and discussed. It turns out that for several light isodoublets the "symmetry" energy $U$ tends to be smaller that $60(T+1){A}^{\ensuremath{-}1}$ MeV.NUCLEAR STRUCTURE $T=\frac{1}{2}$ nuclei; calculated isospin splitting of $E1$ resonance with sum rules, model independent results discussed.
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