Inner product for resonant states and shell-model applications

Romo, W.J.

doi:10.1016/0375-9474(68)90395-3

Cited by 119 publications

(79 citation statements)

References 12 publications

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“…The resonant state generally has a divergent behavior at asymptotic distance, and then its norm is defined by a singular integral using, for example, the convergent-factor method [24,35,36]. In CSM on the other hand, resonances are precisely described as eigenstates expanded in terms of L 2 basis functions.…”

Section: B Complex Scaling Methods (Csm)mentioning

confidence: 99%

Four-body resonances of7B using the complex scaling method

2011

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We study the resonance spectroscopy of the proton-rich nucleus 7 B in the 4 He + p + p + p cluster model. Many-body resonances are treated under the correct boundary condition as Gamow states using the complex scaling method. We predict five resonances of 7 B and evaluate the spectroscopic factors of the 6 Be-p components. The importance of the 6 Be(2 + )-p component is shown in several states of 7 B; this is a common feature of 7 He, a mirror nucleus of 7 B. For only the ground state of 7 B, the mixing of the 6 Be(2 + ) state is larger than that of 6 He(2 + ) in 7 He, which indicates a breaking of mirror symmetry. This is caused by the small energy difference between 7 B and the excited 6 Be(2 + ) state, the origin of which is Coulomb repulsion.

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Section: B Complex Scaling Methods (Csm)mentioning

confidence: 99%

Four-body resonances of7B using the complex scaling method

2011

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“…Here ␦ nn Ј is the Kronecker delta, and the inner product is defined by means of analytic continuation in k of the proper bound-state eigensolutions to the resonance poles in the lower half of the complex k plane [49,50]. The normalization condition takes the form…”

Section: ͑22͒mentioning

confidence: 99%

Feshbach resonances with large background scattering length: Interplay with open-channel resonances

et al. 2004

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“…The resonant state generally has a divergent behavior at asymptotic distances, and its norm then is defined by a singular integral using, for example, the convergent factor method [27,40,41]. In CSM, on the other hand, resonances are precisely described as eigenstates expanded in terms of the L 2 basis functions.…”

Section: B Complex Scaling Methodsmentioning

confidence: 99%

Five-body resonances of8C using the complex scaling method

2012

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We study the resonance spectroscopy of the proton-rich nucleus 8 C in the α + p + p + p + p cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We obtain the ground state of 8 C as a five-body resonance for the first time, which has dominantly the subclosed (p 3/2 ) 4 configuration and agrees with the recent experiment for energy and decay width. We predict the second 0 + state with the excitation energy of 5.6 MeV, which corresponds to the 2p2h state from the ground state. We evaluate the occupation numbers of four valence-protons in the 8 C states and also the J π distribution of proton-pair numbers of the two 0 + states of 8 C. The ground state involves a large amount of the 2 + proton-pair fraction, while the excited 0 + 2 state almost consists of two of the 0 + proton pairs, which can be understood from the (p 3/2 ) 2 (p 1/2 ) 2 configuration. We also discuss the mirror symmetry between 8 C and 8 He with an α+four nucleon picture. It is found that the 0 + states retain the mirror symmetry well for the configuration properties of two nuclei.

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Inner product for resonant states and shell-model applications

Cited by 119 publications

References 12 publications

Four-body resonances of7B using the complex scaling method

Four-body resonances of7B using the complex scaling method

Feshbach resonances with large background scattering length: Interplay with open-channel resonances

Five-body resonances of8C using the complex scaling method

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