On the factorization of the wave function and the green function in the region of isolated poles of the S-function

Unger, H.-J.

doi:10.1016/0375-9474(67)90474-5

Cited by 23 publications

(10 citation statements)

References 3 publications

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“…In the I ν intervals defined above the positive energy wave functions have the largest localization inside a sphere of radius D, where D is of the order of a few times the nuclear radius. Within D the positive energy wave funtions can be related to the scattering wave function at resonant energy ǫ ν through simple factorization formulas [1,[6][7][8]. Following Refs.…”

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confidence: 99%

Resonant continuum in the Hartree-Fock+BCS approximation

2000

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A method for incorporating the effect of the resonant continuum into Hartree-Fock+BCS equations is proposed. The method is applied for the case of a neutron-rich nucleus calculated with a Skyrme-type force plus a zero-range pairing interaction and the results are compared with Hartree-Fock-Bogoliubov calculations. It is shown that the widths of resonant states have an important effect on the pairing properties of nuclei close to the drip line.Comment: 9 pages, 2 figures, comparison with HFB adde

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confidence: 99%

Resonant continuum in the Hartree-Fock+BCS approximation

2000

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“…We now consider the most general case for a multi-channel resonance, i.e., when the resonance width is not very small. For a spherical system having an isolated single-particle resonance at energy E R , Unger [19] has shown that the scattering radial wave function at energy E whose asymptotic form is…”

Section: Factorization Of Scattering Wave Functionsmentioning

confidence: 99%

“…In Ref. [19] the function F (E) is written in terms of a Breit-Wigner function, but for an isolated resonance it is easy to relate this to the derivative of the phase shift with respect to energy, so that the factorization property can be expressed as…”

Section: Factorization Of Scattering Wave Functionsmentioning

confidence: 99%

“…Alternatively, the resonance states can also be found by monitoring the energy derivative of the phase shift along the real energy axis [18], where a maximum appears at the resonance energy. For a scattering wave function in a spherical potential, a simple factorization formula has been derived for its energy and radial dependences in the vicinity of an isolated resonance state [18][19][20]. This factorization property has been used recently in order to estimate the effect of resonant states on pairing correlations in loosely bound nuclei [5].A resonance structure is much more complicated for a deformed system, where several angular momentum components of the single-particle wave function are coupled to each other.…”

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Structure of positive energy states in a deformed mean-field potential

Hagino

Giai

2004

Nuclear Physics A

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We investigate the properties of single-particle resonances in a non-spherical potential by solving the coupled-channels equations for the radial wave functions. We first generalize the box discretization method for positive energy states to a deformed system. As in the spherical case, we find that the discretized energy is stabilized against the box size when a resonance condition is met. Using the wave functions thus obtained, we then discuss the energy and the radial dependences of scattering wave functions in the vicinity of an isolated resonance. In the eigenchannel basis, where the $S$-matrix is diagonal, we propose a generalized expression for the factorization formula for the multi-channel wave function. We find that the factorized wave function agrees well with the exact solution inside the centrifugal barrier when the energy distance from the resonance is less than the resonance width.Comment: 22 pages, 5 eps figures; a figure adde

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“…The width of the HFB resonance states of this kind originates from the coupling between the hole and the particle states due to the off- diagonal components of the pairing potential. Namely, the particle states which have a similar quasi-particle energy as the hole state in the BCS approximation participate in the resonance state so that the quasi-particle wave functions behave similarly between the hole and the particle states within the resonance width [18,19,20]. This important mechanism of the particle-hole couplings is missing in the BCS approximation.…”

Section: Applicability Of the Perturbation Formulasmentioning

confidence: 99%

Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations

Hagino

Sagawa

2005

Phys. Rev. C

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We develop a perturbative model to treat the off-diagonal components in the Hartree-FockBogoliubov (HFB) transformation matrix, which are neglected in the BCS approximation. Applying the perturbative model to a weakly bound nucleus 84 Ni, it is shown that the perturbative approach reproduces well the solutions of the HFB method both for the quasi-particle energies and the radial dependence of quasi-particle wave functions. We find that the non-resonant part of the continuum single-particle state can acquire an appreciable occupation probability when there exists a weakly bound state close to the Fermi surface. This result originates from the strong coupling between the continuum particle state and the weakly bound state, and is absent in the BCS approximation. The limitation of the BCS approximation is pointed out in comparison with the HFB and the present perturbative model.

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On the factorization of the wave function and the green function in the region of isolated poles of the S-function

Cited by 23 publications

References 3 publications

Resonant continuum in the Hartree-Fock+BCS approximation

Resonant continuum in the Hartree-Fock+BCS approximation

Structure of positive energy states in a deformed mean-field potential

Perturbative Hartree-Fock-Bogoliubov model for many-body pairing correlations

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