Single-particle resonances in a deformed relativistic potential

Li, Zhipan; Zhang, Ying; Vretenar, Dario; Meng, J.

doi:10.1007/s11433-010-0161-7

Cited by 15 publications

(9 citation statements)

References 47 publications

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“…In these nuclei, the neutron (or proton) Fermi surface is close to the particle threshold, thus the contribution of the continuum is crucial [60,61,190,[192][193][194][203][204][205][206][207][208][209][210][211][212][213][214][215][216][217][218]. Many approaches developed for resonances [219], e.g., the analytical continuation in coupling constant method [220][221][222][223][224][225], the real stabilization method [226][227][228][229][230][231], the complex scaling method [232][233][234][235], the coupled-channel method [236][237][238], and some others [239,240], have been used to study nuclear single-particle resonant states. Based on some of these methods, the pseudospin symmetry [241]…”

Section: From Bound States To Resonant Statesmentioning

confidence: 99%

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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Symmetry plays a fundamental role in physics. The quasi-degeneracy between single-particle orbitals $(n, l, j = l + 1/2)$ and $(n-1, l + 2, j = l + 3/2)$ indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry (PSS). Since the introduction of the concept of PSS in atomic nuclei, there have been comprehensive efforts to understand its origin. Both splittings of spin doublets and pseudospin doublets play critical roles in the evolution of magic numbers in exotic nuclei discovered by modern spectroscopic studies with radioactive ion beam facilities. Since the PSS was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry (SS) for anti-nucleon, and many new concepts have been introduced. In the present Review, we focus on the recent progress on the PSS and SS in various systems and potentials, including extensions of the PSS study from stable to exotic nuclei, from non-confining to confining potentials, from local to non-local potentials, from central to tensor potentials, from bound to resonant states, from nucleon to anti-nucleon spectra, from nucleon to hyperon spectra, and from spherical to deformed nuclei. Open issues in this field are also discussed in detail, including the perturbative nature, the supersymmetric representation with similarity renormalization group, and the puzzle of intruder states.Comment: Review Article, 242 pages, 58 figures, 10 table

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Section: From Bound States To Resonant Statesmentioning

confidence: 99%

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

2015

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“…Finally, combining Eqs. ( 14), ( 21) and (33), the total upper-component of the wave function (11) becomes…”

Section: Solution Of Radial Part Equationmentioning

confidence: 99%

RELATIVISTIC BOUND STATES IN THE PRESENCE OF SPHERICALLY RING-SHAPED q-DEFORMED WOODS–SAXON POTENTIAL WITH ARBITRARY l-STATES

Ikhdair

Hamzavi

Rajabi

2013

Int. J. Mod. Phys. E

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Approximate bound state solutions of the Dirac equation with q -deformed Woods-Saxon plus a new generalized ring-shaped potential are obtained for any arbitrary lstate. The energy eigenvalue equation and corresponding two-component wave function are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials.A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term 2 ( 1) . l l r   Under some limitations, we can obtain solution for the ring-shaped Hulthén potential and the standard usual spherical Woods-Saxon potential ( 1 q  ).

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“…To explore single-particle resonances, researchers have developed a series of approaches. One technique starts from scattering theory, such as K-matrix theory [11], S-matrix theory [12,13], R-matrix theory [14,15], the Jost function approach [16,17], and the scattering phase shift method [18,19]. Meanwhile, approaches for bound states are also widely used; these include the real stabilization method [20,21], the complex scaling method [22][23][24][25], the analytical continuation of the coupling constant method [26,27], the complex momentum representation method [28,29], and the complexscaled Green's function method [30].…”

Section: Introductionmentioning

confidence: 99%

Searching for single-particle resonances with the Green's function method

Wang,

Sun

2021

Preprint

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Single-particle resonances in the continuum are crucial for studies of exotic nuclei. In this study, the Green's function approach is employed to search for single-particle resonances based on the relativistic-meanfield model. Taking 120 Sn as an example, we identify single-particle resonances and determine the energies and widths directly by probing the extrema of the Green's functions. In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study [Chin. Phys. C, 44:084105 (2020)], which has proven to be very successful, the same resonances as well as very close energies and widths are obtained. By comparing the Green's functions plotted in different coordinate space sizes, we also found that the results very slightly depend on the space size. These findings demonstrate that the approach by exploring for the extremum of the Green's function is also very reliable and effective for identifying resonant states, regardless of whether they are wide or narrow.

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Single-particle resonances in a deformed relativistic potential

Cited by 15 publications

References 47 publications

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

Hidden pseudospin and spin symmetries and their origins in atomic nuclei

RELATIVISTIC BOUND STATES IN THE PRESENCE OF SPHERICALLY RING-SHAPED q-DEFORMED WOODS–SAXON POTENTIAL WITH ARBITRARY l-STATES

Searching for single-particle resonances with the Green's function method

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