Relativistic extension of the complex scaled Green's function method for resonances in deformed nuclei

Shi, Min; Shi, Xin-Xing; Niu, Zhong-Ming; Sun, T.; Guo, Jian-You

doi:10.1140/epja/i2017-12241-6

Cited by 19 publications

(10 citation statements)

References 42 publications

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“…Similar to Refs. [19,[41][42][43], we can further get the CLD, denoted as ∆ρ(ε), by the difference between the density of states ρ(ε) and the density of continuum states ρ 0 (ε). Here, ρ 0 (ε) is obtained from the asymptotic Hamiltonian H 0 in the form of H with r → ∞.…”

Section: Formalismmentioning

confidence: 99%

“…The CLD has been calculated in the nonrelativistic framework [41]. Using the complex scaled Green's function method, the study of CLD has been extended to the relativistic framework in the spherical and deformed nuclei [42,43]. Although such methods can describe the resonant states in an intuitive way, their results are not completely independent on the rotation angle in the actual calculations with a finite basis.…”

Section: Introductionmentioning

confidence: 99%

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Combination of complex momentum representation and Green's function methods in relativistic mean-field theory

2018

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We have combined the complex momentum representation method with the Green's function method in the relativistic mean-field framework to establish the RMF-CMR-GF approach. This new approach is applied to study the halo structure of 74 Ca. All the continuum level density of concerned resonant states are calculated accurately without introducing any unphysical parameters, and they are independent of the choice of integral contour. The important single-particle wave functions and densities for the halo phenomenon in 74 Ca are discussed in detail.

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Section: Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Combination of complex momentum representation and Green's function methods in relativistic mean-field theory

2018

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“…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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“…Based on the conventional scattering theories, many approaches, such as R-matrix theory [26,27], K-matrix theory [28], S-matrix theory [29,30], Jost function approach [31,32], and the scattering phase shift (SPS) method [29,33,34] have been developed to study the single-particle resonant states. Meanwhile, the tech-niques for bound states have been extended for the singleparticle resonant states, such as the analytical continuation of the coupling constant (ACCC) method [23,24,[35][36][37][38][39][40][41][42][43][44][45], the real stabilization method (RSM) [46][47][48][49][50], the complex scaling method (CSM) [51][52][53][54][55][56][57][58][59][60][61][62][63], the complexscaled Green's function (CGF) method [62][63][64][65], and the complex momentum representation (CMR) method…”

mentioning

confidence: 99%

“…Meanwhile, the tech-niques for bound states have been extended for the singleparticle resonant states, such as the analytical continuation of the coupling constant (ACCC) method [23,24,[35][36][37][38][39][40][41][42][43][44][45], the real stabilization method (RSM) [46][47][48][49][50], the complex scaling method (CSM) [51][52][53][54][55][56][57][58][59][60][61][62][63], the complexscaled Green's function (CGF) method [62][63][64][65], and the complex momentum representation (CMR) method [66][67][68][69][70][71][72]. Especially, the SPS [33,34], ACCC [23,38,45], CSM [60]…”

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confidence: 99%

Green's function method for the single-particle resonances in a deformed Dirac equation

et al. 2020

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Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead to improved descriptions of exotic nuclei. In this work, the Green's function (GF) method that can treat the single-particle bound and resonant states on the same footing is applied to solve the coupled-channel Dirac equation with a quadrupole-deformed Woods-Saxon potential for the first time. Detailed formalism for the partial-wave expansion of Green's function is presented. Numerical checks are carried out by comparing with our previous implementation of spherical GF method and the results from the deformed analytical continuation of the coupling constant (ACCC) and scattering phase shift (SPS) methods. Finally, Nilsson levels for bound and resonant orbitals in a halo candidate nucleus 37 Mg from the deformed GF method are calculated over a wide range of deformations and show some decisive hints of p-wave halo formation in this nucleus, namely, crossing between the configurations 1/2[321] and 5/2[312] at deformation parameter β > 0.5 may enhance the probability to occupy the 1/2[321] orbital coming from 2p 3/2 .

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Relativistic extension of the complex scaled Green's function method for resonances in deformed nuclei

Cited by 19 publications

References 42 publications

Combination of complex momentum representation and Green's function methods in relativistic mean-field theory

Combination of complex momentum representation and Green's function methods in relativistic mean-field theory

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

Green's function method for the single-particle resonances in a deformed Dirac equation

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