Decomposition of scattering phase shifts and reaction cross sections using the complex scaling method

Odsuren, M.; Katō, Kiyoshi; Aikawa, Masanori; Myo, Takayuki

doi:10.1103/physrevc.89.034322

Cited by 25 publications

(21 citation statements)

References 42 publications

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“…We also have b = 1 for the HO length parameter, μ = 1 for the reduced mass. It is worth noting that this potential was employed for first time in calculations for the exploration of the direct backrotation and how one could minimize errors associated with it in [53] and later on for CSM calculations of the complex scaled Green operator [58][59][60]. It also provides with a testing bed for other methods as well [55].…”

Section: Backrotation Of Csm Wavefunctionmentioning

confidence: 98%

Calculation of Expectation Values of Operators in the Complex Scaling Method

Papadimitriou

2016

Few-Body Syst

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The complex scaling method (CSM) provides with a way to obtain resonance parameters of particle unstable states by rotating the coordinates and momenta of the original Hamiltonian. It is convenient to use an L 2 integrable basis to resolve the complex rotated or complex scaled Hamiltonian H θ , with θ being the angle of rotation in the complex energy plane. Within the CSM, resonance and scattering solutions have fall-off asymptotics. One of the consequences is that, expectation values of operators in a resonance or scattering complex scaled solution are calculated by complex rotating the operators. In this work we are exploring applications of the CSM on calculations of expectation values of quantum mechanical operators by using the regularized backrotation technique and calculating hence the expectation value using the unrotated operator. The test cases involve a schematic two-body Gaussian model and also applications using realistic interactions.

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Section: Backrotation Of Csm Wavefunctionmentioning

confidence: 98%

Calculation of Expectation Values of Operators in the Complex Scaling Method

Papadimitriou

2016

Few-Body Syst

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“…Through the CLD, we can see a close relation between level structures and scattering phase shifts. In this section, we give a brief explanation of the CLD in relation to the extended completeness relation with complex scaling, which provides the decomposition of the scattering phase shifts into resonance and continuum contributions [157]. We also show the applications of the CLD to nuclear two-and three-body scattering problems associated with the α cluster.…”

Section: Continuum Level Densitymentioning

confidence: 99%

Recent development of complex scaling method for many-body resonances and continua in light nuclei

Myo

Kikuchi

Masui

et al. 2014

Progress in Particle and Nuclear Physics

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126

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The complex scaling method (CSM) is a useful similarity transformation of the Schrödinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the L2L2 basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Green’s functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented

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“…(11), it is seen that a bound state gives a constant shift of π in the phase shift, and a resonant state gives a monotonic increasing function up to π for energy E as discussed in Refs. [4,26]. The phase shift of the virtual state is described by an increasing function of energy FIG.…”

Section: B Virtual State In the Csmmentioning

confidence: 99%

Virtual-state character of the two-body system in the complex scaling method

et al. 2017

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In association with the property of the 1/2 + state observed just above the 8 Be(0 + ) + n threshold energy in 9 Be, we investigate the photodisintegration cross section of an s state in a simple schematic two-body model using the complex scaling method. The photodisintegration cross section, continuum level density, scattering phase shifts, and scattering length are discussed in relation with the virtual state. These scattering observables show strong divergences when a virtual state is located near the physical scattering region.

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Decomposition of scattering phase shifts and reaction cross sections using the complex scaling method

Cited by 25 publications

References 42 publications

Calculation of Expectation Values of Operators in the Complex Scaling Method

Calculation of Expectation Values of Operators in the Complex Scaling Method

Recent development of complex scaling method for many-body resonances and continua in light nuclei

Virtual-state character of the two-body system in the complex scaling method

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