Two- and three-cluster decays of light nuclei within a hyperspherical harmonics approach

Vasilevsky, V. S.; Lashko, Yu. A.; Filippov, G.F.

doi:10.1103/physrevc.97.064605

Cited by 10 publications

(5 citation statements)

References 38 publications

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“…This statement is, for example, demonstrated in Ref. [29]. Thus, oscillator functions with a small value of N sh describe very compact configurations of a three-cluster system with all clusters being close to each other.…”

Section: Supplementary Quantitiesmentioning

confidence: 57%

Systematic investigation of the Hoyle-analog states in light nuclei

2018

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We investigate resonance states in three-cluster continuum of some light nuclei 9 Be, 9 B, 10 B, 11 B and 11 C. These nuclei are considered to have a three-cluster configuration consisting of two alphaparticles and neutron, proton, deuteron, triton and nucleus 3 He. In this study, we make use two different microscopic three-cluster models. The first model employs the Hyperspherical Harmonics basis to numerate channels and describe three-cluster continuum. The second model is the wellknown complex scaling method. The nucleon-nucleon interaction is modeled by the semi-realistic Minnesota and Hasegawa-Nagata potentials. Our main aim is to find the Hoyle-analog states in these nuclei or, in other words, whether it is possible to synthesize these nuclei in a triple collision of clusters. We formulate the criteria for selecting such states and apply them to resonance states, emerged from our calculations. We found that there are resonance states obeying the formulated criteria which make possible syntheses of these nuclei in a stellar environment.

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Section: Supplementary Quantitiesmentioning

confidence: 57%

Systematic investigation of the Hoyle-analog states in light nuclei

2018

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“…Basic ideas of the method were formulated in Reference [2]. In the present paper we will the same notations as in recent publications [1,12,13].…”

Section: Amhhb and Coupled Channels Methodologymentioning

confidence: 99%

“…  of the wave function (5) are subject for boundary conditions, which were discussed in detail in Reference [12]. The total many-particle Hamiltonian Ĥ is split onto the It is important to underline, that within the coupled channel methodology, if we have N ch open channels then for each energy we have N ch independent solutions (wave functions) which describe all possible elastic and inelastic processes.…”

Section: Amhhb and Coupled Channels Methodologymentioning

confidence: 99%

On three-cluster disintegration of 9Be

Vasilevsky¹,

Katö²

2019

Phys. sci. technol.

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We study a process of the photodisintegration of some Borromean light nuclei into three clusters. This study is performed within a three-cluster microscopic model. In Reference [1] this model was applied to obtain parameters of resonance states in 9 Be and 9 B and to establish their nature. Main aim of the present investigations is to describe the dipole transition probability from the ground state of 9 Be to the states of three-cluster α+α+n continuum by using the same model. That model exploits the hyperspherical harmonics basis (HHB) and thus reduces many-channel Schrödinger equation to the algebraic matrix (AM) form. The dipole transitions from the ground 3/2-state to the 1/2+ states of three-cluster continuum were studied in detail. The role of resonance states in three-cluster continuum to this process is investigated in detail. The dominant channels with the maximal dipole strength due to the coupling between the ground and scattering states are discovered.

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“…One can see some illustrations to this statement in Refs. [25,26]. Such a "boundary condition" for the operator r 2 and p 2 is due to the tridiagonal form of these matrices.…”

Section: Proofmentioning

confidence: 99%

Properties of a potential energy matrix in oscillator basis

2019

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Matrix elements of potential energy are examined in detail. We consider a model problem -a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L 2 basis (J-matrix) method for the quantum theory of scattering.

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Two- and three-cluster decays of light nuclei within a hyperspherical harmonics approach

Cited by 10 publications

References 38 publications

Systematic investigation of the Hoyle-analog states in light nuclei

Systematic investigation of the Hoyle-analog states in light nuclei

On three-cluster disintegration of 9Be

Properties of a potential energy matrix in oscillator basis

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