Low-energy behaviour of the proton optical potential of Sn

Gyarmati, B.; Vertse, T.; Zolani, L; Baryshnikov, A.I.; Gurbich, A.F.; Titarenko, N.N.; Yadrovsky, E.L.

doi:10.1088/0305-4616/5/9/007

Cited by 21 publications

(6 citation statements)

References 17 publications

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“…wherep z is the usual momentum operator for the zdirection. The idea of the separable expansion method [18][19][20] is to expand the potentials V s on some basis as,…”

Section: A General Formalismmentioning

confidence: 99%

“…The eigen-values E can be found by requiring that the determinant of the matrix in Eq. (9) vanishes at E [18][19][20]. This method has been employed in several applications in the past.…”

Section: A General Formalismmentioning

confidence: 99%

“…The second approach, on the other hand, is to expand each potential in a two-center potential on some basis and then to shift it with a quantum mechanical shift operator [18,19]. To obtain eigenfunctions for the resultant potential, the single-particle Schrödinger equation is transformed to a linear algebraic equation based on the Lippmann-Schwinger equation, and then the eigen-values are sought by checking the solvability condition of the equation as a function of a single-particle energy [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

“…One also has to use different treatments for bound states and scattering states because of the different boundary conditions of the wave functions [19]. Another point is that the matrix elements of a Green's function have to be constructed at each energy, which may be time consuming if many basis states are included in a calculation, even though one may be able to resort to a recurrence formula [19,20].…”

Section: Introductionmentioning

confidence: 99%

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New and efficient method for solving the eigenvalue problem for the two-center shell model with finite-depth potentials

Hagino

Ichikawa

2017

Phys. Rev. C

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We propose a new method to solve the eigen-value problem with a two-center single-particle potential. This method combines the usual matrix diagonalization with the method of separable representation of a two-center potential, that is, an expansion of the two-center potential with a finite basis set. To this end, we expand the potential on a harmonic oscillator basis, while singleparticle wave functions on a combined basis with a harmonic oscillator and eigen-functions of a one-dimensional two-center potential. In order to demonstrate its efficiency, we apply this method to a system with two 16 O nuclei, in which the potential is given as a sum of two Woods-Saxon potentials.

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“…wherep z is the usual momentum operator for the zdirection. The idea of the separable expansion method [18][19][20] is to expand the potentials V s on some basis as,…”

Section: A General Formalismmentioning

confidence: 99%

“…The eigen-values E can be found by requiring that the determinant of the matrix in Eq. (9) vanishes at E [18][19][20]. This method has been employed in several applications in the past.…”

Section: A General Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New and efficient method for solving the eigenvalue problem for the two-center shell model with finite-depth potentials

Hagino

Ichikawa

2017

Phys. Rev. C

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“…Solution method(approx. 50-250 words):The potential separable expansion (PSE) method using two basis sets of harmonic oscillator functions is employed [2,3]. A method to ensure the volume conservation of the fusing system is used [1].…”

mentioning

confidence: 99%