Scattering of a Klein-Gordon particle by a Woods-Saxon potential

Rojas, Clara; Villalba, Vı́ctor M.

doi:10.1103/physreva.71.052101

Cited by 73 publications

(81 citation statements)

References 17 publications

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“…For given values of the energy and the proper choice of the shape of the effective barrier, the probability of transmission reaches a maximum such as that obtained in the study of superradiance [14], where the amplitude of the scattered solutions by a rotating Kerr black hole is even larger than the amplitude of the incident wave. Analogous phenomena can also be obtained due to the presence of strong electromagnetic potentials [15].Recently, transmission resonances for the Klein-Gordon equation in the presence of a Woods-Saxon potential barrier have been computed [16]. The transmission coefficient as a function of the energy and the potential amplitude shows a behavior that resembles the one obtained for the Dirac equation [4].…”

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confidence: 57%

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Scattering of a relativistic scalar particle by a cusp potential

Villalba

Rojas

2007

Physics Letters A

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We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.PACS numbers: 03.65. Pm, 03.65.Nk, 03.65.Ge The study of low-momentum scattering of nonrelativistic particles by one-dimensional potentials is a well studied and understood problem [1]. Here we have that, as momentum goes to zero, the reflection coefficient goes to unity unless the potential V (x) supports a zero energy resonance. In this case the transmission coefficient goes to unity, becoming a transmission resonance [2]. Recently, this result has been generalized to the Dirac equation [3], showing that transmission resonances at k = 0 in the Dirac equation take place for a potential barrier V = V (x) when the corresponding potential well V = −V (x) supports a supercritical state. Kennedy [4] has shown that this result is also valid for a Woods-Saxon potential. More recently, transmission resonances and half-bound states have been discussed for a Dirac particle scattered by a cusp potential [5,6] as well as for a class of short range potentials [7]. The bound states for scalar relativistic particles satisfying the Klein-Gordon equation are qualitatively different from the previous case. Here, for short-range attractive potentials the Schiff-Snyder effect [8,9,10,11,12,13,14] takes place, i.e for a given potential strength two bound states appear, one with positive norm and another with negative norm. Such states can be associated with a particle-antiparticle creation process. No antiresonant states appear [11,12].The absence of resonant overcritical states for the Klein-Gordon equation in the presence of short-range potential interactions does not prevent the existence of transmission resonances for given values of the potential.Quantum effects associated with scalar particles in the presence of external potentials have been extensively discussed in the literature [10,14]. Among quantum effects, we have that transmission resonance is one of the most interesting phenomena. For given values of the energy and the proper choice of the shape of the effective barrier, the probability of transmission reaches a maximum such as that obtained in the study of superradiance [14], where the amplitude of the scattered solutions by a rotating Kerr black hole is even larger than the amplitude of the incident wave. Analogous phenomena can also be obtained due to the presence of strong electromagnetic potentials [15].Recently, transmission resonances for the Klein-Gordon equation in the presence of a Woods-Saxon potential barrier have been computed [16]. The transmission coefficient as a function of the energy and the potential am...

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confidence: 57%

“…Recently, transmission resonances for the Klein-Gordon equation in the presence of a Woods-Saxon potential barrier have been computed [16]. The transmission coefficient as a function of the energy and the potential amplitude shows a behavior that resembles the one obtained for the Dirac equation [4].…”

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confidence: 74%

Scattering of a relativistic scalar particle by a cusp potential

Villalba

Rojas

2007

Physics Letters A

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“…Moreover Rojas et al studied the KG particle scattering without scalar WSP [30] while Hassanabadi et al with scalar potential [31]. Note that WSP first described by Woods and Saxon in [32] to describe the 20 MeV proton scattering from medium and heavy nuclei.…”

Section: Introductionmentioning

confidence: 99%

Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

2018

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Recently, it has been shown that the generalized symmetric Woods-Saxon potential energy, in which surface interaction terms are taken into account, describes the physical processes better than the standard form. Therefore in this study, we investigate the scattering of Klein-Gordon particles in the presence of both generalized symmetric Woods-Saxon vector and scalar potential. In one spatial dimension we obtain the solutions in terms of hypergeometric functions for spin symmetric or pseudo-spin symmetric cases. Finally, we plot transmission and reflection probabilities for incident particles with negative and positive energy for some critical arbitrary parameters and discuss the correlations for both cases.

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“…It has been used in the study of nuclei outside A = 110−210 [1], high spin states in 146 Gd [2], parametrization of the n-208 Pb mean field [3], two-centre formalism [4], shell model calculations [5], spectra of rotating nuclei [6], confined quantum systems [7], collective models [8] and the wobbling excitations [10]. The solution of the Klein-Gordon equation under the WSP has been obtained in [11]. By using the supersymmetry quantum mechanics the solution of twobody spinless Salpeter equation for the WSP has been reported in [12].…”

Section: Introductionmentioning

confidence: 99%

The Relativistic Transmission and Reflection Coefficients for Woods-Saxon Potential

Yazarloo

Mehraban

2016

Acta Phys. Pol. A

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The relativistic problem of spin-1/2 particles subject to the Woods-Saxon potential is investigated by using the functional analysis method. We obtain scattering and bound state solutions of the one-dimensional Dirac equation with the Woods-Saxon potential in terms of the Jacobi polynomials. We also calculated the transmission and reflection coefficients by using behavior of the wave functions at infinity.

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Scattering of a Klein-Gordon particle by a Woods-Saxon potential

Cited by 73 publications

References 17 publications

Scattering of a relativistic scalar particle by a cusp potential

Scattering of a relativistic scalar particle by a cusp potential

Scattering of Klein-Gordon particles in the background of mixed scalar-vector generalized symmetric Woods-Saxon potential

The Relativistic Transmission and Reflection Coefficients for Woods-Saxon Potential

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