Influence of deformed surface diffuseness on alpha decay half-lives of actinides and lanthanides
Introduction
The alpha decay is one of the most interesting topics of nuclear physics in both theoretical and experimental studies [1], [2]. Alpha decay gives valuable informations about structure of nuclei and fusion–fission reactions. The chains of emitted alpha-particles observed in experiment are evidence of formation of a superheavy element during heavy-ion fusion reaction. Different theoretical models have been introduced for calculation of the alpha decay half-life, such as cluster model [3], multichannel cluster model, generalized density-dependent cluster model [4], [5], density-dependent M3Y effective interaction [6], [7], generalized liquid drop model [8], and unified model for alpha decay and alpha capture [9], [10].
Since most of alpha emitters have deformed shapes, inclusion of nuclear deformation in alpha decay calculations is essential. In recent theoretical investigations, the effects of nuclear deformation and orientation on the alpha decay characteristics have been studied, extensively [9], [11], [12], [13], [14]. The nuclear deformation is usually included in alpha decay calculations by considering deformed Coulomb potential and deformed phenomenological double-folding potential, Woods–Saxon potential, and proximity potentials with deformed radius of interaction between alpha-particle and deformed daughter nucleus. Moreover, in some studies the deformed form of nuclear potential depth and assault frequency have been employed. The surface diffuseness parameter of Woods–Saxon potential, as a crucial parameter in ion–ion nuclear interaction, is considered as a constant in literatures and different values are adopted for this parameter. Deformed shape of nucleus causes deformed surface diffuseness, as well. By using the gradient of the potential at the nuclear surface and the assumption that surface has the form of a spheroid, primitive relation for deformed surface diffuseness has been given [15], [16], [17]. Recently, more accurate and corrected form of deformed surface diffuseness has been introduced [18], [19]. Therefore, we were motivated to investigate the effect of deformed surface diffuseness on effective potential barrier and alpha decay characteristics. In order to calculate and compare the alpha decay half-lives for constant and deformed surface diffuseness we have employed the Wentzel–Kramers–Brillouin (WKB) semiclassical approximation [20].
In this study, our aim is to investigate the role of the deformed surface diffuseness and orientation on the potential barrier and alpha decay half-lives. In Sec. 2. the effective potential barrier, as summation of the deformed Woods–Saxon nuclear potential, deformed Coulomb potential and centrifugal term, is introduced by considering deformed surface diffuseness and taking into account the quadrupole and hexadecapole deformation parameters of the daughter nucleus. By inclusion of the Bohr–Sommerfeld quantization condition, the theoretical calculation of the alpha decay half-life is given based on WKB semiclassical approximation. The obtained results for half-lives of 19 lanthanide alpha emitters and 65 rare-earth alpha emitters are given in Section 3. Finally, the concluding remarks are given in Sec. 4.
Section snippets
Effective potential
The effective potential between axially symmetric deformed daughter nucleus and alpha-particle, including the attractive nuclear potential, the repulsive Coulomb potential, and the additional repulsive centrifugal part, is given by where θ is the orientation angle of the emitted alpha-particle with respect to the symmetric axis of the deformed daughter nucleus and l is the angular momentum carried by the alpha-particle.
The phenomenological deformed Woods–Saxon
Results
The model described in the previous section is now applied to calculate the alpha decay half-lives of some lanthanide and rare-earth alpha emitters.
Fig. 1 displays the variation of the dimensionless quantization factor η as a function of the orientation angle θ for two alpha emitters 160Ta and 236U. These figures show the variation of η with orientation angle is noticeable. However inclusion of the deformed surface diffuseness can change this parameter, slightly.
Fig. 2 shows the effective
Discussion and conclusion
In this theoretical investigation, the effective potential between α particle and deformed daughter nuclei has been calculated by considering the sum of deformed Woods–Saxon nuclear potential, deformed Coulomb potential, and centrifugal potential. The quadrupole and hexadecapole deformations of daughter nuclei have been considered. By including deformed surface diffuseness in Woods–Saxon potential and taking into account the Bohr–Sommerfeld quantization condition the alpha decay half-lives of
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