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We investigate the formation distance ($R_0$) from the center of the radioactive parent nucleus at which the emitted cluster is most probably formed. The calculations are microscopically performed starting from solving the time-independent Schr\"{o}dinger wave equation for the $\alpha$-core system, using nuclear potential based on the Skyrme-SLy4 nucleon-nucleon interaction and folding Coulomb potential, to determine the incident and transmitted wave functions of the system. Our results advocate that the emitted cluster is mostly formed in the pre-surface region of the nucleus, under the effect of Pauli blocking from the saturated core density. The deeper $\alpha$-formation distance inside the nucleus gives rise to less preformation probability, and indicates more stable nucleus of longer half-life. Also, the $\alpha$-particle tends to be formed at a bit deeper region inside the nuclei having larger isospin asymmetry and in the closed shell nuclei. Regarding the emitted nuclei heavier than $\alpha$-particle, we find that the formation distance of the emitted clusters heavier than $\alpha$-particle increases with increasing the isospin asymmetry of the formed cluster, rather than with increasing its mass number. The partial half-life of a certain cluster-decay mode increases upon increasing either the mass number or the isospin asymmetry of the emitted cluster.

We study the impact of the nuclear symmetry energy and its density dependence on the {\alpha}-decay process. Within the frame work of the performed cluster model and the energy density formalism, we use different parameterizations of the Skyrme energy density functionals that yield different equations of state EOSs. Each EOS is characterized by a particular symmetry-energy coefficient (asym) and a corresponding density-slope parameters L. The stepwise trends of the neutron (proton) skin thickness of the involved nuclei with both asym and L do not clarify the obtained oscillating behaviors of the {\alpha}-decay half-life T{\alpha} with them. We find that the change of the skin thickness after {\alpha}-decay satisfactory explains these behaviors. The presented results provide constrains on asym centered around an optimum value asym= 32 MeV, and on L between 41 and 57 MeV. These values of asym and L, which indicate larger reduction of the proton-skin thickness and less increase in the neutron-skin thickness after an {\alpha}-decay, yield minimum calculated half-life with the same extracted value of the {\alpha}-preformation factor inside the parent nucleus., Comment: To be published in Chinese Physics C

We consider the finite size effect on thermo-magnetic properties of charged Bose gases confined in a quasi two-dimentsional potential. A modified semiclassical approach is used, taking into account the finite size correction to guarantee an accurate density of states. The charged spinless Bose gas shows diamagnetic behavior. Temperature dependent magnetization is indicated for the investigated system that condense at a resistive critical temperature in accordance with the applied magnetic field., Comment: 7 pages

Background: The deformation of the nuclei involved in the cluster decay of heavy nuclei affect seriously their half-lives against the decay. Purpose: We investigate the description of the different decay stages in both the optimum orientation and the orientation-averaged pictures of the cluster decay process. Method: We consider the decays of 232,233,234U and 236,238Pu isotopes. The quantum mechanical knocking frequency and penetration probability based on the Wentzel-Kramers-Brillouin approximation are used to find the decay width. Results: We found that the orientation-averaged decay width is one or two orders of magnitude less than its value along the non-compact optimum orientation. The difference between the two values increases with decreasing the mass number of the emitted cluster. Correspondingly, the extracted preformation probability based on the averaged decay width increases with the same orders of magnitude compared to its value obtained considering the optimum orientation. The cluster preformation probabilities (Sc) obtained in the two considered schemes give more or less comparable agreement with the Blendowske-Walliser (BW) formula based on the preformation probability of Sa(ave.) obtained from the orientation-averaging scheme. All the obtained results, including those obtained in the optimum-orientation scheme, deviate substantially from the BW law based on Sa(opt.) obtained using the optimum-orientation scheme. Conclusion: In order to account for deformations of the participating nuclei, it is more relevant to calculate the decay width by averaging over the different possible orientations of the participating deformed nucleus, rather than considering the corresponding non-compact optimum orientation.

The ground-state spin and parity of a formed daughter in the radioactive Alpha-emitter is expected to influence the preformation probability of the Alpha and daughter clusters inside it. We investigate the Alpha and daughter preformation probability inside odd-A and doubly-odd radioactive nuclei when the daughter and parent are of different spin and/or parity. We consider only the ground-state to ground-state unfavored decays. This is to extract precise information about the effect of the difference in the ground states spin-parity of the involved nuclei far away any influences from the excitation energy if the decays are coming from isomeric states. The calculations are done for 161 Alpha-emitters, with Z=65-112 and N=84-173, in the framework of the extended cluster model, with WKB penetrability and assault frequency. We used a Hamiltonian energy density scheme based on Skyrme-SLy4 interaction to compute the interaction potential. The Alpha plus cluster preformation probability is extracted from the calculated decay width and the experimental half-life time. We discussed in detailed steps the effect of angular momentum of the emitted Alpha-particle on the various physical quantities involved in the unfavored decay process and how it is finally increases the half-life time. We found that if the ground states spin and/or parity of parent and daughter nuclei are different, then the preformation probability of the Alpha-cluster inside parent is less than it would be if they have similar spin-parity. We modified the formula that gives the Alpha preformation probability in terms of the numbers of protons and neutrons outside the shell closures of parent, to account for this hindrance in the preformation probability for the unfavored decays between ground states.

The universal curve is one of the simple ways to get preliminary information about the Alpha-decay half-life times of heavy nuclei. We try to find parameterization for the universal curve of Alpha decay based on semi-microscopic calculations, starting from the realistic M3Y-Reid nucleon-nucleon interaction. Within the deformed density-dependent cluster model, the penetration probability and the assault frequency are calculated using the WKB penetration probability. The deformations of daughter nuclei and the ground-state spin and parity of the involved nuclei are considered. We found that it is accurate enough to express the assault frequency, for all studied decays, either as a function of the mass number of the parent nuclei or as a constant average value. The average preformation probability of the Alpha cluster inside four groups of 166 even(Z)-even(N), 117 odd-even, 141 even-odd, and 72 odd-odd Alpha-emitters are obtained, individually. The effect of participating unpaired nucleons in the involved nuclei, as well as the influence of any differences in their ground-state spin and/or parity, appears in the obtained average values of the preformation probability. Based on the calculated WKB penetration probability, we suggested a single universal curve for Alpha decay, with only one parameter. This parameter varies according to the classified four groups. It includes the preformation probability and the average assault frequency, in addition to the pairing contribution., Comment: 14 pages, 5 Figures, Accepted to be published in Phys. Rev. C

Proton and neutron density profiles of 760 nuclei in the mass region of A=16-304are analyzed using the Skyrme energy density for the parameter set SLy4. Simple formulae are obtained to fit the resulting radii and diffuseness data. These formulae may be useful to estimate the values of the unmeasured radii, and especially in extrapolating charge radius values for nuclei which are far from the valley of stability or to perform analytic calculations for bound and/or scattering problems. The obtained neutron and proton root-mean-square radii and the neutron skin thicknesses are in agreement with the available experimental data., Comment: 14 pages,5 figures. arXiv admin note: text overlap with arXiv:1003.5225 by other authors

The parabolic approximation to the equation of state of the isospin asymmetric nuclear matter (ANM) is widely used in the literature to make predictions for the nuclear structure and the neutron star properties. Based on the realistic M3Y-Paris and M3Y-Reid nucleon-nucleon interactions, we investigate the effects of the higher-order symmetry energy on the proton fraction in neutron stars and the location of the inner edge of their crusts and their core-crust transition density and pressure, thermodynamically. Analytical expressions for different-order symmetry energy coefficients of ANM are derived using the realistic interactions mentioned above. It is found that the higher-order terms of the symmetry energy coefficients up to its eighth-order (E$_{sym8}$) contributes substantially to the proton fraction in $\beta$ stable neutron star matter at different nuclear matter densities, the core-crust transition density and pressure. Even by considering the symmetry energy coefficients up to E$_{sym8}$, we obtain a significant change of about 40$\%$ in the transition pressure value from the one based on the exact equation of state. Using equations of state based on both Paris and Reid effective interactions which provide saturation incompressibility of symmetric nuclear matter in the range of 220 MeV$\leq$K$_0$$\leq$270 MeV, we estimate the ranges 0.090 fm$^{-3}$$\leq$$\rho_t$$\leq$0.095 fm$^{-3}$ and 0.49 MeV fm$^{-3}$$\leq$P$_t$$\leq$ 0.59 MeV fm$^{-3}$ for the liquid core-solid crust transition density and pressure, respectively. The corresponding range of the proton fraction at this transition density range is found to be 0.029$\leq$x$_{p(t)}$$\leq$0.032., Comment: 11 pages, 1 table, 1 figure