Woods-Saxon-Gaussian potential and alpha-cluster structures of alpha + closed shell nuclei

The Woods-Saxon-Gaussian(WSG) potential is proposed as a new phenomenological potential to systematically describe the level scheme, electromagnetic transitions, and alpha-decay half-lives of the alpha-cluster structures in various alpha + closed shell nuclei. It modifies the original Woods–Saxon(WS) potential with a shifted Gaussian factor centered at the nuclear surface. The free parameters in the WSG potential are determined by reproducing the correct level scheme of ~(212) Po=~(208) Pb+α. It is found that the resulting WSG potential matches the M3 Y double-folding potential at the surface region and makes corrections to the inner part of the cluster-core potential. It was also determined that the WSG potential, with nearly identical parameters to that of ~(212) Po(except for a rescaled radius), could also be used to describe alpha-cluster structures in ~(20) Ne =~(16) O+α and ~(44) Ti =~(40) Ca+α. In all three cases, the calculated values of the level schemes, electromagnetic transitions, and alpha-decay half-lives agree with the experimental data, which indicates that the WSG potential could indeed capture many important features of the alpha-cluster structures in alpha + closed shell nuclei. This study is a useful complement to the existing cluster-core potentials in literature. The Gaussian form factor centered at the nuclear surface might also help to improve our understanding of the alpha-cluster formation, which occurs in the same general region.     

Bonding potential between two12C nuclei

The potential between two¹²C nuclei in linear chain configuration has been calculated microscopically using the Ali-Bodmerα-α potential. This potential shows a pocket and compares well in the tail region with the phenomenological potential extracted before, from the data on the quasi-molecular resonances of the¹²C +¹²C system. This provides support to the diatomic like rotation-vibration picture of quasi-molecular states.     

VOn±(n=0,1,2)的势能函数与光谱常数研究

用密度泛函B3LYP/6-311++G(d,p)方法和相对论有效实势(Lanl2dz基组)对VO^n±(n=0,1,2)分子离子的势能函数及光谱常数进行了分析. 结果表明它们都能稳定存在, 其基态电子状态分别是:⁴Σ(VO^2-), ³Σ(VO^-), ⁴Σ(VO), ³Σ(VO⁺)和²Σ(VO²⁺). 其中VO^2-和VO²⁺的势能函数曲线呈“火山口”型, 属于亚稳态分子离子. 用七参数Murell-Sorbie势拟合VO^2-和VO²⁺分子亚稳态双原子分子离子势能函数, 发现其拟合曲线与势能函数曲线符合得很好. 同时,讨论了电荷对势能函数和能级的影响. 关键词： 分子离子 密度泛函理论 势能函数 能级     

First determination of isotopically invariant parameters of the negative ion—Hydrogen sulfide anion (SH)

The first isotopically invariant Dunham analysis of a negative ion (the hydrogen sulfide anion SH⁻) that uses all available infrared and sub-millimeter wave experimental data on ³²SH⁻, ³³SH⁻, ³⁴SH⁻, and ³²SD⁻ yields accurate information on Born-Oppenheimer breakdown parameters. The potential constants of expansion of the potential function up to the sixth order were calculated. Differences between the construction of the potential function based on the Morse potential and that on the base of the power series expansion are shown.     

Constructing effective nucleon-nucleon interaction on the basis of the Idaho potential

An effective nucleon-nucleon interaction at an energy of 200 MeV is constructed for the Idaho nucleon-nucleon potential obtained on the basis of the theory of spontaneous chiral-symmetry breaking. This interaction approximates the nonlocal t matrix obtained for free nucleon-nucleon scattering from a solution to the Lippmann-Schwinger equation for the Idaho potential. The exact and approximated t matrices for the Paris potential, Idaho potential, and the von Geramb Hamburg potential are compared. The effective potential obtained in the way outlined above is used to calculate the inelastic scattering of 200-MeV polarized protons that is accompanied by the excitation of the 2⁺ level at 4.44 MeV and the 1⁺ level at 15.11 MeV in the ¹²C nucleus and the 6^? level at 14.1 MeV in the ²⁸Si nucleus. The results are compared with the results of the calculations on the basis of the Paris potential.     

Instabilities of the Conventional Nucleus-Nucleus Interactions for (<Superscript>3</Superscript>H<Superscript>4</Superscript>He) Proton Pickup Cross-Sections

The angular distributions of the ²⁶Mg, ²⁸Si, ³⁰Si(³H, ⁴He) reactions have been analyzed using the exact finite-range DWBA calculations. The optical model potential is assumed to have the conventional spin-orbit potential. The obtained cross-sections with the spin-orbit potential are not significantly different from those calculated using the phenomenological Woods–Saxon form factors in the forward angle regions. The inclusion of the spin-orbit potential gives the best fit to the data and greatly improves the large angle cross-sections. Different reasonable spectroscopic factors are found to account well for the cross-section magnitudes.     

The Reid93 Potential Triton in the Unitary Pole Approximation

The Reid93 potential provides a representation of the nucleon–nucleon (NN) scattering data that rivals that of a partial wave analysis. We present here a unitary pole approximation (UPA) for this contemporary NN potential that provides a rank one separable potential for which the wave function of the deuteron (³S₁-³D₁) and singlet anti-bound (¹S₀) state are exactly those of the original potential. Our motivation is to use this UPA potential to investigate the sensitivity of the electric dipole moment for the deuteron and ³H and ³He to the ground state nuclear wave function. We compare the Reid93 results with those for the original Reid (Reid68) potential to illustrate the accuracy of the bound state properties.     

Accurate calculation of the scattering length for the cooling of hydrogen atoms by lithium atoms

An improved ab initio calculation has been performed for the potential for the LiH a ³Σ⁺ state, using two very large basis sets. The Basis Set Superposition Error (BSSE) correction has been determined for both basis sets and the non-Born-Oppenheimer correction estimated to be negligible. The best potential is approximately 10% deeper than the previous estimate. Vibrational energies and scattering lengths have been calculated for ^6,7LiH(D) with both potentials, with and without the BSSE correction, and also with an estimated potential expected to bracket the true potential. The ⁷LiH scattering length is estimated to be (45 ± 4)a₀ and hence the low-energy cross-section in the best a ³Σ⁺ potential is about half that calculated previously. Enhanced cooling by ⁷Li of trapped H atoms remains feasible. Received 30 April 2001     

Quantum mechanical calculation of rotational constants and Franck-Condon factors of diatomic molecules

In this paper, the question of reliability of the Morse potential as a potential curve for a diatomic molecule is investigated on the basis of calculating the rotational constant. It is shown that the Morse potential describes well potential curves of X¹Σ _q ⁺ and B¹Π_u electronic states of a Na₂ molecule. Calculations of Franck-Condon factors for X¹Σ _q ⁺ ? B¹Π_u band of a Na₂ molecule using wave functions of the Morse potential confirm the known correlation between the values of Franck-Condon factors and rotational constants of combined electronic states.     

An X-ray diffraction study of anharmonic thermal vibrations in the ionic conductor,barium chloride fluoride (BaClF)

Integrated intensities of X-ray reflections from a barium chloride fluoride single crystal were measured at 24, 180, 289, 402, 467 and 610°C. The intensities were used for the determination of the anharmonic potential parameters up to the third order. Harmonic potential parameters for each ion were obtained from the temperature dependence of thermal parameters, and anharmonic potential parameters were determined by the least-squares procedures, utilizing the temperature factor formalism based on the cumulant expansion. As a result, it has been found that the Ba²⁺ and Cl^? ions show an anharmonicity, while no significant anharmonic effect was detected for the F^? ion. From the potential calculated around the Cl^? and F^? ions, it was found that both Cl^? and F^? ions diffuse more easily within the (001) plane than along the c axis.     

Use of Harrison's potential in ZnS,NaCl and CsCl-structure solids

Harrison's overlap repulsive potential has been used for evaluating cohesive energies, bulk modulus and its pressure derivatives, Gruneisen parameter, and the volume derivatives of Gruneisen parameter for cuprous halides, silver halides and thallous halides. This potential has replaced the old and widely used Born-Mayer potential in ionic crystals. The Harrison repulsive potential has been represented by a quantum mechanical analytical potential form derived from the tight binding theory. The parameters involved in this potential form have been determined in terms of valence state energies of outermost d-electrons of Cu⁺, Ag⁺ and Tl⁺ ions. The results calculated in the present study have been found in good agreement with experimental data and better than those predicted from the Born potential model.On leave fromDepartment of Physics, G. B. Pant University, Pant Nagar, U. P., India.     

Potentials for heavy ions scattering from 208Pb

Data for the elastic scattering of ¹²C(96 MeV), ¹⁶O(129.5 and 192 MeV) and ²⁰Ne (161.2 MeV) from ²⁰⁸Pb have been used to deduce properties of the ion-ion potential. In particular, the strength of the absorptive potential in the surface region was found to be comparable to that of the real potential. The importance of small-angle data is emphasized.     

A consistent derivation of the real and imaginary parts of the heavy ion potential below and above the Coulomb barrier

In a model including approximately a large set of non-elastic channels, the real and imaginary potentials are consistently derived. The “anomaly” of the real potential which sharply increases in the vicinity of the Coulomb barrier where the imaginary potential is strongly reduced is studied in ¹⁶O + ⁴⁰Ca and ¹⁶O + ²⁰⁸Pb systems. The results on the imaginary potential are discussed and compared to our previous calculation.     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

Global optical model potential describing 12C-nucleus elastic scattering

We construct a new global optical model potential to describe the elastic scattering of ¹²C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from ²⁴Mg to ²⁰⁹Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.     

Theoretical analysis of <Superscript>6</Superscript>He + <Superscript>12</Superscript>C scattering by means of the model of microscopic optical potential

The ⁶He + ¹²C elastic scattering at E = 3.0, 38.3, and 41.6 MeV/nucleon is analyzed using the microscopic model of optical potential. According to this approach, two or three parameters are fitted that renormalize the depth of real, imaginary, and surface parts of the calculated optical potential. In this case, the ambiguity of the obtained sets of fitting parameters remains, but can be reduced by introducing an additional criterion of selection: the dependence of the volume integrals of the optical potential on the energy. The structure of the obtained optical potential, the role of the nuclear medium, the formation of the imaginary part of the optical potential, and the interconnection between the surface potential and the ⁶He breakup channels are discussed.     

Diffusion of Li ion on graphene: A DFT study

Density functional theory investigations show that the Li⁺ ion is stabilized at the center of hexagonal carbon ring with the distance of 1.84 Å from graphene surface. The potential barrier of Li⁺ ion diffusion on the graphene surface, about 0.32 eV, is much lower than that of Li⁺ ion penetrating the carbon ring which is 10.68 eV. When a vacancy of graphene exists, potential barrier about 10.25 eV for Li⁺ ion penetrating the defect is still high, and the ability of the vacancy to sizing the Li⁺ ion is also observed. Electronic densities of states show that the formation of a localized bond between Li atom and edge carbon of vacancy is the main reason for high potential barrier when Li⁺ ion penetrate a vacancy. While Coulomb repulsion is the control factor for high potential barrier in case of Li⁺ ion penetrating a carbon ring.     

Bestimmung von Potentialparametern für die Wechselwirkung von Ionen und Atomen aus dem Beugungseffekt

This paper is concerned with the determination of the potential parameters from experimental results. The potential parameters are determined from the amplitudes and the positions of the experimental diffraction pattern by applying the general solution of the diffraction effect in [1]. All existing experimental results up to date are referred and evaluated. For the following scattering systems the potential parameters were determined and are presented in a table:⁷Li⁺-He,⁷Li⁺-Ne,⁷Li⁺-Ar,⁷Li⁺-Kr,⁷Li⁺-Xe,⁶Li⁺-Ar and H⁺- Ar.     

Cold valleys of superheavy elements with deformed targets and projectiles

The dependence of the cold driving potential on the deformation of the incoming target and projectile is investigated in the case of the synthesis of the superheavy nuclei ²⁵⁶No, ²⁸⁶112, ²⁹²114, ²⁹⁶116, and ³⁰⁶122. The occurrence of valleys in the driving potential as a function on the interfragment distance and the mass asymmetry is studied for different fixed orientations of the colliding nuclei such as the pole-pole, pole-equator, equator-equator, and equator-equator-crossed and compared to the case when the nuclei are assumed to be spherical or when the potential is averaged over the orientation.     

Screening effects on ~(12)C+~(12)C fusion reaction

One of the important reactions for nucleosynthesis in the carbon burning phase in high-mass stars is the ~(12)C+~(12)C fusion reaction. In this study, we investigate the influences of the nuclear potentials and screening effect on astrophysically interesting ~(12)C+~(12)C fusion reaction observables at sub-barrier energies by using the microscopic α-αdouble folding cluster(DFC) potential and the proximity potential. In order to model the screening effects on the experimental data, a more general exponential cosine screened Coulomb(MGECSC) potential including Debye and quantum plasma cases has been considered in the calculations for the ~(12)C+~(12)C fusion reaction. In the calculations of the reaction observables, the semi-classical Wentzel-Kramers-Brillouin(WKB) approach and coupled channel(CC)formalism have been used. Moreover, in order to investigate how the potentials between ~(12)C nuclei produce molecular cluster states of ~(24)Mg, the normalized resonant energy states of ~(24)Mg cluster bands have been calculated for the DFC potential. By analyzing the results produced from the fusion of ~(12)C+~(12)C, it is found that taking into account the screening effects in terms of MGECSC is important for explaining the ~(12)C+~(12)C fusion data, and the microscopic DFC potential is better than the proximity potential in explaining the experimental data, also considering that clustering is dominant for the structure of the ~(24)Mg nucleus.