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.     

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     

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.     

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.     

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     

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.     

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.     

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.     

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.     

Systematic investigation of light heavy-ion reactions

We introduce a novel coupling potential for the scattering of deformed light heavy-ion reactions. This new approach is based on replacing the usual first derivative coupling potential by a new, second derivative coupling potential in the coupled-channels formalism. This new approach has been successfully applied to the study of the ¹²C+¹²C, ¹²C+²⁴Mg, ¹⁶O+²⁸Si, and ¹⁶O+²⁴Mg systems and made major improvements over all the previous coupled-channels calculations for these systems. This paper also shows the limitations of the standard coupled-channels theory and presents a global solution to the problems faced in the previous theoretical accounts of these reactions.     

Three-alpha force and the 3-α model of12C

We postulate a Gaussian three-body potential amongα particles and adjust its parameters so that, when it is added to the Ali-Bodmerα-α potential, a good fit to experimental energies of low-lying 0⁺ and 2⁺ states of¹²C is achieved. With these potentials we made a linear variational calculation in a basis of harmonic oscillator functions which are translationally invariant, completely symmetric, and have a definite orbital angular momentum. We study the influence of this three-body potential on elastic and inelastic form factors, transition widths, Coulomb energy and charge radius of the 3-α system. The 3-α potential improved results found with the Ali-Bodmer potential alone. We find the 0 ₂ ⁺ state to be a (non-rigid) linear chain and the ground state to be a triangle ofα particles.     

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.     

反应物NO的转动激发对反应N(4S)+NO(X2Π)→N2(X3Σg-)+O(3P)影响的立体动力学研究

采用准经典轨线方法,在碰撞能为0.6 eV时,研究了反应物NO分子的转动激发对发生在³A"和³A'势能面上的反应N(⁴S)+NO(X²Π)→N₂(X³Σ_g^-)+O(³P)的立体动力学性质的影响. 详细讨论了在反应物分子的不同转动态下发生在两个势能面上反应的矢量性质. 结果表明, 反应物分子NO的转动激发对发生在³A′势能面上的立体动力学性质产生重大影响, 这可能与该势能面上存在一个早期势垒有关.     

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.     

高次正幂与逆幂势函数的叠加的径向薛定谔方程的解析解

当薛定谔方程中出现高次非谐振子势，电偶极矩势，分子晶体势，极化等效势等高次正幂与逆幂势函数以及它们的叠加时，薛定谔方程的求解变得非常复杂，采用奇点邻域附近的级数解法与求解渐近解相结合，在多种相互作用幂函数紧密耦合的条件下，得到势函数为V(r)=a₁r⁶+a₂r²+a₃r^{-4关键词： 级数解法 幂势函数 径向波函数 渐近解}     

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.     

Resonance states in 16O+16O, 12C+16O, α+16O and α+12C with modified Morse potentials

The resonance states in ¹⁶O+¹⁶O, ¹²C+¹⁶O, α+¹⁶O and α+¹²C are described using modified Morse potential proposed earlier whose success has already been demonstrated in the case of ¹²C+¹²C system. The general validity of such a potential with long range, shallow depth and repulsive soft core determined from the resonance data itself is being examined through the present study of the resonances in the above four systems. In each system, the experimental data of a large number of states have been successfully described with a modified Morse potential. The success points out a common mechanism of the origin of these states, and reaffirms authentically the diatomic-like rotational and vibrational picture of the nuclear molecular resonances proposed previously. The close resemblance between the physics of diatomic molecules and nuclear molecular resonances extending to the level of potential which is Morse type in both the cases — although belong to two different areas of physics — is further strengthened through the present study.      

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.     

Effect of strong magnetic field on chemical potential and electron capture in magnetar

The chemical potential of electrons in a strong magnetic field is investigated. It is shown that the magnetic field has only a slight effect on electron chemical potential when B 〈 10^11 T, but electron chemical potential will decrease greatly when B 〉 10^11 T. The effects of a strong magnetic field on electron capture rates for ^60Fe are discussed, and the result shows that the electron capture sharply decreases because of the strong magnetic field.     

Diffusion transport of negative ions through the interface between cryogenic liquids

A theory of electron bubble transport through the interface between cryogenic liquids is developed based on a new approach to calculating the potential of interaction of a bubble with the interface. The theory is in good agreement with experiments on the electric-field dependence of the potential barrier near the interface between liquid ⁴He, ³He, and vacuum, as well as at the interface between ³He and ⁴He saturated solutions. It is found that the interaction potential dependence on the distance between the electron bubble and the interface is isotopically invariant to three versions of such an interface. The dependence of the lifetime of negative ions in ⁴He and ³He on the temperature and electric field has been determined using the Kramers theory.