Effects of Parametrization of A Woods–Saxon Potential on Single Particle Orbits in ~(66)Ca

A Woods–Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods–Saxon potential on single particle orbits around the Fermi surface are investigated in66Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness.     

△-Resonances in Ground State Properties of ^40 20Ca Spherical Cold Finite Nucleus at Equilibrium and under Compression

The ground state properties of the spherical nucleus ^40Ca have been investigated by using constrained spherical Hartree Fock （CSHF） approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the △（1236） resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon （N-N） interaction is based on Reid soft core （RSC） potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive △ particles. The number of △ ＇s can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. △ good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of △＇s are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.     

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.     

Accurate calculation of the potential energy curve and spectroscopic parameters of X~2Σ~+ state of ~(12)Mg~1H

High level calculations on the ground state of12Mg1 H molecule have been performed using multi-reference configuration interaction(MRCI) method with the Davidson modification. The core–valence correlation and scalar relativistic corrections are included into the present calculations at the same time. The potential energy curve(PEC) of the ground state, all of the vibrational levels and spectroscopic parameters are fitted. The results show that the levels and spectroscopic parameters are in good agreement with the available experimental data. The analytical potential energy function(APEF) is also deduced from the calculated PEC using the Murrell–Sorbie(M–S) potential function. The present results can provide a helpful reference for the future spectroscopic experiments or dynamical calculations of the molecule.     

Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

Dynamics of the CH4+ O(~3 P) → CH_3(ν= 0) + OH(■= 0) reaction

The dynamics of the ground-state reaction of CH_4+ O(~3P) → CH_3(ν = 0) + OH( ν= 0) have attracted a great deal of attention both theoretically and experimentally. This rapid communication represents extensive quasi-classical trajectory calculations of the vibrational distributions on a unique full-dimensional ab initio potential energy surface for the title reaction, at the collision energy of relevance to previous crossed molecular beam experiments. The surface is constructed using the all electrons coupled-cluster singles and doubles approach plus quasi-perturbative triple excitations with optimized basis sets. A modified Shepard interpolation method is also employed for the construction. Good agreement between our calculations and the available experimental results has been achieved, opening the door for accurate dynamics on this surface.     

Estimation of vector static magnetic field by a nitrogen-vacancy center with a single first-shell ~(13)C nuclear(NV–~(13)C)spin in diamond

We suggest an experimental scheme that a single nitrogen-vacancy(NV) center coupled to a nearest neighbor~(13) C nucleus as a sensor in diamond can be used to detect a static vector magnetic field. By means of optical detection magnetic resonance(ODMR) technique, both the strength and the direction of the vector field could be determined by relevant resonance frequencies of continuous wave(CW) and Ramsey spectrums. In addition, we give a method that determines the unique one of eight possible hyperfine tensors for an(NV–~(13) C) system. Finally, we propose an unambiguous method to exclude the symmetrical solution from eight possible vector fields, which correspond to nearly identical resonance frequencies due to their mirror symmetry about~(14)N–Vacancy–~(13) C(~(14)N–V–~(13) C) plane.     

Quasiparticle structure of superheavy nuclei in α-decay chains of ~(285)Fl and ~(291,293)Lv

Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belonging to the α-decay chains of ~(285)Fl and ~(291,293)Lv are calculated and compared with the available experimental data. Dependence of the splitting of the pseudospin doublets and of the energies of the unique parity neutron one-quasiparticle states on the mean field potential are discussed. As shown, the α-decay spectra could be different in the α-decay chain and at the direct production of the nucleus in a fusion reaction.     

Entrance Channel Mass Asymmetry Effects in Sub-Barrier Fusion Dynamics by Using Energy Dependent Woods-Saxon Potential

The present article highlights the inconsistency of static Woods-Saxon potential and the applicability of energy dependentWoods-Saxon potential to explore the fusion dynamics of ₂₂⁴⁸Ti+₂₈^58,60,64Ni, ₂₂⁴⁶Ti+₂₈⁶⁴Ni, ₂₂⁵⁰Ti+₂₈⁶⁰Ni, and ₉¹⁹F+₄₁⁹³Nb reactions leading to formation of different Sn-isotopes via different entrance channels. Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods-Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations. However, the predictions of one- dimensional Wong formula based upon energy dependent Woods-Saxon potential model (EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy. Therefore, the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.     

Entrance Channel Mass Asymmetry Effects in Sub-Barrier Fusion Dynamics by Using Energy Dependent Woods–Saxon Potential

The present article highlights the inconsistency of static Woods Saxon potential and the applicability of energy dependent Woods Saxon potential to explore the fusion dynamics of ~(48)_(22)Ti+~(58,60,64)_(28)Ni,~(46)_(22)Ti+~(64)_(28)Ti+~(50)_(22)Ti+~(60)_(28)Ni,and~(19)_9F+~(93)_(41)Nb reactions leading to formation of different Sn-isotopes via different entrance channels.Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations.However,the predictions of onedimensional Wong formula based upon energy dependent Woods Saxon potential model(EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy.Therefore,the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.     

Allowance for the shell structure of the 42100 Mo and 46110 Pd nuclei in the synthesis of 84200 Po, 88210 Ra, and 92220 U

The effect of the shell structure of colliding nuclei in calculating the entrance channel on the ensuing evolution of the product system is investigated. The entrance channel is calculated under the assumption of the nose-to-nose orientation of colliding nuclei. The following three reactions involving nuclei that are deformed in the ground state are considered: ₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄¹⁰⁰Po, ₄₂¹⁰⁰Mo + ₄₆¹⁰⁰Pd → ₈₈²¹⁰Ra, and ₄₆¹¹⁰Pd + ₄₆¹¹⁰Pd → ₉₂²²⁰U. The state of the system at the point of touching is determined by the results obtained by calculating the entrance reaction channel. The shape of the system is specified by three collective coordinates (deformation parameters). The evolution of collective coordinates of the system is described in terms of Langevin equations. The potential energy of the system of colliding nuclei is calculated with allowance for their shell structure. It is shown that allowance for individual features of interacting nuclei in the entrance channel of the fusion-fission reactions makes it possible to obtain, for the reactions being considered, cross sections for evaporation-residue formation that are closer to available experimental data than their liquid-drop counterparts.     

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.     

Systematic study of deformation effects on fusion cross-sections using various proximity potentials

The influence of static quadrupole and hexadecapole (positive & negative) deformation of targets are studied using eleven different versions of nuclear potentials. The height and position of the interaction barrier for the reactions induced by spherical projectile (¹⁶O) on the deformed targets such as ¹⁶⁶Er, ¹⁵⁴Sm and ¹⁷⁶Yb have been estimated. It is found that the nucleus-nucleus potential strongly depends on the value of the deformation parameters and orientation of the target. The experimental fusion cross-section of the reactions ¹⁶O + ¹⁷⁶Yb, ¹⁶O +¹⁶⁶Er and ¹⁶O +¹⁵⁴Sm are investigated by applyingWong’s formula using various parameterizations of the proximity potential as well as an assessment of the results of a multi-dimensional barrier penetration model (BPM). The fusion cross-sections by Prox 77, Prox 88, Prox 00, Prox 00DP, Denisov DP, Bass 80, CW 76 and AW 95 potentials are found to be better than the rest in comparison to experimental data.     

Fusion and peripheral reactions in the systems 16O + 148,152Sm at sub-barrier energies

Cross sections for fusion and peripheral reactions in the sub-barrier region obtained with the coupled-channel and equivalent-spheres methods are compared for the systems ¹⁶O + ^148,152 Sm. A barrier-like real potential plus a residual surface-imaginary potential is introduced as an alternative approach which allows the simultaneous fit of elastic, inelastic, fusion and peripheral reaction cross sections.     

16, 18O induced transfer reactions on122, 120Sn

The reactions¹²⁰Sn+72 MeV¹⁸O and¹²²Sn+74 MeV¹⁶O were investigated with time of-flightE-E-telescopes. Data are presented for all quasi-elastic reaction channels. The two neutron stripping and pickup reactions (¹⁸O,¹⁶O), (¹⁸O,²⁰O) and (¹⁶O,¹⁸O) are analyzed in detail. It is shown that these heavy ion induced two neutron transfer reactions proceed with essentially the same type of selectivity as the corresponding light ion induced reactions. The differential cross sections for transfer reactions leaving the^{120, 122}Sn nuclei in their 2⁺ first excited states are shown to be influenced by interference effects due to additional inelastic excitations.     

Dynamic Model Study of Fusion Reactions for 40,48Ca+90,96Zr

Based on the Improved Quantum Molecular Dynamics Model the fusion reactions of ^40,48Ca+^90,96Zr are studied by making a more rigorous treatment of the initial condition. The study shows that:(1) the calculated fusion cross sections for all four reactions of ^40,48Ca+^90,96Zr are in good agreement with experiment data; (2) the sub-barrier fusion for the neutron-rich reaction ⁴⁰Ca+⁹⁶Zr is ubstantially enhanced as compared with the other three reactions. In order to understand the reason why the sub-barrier fusion of the neutron-rich reaction ⁴⁰Ca+⁹⁶Zr is enhanced as compared with the non-neutron-rich reaction ⁴⁰Ca+⁹⁶Zr and that of the neutron-rich reaction ⁴⁸Ca+⁹⁶Zr is not enhanced, the further investigations are carried out, those are: the dynamic fusion barriers for four reactions, the relation between dynamic fusion barrier and nucleon transfer and the relation between nucleon transfer and corresponding reaction Q value. It has been found that positive Q value leads to the strong nucleon transfer which reduces the dynamic fusion barrier and enhances the sub-barrier fusion cross section.