Shell corrections for finite depth deformed potentials. II

Energy shell corrections are derived for the nucleus²³⁸U by means of the new shell correction technique developed for finite depth single-particle potentials and exploiting only the bound states. The results are compared with those obtained by the traditional method.     

利用电子结构数据拟合H2分子的电子壳模型势函数参数

电子壳模型势函数在离子晶体的原子级计算机模拟中有广泛应用,其势参数主要通过拟合晶体的实验数据或电子结构数据得到.提出了通过拟合双原子分子的量子化学从头计算电子结构数据来获得该势函数的方法,并由H₂分子的电子结构数据建立了H原子间的电子壳模型势函数.此外,还应用该势函数对H⁺₂分子离子进行了计算.该势函数拟合方案更适合于共价键型的分子. 关键词： 电子壳模型势 参数拟合 共价键 2分子')" href="#">H₂分子     

Exciton level densities with spin and parity based on random matrix model

Level densities for fixedJ ^π and the exciton number are evaluated for closed shell nuclei⁴⁰Ca and²⁰⁸Pb. The single particle spectra and wave functions are generated by Woods-Saxon potentials. The effects of the residual interaction are taken into account statistically by the method of generating function and Grassmann integral. The matrix elements for the residual interaction are assumed to be random variables with Gaussian distributions whose second moments are calculated by using a zero range interaction. The second moments are evaluated for fixedJ ^π by ignoring the Pauli principle between active nucleons and the spectator. This approximation is shown numerically to be very good. The partial level densities are calculated using the second moments as well as independent particle model spectra. The resulting level densities spread over wider energy ranges, have a smoother energy dependence and are enhanced at low energies compared with the independent particle model densities, although the total level densities do not differ by much.     

The effect of density dependent Av18 effective interaction on the ground state properties of heavy closed shell nuclei

The channel-dependent Argonne Av₁₈ effective two-body interactions (CDEI) which are generated through the lowest order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av₁₈ bare nucleon–nucleon potential are used to calculate the ground state properties of heavy closed shell nuclei such as ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb. The harmonic oscillator basis, and the local density approximation (LDA) are applied to create the relative and the center of mass dependent effective two-body potential. We get more binding with respect to the similar calculation with the Reid types potentials. It is tried to omit the LDA and perform full calculation with the Av₁₈CDEI for light nuclei. The results indicate that the LDA works quite well. It is also shown that in case of heavy closed shell nuclei and unlike our previous report with Reid68Day   interaction, the contributions of higher partial waves (J>2$J>2$) are very important for the calculations with Av₁₈ potential and we get reasonable agreement between our calculated binding energies and RMS radii, with those predicated by the others methods, and the experimental data. Finally, the various aspects of channel and density dependent two-body effective interactions are discussed.     

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.     

The determination of low lying ionization potentials of BN,BN+ and B2N and photodetachment energies of BN− and B2N− using the multiconfigurational spin tensor electron propagator method

The multiconfigurational spin tensor electron propagator method (MCSTEP) is a Green's function based approach for directly calculating accurately the low lying ionization potentials (IPs) and electron affinities (EAs) of highly correlated closed and open shell molecules. The MCSTEP method has been employed to determine the vertical ionization potentials and adiabatic ionization potentials of BN, BN⁺ and B₂N and the photodetachment energies (PDEs) of BN^? and B₂N^?. These systems have had wide industrial applications and have recently been the focus of considerable attention. For BN, the lowest few MCSTEP vertical and adiabatic ionization potentials are in good agreement with other theoretical values previously reported. For BN^? the MCSTEP PDEs are in good agreement with the experimental values and previous theoretical results. MCSTEP vertical and adiabatic IPs for BN⁺ differ for some states compared with other previously reported theoretical values. This is believed to be the first time that the vertical and adiabatic IPs of B₂N have been reported. The MCSTEP PDEs of B₂N are in very good agreement with the experimental values.     

The effect of Fermi momentum cutoff on the binding energy of closed shell nuclei in the LOCV framework

The ground state binding energies of the light symmetric closed-shell nuclei, i.e., ⁴He, ¹²C, ¹⁶O and ⁴⁰Ca and the heavy asymmetric ones, i.e., ⁴⁸Ca, ⁹⁰Zr and ¹²⁰Sn are calculated in the harmonic oscillator (HOS) basis, by imposing the relative Fermi momentum cutoff of two point-like interacting nucleons on the density dependent average effective interactions (DDAEI). The DDAEI are generated through the lowest order constrained variational (LOCV) method calculations for the asymmetric nuclear matter with the operator and the channel dependent type bare nucleon-nucleon potentials, such as the Argonne $Av_{18}^{j_{\max } = 2}$ and the Reid soft core, Reid68, interactions. In the framework of harmonic oscillator shell model, the cutoff is imposed by defining the maximum value of the relative quantum numbers (RQN_max) in two ways: (1) The RQN_max of the last shell and (2) the RQN_max of each shell, in the ground state of the nucleus. It is shown that present results on the binding energies and the root means square radius are closer to the corresponding experimental data than, our previous works with the same DDAEI potentials, but without the cutoff constraint. However, for the light symmetric nuclei, the second scheme gives less binding energy and larger root mean square radius compare to the first one. While the situation is reversed for the heavier nuclei.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

The contribution of nuclear inelastic excitation to the optical potential for heavy ions

Using the plane-wave approximation we derive analytical expressions for both the real and imaginary parts of the polarization potential arising from nuclear inelastic scattering. These potentials and the resulting elastic and inelastic cross sections are compared with exact coupledchannel calculations for ¹³C on ⁴⁰Ca at 68 MeV. The agreement, for the most part, is good. We also briefly discuss the numerical non-local potentials for this system and the imaginary polarization potential for ¹⁶O on ²⁰⁸Pb at 104 MeV.     

Quartet states in the sd and fp shells

Two-proton-two-neutron correlations are studied in psd and fp shell nuclei in the frame of the aligned scheme approximation. Four-particle rotational states are obtained in terms of linear combinations of projected aligned Slater determinants and the resulting excitation energies and wave functions are compared with those of elaborate shell-model calculations. The close agreement obtained both for single j-shell and complete shell configuration spaces shows that rotational or quasi-rotational states are almost entirely generated by aligned configurations. The lowest four-particle states obtained in one j-shell can be explained as the rotational spectrum of an oblate intrinsic state. The lowest four-particle states of ¹⁶O, ²⁰Ne, ⁴⁴Ti and ⁶⁰Zn, calculated in a major shell, correspond to the rotational spectrum of a prolate intrinsic state and fit the existing data. Higher states are the result of a mixed deformation.     

Shell-model calculation of the spectral function for l=0 proton states in12C

The spectral function for the removal of l=0 protons in¹²C is calculated within the framework of the shell model. The techniques used in the calculation exploit, in a novel fashion, certain features of the Lanczos method used in obtaining energies and wave-functions. G ross and fine details of the resulting strength distributions are compared against the results from¹²C(e, e′p)¹¹B experiments.     

Mytilus galloprovincialis as a bioindicator of environmental conditions: the case of the eastern coast of the Adriatic Sea

The marine mussel Mytilus galloprovincialis lives attached to the surface of hard substrata, where its exposure and relative immobility allow it to record changes in ambient seawater. It is also found along the eastern coast of the Adriatic Sea. Oxygen and carbon isotopes were analysed for calcite and aragonite in separate shell layers, while major, minor and trace elements in the bulk shell were analysed to evaluate environmental conditions such as the temperature of carbonate deposition, freshwater influence and locations of anthropogenic pollution. We found that, on average, aragonite is enriched by 1.1‰ in ¹³C and by 0.2‰ in ¹⁸O compared with calcite. The calculated temperatures for M. galloprovincialis shell growth from the investigated area range from 13.4 to 20.9 °C for calcite and from 16.6 to 23.1 °C for aragonite. According to the δ¹⁸O and δ¹³C values of shell layers, we can separate the investigated area into three locations: those with more influence of freshwater, those with less influence of freshwater and those with marine environments. The highest concentrations of manganese, barium, boron, arsenic, nickel and chromium were observed in shells from Omi?, Ba?vice and Zabla?e (Central Adriatic) and Sv. Ivan (South Adriatic), where chemical and heavy industries are located and where sewage is known to be discharged into coastal areas. The highest concentrations of zinc, lead and copper were measured in samples from Pula, Rijeka and Gru?, where there are also ports in addition to industry.     

Isobar configurations in closed shell nuclei

Explicit expressions for one- and two-N¹ isobar configurations in closed shell nuclei have been derived in the impulse approximation and applied to ⁴He and ¹⁶O. Conventional transition potentials with π- and ?-exchange have been used and the influence of potential regularization and short-range correlations have been studied. The dominant isobar configurations are found to be the one- and two-Δ components and originate from two-nucleon pairs in a relative S-state. The probability for finding a nucleon as a Δ-isobar is about 4.5% in ⁴He and about 3.2% in ¹⁶O. These numbers should be considered as upper limits due to uncertainties in off-shell effects of the transition potentials.     

Effective nucleus-nucleus potentials derived from the generator coordinate method

The equivalence of the generator coordinate method (GCM) and the resonating group method (RGM) and the formal equivalence of the RGM and the orthogonality condition model (OCM) lead to a relation connecting the effective nucleus-nucleus potentials of the OCM with matrix elements of the GCM. This relation may be used to derive effective nucleus-nucleus potentials directly from GCM matrix elements without explicit reference to the potentials of the RGM. In a first application local and l-independent effective potentials are derived from diagonal GCM matrix elements which represent the energy surfaces of a two-centre shell model. Using these potentials the OCM can reproduce the results of a full RGM calculation very well for the elastic scattering of two α-particles and fairly well for elastic ¹⁶O-¹⁶O scattering.     

Mass transport in anharmonic potentials

We investigate the effect of nuclear shell structure on the mass transport in low-energy heavy-ion collisions. The shell-correction energy leads to anharmonic driving potentials and thus, to nonlinear drift coefficients in the Fokker-Planck equation. Results for²³⁸U (7.42 MeV/nucleon)+²³⁸U are presented. The drift towards the closed Pb-shell enhances the fluctuations in the mass transport and provides an explanation for the large variances found experimentally. Local maxima in the mass distribution at the shell minima disappear due to the temperature dependence of the driving potential.     

Exactly projected coupled-channel potentials

Polarization effects in heavy-ion potentials are investigated in the coupled-channel framework. Particular emphasis is placed on a study of the effects of a truncation of the full Hubert space. The formalism, based on Feshbach's projection method, is applied to inelastic ¹⁶O + ¹⁶O scattering. The resulting effective diagonal and coupling potentials are discussed. It is shown that the present theory leads naturally to different potentials for different channels as well as to modified coupling strengths.     

The (3He,n) reaction on 16O and 18O

The (³He, n) reaction on ¹⁶O and ¹⁸O has been used to study low-spin states in ¹⁸Ne and ²⁰Ne up to E_x ≈ 8 and 20 MeV, respectively. The measured neutron angular distributions have been analysed using DWBA. By a comparison with shell-model calculations in the (s, d) shell it is found that most of the two-proton transfer strength can be explained within that shell. Important contributions, however, from the (f, p) shell in low-lying negative parity states are also present.     

Thomas-Fermi theory for atomic nuclei revisited

The recently developed semiclassical variational Wigner-Kirkwood (VWK) approach is applied to finite nuclei using external potentials and self-consistent mean fields derived from Skyrme interactions and from relativistic mean field theory. VWK consists of the Thomas-Fermi part plus a pure, perturbative ?² correction. In external potentials, VWK passes through the average of the quantal values of the accumulated level density and total energy as a function of the Fermi energy. However, there is a problem of overbinding when the energy per particle is displayed as a function of the particle number. The situation is analyzed comparing spherical and deformed harmonic oscillator potentials. In the self-consistent case, we show for Skyrme forces that VWK binding energies are very close to those obtained from extended Thomas-Fermi functionals of ?⁴ order, pointing to the rapid convergence of the VWK theory. This satisfying result, however, does not cure the overbinding problem, i.e., the semiclassical energies show more binding than they should. This feature is more pronounced in the case of Skyrme forces than with the relativistic mean field approach. However, even in the latter case the shell correction energy for e.g., ²⁰⁸Pb turns out to be only ∼−6 MeV what is about a factor two or three off the generally accepted value. As an ad hoc remedy, increasing the kinetic energy by 2.5%, leads to shell correction energies well acceptable throughout the periodic table. The general importance of the present studies for other finite Fermi systems, self-bound or in external potentials, is pointed out.     

Bivariate distributions in statistical spectroscopy studies

Orthogonal polynomials in two variables, defined by a bivariate density function, are used to derive series expansions for expectation values with respect to the two variables. The convergence of the resulting polynomial expansion is due to the action of a central limit theorem. The shell model results for fixedE, J occupancies in (ds) ^m=5T=1/2 space are compared with the polynomial expansion results and the agreement is good.