A Reliability Analysis of Calculated Results for Odd-Even and Odd-Odd Nuclei in Relativistic Mean-Field Theory

We calculate the binding energies of Ni, Cu, Xe, Cs, Pt, Au, Np, Pu isotope chains using two interaction parameter sets NL-3 and NL-Z, and compared the relative errors of the even-even nuclei with those of odd-even nuclei and odd-odd nuclei. We find that the errors of binding energy of odd-even and odd-odd nuclei are not bigger than the one of even-even nuclei. The result shows that comparing with even-even nuclei, there is no systematic error and approximation in the calculations of the binding energy of odd-even and odd-odd nuclei with relativistic mean-field theory. In addition,the result is explained theoretically.     

Properties of universal functions in the Wigner mass formula for nuclei

The properties of the empirical functions in the Wigner mass formula for nuclei, which is based on SU(4) spin-isospin symmetry, are considered. It is shown that the origin of the odd-even effect in nuclei can be explained on the basis of an explicit analytic form of the second-degree Casimir operator for even-even and odd-odd nuclides and for nuclei of odd mass number. Experimental data in support of the proposed Wigner origin of the odd-even effect are presented.     

Description of the Superdeformed Bands of the Odd-Odd Nuclei in A～150 Region

With the supersymmetry scheme including many-body interactions, the global property and the ΔI=4 bifurcation in the superdeformed (SD) bands of odd-odd nuclei in A～150 mass region are investigated systematically. Good results for the γ-ray energies, the dynamical moments of inertia, and energy differences ΔE_γ-ΔE_γ^ref are obtained. It shows that this approach is quite powerful in describing not only the SD bands in even-even and odd-A nuclei but also those in odd-odd nuclei in the mass region.     

Intershell beta- and gamma-decay transition rates in the multiparticle shell model

In the framework of the two-group configuration model we obtain formulas for the reduced transition rates for beta and gamma transitions in even-even, odd-odd, even-odd, and odd-even nuclei. We explored dependencies of the transition rates on the occupancies of the involved subshells, as well as on the spin values of the initial and final states. The obtained formulas are useful for the qualitative spectroscopic analysis of experimental data, particulary in the regions of magicity, including the regions of the “remote” nuclei.     

Odd-Even Difference of Moment of Inertia of NuclearSuperdeformed States in A～190 Region

By fitting the E2 transition spectra of superdeformed bands in A～190 region, the coefficients of Bohr-Mottelson's I(I+1) expansion are determined and moments of inertia of band head are calculated out. All results show that the moments of inertia of odd-A nuclei are systematically larger than those of the neighboring even-even nuclei, and the moments of inertia of odd-odd nuclei are systematically larger than those of the neighboring odd-A nuclei. The odd-even difference of moment of inertia of nuclear superdeformed states is obvious.     

Statistical Treatment of Low-Energy Nuclear Level Schemes

The level density parameter and the back shift energy E1 are determined for nuclei with A-values across the whole periodic table from fits to complete level schemes at low excitation energy near the neutron binding energies.We find that the energy back shift E1 shows complicated behavior and depends on the type of the nucleus,even-even,odd mass,and odd-odd.The spin cut-off factor has also been investigated for nuclei mentioned above.The results arecompared with the previous results and different experimental data on level densities.     

用推广的Viola-Seaborg公式计算α衰变寿命

根据Audi等编评的最新核数据表, 对Z≥84, N≥128的核的α衰变实验寿命用Viola-Seaborg公式进行最小方差拟合, 得到一套新参数. 用新拟合参数计算的偶偶核的衰变寿命与实验寿命很好地符合, 平均偏差1.3倍.而对奇A和奇奇核理论寿命与实验寿命相差较远. 考虑到处于基态时奇A和奇奇核与偶偶核的主要区别在于自旋和宇称, 对Viola-Seaborg公式做了推广. 在公式中引入了离心势垒(即α粒子轨道角动量)对衰变寿命的影响. 由推广公式计算的奇A和奇奇核的寿命与实验寿命平均偏差2.5倍,最大偏差5—6倍.     

Description of α-decay half-lives of heaviest nuclei

The accuracy in describing α-decay half-lives T _α of heavy and superheavy nuclei is studied. A simple five-parameter phenomenological formula, expressing T _α as a function of the α-decay energy Q _α, is considered. It is found that such a formula can describe measured values of T _α within a factor of 1.3 for even-even, 2.1 for odd-even, 3.2 for even-odd, and 4.0 for odd-odd nuclei when measured values of Q _α are taken. This accuracy is decreased by a factor of about 4 when theoretical values of Q _α are used. The latter are obtained within a macroscopic-microscopic approach and reproduce the experimental values of Q _α of the same nuclei with an average accuracy of about 190 keV for even-even, 270 keV for odd-even, 260 keV for even-odd, and 330 keV for odd-odd nuclei. In the analysis, 201 nuclei with proton number Z = 84–111 and neutron number N = 128–161, with measured values of both Q _α and T _α, are taken. The text was submitted by the authors in English.     

Microscopic structure of fundamental excitations in N = Z nuclei

An extended mean-field model is presented that describes states of different isospin in odd-odd and even-even nuclei. Excitation energies of the T = 1 states in even-even as well as T = 0 and T = 1 states in odd-odd N = Z nuclei are calculated. It is shown that the structure of these states can be determined in a consistent manner when both isoscalar and isovector pairing collectivity as well as isospin projection (treated here within the isocranking approximation) are taken into account. In particular, in odd-odd N = Z nuclei, the interplay between quasiparticle excitations (relevant for the case of T = 0 states) and isorotations (relevant for the case of T = 1 states) explains the near degeneracy of these states.     

相对论平均场框架下偶-偶核奇-偶核计算误差的系统研究

在相对论平均场理论框架下, 用NL-3和NL-Z两组相互作用参数研究了4个同位素链²⁸Ni,⁵⁴Xe,⁷⁸Pt,⁹⁴Pu的基态性质. 发现,在Hatree近似下奇A核结合能理论计算值与实验值的相对误差反而普遍比偶偶核小. 这说明用相对论平均场理论,即使不考虑矢量介子的空间分量,仍可以比较可靠地计算奇A核结合能.     

On the origin of the Wigner energy

Surfaces of experimental masses of even-even and odd-odd nuclei exhibit a sharp slope discontinuity at N = Z. This cusp (Wigner energy), reflecting an additional binding in nuclei with neutrons and protons occupying the same shell model orbitals, is usually attributed to neutron-proton pairing correlations. A method is developed to extract the Wigner term from experimental data. Both empirical arguments and shell-model calculations suggest that the Wigner term can be traced back to the isospin T = 0 part of nuclear interaction. The structure of the Wigner energy is analyzed in terms of neutron-proton pairs of a given angular momentum and isospin. In particular, we find that the Wigner term cannot be solely explained in terms of correlations between the neutron-proton J = 1, T = 0 (deuteron-like) pairs.     

Beyond mean field approach to the beta decay of medium mass nuclei relevant for nuclear astrophysics

The Gamow-Teller strength distributions for the β decay of the ground state as well as the lowest excited states of the rp-process waiting point nuclei ⁶⁸Se and ⁷²Kr are obtained within the complex Excited Vampir variational approach using realistic effective interactions and a rather large model space. The shape mixing is consistently described for both the states in the even-even parent and the states in the odd-odd daugther nucleus. The influence of the shape mixing accounted by the different effective interactions used and comparison with the available data are presented. The possible influence of the decay of the lowest excited states of the parent nuclei in the astrophysical environment of X-ray bursts is discussed.Gamow-Teller strength distributions, β-decay half-lives, and β-delayed neutron emission probabilities for neutron-rich Zr nuclei are investigated for the first time within the complex Excited Vampir approach using a large model space. Comparison with available data and predictions relevant for the astrophysical r process are presented.     

A=100区奇奇核旋称反转

利用两准粒子加轴对称转子模型,对A=100质量区两个奇奇核¹⁰²Rh和^{9 8}Rh的旋称反转进行了研究.结果表明,在A=160,130,80三个质量区奇奇核的计算中 已得到证实的、可能的旋称反转机制(即低K空间n-p相互作用和科氏力的相互竞争),对 于A=100质量区奇奇核也是适用的.这暗示在不同质量区奇奇核可能存在一种普遍的旋称 反转机制. 关键词： 奇奇核 旋称反转 两准粒子加轴对称转子模型     

用BCS理论计算稀土核转动惯量的奇偶差

用BCS理论计算了稀土区偶偶核和奇A核的转动惯量.计算结果表明,尽管转动惯量的计算值系统地小于实验值,但实验上观测到的转动惯量奇偶差的大幅度变化能够用BCS理论定性地描述. 这个结论与人们普遍认为的BCS理论给出的奇A核转动惯量应比相邻的偶偶核基态转动惯量大15%的看法相悖,但却证实了20多年以前Gregory和Volkov等人得出的结论,有助于人们在BCS平均场理论框架下理解正常形变核中出现全同带的现象.     

Gamma band in transitional nuclei

The obstinate difficulty of the Davydov-Filippov model in obtaining the correct bunching of states in the γ-band of even-even mass transitional nuclei is explained in an extended version of the model which includes the 2-qp excitations and also the coupling between the 0- and 2-qp states. The important result is that the 0–2qp coupling for even spin states is much stronger than that for odd ones. Due to this effect the bunching of even-odd spin states in the Davydov-Filippov model is destroyed producing either an opposite bunching (now odd-even spin states) or a band wherein the states have similar energy spacings.     

Pairing rotations and separation energies

Recent experiments exhibit a strong regularity of the two-neutron (proton) binding energies in superconducting nuclei. Using BCS calculations by Soloviev and by Kisslinger and Sorensen for the rare earth and tin region, respectively, we show that the pairing rotational model accounts for this behaviour provided the deformation does not change appreciably when two neutrons or protons are added to the system. The model relates the degree of pairing to the ground state energies of neighbouring even-even nuclei and supplements the information coming from the odd-even effect.     

Signature and parity splitting in the rotational bands and the chiral bands. Double-minimum potential model

The effects of signature and parity splitting in nuclear spectra and the properties of the chiral bands are analyzed basing on a one-dimensional Schrödinger equation with a double-minimum potential. Rotational bands in odd axial and triaxial nuclei, alternating parity bands in even-even nuclei and the chiral bands in odd-odd nuclei are considered. The results obtained are discussed.     

T = 0 versusT = 1 pairing in 0(36) limit of IBM-4 for heavyN = Z nuclei

In theO(36) limit of the interacting boson model including spin-isospin degrees of freedom (IBM-4), starting with a group chain that preservess andd boson spins and isospins together with a simple mixing hamiltonian, it is shown that the model generates, for heavyN =Z nuclei, even-even to odd-odd staggering in the number ofT = 0 pairs in the ground states for moderate difference in the basicT = 0 andT = 1s-boson pair energies; the staggering disappears when the energy difference is large.