Shell-model calculations on Ni and Cu isotopes

Binding energies, excitation energies and spectroscopic factors have been calculated for^57–67Ni and^58–68Cu in an unrestricted (2p_3/2, lf _5/2,2p_1/2) shell-model space. The effective two-body matrix elements are obtained from the modified surface delta interaction (MSDI) and from a least-squares fit to experimental binding and excitation energies (ASDI). The average deviation between about 100 experimental and calculated energies is 0.14MeV for MSDI and 0.08 MeV for ASDI. Excitation energies of high-spin states are given also. Spectroscopic factors have been calculated for all single-nucleon transfer reactions on stable Ni or Cu targets leading to Ni or Cu isotopes. For spectroscopic factors larger than 0.4 the average deviation between theory and experiment is about 30%. The experimentally observed and calculated spectroscopic strengths are compared by using sum rules and are found to be consistent. An extensive compilation has been made of experimental data on energies,J ^π assignments and spectroscopic factors.     

Shell-model calculations inA=28–32 nuclei

Shell-model calculations for positive-parity levels of A=28–32 nuclei have been performed in a 1d_5/2 2s_1/2 1d_3/2 configuration space. Configuration mixing of at most 250 lowest-lying pure configurations for each (A, J, T) set was taken into account. By a variation of the four effective interaction (MSDI) parameters and three single-particle energies a search was made for the best fit of the calculated energies to the experimental values. The average deviation between theory and experiment for the energies of the 110 fitted levels is 0.44 MeV. By adjusting all the 63 two-body matrix elements (ASDI) and the three single-particle energies, the average deviation of the binding energies was reduced to 0.16 MeV. For the lowest 10–15 levels in all A=28–32 nuclei a one to one correspondence exists between theory and experiment. Electromagnetic transition strengths were calculated both with MSDI and with ASDI wave functions. The ASDI wave functions reproduce the experimental E2 data much better than the MSDI wave functions. For the M1 transition strengths only a minor improvement has been achieved.     

Shell-model calculations in the A = 5 system

The A = 5 structure problem is solved within the framework of the nuclear shell model. The model states are expanded on a basis of properly symmetrized translationally invariant harmonic oscillator eigenstates including states of up to 5(kh)gw of oscillator excitation. Ground and excited levels of the ⁵H, ⁵He, ⁵Li and ⁵Be systems are presented. The two-body interaction is based on the Sussex matrix elements. Model results are in good agreement with measured A = 5 level positions. The model $\text{T =}\text{3}\text{2}$ results lead to a quartet of levels, whose positions are given roughly by the isobaric multiplet mass equation.     

Shell-model calculations with Woods-Saxon wave functions in O and Ca

Two-particle states of ¹⁸O and ⁴²Ca are calculated within the shell model. The nuclear cores are represented by Woods-Saxon potentials, and for the residual interaction, central forces of Yukawa and Gaussian types are used. The wave functions for the low-lying states except for the O₂⁺ and 2₂⁺ states in ⁴²Ca are obtained, and the calculated energy spectra are in good agreement with experiments. Also E2 transitions are calculated and compared with experimental results.     

IBA calculations on the even-even Pt isotopes

By performing least-squares-fit calculations on the energy spectra of the even-even ^186–196Pt isotopes, the IBA model I and the IBA model II are compared on an equal footing. It is found that both model I and model II can fit energy spectra and absolute B(E2) transition rates reasonably well. Model II shows a distinct improvement in the energy spectra of β-bands of heavier nuclei in the isotope series. It is suggested that for regions far from the closed shells model I may be used to simulate model II as a useful phenomenological probing tool.     

Microscopic calculations for Be isotopes within real-time evolution method

The European Physical Journal A - This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A,...     

The interacting boson model: Microscopic calculations for the mercury isotopes

Microscopic calculations of the parameters of the proton-neutron interacting boson model (IBM-2) appropriate to the even Hg isotopes are reported. The calculations are based on the Otsuka-Armia-Iachello boson mapping procedure, which is briefly reviewed. Renormalization of the parameters due to exclusion of the l=4 g boson is treated perturbatively. The calculations employ a semi-realistic shell-model Hamiltonian with no adjustable parameters. The calculated parameters of the IBM-2 Hamiltonian are used to generate energy spectra and electromagnetic transition probabilities, which are compared with experimental data and with the result of phenomenological fits. The overall agreement is reasonable with some notable exceptions, which are discussed. Particular attention is focused on the parameters of the Majorana interaction and on the F-spin character of low-lying levels.     

Exploratory coupled channels calculations for loosely bound carbon isotopes

We have investigated the loosely bound halo candidates ¹⁷C and ¹⁹C in a neutron+core coupling model. A deformed Woods-Saxon potential is used for the neutron-core interaction and the coupled channels equations are solved with Sturmian expansions of the relative motion wave functions for experimental one-neutron separation energies. The r.m.s. matter radii, longitudinal momentum distributions, E1 strength functions, neutron stripping cross sections and electromagnetic dissociation cross sections are calculated. Their sensitivity to the structural assumptions is explored. Available data does not allow final conclusions to be drawn for ¹⁹C but an assessment of the possible character of ¹⁷C and ¹⁹C is made, and in particular, of the role of s-orbital motion between halo-neutron and core.     

Shell-model calculations for the semi-magic nucleus ~(85)Br and systematic features of the N = 50 odd-A isotones

Level structures of ~(85)Br have been investigated using the shell-model code nushellx within a large model space containing the neutron-core excitations across the N = 50 closed shell. The calculated results have been compared with the available experimental data. Reasonable agreement between the experimental and calculated values is obtained, which indicates that the neutron-core excitations are essential to reproduce the level structures of ~(85)Br. The systematic features of neutron-core excitations in the N = 50 isotones are investigated.     

Shell-model Coulomb energies

Analytical expressions have been derived for the total Coulomb energies, for isoscalar, isovector and isotensor Coulomb energies, and for Coulomb energy differences of nuclei with protons and neutrons in equivalent and in different major shell regions. The approach is related to earlier theoretical treatments of Carlson and Talmi and of Hecht. A simple A-dependence is assumed to account for the increase in radius. Introducing average matrix elements for the Coulomb interactions between valence-valence, valence-core, and core-core protons in each of the six major shell regions as adjustable parameters, a global fit with 21 parameters to 288 experimental Coulomb displacement energies with 4 < A < 240 gives good agreement with a standard deviation of σ = 45 keV. The interaction energies display discontinuities particularly at major proton shell crossings, and they generally decrease within shells less rapidly than $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$. The average decrease, however, follows approximately an $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ dependence which explains the success of Coulomb energy equations based on liquid-drop models.     

Fine-grid calculations for stellar electron and positron capture rates on Fe isotopes

The acquisition of precise and reliable nuclear data is a prerequisite to success for stellar evolution and nucleosynthesis studies. Core-collapse simulators find it challenging to generate an explosion from the collapse of the core of massive stars. It is believed that a better understanding of the microphysics of core-collapse can lead to successful results. The weak interaction processes are able to trigger the collapse and control the lepton-to-baryon ratio (Y _e ) of the corematerial. It is suggested that the temporal variation of Y _e within the core of a massive star has a pivotal role to play in the stellar evolution and a fine-tuning of this parameter at various stages of presupernova evolution is the key to generate an explosion. During the presupernova evolution of massive stars, isotopes of iron, mainly ^54–56Fe, are considered to be key players in controlling Y _e ratio via electron capture on these nuclides. Recently an improved microscopic calculation of weak-interaction-mediated rates for iron isotopes was introduced using the proton-neutron quasiparticle random-phase-approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic state-by-state calculation of stellar capture rates which greatly increases the reliability of calculated rates. The results were suggestive of some fine-tuning of the Y _e ratio during various phases of stellar evolution. Here we present for the first time the fine-grid calculation of the electron and positron capture rates on ^54–56Fe. The sensitivity of the pn-QRPA calculated capture rates to the deformation parameter is also studied in this work. Core-collapse simulators may find this calculation suitable for interpolation purposes and for necessary incorporation in the stellar evolution codes.     

Effective boson number calculations in Mo and Cd isotopes

The effects of the neutron-proton interaction on the low-lying levels of Mo and Cd isotopes have been considered in the frame of the IBA-1 model by taking into account an effective boson number (N _eff). Both an empirical procedure based on previous IBA-2 mixing calculations and theN _p N _n scheme provide comparableN _eff values. Level spectra and electromagnetic transitions are investigated. The results support the idea that IBA-1 calculations with a suitableN _eff can largely simulate IBA-2 mixing calculations, taking advantage of simplicity and a smaller number of parameters.     

Interaction of neutrons with zinc and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured for elemental Zn,Zn-compounds and on isotopicly enriched samples for neutron energies from 0.5 meV up to 143 keV using different techniques. From the experimental data the following quantities were obtained:

the coherent scattering lengths (b in fm) of Zn (5.689±0.014);⁶⁴Zn (5.23±0.04);⁶⁶Zn (5.98±0.05);⁶⁷Zn (7.58±0.08;b ₊=9.4±0.5/5.8±0.5;b _?=5.0±0.7/10.1±0.7);⁶⁸Zn (6.04 ±0.03);

the potential scattering radii (R′ in fm) of Zn (6.2±0.2),⁶⁴Zn (6.0±0.3) and⁶⁶Zn (6.2 ±0.3);

the absorption cross sections (σ _γ at 0.025 eV in barn) of Zn (1.11±0.02);⁶⁴Zn (1.1 ±0.1) and⁶⁶Zn (0.62±0.06).

Derived quantities are the “zero energy” scattering cross sections (σ ₀ in barn) for Zn (4.128±0.010) and⁶⁷Zn (7.8±0.3) and the incoherent bound cross sections of Zn (0.061 ±0.023) and⁶⁷Zn (0.6±0.4). In the epithermal region the Zn-cross section can be described by introduction of two strong bound levels of⁶⁷Zn+n for which estimated parameters are given.     

Shell-model calculation with Hartree-Fock condition

Giant resonances and spectroscopic factors of ¹⁶O are studied in the framework of the shell model with (0 + 2)ħω model space. It is found that the Hartree-Fock condition is crucial in order to obtain reasonable excitation energies of giant resonances in ¹⁶O. The calculated spectroscopic factors in ¹⁵N are quenched only by 10% due to the coupling to 1p-2h states. The spectroscopic factor of the s-state in ¹¹B is also discussed.     

探索原子核结构的对称性主导无芯壳模型计算(英文)

揭示隐藏于复杂中的简单性相关的特殊对称性是核理论研究的"圣杯",回顾了其探索历史和当前利用高性能计算设备及应用数学方法进行的从头计算无芯壳模型研究。作为对称性主导无芯壳模型（SA-NCSM）计算的实例,通过对轻核和中重质量区核素的能谱计算及与实验结果的比较,清晰地展示了群论在揭示这些当今最先进计算手段得到结果中所起的重要作用。作为SA-NCSM的有趣推广,从头引入形变的新方法提供了解决所有以探索原子核的集体性质为目的的从头计算方法都要面对的模型空间维数呈组合数增长的处理手段,并且该方法使本理论能用于描述重核及奇特核。Exploiting special symmetries to unmask simplicity within complexity that remains the "holy grail" of nuclear theory is re-examined within the framework of its historical context and current ab initio nocore shell-model approaches that exploit high-performance computing resources and applied math methodologies. Examples using the symmetry-adapted no-core shell model (SA-NCSM) that clearly demonstrate the important role group theory plays in this evolving story will serve to elucidate current state-of-the-art developments in this arena, including comparisons of excitation spectra and transition rates with experimental results for light and medium-mass nuclei. An interesting extension of the SA-NCSM, an advanced method with a novel twist that enables one to incorporate deformation from the onset, will be proffered as a further way to manage the combinatorial growth of model-space dimensionalities that remains the nemesis of all theories that seek an ab initio understanding of nuclear collectivity, and in so doing extends applicability of the theory to heavier and more exotic nuclear species.     

Theoretical calculations of electron densities in zinc chalcogenides and in zinc fluoride

Self-consistent, non-relativistic Hartree-Fock calculations on a finite cluster of atoms with zinc at the center have been performed on the zinc blende compounds ZnTe, ZnSe, ZnS, on ZnO (wurtzite structure), ZnO (NaCl structure), and on ZnF₂ (rutile-type structure) to obtain changes in s electron density (0) at the⁶⁷Zn nucleus. We solved the eigenvalue problem of the dynamic matrix to calculate the second-order Doppler shiftS _SOD using appropriate force constant models and determined the isomer shiftS from the measured center shift for each compound. Our calculations clearly show the importance of the covalency of the Zn-ligand bond for the origin ofS and fully corroborate the experimental linear correlations between decreasingS values and increasing electronegativity of the ligands. The most important contribution to (0) comes from the Zn(4s) electrons, with a smaller but significant contribution from the Zn(3s) electrons. For the change of the mean-square nuclear charge radius for the Mössbauer transition in⁶⁷Zn, we obtain r ²=+(13.9±1.4) × 10^–3 fm².     

The (t,p) reaction on the zinc isotopes

Multichannel spectrograph studies of the (t, p) reaction on the Zn isotopes have provided energy-level data, cross-section measurements and many new spin and parity determinations. The systematics of the energy spectra of the even zinc isotopes are discussed.