Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

The positive-parity yrast bands of ^{79, 81, 83, 85, 87, 89}Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.     

Study of neutron-rich Mo isotopes by the projected shell model approach

The projected shell model (PSM) calculations have been performed for the neutron-rich even–even ^102?110Mo and odd—even ^103?109Mo isotopes. The present calculation reproduces the available experimental data on the yrast bands. In case of even–even nuclei, the structure of yrast bands is analysed and electromagnetic quantities are compared with the available experimental data. The g-factors have been predicted for high spin states. For the odd-neutron nuclei, the structures of yrast positive- and negative-parity bands are analysed and found to be in reasonable agreement with the experiments for ^103?107Mo. The disagreement of the calculated and observed plots for energy staggering quantity clearly establishes the occurrence of sizable triaxiality in ^103,105Mo and also predicts a decrease in the quantum of triaxiality with increasing neutron number and angular momentum for odd mass neutron-rich Mo isotopes.     

Systematic study of odd-mass 151-161Pm and 154,156Pm isotopes using projected shell model

Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass ^151-161Pm and odd-odd ^154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.     

Microscopic study of yrast bands and backbending anomaly in 78-82Kr isotopes

The yrast spectra of ^78-82Kr are studied by using the projected shell model (PSM) approach. The energy states are obtained by taking oblate as well as prolate quadrupole deformations for ^78-82Kr. The structure of yrast states and backbending phenomena are investigated. The theoretical results predict low-lying states in ^{78, 82}Kr to be oblate and coexistence of oblate-prolate shapes for ⁸⁰Kr. The B(E2) transition probabilities and g-factors are obtained and compared with the available experimental data.     

Microscopic study of positive-parity yrast bands of 224−234Th isotopes

The positive-parity bands in ^224???234Th are studied using the projected shell model (PSM) approach. The energy levels, deformation systematics, B(E2) transition probabilities and nuclear g-factors are calculated and compared with the experimental data. The calculation reproduces the observed positive-parity yrast bands and B(E2) transition probabilities. Measurement of B(E2) transition probabilities for higher spins and g-factors would be a stringent test for our predictions. The results of theoretical calculations indicate that the deformation systematics in ^224???234Th isotopes depend on the occupation of low k components of high j orbits in the valence space and the deformation producing tendency of the neutron–proton interaction operating between spin orbit partner (SOP) orbits, the [(2g_9/2) _π –(2g_7/2) _ν ] and [(1i_13/2) _π –(1i_11/2) _ν ] SOP orbits in the present context. In addition, the deformation systematics also depend on the polarization of (1h_11/2) _π orbit. The low-lying states of yrast spectra are found to arise from 0-quasiparticle (qp) intrinsic states whereas the high-spin states turn out to possess composite structure.     

Projected shell model study of yrast bands in even-even 100–118Pd isotopes

The projected shell model (PSM) study of ^100?C118Pd nuclei is carried out. The reliability of the ground-state wave functions is checked by reproducing yrast spectra and electromagnetic properties. The results of calculations indicate that the observed deformation systematics in ^100?C118Pd isotopes depends on the increase of occupation probability of (1h _{11/2 ??} ) orbit and the deformation producing tendency of n-p interaction operating between Spin Orbit Partner (SOP) orbits (d _5/2)_???(d _3/2) _?? and (g _9/2)_???(g _7/2) _?? . Beside this, the results on band diagrams show that the yrast spectra in Pd isotopes do not arise from a single intrinsic state only but also from multi-quasiparticle states.     

E2 transition andQ_{J^ + } systematics of even mass tellurium nucleisystematics of even mass tellurium nuclei

The yrast spectra withJ _max ^π = 6⁺,B(E2) transition probabilities and $Q_{J^ + } $ values are calculated for even-even tellurium isotopes by carrying out Hartree-Fock-Bogoliubov (HFB) anstaz employing a pairing-plus-quadrupole-quadrupole effective interaction operating in a reasonably large valence space outside the¹⁰⁰Sn core. Our calculations reproduce qualitatively the observed parabolic systematics of the low-lying yrast states as a function of mass number for tellurium isotopes. The results onB(E2) transition probabilities predict a dip in the isotopes^114,118,124Te which might be construed to imply different structures for^114,118,124Te as compared to their neighbours. Besides this, our results also reveal that both the HFB technique as well as the quadrupole-quadrupole-plus-pairing model of the two body interaction are fairly reliable in this mass region.     

丰中子锶同位素的投影壳模型研究

利用考虑跨壳激发的投影壳模型（PSM）方法,研究了质子数Z=38、中子数N=63和64大形变丰中子101,102Sr同位素的结构性质。主要计算了转动谱、转动惯量和电磁跃迁性质等（如B（E2）和g因子）,并与相应的实验数据进行系统比较和相关的理论预言。结果表明,PSM可以利用理论计算的能带图解释101,102Sr同位素的转动惯量、电磁跃迁随自旋的变化,分析晕带的结构。PSM理论可以很好地再现实验结果,说明PSM方法及其采用的有效相互作用可以外推研究丰中子核区101,102Sr同位素的原子核结构。对于101,102Sr同位素,核子开始填布质子g_9/2和中子h_11/2轨道,通过更为仔细地分析能带图中来自质子g_9/2和中子h_11/2轨道对各转动带的组态成分的贡献,清晰地表明丰中子核结构性质对不同核子填布的依赖。Recently, we have carried out systematically studies on the structural properties of proton number Z=38, neutron number N=63 and 64 neutron-rich isotopes 101,102Sr by using the projected shell model (PSM) with consideration of cross shell excitation. The rotation spectra, the moment of inertia and the electromagnetic transition properties (such as B(E2) and g-factor) are calculated and compared with the corresponding experimental data in this paper. Furthermore, more high spin states are predicted in the calculation and expected to be confirmed experimentally. The results show that the PSM can not only well analyze the structural properties of yrast bands in 101,102Sr but also interpret the variation of the moment of inertia, electromagnetic transition with spins in terms with the theoretical band diagram. The good agreement with the experimental data suggests that the PSM with the adopted effective interactions can be generalized to study the nuclear structure of 101,102Sr isotopes in neutron-rich mass region. For 101,102Sr isotopes, the nucleons begin to fill proton g_9/2 and neutron h_11/2 orbital, the dependence of nuclear structure and properties on the different orbital occupies is described by carefully analyzing the contribution from proton g_9/2 and neutron h_11/2 orbital to the configuration of rotational bands in band diagram.     

On the parity of the yrast 8+ level in138Ce and an anomaly in theB(E2) values

On the basis of conversion electron andγ-angular distribution measurements new spin and parity assignments in¹³⁸Ce have been made. They lead together with the already known lifetime of the 10⁺ yrast state whose parity was unclear to an extremely low transition probability of the 10⁺→8⁺ transition. A comparison with neighbouring even isotopes is made.     

Microscopic study of low-lying yrast spectra and deformation systematics in neutron-rich <Superscript>98–106</Superscript>Sr isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A = 98–106 strontium isotopes. In this framework, the yrast spectra with J ^Π ≥ 10⁺, B(E2) transition probabilities, quadrupole deformation parameter and occupation numbers for various shell model orbits have been obtained. The results of the calculation for yrast spectra give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in Sr isotopes. Besides this, it is also found that the simultaneous polarization of p _3/2 and f _5/2 proton subshells is a significant factor in making a sizeable contribution to the deformation in neutron-rich Sr isotopes.     

Contrasting high-spin yrast bands in 172Os and 174Os and an unexpected low-frequency anomaly in 172Os

The yrast bands of the neutron deficient isotopes ¹⁷²Os and ¹⁷⁴Os have been identified to spins of about 24. The yrast band in ¹⁷⁴Os shows no bandcrossing anomalies, confirming the shell effect observed in other N = 98 nuclei. In contrast, a strong backbend observed at a frequency of about 0.26 MeV in ¹⁷²Os is attributed to the s-band crossing. A weaker band-crossing is also observed at a lower frequency, about 0.24 MeV, in ¹⁷²Os. This unexpected anomaly may be due to either a deformation effect, or to a change in the s-band structure.     

High-spin states in 208Rn

The yrast decay scheme of ²⁰⁸Rn has been investigated up to spin $\text{≈ 20}\text{h}\text{?}$ and an excitation energy of ≈ 6 MeV. Several different γ-ray spectroscopic techniques were used to determine the properties of excited states and transitions in the nucleus. Significant changes to the previously established level scheme are proposed, based on the existence of an unobserved 3.1 keV transition. Simple empirical shell-model calculations of level energies aided in the assignment of shell-model configurations to excited states and the decay scheme is discussed in terms of these configurations. The energy level systematics for the even radon isotopes, from A = 206 to 212 are discussed, as are core polarization effects in the even radon isotopes (A = 204 to 210) and polonium isotopes (A = 202–208).     

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

Chiral geometry in multiple chiral doublet bands

The chiral geometry of multiple chiral doublet bands with identical configuration is discussed for different triaxial deformation parameters γ in the particle rotor model with πh_(11)/2γh_(11/2)~(-1).The energy spectra,electromagnetic transition probabilities B(M1) and B(E2),angular momenta,and K-distributions are studied.It is demonstrated that the chirality still remains not only in the yrast and yrare bands,but also in the two higher excited bands whenγ deviates from 30°.The chiral geometry relies significantly on γ,and the chiral geometry of the two higher excited partner bands is not as good as that of the yrast and yrare doublet bands.     

g-Factor Measurements of Rotational States in 84,86Zr

The g-factors of the positive parity yrast rotational states in ^84,86Zr have been precisely measured using a TMF-IMPAD method. The measured g factors indicate the proton alignment followed by neutron alignment in the g _9/2 high-j shell for ⁸⁴Zr and the neutron alignment followed by proton alignment for ⁸⁶Zr. The present results also reveal the structure transition at N=46 for Zr isotopes. This revised version was published online in September 2006 with corrections to the Cover Date.     

Structure of negative parity yrast bands in odd mass <Superscript>125–131</Superscript>Ce nuclei

The negative parity yrast bands of neutron-deficient ^125–131Ce nuclei are studied by using the projected shell model approach. Energy levels, transition energies and B(M1)/B(E2) ratios are calculated and compared with the available experimental data. The calculations reproduce the band-head spins of negative parity yrast bands and indicate the multi-quasiparticle structure for these bands.     

Microscopic study of low-lying yrast spectra in <Superscript>100–108</Superscript>Mo isotopes

Variation-after-projection (VAP) calculations in conjunction with Hartree-Bogoliubov (HB) ansatz have been carried out for A=100−108 molybdenum (Mo) isotopes. In this framework, the yrast spectra with J _max ^π ≥10⁺, B(E2) transition probabilities, quadrupole (β₂) and hexadecapole (β₄) deformation parameters, moment of inertia (I) and square of cranking frequency (ω²) for even-even Mo isotopes have been obtained. The results of the calculation give an indication that it is important to include the hexadecapole-hexadecapole component of the two-body interaction for obtaining various nuclear structure quantities in these Mo isotopes.     

On the structure of two-quasiparticle states in even-A Xe isotopes

The excitation energies of proton and neutron two-quasiparticle states in even-A xenon isotopes are studied within the shell-model framework. The results suggest that in the lighter isotopes (A≦126) the proton excitations might be yrast, whereas in the heavier ones (A≧130) the neutron-hole excitations dominate at lower energies. This finding would then explain the complex excitation spectra found in^{126, 128, 130}Xe, where the two excitation modes occur at comparable energies.     

Study on 222–226Th Isotopes in the Cranking Framework

The yrast spectra, quadrupole moments, quadrupole deformation parameters (β ₂), non-axiality parameters (γ), root mean-square radii for protons and neutrons, occupation probabilities, moment of inertia (I), and B(E2) transition probabilities are calculated for ^222–226Th in the cranked Hartree–Bogoliubov framework. The calculations employ a quadrupole-quadrupole plus pairing model of residual interaction operating in a reasonably large valence space outside the ¹⁶⁴Pb core. Our calculations reproduce qualitatively the observed yrast spectra in ^222–226Th up to spin 20⁺. The calculated results indicate that the non-axiality parameter decreases as one moves along the yrast states. The observed increase in deformation from ²²²Th to ²²⁶Th is due to the increase in the occupation of low-k components of $(2g_{9/2})_{\pi }$ and $(1j_{{15/2}})_{\nu }$ orbits. The model parameters reproduce not only the moment of inertia, deformation, and transition probabilities but also the proton and neutron pairing gaps and are the most appropriate for cranking studies in this region.