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.     

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.     

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.     

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.     

Projected Shell Model Description of Positive Parity Band of <Superscript>130</Superscript>Pr Nucleus

Theoretical investigation of positive parity yrast band of odd-odd ¹³⁰Pr nucleus is performed by applying the projected shell model. The present study is undertaken to investigate and verify the very recently observed side band in ¹³⁰Pr theoretically in terms of quasi-particle (qp) configuration. From the analysis of band diagram, the yrast as well as side band are found to arise from two-qp configuration πh _11/2???νh _11/2. The present calculations are viewed to have qualitatively reproduced the known experimental data for yrast states, transition energies, and B(M1) / B(E2) ratios of this nucleus. The recently observed positive parity side band is also reproduced by the present calculations. The energy states of the side band are predicted up to spin 25⁺, which is far above the known experimental spin of 18⁺ and this could serve as a motivational factor for future experiments. In addition, the reduced transition probability B(E2) for interband transitions has also been calculated for the first time in projected shell model, which would serve as an encouragement for other research groups in the future.     

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.     

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.     

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.     

Analytical approach to particle-rotor model for single <Emphasis Type="Italic">j</Emphasis> configuration, <Emphasis Type="Italic">γ</Emphasis> = 30°

The analytical method is developed to describe yrast states in odd triaxial nuclei. Simple expressions for the energies and the wave functions are obtained. B(M1) transition probabilities inside the yrast band are considered. The text was submitted by the authors in English.     

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.     

Systematic behavior ofB(E2) values in the yrast bands of doubly even nuclei

The experimental information onB(E2) transition rates in the yrast bands of doubly even nuclei (126≦A≦184) is systematized. The strength functionS _exp≡B(E2,I→I?2)×E(I→I?2) is found to reveal characteristic behavior significant for structure studies of yrast bands. The energy-weightedB(E2,I→I?2) values (S _exp) and 2?/?²(?: moment of inertia) are plotted versus the rotational frequency squared ?²ω² for each nucleus. In strongly deformed nuclei (N≧90), theS _exp curves smoothly increase for low rotational frequencies suggesting that up to spin valuesI≈8 the ratioQ ₀ ² ? is nearly constant (Q ₀: quadrupole moment). This is not the case in nuclei with a soft core (N≦88). In the relevant discussion, the hydrodynamical model as well as the CAP effect are considered. The results in the backbending region are qualitatively discussed in terms of the two-band crossing model. Evidence is found supporting the prediction of an oscillating behavior of the yrast-yrare interaction.     

The spin(6) scheme and electromagnetic transitions in 191Ir and 193Ir

The Coulomb excitation of natural Ir and Pt targets has been measured with protons and α-particles of energies between 5.0 and 6.0 MeV. Accurate γ-ray angular distributions were taken to determine the relative yields of observed γ-rays. Using ¹⁹⁴Pt as standard the reduced electric quadrupole transition probabilities to the ground states from Coulomb excited levels in the Ir and Pt isotopes were determined. Other B(E2) and B(M1) values were determined from the decay schemes obtained and from mixing ratios deduced from γ-ray angular distributions or from previously measured internal conversion coefficients. The detailed sets are compared with calcula- tions based on the Spin(6) scheme, which predicts several symmetries in ¹⁹¹Ir and ¹⁹³Ir. The possible existence of wider supersymmetry multiplets in this region of nuclei is examined on the basis of comparison of electromagnetic properties of Ir nuclei with those of Pt and Os isotopes.     

Feeding and lifetimes of yrast levels in Hf nuclei

Feeding intensities and times, as well as lifetimes of yrast levels in doubly even ^{166, 168, 170}Hf nuclei have been measured. The reactions ^{122, 124}Sn(^{48, 50}Ti, 4n)^166–170₇₂Hf have been investigated using the recoil-distance Doppler-shift method. The lifetimes, and hence the B(E2) values measured, show the same trends of rather small deviations from the rigid rotor as in the known ₆₈Er and ₇₀Yb cases. In addition to the fast feeding component, showing behaviour rather similar to that of the Yb nuclei, another type of slow feeding, related to the low spin yrast levels, is observed.     

Microscopic description of collective states near the yrast line of nuclei with stable octupole deformation

Collective states near the yrast line in nuclei with stable octupole deformation are discussed in the framework of the random phase approximation (RPA) based on the cranking model. These vibrational states are characterized by the quantum number of generalized signature (eigenvalue of the operator S_x = PR_x^?1(π)). In the zero-octupole deformation limit the RPA equations of motion are reduced to the well-known ones characterized by both values of parity and signature, respectively. The connection of the translational and rotational symmetry of the model hamiltonian with the spurious solutions of the RPA equation of motion is discussed. Expressions for the reduced probabilities B(E1), B(E2) and B(E3) are obtained. These expressions confirm the conclusions of phenomenological models for the strong E1 and E3 intraband transitions in nuclei with stable octupole deformation.     

Multiple Coulomb excitation of198Hg and200Hg

Multiple Coulomb excitation measurements on^{198, 200}Hg have been performed with 5MeV/amu²⁰⁸Pb projectiles andB(E2)-values are determined for transitions between states up to spin 8⁺. In¹⁹⁸Hg a reduction of theB(E2)-value for the yrast transition 8⁺→6⁺ by a factor of 3 as compared to the rigid rotor prediction is observed, which supports the earlier proposed idea that the ground state band is crossed between the 6⁺ and 8⁺ state by a weakly interactingvi ₁₃ ^2/2 rotation aligned band. In each of the two nuclei,¹⁹⁸Hg and²⁰⁰Hg, a state with a possibleI ^π=8⁺ assignment is observed, which is tentatively interpreted as the 8⁺ member of the ground state band.     

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.     

Boson description of nuclear collective motion

Nuclear system interacting via quadrupole and octupole particle-hole forces is studied by the boson expansion technique. Energy spectra of the negative parity yrast band and the ground state band are calculated and compared with experiment for¹⁰⁰Ru,¹¹²Cd,¹⁵⁰Sm and¹⁵⁰Gd. ExperimentalB(E1)/B(E2) ratios show strong hindrance for E1 transitions, and are used to deduce the static polarizability of E1 transitions.