Dipole γ-ray transition rates in 238U

M1 and E1 transition rates from the ground to excited states and between excited states in ²³⁸U are calculated within the quasiparticle-phonon nuclear model with the wave functions consisting of one- and two-phonon terms. We show that there are relatively large M1 transitions between 2⁺ states in the low-energy region. The fragmentation of the one-phonon states strongly affects M1 and E1 strength distributions. The correlation takes place between E1 and E3 transition strengths. We show that there are fast E1 and M1 transitions between large components of the wave functions differing by an octupole or quadrupole phonon.     

On collective two-phonon states in deformed nuclei

The centroid energies of the two-phonon states in doubly even deformed nuclei are calculated within the quasiparticle-phonon nuclear model taking into account the Pauli principle in the two-phonon components of the wave functions. It is shown that the collective two-phonon energies are shifted by 1–2 MeV to higher energies due to the Pauli principle. A strong fragmentation of the two-phonon collective states over many nuclear levels occurs at the excitation energies of 3–4 MeV. It is concluded that the two-phonon states cannot exist in deformed nuclei. The analysis of the available experimental data on the two-phonon states shows that the experimental data do not contradict the results of these calculations.     

Non-normal parity states in mass 10–15 nuclei

The modified surface delta interaction (MSDI) is used as the effective two-nucleon residual interaction in extensive shell-model calculations forA=10–15 nuclei; a He-4 core andj-j coupled extra-core nucleon configurations of the formP _3/2 ⁿ P _1/2 ^m (1d _5/2,2s _1/2)¹ are employed. Level energies and wave functions for low-lying non-normal parity states are first obtained from a simultaneous fit to experimental energies over the entire 10–15 mass range. The wave functions are next tested by comparing predicted nuclear properties with experimental data: single-nucleon spectroscopic factors, beta decay lifetimes,M1 andE2 radiative transition widths as well asE1 andM2 radiative widths are calculated. In general good agreement between experiment and theory is obtained.     

Thermal neutron capture in isotopes of nickel

The gamma-ray spectra associated with thermal neutron capture in targets of⁵⁸Ni,⁶⁰Ni,⁶²Ni, and⁶⁴Ni have been observed with a high-sensitivity pair-spectrometer. Level schemes for the four product nuclei are discussed, correlation of widths with neutron single-particle states examined, and estimates forM1 andE2γ-ray strength functions obtained.     

Description of low-lying vibrationalK π≠0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in¹⁶⁸Er,¹⁷²Yb and¹⁷⁸Hf are found to be in reasonable agreement with experimental data. It is shown that distribution of theEλ strength in some deformed nuclei differs from the standard one. There are cases when for a givenK ^π theEλ strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed.     

Description of high-spin isomers in theN=82 region

The high spin states and of those especially the yrast isomers are studied in the region near the rare earth nuclei. The deformation energy surface is calculated with a method modelled in principle according to a shape constrained cranked HF theory (CHF). In practice, the expectation value of the many-body Hamiltonian is calculated with cranked Nilsson functions. One finds rotation around a slightly deformed oblate or prolate symmetry axis in front or behind the rare earth region, respectively. Near the Hf isotopes strongly prolate deformed nuclei rotating around the symmetry axis are found in agreement with the knownK isomers in this region. These results are explained also qualitatively with the help of the MONA (Maximisation of theOverlap ofNucleonic wave functions byAlignment of single particle angular momenta) effect. In the second part high spin states and yrast isomers in theN=82 region are calculated in the cranked Hartree-Fock-Bogoliubov approach with four and six quasi-particle excitations. For the excitation energies in¹⁴⁶Gd and¹⁵²Dy and a measuredg factor one finds satisfactory agreement.     

Description of high-spin isomers in theN=82 region

The high spin states and of those especially the yrast isomers are studied in the region near the rare earth nuclei. The deformation energy surface is calculated with a method modelled in principle according to a shape constrained cranked HF theory (CHF). In practice, the expectation value of the many-body Hamiltonian is calculated with cranked Nilsson functions. One finds rotation around a slightly deformed oblate or prolate symmetry axis in front or behind the rare earth region, respectively. Near the Hf isotopes strongly prolate deformed nuclei rotating around the symmetry axis are found in agreement with the knownK isomers in this region. These results are explained also qualitatively with the help of the MONA (Maximisation of theOverlap ofNucleonic wave functions byAlignment of single particle angular momenta) effect. In the second part high spin states and yrast isomers in theN=82 region are caluclated in the cranked Hartree-Fock-Bogoliubov approach with four and six quasi-particle excitations. For the excitation energies in¹⁴⁶Gd and¹⁵²Dy and a measuredg factor one finds satisfactory agreement.     

Rotation of nuclei around a prolate symmetry axis at very high spin states

Classically one expects that nuclei rotate at very high spins (30≦I≦80) around an oblate symmetry axis. It is shown that strong shell correction energies yield for some nuclei at the end of the rare earth region and in the Pb-region yrast states for a rotation around a prolate symmetry axis. Like for the rotation around an oblate symmetry axis one expects also here yrast traps. The deformation energy surfaces for very high spin states are calculated by the Strutinsky method using a Saxon-Woods potential and by a microscopic method built on constraint Nilsson functions. Both methods agree qualitatively. Yrast traps are studied for these nuclei. It is shown that the MONA (Maximisation of theOverlap ofNuclear wave functions byAlignment) effect prefers at high spin rotation around the symmetry axis of a negative deformed shape at the beginning of the shell and of positive deformation at the end of the shell.     

Core excitation in79Br and81Br

TheE2 andM1 reduced transition probabilities between the low lying levels, in the case of⁷⁹Br and⁸¹Br, have been calculated on the core-excitation model. To account for the observed M1 transition probabilities admixture among the like spin states is considered. In addition, the ground state static moments have been computed. For the same amount of admixture among the like spin states, a good agreement with the experimental results is obtained, for both⁷⁹Br and⁸¹Br. The results are compared with other existing theoretical calculations. From our analysis, we obtain, the quadrupole moment of the first excited 2⁺ state in the neighbouring even-even nuclei. It is in good agreement with the value calculated on the basis of the anharmonic vibrational model.     

Directional correlations in the decay of 1200y 166Ho

γγ-directional correlations have been measured between the ground state band transitions 6→4, 4→2 and 2→0 and the γ-rays depopulating the levels of the gamma vibrational band and the negative parity states of¹⁶⁶Er. Thereby angular momenta could be assigned to the latter states andM2/E1 multipole mixtures determined for the depopulating γ-transitions. TheE2/M1 mixing ratios were obtained for a series ofI _γ→I _g transitions up toI _γ=8⁺. These are used to investigate the angular momentum dependence of theE2/M1 admixtures.     

Particle plus octupoleM2/E3 isomers and high-spin particle-hole states in147Tb and148Tb

The level structures of theN=82 andN=83 nuclei¹⁴⁷Tb and¹⁴⁸Tb have been studied by means of (α, 8n) and (α,7n) reactions induced by 68 to 110 MeVα particle bombardments of¹⁵¹Eu targets. In-beam conversion electron measurements have established that isomers withT _1/2=4.8(6)ns in¹⁴⁷Tb andT _1/2=22(1)ns in¹⁴⁸Tb decay byM2+E3 transitions to the ground states. The measuredB(E3) values show that the isomeric states arise from the coupling of the valence nucleon(s) to the¹⁴⁶Gd core octupole. Particlephonon coupling in these nuclei and in the one-neutron nucleus¹⁴⁷Gd is discussed and compared with well known cases involving the²⁰⁸Pb core. The higher lying yrast states in the two Tb nuclei are described as shell-model particle-hole excitations using empirical single particle energies and nucleon-nucleon interactions.     

Chaotic properties of multipoint correlation functions of an Ising model with long-range interactions on the Sierpiński—Gasket lattice

A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ ₁=Q,l=1,2,..., on the Sierpiski-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM _k-spin correlation functions, whereM _k=3 ^k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM _k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM _k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.     

Microscopic calculation of pion production in nucleus-nucleus collisions around 1 GeV·A

New phonon operators are introduced for describing deformed nuclei which consist of the electric and magnetic parts. The Hamiltonian of the quasiparticle-phonon nuclear model is constructed and the basic equations for the finite rank separable isoscalar and isovector multipole and spin-multipole particle-hole and particle-particle interactions between quasiparticles are derived. It is shown that calculations of one-phonon states in the RPA encounter some difficulties due to the finite rankn _max>1 separable interaction of the electric and magnetic type. The use of complex separablen _max>1 interactions does not lead to complication of the QPNM equations for describing fragmentation of vibrational states. The matrix elements are obtained for describingE- andM- transitions between excited states of deformed nuclei. It is stated that the QPNM can serve as a basis for calculating many characteristics of excited states of deformed nuclei.     

The low-energy level structure and the electromagnetic properties of191Ir and193Ir

TheM 1 andE 2 reduced transition probabilities in¹⁹¹Ir and¹⁹⁹Ir have been calculated on the weak particle-core coupling model. The static moments of the ground state and the first three low-lying excited states have been computed. The theoretical values are in good agreement with the experimental results, in particular, the existing discrepancy between the theoretical and the experimental value for the magnetic moment of the first excited 5/2⁺ state, in both these nuclei, has been removed. The predicted sign of the quadrupole moment of the 2⁺ state in the neighbouring even-even nuclei is consistent with the results reported for Platinum nuclei. The level structure of both these nuclei has been calculated assuming the particle-core interaction to be dipole-dipole and quadrupole-quadrupole type.     

Octupole vibrations of deformed nuclei

The octupole vibrations of deformed nuclei are studied. A strong coupling between the harmonic octupole vibrations and the quadrupole ellipsoid is assumed. This interaction gives rise to a splitting of octupole bands with different projection quantum numberK. TheE1-transitions of the octupole states are explained within the frame of the Dynamic Collective Theory ofDanos andGreiner by calculating the Coulomb interaction between octupole vibrations and giant resonances. Furthermore, theE2- andE3-transitions of the octupole states are studied. The spectrum of W¹⁸² is investigated in detail. A fair agreement between theory and experiment is obtained. Predictions for the octupole spectra of Sm¹⁵² and Gd¹⁵⁶ are given.     

A quantitative evaluation of the reliability of calculated decay properties of nuclei in the mass region A=24−28

Electromagnetic transition rates and logft values were calculated for transitions between positive-parity states in theA=24?28 mass region. The wave functions used were taken from a previous paper. In general we found satisfactory agreement with experiment. In order to have a measure of the stability of the results against changes in the Hamiltonian a method was developed for assigning errors to calculated transition properties. The renormalized single-particle matrix elements of theE2 andM 1 transition operators were determined in a phenomenological way. To this end use was made of the errors just mentioned. It was found that good agreement was obtained with bare-nucleonM 1 singleparticle matrix elements and a state independent effective isoscalar charge for theE 2 operator. Predictions for static moments are given.     

Nuclear Structure of 12,14Be Within Deformed Quasi-Particle Random Phase Approximation (DQRPA)

We developed a deformed quasi-particle random phase approximation (DQRPA) to describe the Gamow–Teller (GT) transitions on even–even neutron-rich nuclei. To describe deformed nuclei, we exploited the deformed axially symmetric Woods–Saxon potential, the deformed BCS, and the deformed QRPA with realistic two-body interaction calculated by Brueckner G-matrix based on Bonn CD potential. The deformed single particle states are expanded in terms of the spherical harmonic oscillator basis in order to take the realistic G-matrix stored in the spherical basis. We calculated GT strength distributions, B(GT), of two nuclei ^12,14Be for many different deformation parameter β ₂ values as a function of the excitation energy E _ex w.r.t. the ground state of a parent nucleus. Our results for ¹²Be predict to prefer a prolate shape and B(GT) results of ¹⁴Be turn out to be independent of the β ₂ values.     

Studying parity-nonconservation effect in the conversion transition between the levels of the (5/2)± doublet in the 229Pa nucleus

Effects of weak nucleon interaction are calculated for the ground-state doublet of 5/2^± levels of the strongly deformed nucleus ²²⁹Pa₉₁. A parity-nonconservation effect in the doublet states can be observed in the conversion spectrum for the isomeric transition between the doublet levels. By using a generalized model of the nucleus, the matrix element of the effective one-nucleon weak-interaction potential, which determines the weight of the opposite parity admixture in the doublet components is estimated in the single-particle approximation. The reduced probabilities of the E1 and M1 nuclear transitions between the doublet states are calculated within various models of the deformed nuclear potential. The effect of Coriolis forces on the dipole electric transition in question is considered. The lifetime of the upper doublet state is estimated.     

Number-conserving treatment of the BCS-Tamm-Dancoff approximation for deformed rare-earth nuclei

The formulation for the exact number-conserving treatment of the BCS-Tamm-Dancoff approximation (NTDA) in deformed even nuclei is given. It is applied to theK ^π=0^? octupole vibrations of rare-earth nuclei and is also compared with the ordinary TDA or RPA method based on the Bogoliubov transformation which has the defect of mixing of the particle number in the wave functions. The excitation energies andB(E3) calculated by NTDA method show rather stronger dependence on the Nilsson orbits than those calculated by the usual TDA or RPA methods, especially atN=94 nuclei.