Improved description of M1 transitions by special hamiltonians of the proton-neutron interacting boson model

The proton-neutron interacting boson model (IBM-2) describes energies, B(E2) and B(M1) values of nuclei. In order to reduce the great number of free IBM-2 parameters two special IBM-2 hamiltonians are proposed which allow a decoupling of the energy and B(E2) fit from the determination of the B(M1) values and the energy of the lowest mixed symmetry 1⁺ state. This property allows a simple fit procedure of the IBM-2 parameters in both cases.     

Lifetimes of unresolved transitions from very high spin states in nuclei nearN=82

Average lifetimes of unresolved transitions deexciting very high spin states populated in²⁸Si(^{136, 129}Xe,xn)^164? x, 157?xEr reactions have been determined by a Doppler shift attenuation method. We find that the yrast bump region between 1.0 and 1.6 MeV contains a majority of strongly collectiveE2 transitions with very short lifetimes (a few tens of fsec) in the well deformed nuclei around¹⁵⁹Er and, with less certainty, almost comparably short lifetimes in the more spherical nuclei around¹⁵²Er. In the high energy region of 2.0–3.2 MeV we observe transitions which depopulate longer lived states in the nuclei nearN=82 than in the well deformed systems.     

Nuclear pears: Recent developments and future prospects

We report studies of examples of reflection-asymmetric nuclei which are difficult to access using compound nucleus reactions. The octupole radium isotopes withN>132 and radon isotopes are not accessible by reactions employing stable targets and beams; we have shown that multinucleon transfer reactions can populate these nuclei with sufficient yield for their structure to be determined. We report high-spin studies in^{218, 220, 222}Rn and^{222, 224, 226, 228, 230}Ra: these show that the Ra isotopes withA<228 have the characteristics of octupole deformed nuclei whereas the Rn isotopes behave like octupole vibrators. Measurements of theB(E1)/B(E2) ratios indicate that the electric dipole moment in these nuclei is constant with spin. The most octupole deformed nuclei are predicted to be uranium isotopes withN≈132; measurements of the very fissile nucleus²²⁶U suggest that it is octupole deformed and has a large intrinsic electric dipole moment. Finally, we speculate that the best examples of pear shapes are the hyperdeformed minima predicted to lie low in uranium isotopes withN≈140; their signature of high-multiplicity low-energyE1 photon cascades should be detectable using present-day high-efficiency germanium arrays.     

Anharmonicities of γ-vibrations in deformed nuclei

The anharmonicities of γ-vibrations are studied within the multiphonon method in different even-even deformed nuclei where the first K^π = 2⁺ vibrational state appears well below the energy gap: ¹³⁰Ce, ^162–164Dy, ^164–168Er, ¹⁸⁶Os. The anharmonicities previously obtained in ¹⁶⁸Er appear to be a general property of these nuclei.     

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.     

Study of transitional odd-odd mass nuclei

The low lying high spin states in the transitional odd-odd mass nuclei are studied systematically in the framework of gamma deformed rotor model. The two odd particles, a proton and a neutron, are treated as the BCS quasi particles moving in a triaxially deformed field. The calculations are confined to smallβ-deformation which is typical of the transitional nuclei. Moreover, we consider only the case where two odd particles are in singlej-shells. Results for the excitation energy covering the various physical situations are presented as a function of theβ-deformation, the asymmetryγ, and the Fermi energiesλ _p andλ _n . Electromagnetic transitions and moments are also calculated. Certain features well known in the odd mass nuclei are shown to persist also in the odd-odd mass system. Trends in the level systematics and the electromagnetic properties are predicted for the case where both particles decouple or remain strongly coupled, and for the case where one decouples and the other couples strongly with the core. Measurements which are getting now available show encouraging agreement with the theoretical results.     

Majorana neutrinos in rare meson decays

The rare meson decays K ⁺ → π ^??⁺?′⁺ and D ⁺ → K ^??⁺?′⁺ (?, ?′ = e, μ), which are induced by Majorana neutrino exchange and which are accompanied by lepton-number nonconservation, are considered. The effects of the meson structure are taken into account on the basis of the Gaussian model for the respective Bethe-Salpeter amplitudes. It is shown that existing direct experimental constraints on the decay branching ratios are overly lenient and therefore give no way to set realistic limits on effective Majorana masses. On the basis of the constraints on the lepton-mixing parameters and neutrino masses from precision measurements of electroweak processes, neutrino-oscillation experiments, searches for neutrinoless double-beta decay of nuclei, and cosmological data, indirect constraints on the branching ratios for the decays in question are obtained and found to be much more stringent than the above direct constraints.     

M1 Character of unresolved continuum transitions from X-ray multiplicity measurements

We have measured the X-ray multiplicities of the transitions deexciting the quasi-continuum region as a function of the input spin for deformed and transitional erbium isotopes obtained in (⁴⁰Ar,xn) reactions. Combined withγ-ray angular distribution studies, these measurements clearly show the occurrence of a magnetic dipole component in the energy region 300–800keV. The spin dependence of this “bump” is quite different in deformed and transitional nuclei. In the latter case, a sudden increase in the quasi-continuumK electron multiplicity arises for spins higher than 35? and is strongly correlated to the occurrence of collective modes in these nuclei at the same spins. It is suggested to correspond to collective behavior of bands built on yrast states of single particle nature.     

Collective gyromagnetic ratio from density dependent hartree-fock calculations: (II). Odd nuclei

The collective gyromagnetic ratio and moment of inertia of deformed odd-proton and oddneutron axially symmetric nuclei have been calculated in the cranking approximation using wave functions obtained with the Skyrme force SIII. Good agreement with experiment is found for g_R. Our parameter-free cranking results are better than those of Prior, Boehm and Nilsson where effective charges were used. The cranking formula leads to better results than the projection method (in which one simply takes the expectation value of the relevant operator in the deformed HF ground state, neglecting corrections of relative order 1/〈J²〉. In particular, the cranking results follow nicely the exceptionally large/small g_R for the odd-proton/neutron nuclei around mass 153–167.     

Deformation and shape coexistence in medium mass nuclei

Emerging evidence for deformed structures in medium mass nuclei is reviewed. Included in this review are both nuclei that are ground state symmetric rotors and vibrational nuclei where there are deformed structures at excited energies (shape coexistence). For the first time. Nilsson configurations in odd-odd nuclei within the region of deformation are identified. Shape coexistence in nuclei that abut the medium mass region of deformation is also examined. Recent establishment of a four-particle, four-hole intruder band in the doublesubshell closure nucleus⁹⁶Zr₅₆ is presented and its relation to the Nuclear Vibron Model is discussed. Special attention is given to the N=59 nuclei where new data have led to the reanalysis of⁹⁷Sr and⁹⁹Zr and the presence of the [404 9/2] hole intruder state as isomers in these nuclei. The low energy levels of the N=59 nuclei from Z=38 to 50 are compared with recent quadrupole-phonon model calculations that can describe their transition from near-rotational to single closed shell nuclei. The odd-odd N=59 nuclei are discussed in the context of coexisting shape isomers based on the (p[303 5/2]n[404 9/2])2^– configuration. Ongoing in-beam (t.p conversion-electron) multiparameter measurements that have led to the determination of monopole matrix elements for even-even₄₂Mo nuclei are presented, and these are compared with initial estimates using lBA-2 calculations that allow mixing of normal and cross subshell excitations. Lastly, evidence for the neutron-proton³S₁ force's influence on the level structure of these nuclei is discussed within the context of recent quadrupole-phonon model calculations.Work supported by USDOE contract Nr.W-7405-Eng-48 and NATO Grant Nr.RGO565/82.     

A correspondence between IBA-1 and IBA-2 models and electromagnetic transitions in the decay of some erbium isotopes

The interacting boson approximation IBA-1 model space, in which neutron and proton degrees of freedom are not distinguished, can be considered as a subspace of the IBA-2 model space. Using the microscopic background of the IBA-2 model, a correspondence can be established between IBA-1 and IBA-2 model space. Since the space of the IBA-1 model can be regarded as a subspace of the IBA-2 model there is a unique way to ‘Project’ the operators of the IBA-2 model onto those of IBA-1. This projection can be carried out using theF-spin formalism. In the IBA-2 model, the lowest states are indeed fully symmetric, and using the calculations with the help of this projection, we explore the energy levels and the electric quadrupole transition probabilitiesB(E2; {ie393-01}) and γ-ray E2/M1 mixing ratios for selected transitions of^{162, 164, 166, 168, 170}Er. Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (ε) and (κ). This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for^{162, 164, 166, 168, 170}Er isotopes are reasonably in good agreement with the previous experimental values.     

Are nuclei withN∼43 deformed?

The level schemes of⁷⁵Se and⁷⁹Kr have been established through gamma ray and conversion electron spectroscopy following⁷⁵As (p, nγ ^?e) and⁷⁹Br (p, nγe^?) reactions. The data on these nuclei and the nuclei in the neighbourhood of this mass region are discussed and evidence is presented to show that the nuclei withN～43 are deformed.     

Fragmentation of giant multipole resonances in deformed nuclei

The fragmentation of the giant monopole resonance in deformed nuclei is first studied by coupling the monopole oscillation with the quadrupole oscillation by means of the variational procedure for resonance frequencies. It is shown that, for non-axial symmetry, the monopole oscillation couples with both m = 0 and 2 modes of the quadrupole oscillation and the giant monopole resonance is split into three components, whereas for axial symmetry, the fragmentation is given by E₀(1 + 0.86δ² ± 1.25δ³) and E₀(0.74 ± 0.22δ ? 0.21δ² ± 0.57δ³), where E₀ is the g monopole resonance energy for spherical nuclei, δ is the deformation parameter, and the upper and lower signs stand for prolate and oblate deformations, respectively. The initial fragmentation of the giant quadrupole resonance is seen to be little modified by the coupling, except for the m = 0 mode which is split into two components. The variational method is extended to general multipoles for an ellipsoid and the fragmentation of giant multipole resonances in deformed nuclei is investigated for both axial and non-axial symmetries. A brief discussion is also made about the meaning of the energy eigenvalue involved in the model wave equation in terms of multipole sum rules. The giant dipole resonance for the static octupole deformation is shortly considered. The giant E0 and E3 resonances for largely deformed nuclei are finally examined by solving the spheroidal eigenvalue equation and they are compared with the results of the giant dipole and quadrupole resonances.