Commutation superoperator of a state and its applications to the noncommutative statistics

For a normal state on a von Neumann algebra the space of square-integrable operators is introduced. As distinct from the L² space in the classical probability theory, it possesses an additional skew-symmetric form and the associated superoperator, which is a convenient tool to describe commutation properties in L². It is shown that a state on the algebra of canonical commutation relations is Gaussian (quasi-free) iff the space of canonical observables is an invariant subspace of the corresponding commutation superoperator. Basing on these ideas a new approach to some problems in the noncommutative statistic is developed.     

Beyond mean field approach to the beta decay of medium mass nuclei relevant for nuclear astrophysics

The Gamow-Teller strength distributions for the β decay of the ground state as well as the lowest excited states of the rp-process waiting point nuclei ⁶⁸Se and ⁷²Kr are obtained within the complex Excited Vampir variational approach using realistic effective interactions and a rather large model space. The shape mixing is consistently described for both the states in the even-even parent and the states in the odd-odd daugther nucleus. The influence of the shape mixing accounted by the different effective interactions used and comparison with the available data are presented. The possible influence of the decay of the lowest excited states of the parent nuclei in the astrophysical environment of X-ray bursts is discussed.Gamow-Teller strength distributions, β-decay half-lives, and β-delayed neutron emission probabilities for neutron-rich Zr nuclei are investigated for the first time within the complex Excited Vampir approach using a large model space. Comparison with available data and predictions relevant for the astrophysical r process are presented.     

Classical simulations of heavy-ion fusion reactions and weakly-bound projectile breakup reactions

Heavy-ion collision simulations in various classical models are discussed. Heavy-ion reactions with spherical and deformed nuclei are simulated in a classical rigid-body dynamics (CRBD) model which takes into account the reorientation of the deformed projectile. It is found that the barrier parameters not only on the initial orientations of the deformed nucleus, but also on the collision energy and the moment of inertia of the deformed nucleus. Maximum reorientation effect occurs at near- and below-barrier energies for light deformed nuclei. Calculated fusion cross-sections for ²⁴Mg + ²⁰⁸Pb reaction are compared with a static-barrier-penetration model (SBPM) calculation to see the effect of reorientation. Heavy-ion reactions are also simulated in a 3-stage classical molecular dynamics (3S-CMD) model in which the rigid-body constraints are relaxed when the two nuclei are close to the barrier thus, taking into account all the rotational and vibrational degrees of freedom in the same calculation. This model is extended to simulate heavy-ion reactions such as⁶Li + ²⁰⁹Bi involving the weakly-bound projectile considered as a weakly-bound cluster of deuteron and ⁴He nuclei, thus, simulating a 3-body system in 3S-CMD model. All the essential features of breakup reactions, such as complete fusion, incomplete fusion, no-capture breakup and scattering are demonstrated.     

Ground state reorientation effects in elastic scattering cross sections

Elastic scattering cross sections are shown to be quite sensitive to ground state reorientation amplitudes and cross sections. These effects are dramatically evident when comparing scattering from even-even nuclei with that from high-spin odd-A nuclei, and may affect choices of potentials for odd versus even nuclei. Neutron scattering data from ²³⁵U and ²³⁸U are analyzed via coupled channels methods. The diffraction minima in elastic scattering from ²³⁵U are found to be dominated by reorientation cross sections. The majority of this reorientation is shown to follow from second order virtual nuclear excitations rather than proceeding through amplitudes for direct ground state reorientation.     

Pseudobands in non-SU(3) odd-mass nuclei and coherent state structures of quadrupole phonons

Ground state symmetric rotor bands are described as coherent-state structures of deformation in a quadrupole-phonon model. These structures are shown to be very different from the phonon composition of pseudobands which are culled from the excited state spectrum of nuclei such as⁷⁵Se,⁷⁵Kr, and⁷⁷Kr. The pseudobands are shown to be only a subset of more complete excitation spectra, which occur in most unique-parity odd-nucleon nuclei with a transitional core and can be expected to occur throughout the chart of the nuclides.     

Mechanisms of transfer reactions in low-energy collisions with neutron-enriched nuclei

A mechanism of neutron transfer between nuclei in close low-energy collisions is established. It includes three stages: the transformation of the initial one-nuclear state into a two-nucleus state, the transitions of this state to other molecular states, and the transformation of those states into one-nuclear states in which nuclei are separated from one another. An explanation is offered for the fusion of nuclei in the ¹⁸O + ⁵⁸Ni reaction exceeding the cross section, relative to the ¹⁶O + ⁶⁰Ni reaction.     

Solid4He as an ensemble of superradiating nuclei

Summary We explore the possibility that the crystalline⁴He state is related to the onset of ?superradiance? (coherent oscillation in phase with particular classical modes of the electromagnetic field) for the ensemble of⁴He nuclei. Working at zero-temperature we find evidence for this phenomenon and compute the correct liquid-solid transition pressure and the correct energetics.     

Calculated properties of superheavy nuclei

Ground-state properties of the heaviest nuclei are analyzed within a macroscopic-microscopic approach. The main attention is paid to such properties as deformation, deformation energy, energy of the first rotational state 2⁺ of a nucleus, and the branching ratio of α decay to this 2⁺ state with respect to the decay to the ground state 0⁺. The analysis concerns the problem of experimental confirmation of theoretically predicted deformed shapes of superheavy nuclei situated in the region around the nucleus ²⁷⁰Hs. A large region of even-even nuclei with proton, Z=82–128, and neutron, N=126–190, numbers is considered.     

Finite nuclei to nuclear matter: a leptodermous approach

The liquid drop model (LDM) expansions of energy and incompressibility of finite nuclei are studied in an analytical model using Skyrme-like effective interactions to examine, whether such expansions provide an unambiguous way to go from finite nuclei to nuclear matter, and thereby can yield the saturation properties of the latter, from nuclear masses. We show that the energy expansion is not unique in the sense that, its coefficients do not necessarily correspond to the ground state of nuclear matter and hence, the mass formulas based on it are not equipped to yield saturation properties. The defect is attributed to its use of liquid drop without any reference to particles as its basis, which is classical in nature. It does not possess an essential property of an interacting many-fermion system namely, the single particle property, in particular the Fermi state. It is shown that, the defect is repaired in the infinite nuclear matter model by the use of generalized Hugenholtz–Van Hove theorem of many-body theory. So this model uses infinite nuclear matter with well defined quantum mechanical attributes for its basis. The resulting expansion has the coefficients which are at the ground state of nuclear matter. Thus a well defined path from finite nuclei to nuclear matter is found out. Then using this model, the saturation density 0.1620 fm⁻³ and binding energy per nucleon of nuclear matter 16.108 MeV are determined from the masses of all known nuclei. The corresponding radius constant r₀ equal to 1.138 fm thus determined, agrees quite well with that obtained from electron scattering data, leading to the resolution of the so-called ‘r₀-paradox’. Finally a well defined and stable value of 288±20 MeV for the incompressibility of nuclear matter K_∞ is extracted from the same set of masses and a nuclear equation of state is thus obtained.     

Two-phonon states in doubly even nuclei with 30 ≦ Z ≦ 52

Results of a survey of energies of two-phonon states are presented. Systematic trends are extracted and parametrized with the anharmonic vibrator model. The doubly even nuclei with anomalous 0⁺ first excited states are fitted into a general pattern indicating profound influence of both proton and neutron shell closure on the lowering of the 0^+' state energies. A sharp transition from anharmonic vibrational to almost pure rotational motion in this nuclear region is suggested for nuclei with first excited 2⁺ state energy ≈ 130 keV. Such a possible transition and similar ones already well known in the rare earth and heavy element regions are well described by the model.     

Allowance for the shell structure of colliding nuclei in the fusion-fission process

The motion of two nuclei toward each other in fusion-fission reactions is considered. The state of the system of interacting nuclei is specified in terms of three collective coordinates (parameters). These are the distance between the centers of mass of the nuclei and the deformation parameter for each of them (the nose-to-nose orientation of the nuclei is assumed). The evolution of collective degrees of freedom of the system is described by Langevin equations. The energies of the Coulomb and nuclear (Gross-Kalinovsky potential) interactions of nuclei are taken into account in the potential energy of the system along with the deformation energy of each nucleus with allowance for shell effects. The motion of nuclei toward each other are calculated for two reaction types: reactions involving nuclei that are deformed (₄₂¹⁰⁰Mo + ₄₂¹⁰⁰Mo → ₈₄²⁰⁰Po) and those that are spherical (₈₂²⁰⁸Pb + ₈¹⁸O → ₉₀²²⁶Th) in the ground state. It is shown that the shell structure of interacting nuclei affects not only the fusion process as a whole (fusionbarrier height and initial-reaction-energy dependence of the probability that the nuclei involved touch each other) but also the processes occurring in each nucleus individually (shape of the nuclei and their excitation energies at the point of touching).     

Dipole excitations in 122Te, 126Te and 130Te

Excited states of the nuclei ¹²²Te, ¹²⁶Te and ¹³⁰Te were populated via the (γ, γ') reaction at endpoint energies of the bremsstrahlung between 4.5 and 5.5 MeV. Gamma rays were detected with a EUROBALL-CLUSTER detector and a single detector. In all nuclei several dipole transitions were identified at energies around 3 MeV. The lowest corresponding J = 1 states are interpreted as two-phonon excitations. Quasiparticle-phonon-model calculations predict one 1^? state arising from the coupling of the first quadrupole and the first octupole phonon and one 1⁺ state arising from the coupling of the first and the isovector second quadrupole phonon at about 3 MeV. The calculated transition strengths are compatible with experimental ones.     

Quantum mechanical version of classical Liouville theorem

In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of coherent state from |z〉to |sz-rz^*〉angle corresponds to the motion from a point z(q,p) to another point sz-rz^* with |s|²-|r|²=1. The evolution is governed by the so-called Fresnel operator U(s,r) recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation and obeys the group product rules. In another word, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics.     

Decay of heavy and superheavy nuclei

We present here, an overview and progress of the theoretical works on the isomeric state α decay, α decay fine structure of even–even, even–odd, odd–even and odd–odd nuclei, a study on the feasibility of observing α decay chains from the isotopes of the superheavy nuclei Z = 115 in the range 271 ≤A ≤ 294 and the isotopes of Z = 117 in the range 270 ≤A ≤ 301, within the Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed half-lives of the favoured and unfavoured α decay of nuclei in the range 67 ≤Z ≤ 91 from both the ground state and isomeric state, are in good agreement with the experimental data and the standard deviation of half-life is found to be 0.44. From the α fine structure studies done on various ranges of nuclei, it is evident that, for nearly all the transitions, the theoretical values show good match with the experimental values. This reveals that CPPMDN is successful in explaining the fine structure of even–even, even–odd, odd–even and odd–odd nuclei. Our studies on the α decay of the superheavy nuclei ^271?294115 and ^270?301117 predict 4 α chains consistently from ^284,285,286115 nuclei and 5α chains and 3α chains consistently from ^288?291117 and ²⁹²117, respectively. We thus hope that these studies on ^284?286115 and ^288?292117 will be a guide to future experiments.     

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.     

Particle Production in Non-equilibrium Thermodynamic States in Nucleus-Nucleus Collisions

The formation of nonequilibrium thermodynamic system is assumed during the collision of relativistic heavy ions with target nuclei. A simple classical solution of the Boltzmann equation is found and compared with the spectra of particles produced in the Ne-U²³⁸ reaction at lab. energies of 250 and 400 MeV per nucleon. The model contains only one fitting parameter t_c which is the time required by the system to reach the equilibrium state.     

Electronic structure of the H+2 molecule

Main results of investigations aimed at a construction of the classical model of the H⁺₂ molecule are presented. The form of the orbit of the electron, binding two nuclei of the H⁺₂ molecule together has been deciphered. Theoretical value of the structural parameter, which is the distance between nuclei times the binding energy of the electron, was found to be equal with a high accuracy to that experimentally measured.     

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.