Nuclear Moment Of Inertia Research Articles

Moment of inertia of even–even proton-rich nuclei using a particle-number conserving approach in the isovector neutron–proton pairing case

An expression of the particle-number projected nuclear moment of inertia (MOI) has been established in the neutron–proton (np) isovector pairing case within the cranking model. It generalizes the one obtained in the like-particles pairing case. The formalism has been, as a first step, applied to the picket-fence model. As a second step, it has been applied to deformed even–even nuclei such as [Formula: see text] and of which the experimentally deduced values of the pairing gap parameters [Formula: see text], [Formula: see text], are known. The single-particle energies and eigenstates used are those of a deformed Woods–Saxon mean-field. It was shown, in both models, that the np pairing effect and the projection one are non-negligible. In realistic cases, it also appears that the np pairing effect strongly depends on [Formula: see text], whereas the projection effect is practically independent from the same quantity.

Application of the triaxial quadrupole–octupole rotor to the ground and negative-parity levels of actinide nuclei

In this work, we examine the possibility to describe yrast positive- and negative-parity excitations of deformed even–even nuclei through a collective rotation model in which the nuclear surface is characterized by triaxial quadrupole and octupole deformations. The nuclear moments of inertia are expressed as sums of quadrupole and octupole parts. By assuming an adiabatic separation of rotation and vibration degrees of freedom, we suppose that the structure of the positive- and negative-parity bands may be determined by the triaxial-rigid-rotor motion of the nucleus. By diagonalizing the Hamiltonian in a symmetrized rotor basis with embedded parity, we obtain a model description for the yrast positive- and negative-parity bands in several actinide nuclei. We show that the energy displacement between the opposite-parity sequences can be explained as the result of the quadrupole–octupole triaxiality.

Nuclear moment of inertia as an indicator of the phase transition in a finite system

The purpose of this article is to derive the analytic expression for the angular-momentum dependence ($I$ dependence) of the moment of inertia in microscopic mean-field theory for both even-even and odd-mass nuclei. Based on the constrained Hartree-Fock-Bogoliubov theory, the Coriolis antipairing effect is taken into account as the second-order perturbation to the BCS basis together with the blocking effect. Instead of integration, an asymptotic series expansion is applied to the quantity in which finiteness of the nuclear system becomes tangible in the high-spin region, where the gap parameter $\ensuremath{\Delta}$ becomes much smaller than the average single-particle level distance $d$. As a result, $\ensuremath{\Delta}$ keeps a small but finite value even for high-spin states, showing that there is no sharp phase transition in the nucleus. Analytic formulas are derived for the $I$ dependence of the moment of inertia for different regions of $\ensuremath{\Delta}\ensuremath{\ge}d/2$ and $\ensuremath{\Delta}<d/2$.

Temperature-dependent particle-number projected moment of inertia

Expressions of the parallel and perpendicular temperature-dependent particle-number projected nuclear moment of inertia have been established by means of a discrete projection method. They generalize that of the FTBCS method and are well adapted to numerical computation. The effects of particle-number fluctuations have been numerically studied for some even-even actinide nuclei by using the single-particle energies and eigenstates of a deformed Woods-Saxon mean field. It has been shown that the parallel moment of inertia is practically not modified by the use of the projection method. In contrast, the discrepancy between the projected and FTBCS perpendicular moment of inertia values may reach 5%. Moreover, the particle-number fluctuation effects vary not only as a function of the temperature but also as a function of the deformation for a given temperature. This is not the case for the system energy.

NEUTRON-PROTON ISOVECTOR PAIRING EFFECT ON THE NUCLEAR MOMENT OF INERTIA

The neutron-proton (n-p) isovector pairing effect on the nuclear moment of inertia has been studied within the framework of the BCS approximation. An analytical expression of the moment of inertia, that explicitly depends upon the n-p pairing, has been established using the Inglis cranking model. The model was first tested numerically for nuclei such as N = Z and whose experimental values of the moment of inertia are known (i.e. such as 16 ≤ Z ≤ 40). It has been shown that the n-p pairing effect is non-negligible and clearly improves the theoretical predictions when compared to those of the pairing between like particles. Secondly, predictions have been established for even-even proton-rich rare-earth nuclei. It has been shown that the n-p pairing effect is non-negligible when N = Z and rapidly decreases with increasing values of (N-Z).

Nuclear structure and dynamics from heavy - ion induced fission reactions

The study of heavy - ion fusion and fission reactions at near - barrier energies continues to be a rich source of information as regards nuclear structure and dynamics. From a comprehensive statistical model analysis of the fusion and the fission data including information on the pre - scission neutrons, for a large number of compound nuclei with masses around 200, it has been possible to determine reliably the fission barrier, the nuclear moment of inertia and the shell correction at the saddle point. Interestingly, it is found that for the nuclei in the mass region around 200, a significantly large fraction of the ground state shell correction persists at the deformed saddle - point. Systematic measurements of the fission fragment angular distributions spanning a range of projectiles with A = 9 to 19, bombarding the Th,U and Np targets have clearly brought out role of the entrance channel dynamics involving a new type of non - equilibrium fission, which we call pre - equilibrium fission comempeting with the equilibrium compound nucleus fission. A new model which takes into account the deformation and the spin values of the target and the projectile, the orientation and the entrance channel mass asymmetry dependence of the interacting nuclei has been developed which provides a good description of the fission fragment angular distribution data both at above and below barrier energies.

Publisher’s Note: Nuclear moments of inertia and wobbling motions in triaxial superdeformed nuclei [Phys. Rev. C69, 034325 (2004)

The wobbling motion excited on triaxial superdeformed nuclei is studied in terms of the cranked shell model plus random phase approximation. Firstly, by calculating at a low rotational frequency the \gamma-dependence of the three moments of inertia associated with the wobbling motion, the mechanism of the appearance of the wobbling motion in positive-\gamma nuclei is clarified theoretically -- the rotational alignment of the \pi i_{13/2} quasiparticle(s) is the essential condition. This indicates that the wobbling motion is a collective motion that is sensitive to the single-particle alignment. Secondly, we prove that the observed unexpected rotational-frequency dependence of the wobbling frequency is an outcome of the rotational-frequency dependent dynamical moments of inertia.

Nuclear moments of inertia and wobbling motions in triaxial superdeformed nuclei

The wobbling motion excited on triaxial superdeformed nuclei is studied in terms of the cranked shell model plus random phase approximation. First, by calculating at a low rotational frequency the $\ensuremath{\gamma}$ dependence of the three moments of inertia associated with the wobbling motion, the mechanism of the appearance of the wobbling motion in positive-$\ensuremath{\gamma}$ nuclei is clarified theoretically---the rotational alignment of the $\ensuremath{\pi}{i}_{13∕2}$ quasiparticle(s) is the essential condition. This indicates that the wobbling motion is a collective motion that is sensitive to the single-particle alignment. Second, we prove that the observed unexpected rotational-frequency dependence of the wobbling frequency is an outcome of the rotational-frequency dependent dynamical moments of inertia.

Quantized wobbling excitations with alignments

The wobbling excitations in the presence of an appreciable amount of alignment are expected to appear more easily at lower angular momenta of the yrast spectra, compared with those in the textbook example. The large B(E2;I-->I-1) value for Delta(n) over cap =1 transitions where (n) over cap expresses the number of wobbling phonons is shown to be a strongly increasing function of the triaxiality parameter gamma, especially for gammagreater than or similar to+20degrees, while it is relatively independent of moments of inertia. On the other hand, the relation of the wobbling phonon energy to the total angular momentum may be used to extract quantitative information on nuclear moments of inertia. It is concluded that the gamma value of the triaxial, strongly deformed bands in Lu-163 is about equal to +20degrees and may be slightly increasing as a function of I. (Less)

Nonadditivity in nuclear moments of inertia and interference between blocking effects

The experimentally observed obvious nonadditivity in the nuclear moment of inertia and angular momentum alignment of multiquasiparticle rotational bands, both in normally deformed and superdeformed nuclei, presents a serious challenge to the traditional BCS treatment for nuclear pairing. It is shown that the systematically observed nonadditivity mainly comes from the destructive interference between blocking effects, and can be satisfactorily accounted for by the particle-number conserving method, in which the blocking effects are treated consistently and exactly.

THE SINGLE PARTICLE SCHRÖDINGER FLUID AND MOMENTS OF INERTIA OF THE NUCLEI 24Mg, 25Al, 27Al, 183W AND 238Pu

The single particle Schrödinger fluid is applied to study the rotational motion of independent nucleon systems. Accordingly, we have applied the description of this Schrödinger fluid to the calculations of the moments of inertia of the axially deformed nuclei. As examples for the application of this concept to the calculations of the nuclear moments of inertia we have calculated the cranking-model, the rigid body-model and the equilibrium moments of inertia of the axially deformed nuclei 24 Mg , 25 Al , 27 Al , 183 W and 238 Pu . The variations of the moments of inertia of these nuclei with the deformation parameter β have also been given.

K pi =1(+) pairing interaction and moments of inertia of superdeformed rotational bands in atomic nuclei.

The effect of the pairing interaction coming from the rotationally induced [ital K][sup [pi]]=1[sup +] pair-density on the nuclear moments of inertia is studied. It is pointed out that, contrary to the situation at normal deformations, the inclusion of the [ital K][sup [pi]]=1[sup +] pairing may appreciably modify the frequency dependence of the moments of inertia at superdeformed shapes.

On the parallel axis theorem for cranking moments of inertia

The validity of the parallel axis theorem for nuclear moments of inertia is examined within the framework of the cranking model. It is shown that this theorem applies only when a requirement of self-consistency between potential and density distribution is imposed. In this case, the theorem follows as a consequence of a gauge invariance property of the cranking model Schrodinger equation.

Microscopic calculation of the restoring force for scissor isovector vibrations

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.

Nuclear moments of inertia at high spins

Nuclei with highest angular momentum are discussed. The production of high spin states, and the basic ideas associated with high spin physics are reviewed. Recent developments from “continuum” γ-ray studies are presented: the measurement of different average moments of inertia gives new information on the interplay between collective and single particle aspects at high spins. Finally, the exciting possibility of resolving the “continuum” spectra with new detector systems is examined.

Microscopic theory of nuclear collective rotation. V. Connection between nuclear moments of inertia and the definition of a body-fixed frame

For pt.IV see ibid., vol.6, p.1347-58 (1980). Various methods for calculating nuclear moments of inertia are investigated from the point of view of their possible connection with special choices of collective variables. The theoretical tool for this investigation is the method of specific decoupling. For any definition of the body-fixed frame, the authors method provides, in an elegant way, a well defined expression for the moment of inertia. The internal degrees of freedom are described using intrinsic densities and intrinsic wavefunctions. Several frequently used formulae for calculating the moment of inertia can be traced back to specific definitions of the internal frame. The extremum principle of specific decoupling makes possible a very lucid evaluation of the magnitudes of these moments of inertia relative to each other as well as with respect to the corresponding values of the rigid and the irrotational moments of inertia.

Exponential model with pairing attenuation and the backbending phenomenon

Rotational energy calculations with an exponential dependence of the nuclear moment of inertia on pairing correlations coupled with an explicit spin dependence of the effective pairing gap analogous to that used in superconductivity give an excellent fit to the experimental data on excitation energies of yrast band levels in well-deformed even-even nuclei and also reproduce the backbending feature satisfactorily. The variation of the pairing gap parameter with spin is found to be gradual and smooth as compared to the abrupt variation evidenced in the pairing collapse treatment. Variations of the limiting moments of inertia parameter with mass number derived from our model exactly match with those coming out of the cranking model calculations for neutrons and are in no way related to the proton results; for lighter rare earth nuclei also the fluctuations in the values of the moment of inertia are found to correspond to those of the neutron single particle level spacings in this region.

Nuclear moments of inertia in the absence of pairing

The nuclear moments of inertia in the absence of pairing are not equal to the rigid-body values because of quantal corrections due to the finite size of the system.

Isomeric cross section ratios in the 197Au(n, 2n) 196Au reaction

The cross section ratios of 196Au isomers produced in the 197Au(n, 2n) reaction have been measured at 14.7 MeV neutron energy and compared with the values reported previously. The results have also been compared with the theoretical calculations based upon the statistical model and predictions have been made of the spin-cut-off factor and the nuclear moment of inertia

MOMENS OF INERTIA OF EXCITED BANDS AND THE EVEN-ODD DIFFERENCE

The formulae for calculating nuclear moments of inertia with the particle-numbes-conserving method for treating pairing forces are presented. Taking 170 Yb and 169 Yb as typical examples, the even-odd difference of the moments of inertia and the dif-ference in moment of inertia between excited bands and the ground band are treated with this method, which automatically takes the blocking effect into account. The calculated results agree relatively well with the experiments.