Narrow Results

We deal with the application of the nuclear Born–Oppenheimer (NBO) method to the study of nuclear collective motion. In particular, we look at the description of nuclear rotations and vibrations. The collective operators are specified within the NBO method only to the extent of identifying the type of collective degrees of freedom we intend to describe; the operators are then determined from the dynamics of the system. To separate the collective degrees of freedom into rotational and vibrational terms, we transform the collective tensor operator from the lab fixed frame of reference to the frame defined by the principal axes of the system; this transformation diagonalizes the tensor operator. We derive a general expression for the NBO mean energy and show that it contains internal, collective and coupling terms. Then, we specify the approximations that need to be made in order to establish a connection between Bohr's collective model and the NBO method. We show that Bohr's collective Hamiltonian can be recovered from the NBO Hamiltonian only after adopting some rather crude approximations. In addition, we try to understand, in light of the NBO approach, why Bohr's collective model gives the wrong inertial parameters. We show that this is due to two major reasons: the ad hoc selection of the collective degrees of freedom within the context of Bohr's collective model and the unwarranted neglect of several important terms from the Hamiltonian.

Rotationally single-particle and vibrational excitations of deformable odd non-axial odd nuclei are investigated with allowance for the interaction of collective and single-particle states. The ratios of excitation energies, of reduced probabilities of E2 transitions, and of quadrupole moments for deformable non-axial odd nuclei are calculated up to high-spin states.

The unusual structure of ¹¹Li, the first halo nucleus found, is analyzed by the Preparata model of nuclear structure. By applying coherent nucleus theory, we derive a new interaction potential for the halo-neutrons that correctly reproduces the fundamental state of the system.

Excited states deformable odd nuclei with small triaxiality are investigated with allowance for the interaction of collective and single-particle states. Possibility of describing excited states properties of deformable odd nuclei with small triaxiality within non-adiabatic theory of odd nuclei is considered, including states up to high spins. Exponential type of potential is used for the longitudinal vibrations of the nucleus surface.

We present a new study of the low-lying states in ¹²⁴Te nucleus by γ-ray spectroscopy following ¹²⁴Iβ⁺/ε decay. The β radioactive sources were produced in the ¹²⁴Te(p, n)¹²⁴I reaction induced by 11 MeV protons, delivered by the Bucharest FN Tandem Accelerator. The γ-rays were measured in a low background area with three large volume HPGe detectors. A total number of 276 milion double coincidence events were recorded in a six-day run. Most of the gamma line intensities previously measured were confirmed with improved accuracy and several gamma lines were obtained for the first time. Our results, combined with those from a recent (n, γ) study are compared with the predictions of the E(5) critical point symmetry model and numerical IBA-1 model calculations at the critical point of the U(5)–O(6) phase transition.

For the Riemannian space, built from the collective coordinates used within nuclear models, an additional interaction with the metric is investigated, using the collective equivalent to Einstein's curvature scalar. The coupling strength is determined using a fit with the AME2003 ground state masses. An extended finite-range droplet model including curvature is introduced, which generates significant improvements for light nuclei and nuclei in the trans-fermium region.

Optical potentials for the scattering of K^± from ⁶Li and ¹²C nuclei are calculated using the Watanabe superposition model in terms of the alpha-particle and deuteron optical potentials. The elastic and inelastic scattering differential cross-sections obtained using these potentials are compared with experimental data. Good fits are obtained without modifying any of the parameters. Further measurements for K^± scattering from ⁶Li are stressed.

Beyond the shape phase transition from the spherical vibrator to the deformed rotor regime at $N=90$, the interplay of $\beta$- and $\gamma$-degrees of freedom becomes important, which affects the relative positions of the $K^{\pi }=0^{+}\beta$- and $K^{\pi }=2^{+}\gamma$-bands. In the microscopic approach of the dynamic pairing plus quadrupole model, a correlation of the strength of the quadrupole force and the formation of the $\beta$- and $\gamma$-bands in ${}^{158}$Dy is described. The role of the potential energy surface is illustrated. The $E2$ transition rates in the lower three $K$-bands and the multi-phonon bands with $K^{\pi }=0^{+},2^{+}$ and $4^{+}$ are well reproduced. The absolute $B(E2,2_{\mathrm{\text{i}}}^{+}=0_2^{+})$$(i=2,3)$ serves as a good measure of the quadrupole strength. The role of the single particle Nilsson orbits is also described.

In the collective spectra of atomic nuclei, the level energy $E(2_1^{+})$ varies with atomic number $Z$ and neutron number $N$. Also the $E$2 decay-reduced transition probability $B(E2,0_1^{+}\to 2_1^{+})$ is related to the energy $E(2_1^{+})$. The product $E(2_1^{+})\times B(E2)\uparrow$ is constant according to Grodzins product rule, independent of the vibration or rotational status of the nucleus. The product rule is often used for determining $B(E2)$ from the known $E(2_1^{+})$. However, the variation of the product with various parameters is also suggested in the literature. Hence, a detailed global study of this rule for $(Z=54--78,66<N<126)$ region is warranted. We use a novel method of displaying the linear relation of $B(E2)\uparrow$ with $1/E(2_1^{+})$ for the isotopes of each element (Xe–Pt), instead of their variation with $N,Z$ or $A$. Through our work, we firmly establish the global validity of the Grodzins relation of $B(E2)$, being proportional to the moment of inertia, except for the deviation in specific cases. Our $B(E2)\uparrow$ versus $1/E$ plots provide a transparent view of the variation of the low-energy nuclear structure. This gives a new perspective of their nuclear structure. Also the various theoretical interpretations of $B(E2)$s and the energy $E(2_1^{+})$ are reviewed.

The nuclei in the $A=130,$$100$ and $80$ regions, lying on both sides of the $\beta$-stability line, continue to be of interest for their complex nuclear structures. The Grodzins product rule (GPR) viz. $[E(2_1^{+})\times B(E2,0_1^{+}\to 2_1^{+})=\mathrm{\text{constant}}\times Z^2{A}^{-2/3}]$, for the ground bands of even-$Z$ even-$N$ nuclei provides a useful approach to study these structures. The utility of our method, displaying the linear relation of $B(E2)$ to $[1/E(2_1^{+})]$, is illustrated for the $Z=30$ Zn to $Z=48$ Cd series of isotopes. The spread of the data on the linear plots enables a quick view of the shape phase transitions. The role of the shells and the subshells, at spherical and deformed shell gaps for neutrons and protons, with their mutual re-inforcement and the shape phase transition are vividly visible on our plots. The development of collectivity in this region is also linked to the effective number of valence nucleons above the magic number of $Z=20$, and 28 rather than $Z=40$, for Mo to Cd isotopes for a microscopic calculation.

The Kr isotopes lying in between the lighter isotopes of (Zn, Ge and Se) and the heavier isotopes of (Sr and Zr) in the $A=70$–80 region exhibit very interesting spectral features. The spectra of ${}^{72-84}$Kr isotopes display a striking contrast from those of Zn, Ge and Se isotopes. The role of spherical and oblate and prolate deformed subshell gaps at specific $Z$ and $N$ and the resulting re-inforcement are strikingly evident in these contrasting features, with variation in $Z$ or $N$. The evolution of the spectral features in Kr isotopes with $N$ as reflected in the quadrupole deformation, $K$-band structures, $E$0 decay, $B(E$2) values, $\beta$-softness of the nuclear core and odd–even staggering in $K^{\pi }=2^{+}\gamma$-bands is studied to explore the role of the under lying nuclear interactions. The correlations with odd–$A$ isotopes are explored. The shape co-existence displayed in some Kr isotopes is studied. The large deformation observed in the ground bands of ${}^{74,76}$Kr, as exhibited in the $B(E$2) values, is especially interesting.

The validity of the extended Grodzins product rule (GPR) for higher spins in the ground bands of even $Z$, even $N$ nuclei of the light mass region of Cd to Zn chain of isotopes is studied. The plots of $B(E$2, $I\to I-2$) versus [1/$E_{\gamma }(I\to I-2)$] ($I^{\pi }=4_1^{+}$, 6${}_1^{+})$ provide test of the linear relationship of the two entities. There seems to be a good correlation of the two entities at these higher spin states for most of the nuclei studied here. The deviations from linearity in specific cases are found to be useful for studying the variations in the nuclear structures involved. From these linearity plots, the structural change at higher spin in some nuclei involving subshell gaps, as reflected in the anomalous rise or saturation, leads to further insight into the under lying microscopic structure.

The structure of even-mass isotopes ${}^{70-88}$Ge is described in the framework of the five-dimensional Bohr collective Hamiltonian with the microscopic input from a self-consistent mean-field calculation based on the multidimensional constrained covariant density functional theory. The relativistic functionals PC-PK1 and NL3 supplemented by a finite-range pairing force are used to perform constrained mean-field calculations of potential energy surfaces and collective inertia as functions of quadrupole deformation parameters. Results of calculations manifest the spherical-oblate-prolate shape transition in neutron-rich Ge isotopes. The properties of low-lying collective states are calculated and compared with the available experimental data. In particular, for ${}^{74,76,78,80}$Ge isotopes excitation spectra are accurately reproduced. The results represent a significant advancement in understanding the peculiar structure of the Ge isotopes.