The droplet model energy of axially asymmetric nuclei

The shape dependent factors of the droplet model energy are evaluated for the special case of an ellipsoid and expressed in terms of four incomplete elliptic integrals. Generalization to other axially asymmetric shapes is considered.     

Solution of Bohr's collective Hamiltonian for transitional odd-mass nuclei

A numerically feasible method, based on the use of deformed phonons, is developed for the diagonalization of the collective quadrupole Hamiltonian for a system with an odd particle coupled to an anharmonic even core. Examples: the transition from prolate to oblate via γ-unstable shapes and furthermore the $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ spectra of the nuclei ¹⁸⁷Ir and ¹⁹⁷Tl.     

Generator coordinate amplitude for scattering

In the generator coordinate method for scattering the proper boundary condition is accomplished by requiring the GC amplitude to satisfy an integral equation of the first kind. Attempts to solve this problem are first reviewed and then an improved approximation is proposed which is applicable to a wider class of scattering problems in addition to the Coulomb scattering.A better approximation is obtained in the asymptotic region, where the generator coordinate, i.e., the distance between two shell-model wells of the fragments, is larger than the touching distance of the colliding nuclei, by deriving partial differential equations of first order for the terms of an asymptotic series in $\text{1}\text{E}$, where E is the scattering energy.Extracting the information on the GC amplitude for small values of the generator parameter from the integral equation of the first kind is an ill-posed problem. It is shown that the method of statistical regularization offers a powerful and controllable procedure to uncover the GC amplitude. The unknown GC amplitude is treated as a random function with an a priori distribution of probability which is based on the assumption that the amplitude is bounded and that the errors in the input are random with zero expectation value. A useful procedure is found for fixing parameters of the a priori distribution. The solution for small values of the GC parameter is expressed in the form of a Dini series.The method is applied to the calculation of the GC amplitude for scattering of two α-particles at 15 MeV c.m. energy. The measure of the accuracy is the difference between the input wave function of relative motion and the result of folding of the GC amplitude with the kernel of the integral equation. The prescribed accuracy is reached with this method on a much larger interval than with any previously proposed method.     

Fusion oscillations for symmetric light heavy-ion systems

The low-energy fusion cross section for ²⁰Ne+²⁰Ne has been measured. The data extend the systematics on fusion oscillations for such light symmetric systems. A simple extension of the usual barrier penetration model displays the decisive role of the symmetrisation of the system. It is also capable of qualitatively explaining the trends in this effect, in particular its decreasing importance as the mass of the system increases. The structure is essentially due to the sharpness of the cut-off of transmission coefficients as a function of angular momentum. The curvature of the Coulomb barrier is important in determining these coefficients and it is shown that the required values of this quantity are consistent with reasonable values of the surface diffuseness of the nuclear potential.     

Study of the inertial functions for rare-earth nuclei

Vibrational (B_ββ, B_βγ, B_γγ) and rotational (B_x, B_y, B_z) inertial functions of Bohr's collective Hamiltonian are studied microscopically as functions of deformation. The study is extended to the inertial functions of the Hamiltonian appropriate for the phonon expansion treatment. The cranking approximation is used. The results are compared with those of the pairing-plus-quadrupole model. Non-adiabatic effects are discussed.     

A phenomenological woods-saxon potential for p-shell nuclei

The parameters of a Woods-Saxon potential well have been determined for ten p-shell nuclei by fitting the electron scattering form factors and single-particle binding energies. The resulting radius shows, for all but very light nuclei, a regular $\text{A}\text{1}\text{3}$ dependence while the depth smoothly decreases with the increasing proton energy. The observed energy dependence may be ascribed to the non-locality of the HF potential. An energy-independent non-local potential, compatible with elastic electron and proton scattering, is proposed in the energy range ?50 to +50 MeV.     

Collective gyromagnetic ratio and moment of inertia from density-dependent Hartree-Fock calculations

The collective gyromagnetic ratio and moment of inertia of deformed even-even axially symmetric nuclei are calculated in the cranking approximation using wave functions obtained with the Skyrme force S-III. Good agreement is found for g_R, while the moment of inertia is about 20 % too small. The cranking formula leads to better agreement than the projection method.     

Investigation of spin dependence of neutron cross sections and of strength functions for rare earth nuclei in experiments with polarized neutrons and nuclei

Experiments on the spin dependence of the interaction of resonance neutrons (up to 100 keV) with the rare earth nuclei ¹⁴¹Pr, ¹⁵⁹Tb, ¹⁶⁵Ho, ¹⁶⁷Er and ¹⁶⁹Tm are reported. The measurements were performed with polarized neutrons and nuclei. The spin dependence of S-wave strength functions was investigated, and the imaginary part of the spin-spin potential (W_ss = 0.10 ± 0.06 MeV) was estimated in optical-model calculations with a potential in the form of a rectangular well. The energy dependence of the difference of strength functions for two J-states shows possible intermediate states in the formation of the compound nucleus. The J-values of about 230 resonances were determined.     

Search for highly excited states in light nuclei with three-body reactions

Various three-body break-up reactions resulting from the bombardment of ⁷Li with 120 MeV ³He have been measured simultaneously in a kinematically complete experiment. Missing-mass spectra have been deduced for ⁴H, ⁴He, ⁴Li, ⁵He, ⁵Li, ⁶He, ⁶Li and ⁷Li. The ground states of ⁴H and ⁵He are well described as n-t and n-α P-wave final-state interactions, respectively. Evidence is found for relatively narrow states at very high excitation energies in several nuclei. The results are compared with those of other authors and with various theoretical predictions.     

Nucleon channel coupling in electrodisintegration of nuclei

The process of nuclear excitation above threshold for nucleon decay in high energy electron scattering is considered. On the basis of the particle-hole shell model a formalism is proposed which allows one to describe electroexcitation of nuclei in a unified manner both in the resonance and quasielastic scattering regions. Numerical calculations were made for the ¹²C nucleus taking into account the mixing of proton and neutron configurations (channels) of the particle-hole type in the continuum.     

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30? have been measured in the nuclei ¹⁵⁶Dy, ¹⁵⁷Dy, and ^ll58Dy using the recoil-distance technique together with inverse reactions of the type $\text{Mg}\text{(}{}^{136}\text{Xe}\text{, x}\text{n}\text{)}$. The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of ^{156, 158}Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.     

Hexadecapole deformation in the wolfram nuclei

The (τ, α) and (d, t) reactions have been used to investigate the positive-parity intrinsic excitations in ^{179, 181, 183, 185}W stemming form the i_{$\text{13}\text{2}$} spherical shell-model state. The $\text{13}\text{2}{}^{\mathrm{+}}$ members of the rotational bands built on each of these orbitals are expected to be populated strongly in neutron-transfer reactions due to the near-unity values of the $\text{C}{}_{\mathrm{j}}\text{=}\text{13}\text{2}$ coefficients. These states were populated in the (τ, α) reaction which favours transfer of high angular momentum. The assignments of l-values were based on the measured ratio of (τ, α) to (d, t) cross sections populating the same state. The Nilsson model, with the inclusion of pairing and Coriolis mixing, was unable to account for the experimental results, namely the observation of all the expected strength localized in only two or four states below 2 MeV of excitation. Much better agreement with experiment was obtained if the extended Nilsson model including a hexadecapole deformation of ε₄ ≈ +0.06 was used as a starting point for a Coriolis-coupling calculation.     

One-nucleon transfer reactions in deformed nuclei

The one-nucleon transfer reaction on deformed nuclei has been computed with the inclusion of indirect inelastic transitions that go through intermediate rotational states. The specific examples considered are¹⁷¹Yb(d, p), ¹⁷²Yb(p, d) and ¹⁸⁶W(p, d). Anomalies in the shapes of of experimental angular distributions with respect to predictions of the distorted-wave Born approximation are shown to be reproduced when these higher-order inelastic processes are taken into account. Consideration is also given to the deuteron optical potential needed for these studies.     

Solution of the Hartree-Fock equations

We suggest to use the Newton iteration method for constructing a (locally unique) solution of the atomic and nuclear Hartree-Fock equations for an arbitrary number of particles. Our proposal is based on a theorem by Kantorovi and rests on the following points: 1) the two-body potential must satisfy a boundedness condition; 2) the zero-order approximation, used to start the iteration sequence, must satisfy certain conditions, to be proved numerically. Condition 1) holds, for instance, for all local potentials, defined by a bounded function and for a class of nonlocal potentials; it does not hold for local potentials, behaving as 1/r near the origin.This work has been supported in part by Istituto Nazionale di Fisica Nucleare (Sezione di Catania) and by Centro Siciliano di Fisica Nucleare e di Struttura della Materia (Catania).     

Electromagnetic transitions in some odd-neutron deformed nuclei

Using the reactions ^{155, 157}Gd(α,2n), ¹⁷⁸Hf(n,γ) and ^{177Hf(α, 2n}, the following half-lives of excited nuclear states have been measured: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(188.1}\text{keV in}{}^{157}\text{Dy}\text{) = 1.00 ± 0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(161.9}\text{keV in}{}^{157}\text{Dy}\text{) = 1.3 ± 0.2 μ}\text{S}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(177.6}\text{keV in}{}^{159}\text{Dy}\text{) = 9.0 ± 0.5}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(614.3}\text{keV in}{}^{179}\text{Hf}\text{) = 0.50 ± 0.15}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(720.7}\text{keV in}{}^{179}\text{Hf}\text{) ≦ 0.3}\text{ns}$, $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(516.4}\text{keV in}{}^{179}\text{Hf}\text{) < 0.2}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(309.0}\text{keV in}{}^{179}\text{W}\text{) = 1.53 ± 0.10}\text{ns}$. A Ge(Li) timing system was employed. Electromagnetic transition probabilities are calculated in the Nilsson model including pairing and band mixing effects. Comparisons between theoretical and experimental results are performed.     

Evidence from inelastic proton scattering for a giant quadrupole vibration in spherical nuclei

A systematic study of inelastic proton continuum spectra produced at small angles by bombardment of ²⁷Al, ⁵⁴Fe, ¹²⁰Sn and ²⁰⁹Bi with 62 MeV protons suggests the existence of a collective region in the continuum with properties of a giant quadrupole vibration.     

Possible rotational states in odd In nuclei

Levels and transitions in ¹⁰⁷In and ¹⁰⁹In have been studied in in-beam spectroscopy on the reactions ¹⁰⁶Cd(d, nγ)¹⁰⁷In and ¹⁰⁸Cd(d, nγ)¹⁰⁹In. Low-lying $\text{1}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}$ states resembling the possible rotational bands observed in the heavier In isotopes are seen in both nuclei. The potential energy has been calculated for ^107–121In with the odd proton in different orbitals, using the Strutinsky normalization procedure. A prolate minimum at a deformation ε ≈ 0.2 is obtained for the lowest $\text{1}\text{2}{}^{\mathrm{+}}$ orbital, which is in good agreement with the experimental data for ^115–119In. The excitation energy of the $\text{1}\text{2}{}^{\mathrm{+}}$ minimum shows a fairly good agreement with experimental data.     

Four-body Yakubovsky differential equations for identical particles

The differential equations for Yakubovsky components of the four-body wave functions are derived. An asymptotic form of these components is described. A symmetrized form of the Yakubovsky differential equations for four identical particles is given and its angular analysis is performed. Bound-state calculations are presented for various potentials.