A.K. Kerman

Nuclear deformation energy curves with the constrained Hartree--Fock method.

Abstract Calculations of the deformation energy curves of relatively heavy deformed nuclei — Ce isotopes — have been performed using the constrained Hartree-Fock technique. The two-body interaction is the Skyrme force, and pairing effects are taken into account. Different possible choices for the external field form are investigated and the advantage of a non-linear dependence of the constraint is shown. One of the advantages of this type of calculation is that deformation energy curves can be calculated without making a complete map of the deformation energy surface. A discussion of the numerical techniques and uncertainties, particularly those connected with truncation effects is given. General trends of the deformation energy curves, calculated for the Ce isotopes as a function of the quadrupole moment, are found to be in good agreement with available experimental information. Associated physical quantities are discussed and a comparison is made with the results of phenomenological calculations using the liquid-drop model and the Strutinsky prescription.

Shape transition in the neutron rich sodium isotopes

Abstract Mass spectrometer measurements of the neutron rich sodium isotopes show a sudden increase at 31Na in the values of the two-neutron separation energies. The spherical shell model naturally predicts a sudden decrease at 32Na after the N = 20 shell closure. We propose that the explanation for this disagreement lies in the fact that sodium isotopes in this mass region are strongly deformed due to the filling of negative parity orbitais from the 1f 7 2 shell. Hartree-Fock calculations are presented in support of this conjecture.

SOFT-CORE NUCLEON-NUCLEON POTENTIAL

Abstract The hard cores of the Hamada-Johnston1) (HJ) nucleon-nucleon potential are replaced by finite square wells of larger radius (0.7 fm), and it is demonstrated that the nucleon-nucleon scattering and deuteron data are very well fit by this specific static potential. Outside of the square-well radius the potential is the same as that of HJ except for a few small changes in some of their parameters. The pion masses differ from that of HJ in a charge-dependent way such that charge symmetry is retained. The radius of the square finite cores, which is about 0.7 fm, also has a small charge dependence such that charge symmetry is retained but charge dependence is violated. The strengths of the square cores for n-p and p-p scattering are determined by a computer search. The search routine utilizes a chi-squared test in which the scattering and deuteron data are fit directly. The current best fit obtained in the p-p case has a chi-squared value of about 2.0 per data point, which is smaller than that for any other potential tested against the p-p data set of Signell et al.2).

Self-consistent calculation of the fission barrier of 240Pu

Abstract Completely self-consistent calculations using the Skyrme force have been carried out for the fission energy curve of 240 Pu. We use a deformed oscillator basis including 13 major shells and convergence has been checked by extending the size of the basis to 15 shells. We obtain a double humped barrier with energies E A = 9 MeV for the first barrier, E B = 13 MeV for the second barrier and E II = 4 MeV for the isomeric state. Corrections to our calculation, such as inclusion of non-axial and symmetric shapes and zero-point rotational motion, are likely to improve quantitative agreement with experimental data.

DAMPING OF ISOBARIC ANALOGUE STATES

Abstract The spreading width of analogue states due to the Coulomb interactions in a nucleus is calculated. The coupling to single-particle, two-particle-one-hole and three-particle-two-hole configurations is considered. The effect of nuclear interactions is taken account in the large energy separation between the analogue and the configuration states (symmetry energy displacement) and in the natural distribution of the latter representing their fragmentation. The spreading widths are found to be small, less than 3 keV in 89 Y and 91 Nb.

Study of the 138Ba(d, p)139Ba reaction for incident energies below the coulomb barrier

Abstract The 138 Ba(d, p) 139 Ba reaction has been studied with incident deuteron energies between 5.0 and 7.5 MeV in steps of 0.5 MeV. Proton groups observed at 7.5 MeV corresponding to states in 139 Ba up to 4.0 MeV excitation are reported. The differential cross sections of proton groups corresponding to the ground state, first and second excited states have been measured. The stripping analysis for those transitions is discussed using a DWBA formalism, and values for the reduced normalization and spectroscopic factors versus deuteron energy are given.

TWO BODY FORCES IN LIGHT DEFORMED NUCLEI

Abstract There is evidence that the light nuclei in the aluminium region have rotational states. It is well known from studies of heavy rotating nuclei that an independent particle model for a deformed well as used by Nilsson is a surprisingly good approximation for many of the properties of these collective states. However, it has been clear for some time that two body correlations are important for a more complete understanding of the situation. Because the number of single particle states for the light nuclei is relatively small and because isobaric spin is a good quantum number, we have undertaken some studies on the effect of two body forces on binding energies and energy levels. In particular we have employed the method of Bacher and Goudsmit to find relations among binding energies which depend only upon the existence of two body forces and the assumption that the deformed wave function coupling scheme is a good first approximation. The relations so obtained are remarkably well fulfilled by the data while corresponding relations obtained for the spherical shell model are not. Some of the possible excited states in these nuclei are also discussed and estimates made of their energies.

Nuclear rotations studied by the time-dependent variational method☆

Abstract A general nuclear rotation including precession and wobbling motion is studied by the time-dependent variational method and a classical equation of motion is derived. The intrinsic wave function associated with the general rotational motion is constructed by making use of the constrained Hartree-Fock method and variables necessary in solving the equation are calculated. The method developed here is applied to a schematic extension of the Nilsson model.

The effects of truncation in nuclear Hartree-Fock calculations

Abstract Hartree-Fock calculations were carried out for the doubly even nuclei with A = 4 to A = 80 in a space consisting of the 1 s 1 2 to the 1 i 1 2 harmonic oscillator states inclusive. The results are compared to results of a previous HF calculation in which the space was truncated at the top of the 2p-1f shell. The effects of the truncation are found to be more pronounced for deformed nuclei than for the spherical nuclei, where convergence has been previously studied. As expected, the quadrupole moment is found to be quite sensitive to this extension of the space, while the binding energy, r.m.s. radius and the kinetic energy per particle are not. Center-of-mass effects, compressibility and deformability are also studied, and a few nuclei with 80 ≦ A ≦ 208 are considered.

On the spheroidal bag

Abstract We derive the eigenmodes of quarks and gluons moving in a statically deformed spheroidal cavity satisfying the linear boundary condition of the MIT bag model. Using the gluon propagator of the deformed cavity we determine the quark-quark interaction via one-gluon exchange for massless quarks in the ground state. The model is then applied to nonstrange baryons, and the ground state energy of this three-quark system is calculated as a function of the deformation. With non-interacting quarks the nucleon and the Δ-isobar turn out to be spherically symmetric, as expected. Switching on the one-gluon-exchange interaction, the nucleon still remains spherically symmetric, while the Δ-resonance develops a large oblate or prolate deformation depending on the spin projection on the symmetry axis.