B. F. Bayman

A derivation of the pairing-correlation method

Abstract A discussion is given of the problem of a system of fermions moving in a set of single-particle orbits, and interacting by means of a pairing force. The Bardeen-Cooper-Schrieffer equations are derived by a method which exhibits their approximation as that inherent in the saddle-point method, and without the introduction of fluctuations in the number of particles.

On the connection between the cluster model and the SU3 coupling scheme for particles in a harmonic oscillator potential

Abstract It is shown that the cluster model of Wildermuth and Kanellopoulos provides an alternative description of certain states in the SU 3 coupling scheme of Elliott.

Finite-range calculation of the two-neutron transfer reaction

Abstract Distorted-wave Born approximation calculations have been done for two-neutron transfer reactions, in which the total angular momentum transferred was zero. A finite-range interaction was used, which acted between the proton and each transferred neutron. The results support the conclusions of zero-range calculations, both with respect to the shapes of the angular distributions, and the relative cross sections for transfer into different shells. However, the absolute cross sections, calculated for the 40, 48 Ca(t, p) 42, 50 Ca(g.s.) reactions, were only about a third as large as those observed.

A generalization of the spherical harmonic gradient formula

The familiar gradient formula is generalized by replacing the gradient operator by an arbitrary solid harmonic of the gradient operator. The result is applied to various multipole expansions of angular momentum eigenstates.

Monte Carlo calculations of two-neutron transfer cross sections

Abstract Differential cross sections for (t, p) and (p, t) reactions have been calculated in finite-range distorted-wave Born approximation, with the Monte Carlo method used to evaluate the six-dimensional integrals. The use of the Monte Carlo method makes it possible to treat cases of non-zero angular momentum transfer. Angular distributions and relative cross sections are in good agreement with those given by the zero-range approximation. The cross sections of unnatural-parity transitions, as calculated by our one-step finite-range DWBA, are several orders of magnitude smaller than experimental data, suggesting the importance in these reactions of two-step processes.

Anomalons in relativistic heavy-ion collisions

Abstract By reviewing experimental results from many anomalon searches, one can reasonably conclude that anomalons, if they exist, are preferentially produced in peripheral collisions, signified by low values of N h and δ Z . For Z ≥ 3, the experimental picture about the existence of anomalons is not very clear at this moment. In the Z = 2 case, however, there are reasonably convincing indications that anomalons do seem to be present in fragments produced by light projectile nuclei such as 12 C.

Model of the behavior of solid objects during collision

When two hard solid objects collide, acoustic waves are generated at the point of impact. The deformation of the objects and their subsequent separation are associated with the propagation of these acoustic waves through the objects and their reflection from the surfaces. In this paper we follow the time development of these processes in detail for one‐dimensional collisions involving Hooke’s law springs. We calculate the degree of inelasticity of the collision from the state of internal excitation of the springs after separation occurs. An attempt is made to generalize the conclusions obtained in this one‐dimensional model to the qualitative description of the collision of hard spheres.

Spin-dependent effects in heavy-ion reactions

Abstract The 40 Ca( 13 C, 14 N) 39 K reaction at 60 and 68 MeV has been investigated in the no-recoil approximation to the DWBA. Reorientation effects arising from the quadrupole moments of 14 N and 39 K were found to be small. The use of spin-orbit components in the optical potentials was found to shift the phase of the angular distribution into agreement with experiment, while maintaining a fit to the elastic data. This was understood from a generalization of the Strutinsky model. For the 40 Ca( 13 C, 12 C) 41 Ca reaction at 60 and 68 MeV a smaller shift in phase was obtained which was desirable, but the damping of the magnitude of the oscillations was disturbing.

Quasibound‐state resonances for a particle in a two‐dimensional well

The problem of a particle moving in a two‐dimensional potential well is used to illustrate many of the features of collisions between systems with internal structure. Resonance phenomena are shown to occur when the total energy is close to the energy of a quasibound state, and the width of the resonance is related to the coupling between the quasibound state and the open channels. Explicit calculations are performed for a rectangular potential well.

Spectroscopy with the 45Sc(α, p)48Ti reaction at 26 MeV

Abstract The 45 Sc(α, p) 48 Ti reaction has been studied at 26 MeV bombarding energy with an overall energy resolution of 30 keV. Angular distributions for 31 transitions were recorded and analyzed, covering excitation energies below 6 MeV. A formalism has been developed which allows the computation of fully microscopic zero-range three-particle transfer form factors without expansion in harmonic oscillator wave function bases. The low-lying ( f 7 2 ) 3 dominated transitions have been analyzed using f 7 2 shell model wave functions and a DWBA code. It is concluded that the cross-conjugation conjugation symmetry of the f 7 2 model breaks down for the 6 + states, while the transitions to 0, 2, 3 and 4 + states are well accounted for. A comparison of (α, p) transition intensities to 48 Ti 0 + states with the corresponding 46 Ti(t, p) 48 Ti intensities suggests a strong correlation between the two reactions, a correspondence that is also evident from the structure of the form factors.