Arthur K. Kerman

Intermediate structure and doorway states in nuclear reactions

Abstract Intermediate structure in the energy dependence of cross sections is interpreted in terms of an intermediate model, which describes the transition amplitude averaged over an energy interval which is much larger than the width and spacing of the compound nuclear levels, but which is much smaller than the widths of the structure in the optical model cross sections. The intermediate structure is ascribed to resonances in the intermediate amplitude, which in turn are assumed to be the consequence of the existence of doorway states which are described and defined. A formalism is developed which takes the existence of these states explicitly into account. The resultant amplitude is then averaged and the intermediate model obtained. For an isolated doorway state this amplitude can be divided into a slowly varying part and a rapidly varying resonant part. The energy width of the resonant term equals the width of the doorway state, which is composed of an escape width into open channels, and a decay width into more complex excitations. Strength functions are shown to exhibit intermediate structure. These results are generalized to the case of overlapping doorways. Reactions as well as elastic scattering are discussed. The results are put in a form which permits the analysis of experimental data in terms of intermediate model resonances, and the quantum numbers of the doorway states extracted. Experimental situations which would tend to exhibit intermediate structure, and the identification of such structure as an intermediate model resonance, are outlined. Some examples of intermediate structure are discussed.

Hamiltonian formulation of time-dependent variational principles for the many-body system☆

Abstract We discuss a canonical Hamiltonian formulation for the general time-dependent variational principle associated with the Schroedinger equation. It is expected that such methods will be useful for a wide range of systems including the many body problem and field theory. It is hoped that the canonical formulation will be an aid in identifying useful further approximation schemes for complicated systems; for example, the reduction to some sort of fluid dynamics for the many body scattering problem or the identification of suitable dissipation terms in a reduced description by the use of statistical arguments.

Pairing forces and nuclear collective motion

Abstract The influence of pairing forces on the collective vibrations in nuclei is studied using a perturbation expansion. The result is found to agree with that given by Belyaev using the superconductivity approximation except that here the number of particles is conserved. A general discussion is given of the collective quadrupole energy surface. In particular the anharmonic terms in the expansion about zero deformation and the general character of the stability of axially symmetric deformed systems are discussed.

Prospect of creating a composite Fermi–Bose superfluid

Abstract We show that composite Fermi–Bose superfluids can be created in cold-atom traps by employing a Feshbach resonance or coherent photoassociation. The bosonic molecular condensate created in this way implies a new fermion pairing mechanism associated with the exchange of fermion pairs between the molecular condensate and an atomic fermion superfluid. We predict macroscopically coherent, Josephson-like oscillations of the atomic and molecular populations in response to a sudden change of the molecular energy, and suggest that these oscillations will provide an experimental signature of the pairing.

Time-dependent variational principle and the effective action

Abstract The time-dependent variational principle used in derivations of time-dependent Hartree-Fock theory gives a variational definition for the effective action - the generating functional of single particle irreducible n -point functions.

Modification of Hauser-Feshbach calculations by direct-reaction channel coupling

Abstract If open channels are strongly coupled by direct reactions, the traditional Hauser-Feshbach method of calculating fluctuation cross sections is invalid, because of non-statistical correlations which the direct channel-coupling induces between resonance partial widths in different channels. The fluctuation cross sections can still be computed from the optical S-matrix elements, however, and the formulas necessary for doing so are obtained here with the aid of an “optical background” representation of the full S-matrix. The resulting compound-elastic cross section is increased over the Hauser-Feshbach expression by a factor of 2(Γ ⪢ D) or 3(Γ ⪡ D) in the large-N limit, and compound-reaction cross sections are increased by roughly a factor of (N + 1) N , where N is the number of directly-coupled open channels.

Time-Dependent Variational Principle forφ4Field Theory: RPA Approximation and Renormalization (II)☆

Abstract The Gaussian time-dependent variational equations are used to explored the physics of ( φ 4 ) 3+1 field theory. We have investigated the static solutions and discussed the conditions of renormalization. Using these results and stability analysis we show that there are two viable non-trivial versions of ( φ 4 ) 3+1 . In the continuum limit the bare coupling constant can assume b →0 + and b →0 − , which yield well-defined asymmetric and symmetric solutions, respectively. We have also considered small oscillations in the broken phase and shown that they give one and two meson modes of the theory. The resulting equation has a closed solution leading to a “zero mode” and vanished scattering amplitude in the limit of infinite cutoff.

Studies in isobaric analog resonances. I. Gross properties

Abstract The gross-structure of isobaric analog resonances in the N, Z + 1 system is described in terms of the intermediate structure associated with the analogs of the low-lying states of the N + 1, Z nucleus. These analog states are shown to act as “doorway states” of a rather special nature in producing generally asymmetric gross anomalies in the elastic and inelastic scattering. This description leads to a model-independent parametrization of the isobaric analog resonances. A discussion of (p, n) processes involving isobaric analog resonances is also given.

STRANGENESS ANALOG RESONANCES.

Strangeness analog resonances in hypernuclei are defined by analogy to the well-known isobaric resonances. Their relationship to the Sakata SU(3) model is discussed. Estimates are made for their energies and total widths. It is suggested that the excited states of ΛC12 and ΛN14 seen in stopped Kaon experiments are examples.

The chirped-pulse inverse free-electron laser: A high-gradient vacuum laser accelerator

The inverse free-electron laser (IFEL) interaction is studied theoretically and computationally in the case where the drive laser intensity approaches the relativistic regime, and the pulse duration is only a few optical cycles long. The IFEL concept has been demonstrated as a viable vacuum laser acceleration process; it is shown here that by using an ultrashort, ultrahigh-intensity drive laser pulse, the IFEL interaction bandwidth and accelerating gradient are increased considerably, thus yielding large energy gains. Using a chirped pulse and negative dispersion focusing optics allows one to take further advantage of the laser optical bandwidth and produce a chromatic line focus maximizing the gradient. The combination of these novel ideas results in a compact vacuum laser accelerator capable of accelerating picosecond electron bunches with a high gradient (GeV/m) and very low energy spread.