This Brief Report deals with the solution of the shell-model Hamiltonian in the boson representation. In the present approach, the fermion Hamiltonian is exactly mapped to the boson space using the Dyson boson mapping. The problem of mapping the basis states is resolved by employing the intrinsic boson basis. The method has been applied to a model Hamiltonian consisting of a monopole pairing and a deformation force. It is observed that only s and d bosons are dominant in the intrinsic wave function for the model case studied. This is synonymous to the interacting boson model approach.

In addition to its two known hadronic decay modes—alpha decay (half-life 88 yr) and spontaneous fission (5×${10}^{10}$ yr)—we have found that ${}_{}{}^{238}{}_{}{}^{}\mathrm{Pu}$ also decays by emission of a Mg nucleus (∼2×${10}^{18}$ yr) and by emission of a Si nucleus (∼6×${10}^{17}$ yr). This extends to four (the other two being ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$ emission and Ne emission) the number of known modes of decay by emission of a fragment of mass between that of an alpha particle and that resulting from fission. The branching ratios relative to alpha decay are the lowest yet observed: ∼6×${10}^{\mathrm{-}17}$ for Mg emission and 1.4×${10}^{\mathrm{-}16}$ for Si emission.

A superdeformed band was found in the nucleus ${}_{}{}^{150}{}_{}{}^{}\mathrm{Tb}$ following the reaction ${}_{}{}^{31}{}_{}{}^{}\mathrm{Sn}$ at 160 MeV. This is the first odd-odd nucleus in the mass 150 region where such a band has been found. Its observed properties do not differ significantly from those of other cases in this mass region. From a systematic study of this region, we have determined experimentally the contribution to the moment of inertia ${\mathrm{scrI}}^{\mathrm{}\left(2\right)\mathrm{}}$ in each of the last particles ion these nuclei. At present, this seems to us the best way to identify the orbitals occupied by these particles.

We have measured the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$(n,p${)}^{14}$C cross section from 61 meV to 34.6 keV. Our data are in agreement with previous measurements made via the inverse reaction, but are approximately a factor of 2.5 larger than a recent direct measurement. As a result, our data support the astrophysical reaction rate used in most previous nucleosynthesis calculations over the recently recommended three-fold reduction in this rate. Astrophysical implications of our new measurements are discussed.

The strength function of the $d_{5/2}$ hole state in ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$ has been determined from the (p→,d) reaction at 65 MeV. The $d_{5/2}$ hole state consists of three strongly excited states at the excitation energies of 5–6 MeV with strengths of 41% of the sum-rule limit and a group of several tens of weakly excited states instead of six or seven peaks as in previous data, distributed in the excitation energy region from 6 to 10 MeV with 38% of the sum-rule limit. This is evidence for the general feature of the fragmentation of deeply bound hole states, proved by peak-by-peak analysis. The strength quenching of the stretched $6^{\mathrm{-}}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(p,n) reaction is discussed with the strength fragmentation of the $d_{5/2}$ hole state.

Neutron strength distributions of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ have been obtained from a high resolution study of the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$(d→,p) reaction. They agree well with quasiparticle-phonon coupling calculations in a large configuration space including major shell mixing. We see no evidence of strong depopulation of closed shell orbitals.

A strong correlation is found to exist between the phenomena of heavy-fragment radioactivity and high transparency in the molecular window for the same nuclei taken, in turn, as emitters and composite systems. Such a correlation sheds new light on the nature of heavy-fragment radioactivity and provides a new way in searching for possible resonant phenomena in heavy nuclei.

The Coulomb sum rule is studied using the random-phase approximation to the relativistic σωρ model. The addition of the ρ meson to the σω model has a large effect on the quenching of the sum rule because of its random-phase approximation correlation and its coupling with the isovector anomalous magnetic moment of the nucleon. The low-density surfaces of finite nuclei have a larger response than their interior so that the quenching of the Coulomb sum rule is not as significant as in the nuclear matter ground state. Calculations for finite nuclei using the local density approximation agree with existing experimental data on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$.

Multipole excitations ${\lambda }^{\pi }$${=2\mathrm{}}^{+}$ and $3^{\mathrm{-}}$, in ${}_{}{}^{116}{}_{}{}^{}\mathrm{Sn}$ and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$, are calculated within the formalism of the finite-temperature linear response theory. Low- and high-energy strength distributions, for quadrupole and octupole vibrations, are shown as a function of the nuclear temperature. The resulting energy-weighted sum rules, for the associated multipole operators, are found to be weakly varying functions of the temperature T, in the interval 0≤T≤2 MeV, provided off-diagonal blocks of the response matrix are included in the formalism.

Particle-hole excitations are studied in terms of a single-particle representation consisting of bound states and resonant solutions (Gamow resonances) of a ‘‘realistic’’ Woods-Saxon potential. Within this representation a particle-hole resonant random phase approximation is developed. Using the resonant random phase approximation the escape widths of the multipole giant resonances in ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ are calculated and reasonable agreement with available experimental data is obtained.

Properties of chirally-invariant models of nuclear matter are calculated with the relativistic Hartree approximation. Our emphasis is on the behavior of the effective σ meson mass. We find that the effective σ mass does not scale with the effective nucleon mass, which in these calculations is proportional to the expectation value of the σ field, i.e., the chiral order parameter. These results suggest that a decrease in the effective σ mass with increasing nucleon density is not a generic feature of chiral models. We also find that the incompressibility of nuclear matter is lower for those models with higher effective σ masses.

An interacting cylindrical boson model, describing rotating cylindrical intrinsic states, is utilized to study the bandhead states of the rotational bands in rare-earth nuclei. The three fundamental quasispin (Λ) bosons, $p_s$ (Λ=0) and $p_{\lambda }$ (Λ=(1/2), are introduced and used to solve Hamiltonians with cylindrically broken SU(3) symmetry. This approach, simply incorporated into the interacting boson model SU(3) rotational limit, gives some new results in four areas of interest: changes in order of the strict SU(3) bandhead sequences, explanations for observed low-lying $0^{+}$ rotational bands not accounted for in the pure SU(3) limit, certain bandhead mixing effects, and analytical expressions for E2 transition rates between bandhead states. We also obtain further insights into the interacting boson model SU(4) sp¯ boson model of Chen and Arima. We illustrate with new results for ${}_{}{}^{156}{}_{}{}^{}\mathrm{Gd}$, ${}_{}{}^{168}{}_{}{}^{}\mathrm{Yb}$, and ${}_{}{}^{168}{}_{}{}^{}\mathrm{a}$ sequence of well-studied nuclei having increasing interacting boson approximation valence boson number.

The dynamics of three- and n-body systems is frequently described by central two-body interactions, functions of the moduli of the relative coordinate vectors. The center-of-momentum closure relation allows one to transform the kinetic energy into a pure quadratic form in the two-body relative momenta. Defining generalized two-body relative momenta the Hamiltonian acquires a simple form, albeit in redundant variables. Symmetric systems with harmonic and short-range interactions are discussed, as well as exotic atomic systems, such as kaonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, antiprotonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and others. A solution in terms of symmetric coordinates is also constructed.

A specific linearization procedure is carried out for the time-independent Schrödinger equation in which the Hamiltonian possesses dynamical symmetry. It is found that the solution of the linearized ‘‘Schrödinger equation’’ carries an additional spin. This linearization procedure is used to study the relationship between even-even and even-odd nuclei.

A new and simple algorithm is presented to solve the fermion dynamical symmetry model numerically in the heritage-zero subspace for neutron-proton systems. The algorithm is based on a shell-model approach using the fermion pair operators as building blocks for the many-body wave functions. The same algorithm applies to all possible neutron and proton Hamiltonians. The results of all known dynamical symmetries are reproduced. Typical approximate vibrational and rotational spectra are presented for cases where dynamical symmetries cannot be found from group chain decompositions.

The ground states of nuclear matter and finite nuclei are calculated for a one-dimensional model having a two-body potential with strong short-range repulsion and long-range attraction. Mean-field theory with a phenomenological density-dependent interaction is shown to yield a good approximation to the exact binding energies and density distributions when appropriate center-of-mass corrections are applied. This model thus provides a framework for quantitative study of corrections to mean-field theory.

The procedure developed recently to calculate single-shell wave functions and matrix elements for multiple angular momentum shell-model calculations is extended to the multishell case. This was based on a factorization procedure introduced by Jahn. As a consequence of the factorization, coefficients of fractional parentage between states of arbitrary symmetry must be constructed to build up single-shell N-particle states from single-shell N-1-particle states. Multishell N-particle states are built up recursively from multishell N-1-particle states by using outer-product isoscalar factors. Symmetrized multishell states in one angular momentum subspace are combined with states of conjugate symmetry in a second angular momentum subspace to construct fermion wave functions. This is done using inner-product isoscalar factors. The coefficients of fractional parentage, outer-product isoscalar factors, and inner-product isoscalar factors are computed recursively using a matrix diagonalization algorithm. Shell-model matrix elements are constructed from these factors by using a new sum over path overlaps method. This computational procedure involving factorization is substantially more efficient than computational procedures which do not exploit factorization.