The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.

We present results for the ${}^3{P}_2{-}^3{F}_2$ pairing gap in neutron matter with several realistic nucleon-nucleon potentials, in particular with recent phase-shift-equivalent potentials. We find that their predictions for the gap cannot be trusted at densities above $\rho \approx 1.7{\rho }_0,$ where ${\rho }_0$ is the saturation density for symmetric nuclear matter. In order to make predictions above that density, potential models which fit the nucleon-nucleon phase shifts up to about 1 GeV are required.

The large variety of experimental data around the pion-production threshold are compared with a meson-exchange isobar model which includes the pion-nucleon interaction in $s$ and $p$ waves. Theoretical results obtained with two different $\mathrm{NN}$ potentials (Bonn and Paris) indicate that the behavior of the excitation function at threshold is sensitive to the details of the $\mathrm{NN}$ correlations. The complete model presented, while developed originally to reproduce the reaction around the Δ resonance, is shown to describe well the integral (Coulomb-corrected) cross section at threshold along with its angular distribution. At low energies the angular dependence of the analyzing power $A_{y0\mathrm{}}$ is well reproduced also. Finally, the energy dependence of the analyzing power for $\theta =90\mathrm{}°$ from threshold up to the Δ resonance is considered and discussed.

We show the necessity of two-nucleon axial currents and associated pion emission or absorption operators for the partial conservation of the axial current (PCAC) nuclear matrix elements with arbitrary nuclear dynamics described by a nonrelativistic Schrödinger equation. As examples we construct such nonrelativistic axial two-body currents in the linear- and the heterotic ${(g}_A=1.26)\hspace{0.5em}\sigma$ models, with an optional isoscalar vector $\left(\omega \right)$ meson exchange. The nuclear axial current matrix elements obey PCAC only if the nuclear wave functions used in the calculation are solutions to the Schrödinger equation with the static one-meson-exchange potential constructed in the respective $\left(\sigma \right)$ model. The same holds true for the nuclear pion production amplitude, since it is proportional to the divergence of the axial current matrix element, by virtue of PCAC. Thus we found a consistency condition between the pion creation or absorption operator and the nuclear Hamiltonian. We present examples drawn from our models and discuss the implication of our results for one-pion-two-nucleon processes.

We analyze the SM97 partial wave amplitudes for nucleon-nucleon $\mathrm{}\left(\mathrm{NN}\right)\mathrm{}$ scattering to 2.5 GeV, in which resonance and meson production effects are evident for energies above the pion production threshold. Our analyses are based upon boson exchange or quantum inversion potentials with which the subthreshold data are fit perfectly. Above 300 MeV they are extrapolations, to which complex short-ranged Gaussian potentials are added to form a complex optical model potential. The data to 2.5 GeV are all well fit. The energy dependences of these Gaussians are very smooth save for precise effects caused by the known Δ and $N^{\star }$ resonances. With this optical model approach, we confirm that the geometrical implications of the profile function found from diffraction scattering are pertinent for the geometrical interpretation of the optical model absorption in the regime 300 MeV to 2.5 GeV. The overwhelming part of meson production comes from the QCD sector of the nucleons when they have a separation of their centers of 1 to 1.2 fm.

The neutron-rich nuclei ${}^{109,111}\mathrm{Pd}$ have been produced as fission fragments following the fusion reactions ${}^{28,30}\mathrm{Si}+{}^{176}\mathrm{Yb}$ at 145 MeV and studied with the EUROGAM2 array. Two signature branches of a new band built on the $\nu h_{11/2}$ orbital have been identified in ${}^{109}\mathrm{Pd}$ and the favored signature of the $\nu h_{11/2}$ band has been observed for the first time in ${}^{111}\mathrm{Pd}.$ The spectroscopic properties as well as the rotational behavior of these bands are characteristic of bands expected for a prolate nuclear shape in this mass region. The effect of blocking of the first $h_{11/2}$ quasineutron in the odd-$A$ Pd nuclei supports the interpretation of the first crossing in the yrast bands of ${}^{110,112}\mathrm{Pd}$ as due to a $\nu {(h}_{11/2}{)}^2$ pair.

The $\beta$ decay of ${}^{50}\mathrm{K}$ and ${}^{38}\mathrm{Ca}$ has been investigated with the main motive of determining more accurately the first-forbidden $\beta$ branches, in particular the rank-0, $\Delta J=0,\hspace{0.5em}\beta$ transitions. ${}^{50}\mathrm{K}$ and ${}^{38}\mathrm{Ca}$ have been produced by fragmentation of U and Ti targets, respectively, with a 1 GeV proton beam and subsequent on-line mass separation. For ${}^{50}\mathrm{K},\hspace{0.5em}\gamma$-ray spectroscopy, as well as delayed neutron spectroscopy by time of flight, was carried out to obtain a detailed decay scheme to 20 (bound and unbound) levels in ${}^{50}\mathrm{Ca}.$ The level structure of ${}^{50}\mathrm{Ca}$ can be compared to recent calculations which incorporate one-particle–one-hole excitations from the $f_{7/2}$ shell. The first-forbidden ${\beta }^{-}$ transition ${}^{50}\mathrm{K}\left(0^{\mathrm{-}}\right){\to \mathrm{}}^{50}\mathrm{Ca}{(0\mathrm{}}^{+})$ ground state has been evaluated for the first time by a direct measurement of $\beta$ and $\gamma$ activities. Its strength $(61.0\mathrm{}\pm 7.4\%)$ is interpreted as an effect of the meson-exchange current (MEC) leading to an enhancement factor of 62(5)% in comparison with the value predicted by shell-model calculations using the impulse approximation. For the ${}^{38}{\overrightarrow{\mathrm{Ca}}}^{38}\mathrm{K}$ decay, chemical selective production was obtained through separation of the molecular ion ${\mathrm{CaF}}^{+}$ without contamination by isobars. In these conditions, the measurement of very weak $\beta$ branches, at a level of ${10}^{-3}$ per 100 decays, could be made and a limit, at the $2\sigma$ confidence level, has been obtained for the $0^{+}\to 0^{-}$ branch to the level at $E_x=2993\mathrm{}\hspace{0.5em}\mathrm{keV}\hspace{0.5em}{(I}_{\beta }<0.0046\%).\mathrm{}$ Implications of these results on the general trend of meson-exchange enhancements of first-forbidden transitions within the framework of the spherical shell model are discussed.

The low-lying levels of Cu and Zn isotopes were excited with 2.0–4.5 MeV proton beam. The deexcited γ rays from these levels were detected and identified in the singles spectra recorded with a 57 c.c. Ge(Li) detector. The safe energies for Coulomb excitation process with protons for these nuclei have been determined from the relative contributions of compound nucleus formation and Coulomb excitation cross sections. The reliable values of transition probabilities for the low-lying levels have also been measured by Coulomb excitation technique using safe bombarding energies. The present results have been compared with the reported measurements and various nuclear model calculations.

Directional distribution of γ rays following the decay of ${}^{160}{\mathrm{Ho}}^{g+m}$ oriented in a gadolinium host at low temperature has been studied. The γ-ray anisotropies of transitions from the levels below 3 MeV in ${}^{160}\mathrm{Dy}$ were measured and multipole mixing ratios δ were determined. The variations in both sign and magnitude of δ for the $M1+E2\mathrm{}$ transitions between the γ-vibrational ${(K}^{\pi }{=2\mathrm{}}^{+})$ and ground-state ${(K}^{\pi }{=0\mathrm{}}^{+})$ bands were observed. The $E2/M1\mathrm{}$ mixing ratios for the $\overrightarrow{2}2$ and $\overrightarrow{4}4$ transitions from the β-vibrational ${(K}^{\pi }{=0\mathrm{}}^{+})$ band to the ground-state band were determined, and the $E0/E2\mathrm{}$ probability ratios obtained are consistent with the values for the β-vibrational bands. The $E2/M1\mathrm{}$ mixing ratios of the $\overrightarrow{\gamma }g$ transitions in ${}^{160}\mathrm{Dy}$ obtained previously by the nuclear orientation of ${}^{160}\mathrm{Tb}$ are compared with the present results. The dynamic deformation model is employed to calculate the collective bands, electromagnetic moments, transition probabilities, and mixing ratios in ${}^{160}\mathrm{Dy}.$ A sign change of the $E2/M1\mathrm{}$ mixing ratio is predicted for the ${10}_{\gamma }\to {10}_g$ transition. Our experimental results give such a sign change for the $4_{\gamma }\to 4_g$ and $6_{\gamma }\to 6_g$ transitions. Comparison with the presently determined experimental values of $X(E0/E2\mathrm{})\mathrm{}$ for $\overrightarrow{\gamma }g$ and $\overrightarrow{\beta }g$ transitions is also given.

The level structures of several Ru isotopes near $A=104\mathrm{}$ have been studied in the fission of the compound nucleus ${}^{197}\mathrm{Pb},$ formed in the ${}^{24}{\mathrm{Mg}\mathrm{}+}^{173}\mathrm{}\mathrm{Yb}$ reaction at 134.5 MeV. A sequence of five transitions, observed in coincidence with known transitions in the ${}^{86}\mathrm{Sr}$ and ${}^{87}\mathrm{Sr}$ complementary fragments, has been assigned to ${}^{105}\mathrm{Ru}.\mathrm{}$ Comparison with the neighboring odd-mass Ru isotopes supports assignment of this sequence as built on the $h_{11/2}$ excitation in ${}^{105}\mathrm{Ru}.$ The positive-parity band built on the ${7/2}^{+}$ state of ${}^{103}\mathrm{Ru}$ has been extended above the backbending induced by the alignment of two $h_{11/2}$ neutrons. In addition, the ground-state bands of ${}^{104}\mathrm{Ru}$ and ${}^{106}\mathrm{Ru}$ have been extended to higher spins.

The high-spin structure of the nucleus ${}^{133}\mathrm{Nd}$ has been studied with the GASP array using the ${}^{104}\mathrm{Pd}{(}^{32}\mathrm{S},2pn)$ and ${}^{105}\mathrm{Pd}{(}^{32}\mathrm{S},2p2n)$ reactions. The observed levels have been organized into nine rotational bands including the well-known highly deformed band which has been linked to the states at normal deformation. The bands, which have been classified as being built on different Nilsson orbitals, are discussed in the framework of the interacting boson fermion, particle-plus-triaxial rotor, and cranked shell models.

We investigate the momentum dependence of the nucleon self-energy in nuclear matter. We apply the relativistic Brueckner-Hartree-Fock approach and adopt the Bonn A potential. A strong momentum dependence of the scalar and vector self-energy components can be observed when a commonly used pseudovector choice for the covariant representation of the T matrix is applied. This momentum dependence is dominated by the pion exchange. We discuss the problems of this choice and its relations to on-shell ambiguities of the T matrix representation. Starting from a complete pseudovector representation of the T matrix, which reproduces correctly the pseudovector pion-exchange contributions at the Hartree-Fock level, we observe a much weaker momentum dependence of the self-energy. This fixes the range of the inherent uncertainty in the determination of the scalar and vector self-energy components. Comparing to other work, we find that extracting the self-energy components by a fit to the single particle potential leads to even more ambiguous results.

In this paper we extend the shell model calculations previously made for the very neutron-rich nuclei with $Z>~14$ to Al, Mg, Na, Ne, F, and O, using the same valence space and effective interaction. Predictions are made for the neutron separation energies and for the location of the neutron drip line. We find that the isotopes of Ne, Na, and Mg are deformed for $N>~22.$ In ${}^{40}\mathrm{Mg},$ which is at the edge of the drip line, the $N=28\mathrm{}$ shell closure does not stand. By enlarging the valence space to include intruder states we are able to account for the vanishing of the $N=20\mathrm{}$ neutron shell closure in a small region around ${}^{31}\mathrm{Na}$ that we delineate. The dominance of the intruders explains the collective features experimentally found in this region.

The quadrupole deformation parameter ${\beta }_2,$ and energies of yrast states have been calculated in the microscopic frameworks, using the quadrupole-quadrupole-plus-pairing model of a two-body interaction for the even-even isotopic mass chain of xenon isotopes. Results obtained indicate that ground-state deformation systematics are satisfactorily reproduced and there is a breaking of axial symmetry as we move along the yrast states. Besides this, the observed backbending in some of these isotopes is explained in terms of the partial rotational alignment of a pair of neutrons in the ${(1h}_{11/2}{)}_{\nu }$ orbit.

We compare exotic cluster model predictions of the properties of 19 even-even actinide nuclei with experimental data. We restrict our attention to clusters which have been observed in exotic decay (i.e., ${}^{14}\mathrm{C},{}^{20}\mathrm{O},{}^{24}\mathrm{Ne},{}^{28}\mathrm{Mg},$ and ${}^{32}\mathrm{Si})\mathrm{}$ and concentrate on nuclei which may be modeled as Pb cores combined with these clusters, i.e., isotopes of Ra, Th, U, Pu, and Cm, respectively. Using fixed parameter values for all cases, we examine the energies of the states in the lowest $J^{\pi }{=0\mathrm{}}^{+}{,2\mathrm{}}^{+}{,4\mathrm{}}^{+},\dots$ and $J^{\pi }{=1\mathrm{}}^{-}{,3\mathrm{}}^{-}{,5\mathrm{}}^{-},\dots$ bands, the $B\left(E2\mathrm{}\hspace{0.5em}\downarrow \right)$ transition strengths in the positive parity bands, and the values for $B(E3\mathrm{}\hspace{0.5em}\uparrow {;0\mathrm{}}^{+}\to 3^{-})$ and $B(E4\mathrm{}\hspace{0.5em}\uparrow {;0\mathrm{}}^{+}\to 4^{+}).\mathrm{}$ The level of agreement between calculated and measured values is generally good.

$M1\mathrm{}$ and $E2\mathrm{}$ transition probabilities from the $K=1\mathrm{}$ band, which is lowest in energy among the mixed-symmetry bands, to fully symmetric states are derived analytically within the framework of the SU(3) limit of the neutron-proton interacting boson model. To derive the electromagnetic transitions in closed forms, the tensorial characters of the electromagnetic transition operators, which are taken in terms of SU(3) generators, are investigated in the pure SU(3) limit. The properties of $M1\mathrm{}$ and $E2\mathrm{}$ intrinsic matrix elements in the classical limit of the present model and the $E2/M1\mathrm{}$ mixing ratios for transitions of the $K=1\mathrm{}$ band to fully symmetric states are also studied.

The decay out of superdeformed states through $E0\mathrm{}$ electric monopole transition is investigated for even-even nuclei in the $A=190\mathrm{}$ mass region. Transition rates are evaluated within the generator coordinate method based on Hartree-Fock plus BCS wave functions. For light isotopes of mercury and lead, $E0\mathrm{}$ transitions appear to be strongly enhanced due to large monopole transition matrix elements.

A microscopic formalism to treat α decay from superdeformed nuclei is given within the framework of the Hartree-Fock-Bogoliubov approximation. The process of penetration through the deformed barrier is described exactly. The influence of the deformation on the formation amplitude and on the penetrability is analyzed. It is found that the results of the WKB approximation differ strongly from the exact ones as the deformation increases for ${\beta }_2$ larger than 0.3. The most favorable case that we found corresponds to a superdeformed band in ${}^{192}\mathrm{Pb},$ for which the α decay probability is very large, making this a likely mechanism to feed the daughter nucleus ${}^{188}\mathrm{Hg}.$

The energy factor method that generalizes the definition of identical bands was extended to normal deformed bands. More than 300 rotational bands were analyzed by means of this method and the number of identical bands as a function of criteria is presented. The statistics study shows that the quantization behavior of incremental alignments is completely different from one in superdeformed nuclei, and the alignment in normal deformed nuclei is not quantized.

The transformed harmonic oscillator basis (THO) is derived by a local scaling-point transformation of the spherical harmonic-oscillator radial wave functions. The unitary scaling transformation produces a basis with improved asymptotic properties. The THO basis is employed in the solution of the relativistic Hartree-Bogoliubov (RHB) equations in configurational space. The model is applied in the self-consistent mean-field approximation to the description of the neutron halo in Ne isotopes. It is shown that an expansion of nucleon spinors and mean-field potentials in the THO basis reproduces the asymptotic properties of neutron densities calculated by finite element discretization in the coordinate space. In the RHB description of neutron skins and halos, THO bases in two or three dimensions can be a useful alternative to technically complicated solutions on a mesh in coordinate space.