We calculate the total cross section as well as single and double differential cross sections of the reaction ${\pi }^{-}\overrightarrow{d}\eta \mathrm{nn}$ for incident pion kinetic energies between threshold and 1500 MeV. Our model is based in a fully covariant formalism which includes the dominant single-scattering diagram as well as the nucleon-nucleon final-state interaction diagram.

Differential cross sections for the electro-disintegration process ${e+}^4{\overrightarrow{\mathrm{He}}}^3\mathrm{H}{+p+e}^{\prime }$ are calculated, using a model in which the final-state interaction is included by means of a nucleon-nucleus $\mathrm{}(3+1)\mathrm{}$ potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach. In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p^3\mathrm{H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our plane-wave impulse approximation results exhibit, similarly to other calculations, a dip in the fivefold differential cross section around a missing momentum of $\sim 450\hspace{0.5em}\mathrm{MeV}/c,$ it is argued that this is an artifact of the omission of rescattering four-nucleon processes.

The decays of $T_z=1/2\mathrm{}$ series nuclei ${}^{81}\mathrm{Zr}$ and ${}^{85}\mathrm{Mo}$ have been restudied via their $\beta$-delayed proton decay by using p-$\gamma$ coincidence measurements. The $\beta$-delayed proton spectra populating the first excited states of the final nuclei have been obtained. By using statistical model calculations with level densities calculated with a backshifted Fermi gas model, the spin and parity for the ground state of ${}^{81}\mathrm{Zr}$ have been tentatively assigned to be ${3/2}^{-}$ and those for ${}^{85}\mathrm{Mo}$ to be ${1/2}^{-}.$ Their $Q_{\mathrm{e}.\mathrm{c}.\mathrm{}}-B_p$ values are $4.7\pm 0.2$ and $5.1\pm 0.2\hspace{0.5em}\mathrm{MeV},$ which correspond to mass excesses of $-58.3\pm 0.2\hspace{0.5em}\mathrm{MeV}$ for ${}^{81}\mathrm{Zr}$ and of $-59.1\pm 0.4\hspace{0.5em}\mathrm{MeV}$ for ${}^{85}\mathrm{Mo},$ respectively. Combining the measured half-lives with the calculated partial ones yields branches of $\beta$-delayed proton decay for ${}^{81}\mathrm{Zr}$ and ${}^{85}\mathrm{Mo}$ of $(1.2\mathrm{}\pm 0.2)\times {10}^{-3}$ and $(1.4\mathrm{}\pm 0.2)\times {10}^{-3},$ respectively.

${}^{167}\mathrm{Hf}$ was populated at low and high spins via the heavy-ion fusion reactions ${}^{155}\mathrm{Gd}{(}^{16}\mathrm{O},4n)$ at 85 MeV and ${}^{146}\mathrm{Nd}{(}^{26}\mathrm{Mg},5n)$ at 142 MeV, respectively. Seven rotational bands were observed; four of them are new, and the known bands are extended to much higher spin. A total Routhian surface plus a cranked shell-model calculation enabled quasiparticle configurations to be assigned to the respective bands via comparison with the extracted alignment gains and Routhians from experiment. Evidence is presented for the observation of a quasiproton crossing at $ħ\omega =0.51\mathrm{}\hspace{0.5em}\mathrm{MeV}$ in ${}^{167}\mathrm{Hf}.$ The $\gamma$-ray flux appears to fractionate above this frequency.

$\beta$-decay studies of the neutron-deficient ${}^{54,55}\mathrm{Ni}$ isotopes have been performed at the Leuven isotope separator on-line facility (LISOL) at Louvain-la-Neuve. The nuclei of interest are produced using an element-selective laser ion source coupled to the on-line mass separator. The half-life of ${}^{55}\mathrm{Ni}\hspace{0.5em}{(T}_{1/2}=\hspace{0.5em}204\pm 3$ ms) was remeasured precisely and the ${\beta }^{+}$ decay of ${}^{54}\mathrm{Ni}$ was observed for the first time. The ${\beta }^{+}$-decay Gamow-Teller strength [B(GT)] associated with the ${(J}^{\pi }{=1\mathrm{}}^{+})$ level at 937.2 keV in the daughter nucleus ${}^{54}\mathrm{Co}$ was deduced. The ${\beta }^{+}$ GT strength of $1.09\pm 0.25$ obtained from the measured half life of ${}^{54}\mathrm{Ni}{(T}_{1/2}=106\mathrm{}\pm 12$ ms) and branching ratio ${(I}_{\beta }=22.4\mathrm{}\pm 4.4\%)$ towards this level is in agreement with the GT strength obtained from $\mathrm{}(p,n)\mathrm{}$ reaction studies on ${}^{54}\mathrm{Fe}\left[\mathrm{B}\right(\mathrm{GT}-)=1.172\mathrm{}\pm 0.078].$

The decays of ${}^{183}{\mathrm{Pt}}^m$ (43 s, $J^{\pi }={\frac{7}{2}}^{-})$ and ${}^{183}{\mathrm{Pt}}^g$ (6.5 min, $J^{\pi }={\frac{1}{2}}^{-})$ have been studied with mass-separated sources from the UNISOR facility. Multiscaled spectra of $\gamma$ rays, x rays, and conversion electrons, as well as $\gamma \gamma t,$ $\gamma Xt,$ $e\gamma t,$ and $\mathrm{eXt}$ coincidences, were obtained. A revision of the low-lying positive-parity states is necessary in order to accommodate a strong 58 keV transition which is previously unreported. Other additions are made to the low-energy part of the ${}^{183}\mathrm{Ir}$ scheme. The systematic features of the neutron-deficient odd-mass Ir isotopes are discussed.

Ultraprecise energies and absolute $B\left(E2\mathrm{}\right)\mathrm{}$ values associated with ${K=0\mathrm{}}^{+}$ excitations in ${}^{158}\mathrm{Gd},$ measured with the GRID technique, reveal significant information relating to the possible existence or absence of two-phonon vibrational excitations in deformed nuclei. A strong ${B(E2:K=0\mathrm{}}_2^{+}\to \gamma )$ is observed but reflects band mixing rather than a $\gamma \gamma$ mode. For the ${K=0\mathrm{}}_3^{+}$ band, measurement of precise $\gamma$ transition energies shows that suggested existing placements of strong deexcitation transitions are incorrect and that there is, again, no evidence for $\gamma \gamma$-phonon character in this band either. A weak ${B(E1:K=1\mathrm{}}^{-}\to {K=0\mathrm{}}_1^{+})$ value is interpreted in terms of the microscopic structure of ${K=0\mathrm{}}^{-}$ and ${K=1\mathrm{}}^{-}$ excitations.

The high spin structure in the nucleus ${}^{62}\mathrm{Cu}$ has been studied using the reaction ${}^{50}\mathrm{Cr}{(}^{16}\mathrm{O},3pn)$ at a beam energy of 75 MeV. Most of the levels known from earlier experiments have been confirmed and the spin parity assignments of a few of them have been verified. A number of levels have been proposed extending the energy scheme up to about 7.6 MeV. A simple interacting boson-fermion-fermion model calculation has been performed to explain the observed energy spectrum.

An in-beam $\gamma$-ray spectroscopic study of the nuclear structure $\mathrm{of}{}^{125}\mathrm{I}$ has led to extensions and alterations of the level scheme of this nucleus. Several new intraband and interband transitions are observed in the positive parity bands based on $\pi d_{5/2}$ and $\pi g_{7/2}$ configurations, indicating mixing of the two configurations in these bands. The strongly coupled $\pi g_{9/2}$ band has also been extended and characteristic quadrupole crossover transitions, hitherto unreported, have been observed, providing estimates of the $B(M1;\overrightarrow{I}I-1)/B(E2;\overrightarrow{I}I-2)$ ratios for transitions in this band. New experimental results are presented concerning the three-quasiparticle structure and likely members of the unfavored signature of the prolate $\pi h_{11/2}$ band, showing excellent agreement with the theoretical results. Experimental results are discussed in relation to the systematics of the neighboring odd-$A$ nuclei.

The properties of negative-parity states in the 2.5 MeV region in ${}^{112}\mathrm{Cd}$ have been investigated with the ${(n,n}^{\prime }\gamma )$ reaction. For many of these levels, lifetimes have been measured, and $B\left(E1\mathrm{}\right)\mathrm{}$ and $B\left(E2\mathrm{}\right)\mathrm{}$ values for their decays have been determined. Several transitions exhibit enhanced $B\left(E2\mathrm{}\right)\mathrm{}$ values for decay to the $3_1^{-}$ octupole state, indicative of quadrupole-octupole coupled ${(2\mathrm{}}^{+}\otimes 3^{-})$ states. The $B\left(E1\mathrm{}\right)\mathrm{}$ values observed are typically in the range of 1–$5\times {10}^{-4}$ Weisskopf units (W.u.), irrespective of the final state.

This paper discusses several mechanisms that could be responsible for nuclear excitation in a plasma of temperature of order 10–100 eV. Four mechanisms discussed in detail are nuclear excitation by a resonant electronic transition from an excited bound state to a lower-lying bound state, nuclear excitation by electron capture from the continuum, photoexcitation, and inelastic electron scattering. Estimates of the rates for these different processes are presented for the excitation of ${}^{235m}\mathrm{U}$ for which the present experimental data lacks adequate theoretical interpretation.

We demonstrate the feasibility of realistic shell-model Monte Carlo (SMMC) calculations spanning multiple major shells, using a realistic interaction whose bad saturation and shell properties have been corrected by a newly developed general prescription. Particular attention is paid to the approximate restoration of translational invariance. The model space consists of the full $\mathrm{sd}-\mathrm{pf}$ shells. We include in the study some well-known $T=0\mathrm{}$ nuclei and several unstable neutron-rich ones around $N=20,28\mathrm{}$. The results indicate that SMMC calculations can reproduce binding energies, $B\left(E2\mathrm{}\right)\mathrm{}$ transitions, and other observables with an interaction that is practically parameter free. Some interesting insight is gained into the nature of deep correlations. The validity of previous studies is confirmed.

Recently it has been shown that pseudospin symmetry has its origins in a relativistic symmetry of the Dirac Hamiltonian. Using this symmetry we relate single-nucleon relativistic magnetic moments of states in a pseudospin doublet to the relativistic magnetic dipole transitions between the states in the doublet, and we relate single-nucleon relativistic Gamow-Teller transitions within states in the doublet. We apply these relationships to the Gamow-Teller transitions from ${}^{39}\mathrm{Ca}$ to its mirror nucleus ${}^{39}\mathrm{K}.$

Wick’s theorem for the expectation value of an operator between many-particle states is generalized to the case of a homogeneous linear transformation operator $Ô$, which leaves invariant the $2N$-dimensional linear space composed of the annihilation and the creation operators for the N fermion or boson single-particle basis. Such a transformation generally belongs to the group $\mathrm{SO}\mathrm{}(2N,C)\mathrm{}$ for the case of fermion, or the group $\mathrm{Sp}\mathrm{}(2N,C)\mathrm{}$ for the case of boson. This theorem is applied to derive a reduction theorem for the matrix element of the type $〈\alpha |{\alpha }_1{\alpha }_2\cdot \cdot \cdot {\alpha }_mÔ{\beta }_{m+1\mathrm{}}^{†}{\beta }_{m+2\mathrm{}}^{†}\cdot \cdot \cdot {\beta }_{2n}^{†}|\beta 〉,$ whose many-quasiparticle states and vacua appearing in both sides are represented in different quasiparticle pictures as indicated by $\alpha$ and $\beta .$ The reduction formula is useful in calculating any nuclear transition matrix element for the quantum-number projection calculation associated with the constrained Hartree-Fock-Bogoliubov solutions, and also the generator coordinate method with quantum number projection.

We present a functional integral formulation in the canonical ensemble for Hamiltonians containing pairing interactions, equally applicable for even-even, even-odd, and odd-odd nuclei. A general stabilization technique, necessary for Monte Carlo calculations is discussed and applied, within the Gaussian path Monte Carlo method, to nuclei in the rare-earth region. Approximations, such as the Hartree-Bogoliubov mean-field, and the static path approximations, defined directly in the canonical ensemble, are discussed.

With a perturbation possessing the ${\mathrm{SO}}_{\mathrm{sdg}}\mathrm{}\left(5\right)\mathrm{}$ [or ${\mathrm{SU}}_{\mathrm{sdg}}\mathrm{}\left(5\right)\mathrm{}]$ symmetry being included in the supersymmetry scheme with many-body interactions, the superdeformed (SD) bands of the odd-$A$ nuclei in the $A=150\mathrm{}$ mass region are investigated and quantitatively good results are obtained. It shows that the many-body interactions play crucial roles in the SD states and the $\Delta I=4\mathrm{}$ bifurcation may result from the perturbation holding the ${\mathrm{SO}}_{\mathrm{sdg}}\mathrm{}\left(5\right)\mathrm{}$ [or ${\mathrm{SU}}_{\mathrm{sdg}}\mathrm{}\left(5\right)\mathrm{}]$ symmetry. Moreover, to describe the identical SD bands well, both the supersymmetry and the single particle Routhian should be considered.

Shell-model wave functions for many states of ${}^{208}\mathrm{Pb}$ have been derived in a strictly empirical way from measured spectroscopic factors and branching ratios of γ transitions. It was assumed that the lowest n states of a given $I^{\pi }$ can be described by an orthonormal superposition of the n lowest one-particle one-hole configurations for this $I^{\pi }.$ The often highly redundant data are well reproduced. The matrix elements of the residual interaction were calculated from the wave functions by inverting the Schrödinger equation. The diagonal matrix elements show clear and reasonable trends. The set of empirical $M1\mathrm{}$ and $E2\mathrm{}$ single particle matrix elements that has been used is presented.

Within the framework of self-consistent cranked Hartree-Fock-Bogoliubov theory (one dimensional) we predict a second backbend in the yrast line of ${}^{182}\mathrm{Os}$ at $I\approx 40ħ$, which is even sharper than the first one observed experimentally at $I\approx 14ħ$. Around such a high spin the structure becomes multiquasiparticle type, but the main source of this strong discontinuity is a sudden large alignment of $i_{13/2}$ proton orbitals along the rotation axis followed soon by the alignment of $j_{15/2}$ neutron orbitals. This leads to drastic structural changes at such high spins. When experimentally confirmed, this will be observed for the first time in this mass region, and will be at the highest spin so far.

Relativistic mean field theory has been used to study different isotopes of Zn and Ge in the mass 60–70 region. The mean field equations are expanded in an angular basis assuming axial symmetry and reflection symmetry. The binding energy, charge quadrupole moment, and root mean square radius of a number of nuclei in the studied region have been calculated and compared with experimentally observed values wherever available. The effect of the cutoff value in the angular expansion is investigated and it is found that a value of 4 is sufficient to describe nuclei in this mass region. A study of Zn isotopes indicates that the restriction imposed by the assumption of axial symmetry may be too severe and a triaxial calculation may be necessary.

The stability of the nuclear matter system with respect to density fluctuations is examined exploring in detail the pole structure of the electronuclear response functions. Making extensive use of the method of dispersion integrals we calculate the full polarization propagator not only for real energies in the spacelike and timelike regime but also in the whole complex energy plane. The latter proved to be necessary in order to identify unphysical causality violating poles which are the consequence of the neglect of vacuum polarization. On the contrary it is shown that Dirac sea effects stabilize the nuclear matter system, shifting the unphysical pole from the upper energy plane back to the real axis. The exchange of strength between these real timelike collective excitations and the spacelike energy regime is shown to lead to a reduction of the quasielastic peak as it is seen in electron scattering experiments. Neglecting vacuum polarization one also obtains a reduction of the quasielastic peak but in this case the strength is partly shifted to the causality violating pole mentioned above which consequently cannot be considered as a physical reliable result. Our investigation of the response function in the energy region above the threshold of nucleon-antinucleon production leads to another remarkable result. Treating the nucleons as pointlike Dirac particles we show that for any isospin-independent $\mathrm{NN}$ interaction random phase approximation correlations provide a reduction of the production amplitude for $p\overline{p}$ pairs by a factor of 2.