We develop the relativistic Rankine-Hugoniot relations for a three-dimensional plane shock and a three-dimensional oblique shock. Using these discontinuity relations together with various equations of state for nuclear matter, we calculate the temperatures and the compressibilities attainable by shock compression for a wide range of laboratory kinetic energy of the projectile.

NUCLEAR REACTIONS Equation of state of nuclear matter, hydrodynamics of relativistic heavy ion collision.

An anisotropic directional correlation between gamma rays and $L$ x rays following internal conversion is reported for the first time. Using four detectors, two coaxial and two planar Ge detectors, the spectrum of $L$ x rays was recorded in coincidence with the 1178 keV gamma ray in the decay of ${}_{}{}^{160}{}_{}{}^{}\mathrm{Tb}$. The resulting anisotropies are $A(1178\mathrm{}\gamma -L1)=-0.03\left(3\right)\mathrm{}$, $A(1178\mathrm{}\gamma -L\alpha )=0.009\mathrm{}\left(5\right)\mathrm{}$, $A(1178\mathrm{}\gamma -L\beta )=0.003\mathrm{}\left(3\right)\mathrm{}$, and $A(1178\mathrm{}\gamma -L\gamma )=0.00\mathrm{}\left(1\right)\mathrm{}$. The measured anisotropy for the $L\alpha$ peak is in significant disagreement with the theoretical prediction $A(1178\mathrm{}\gamma -L\alpha )=-0.003\mathrm{}$.

RADIOACTIVITY ${}_{}{}^{160}{}_{}{}^{}\mathrm{Tb}$, measured $\gamma -L\mathrm{x}\left(\theta \right)$, deduced anisotropy, Ge(Li) detectors.

It is found that, if the off-shell form factors for nucleons can be invoked to ensure current conservation during the instantaneous absorption of the four-momentum transfer by a particular constituent nucleon, the nuclear current in the resultant impulse approximation is conserved in the operator sense. It is also found that, if we start with a relativistic second-quantized operator representation of a given current, a precise definition can be ascribed to the nonrelativistic impulse approximation.

RADIOACTIVITY Impulse approximation with current conservation, the off-shell form factors for nucleons; formulation of the nonrelativistic impulse approximation.

An equations-of-motion method is presented for treating pairing correlations in doubly even nuclei. A simple technique is developed to overcome the problem of the spurious states arising from the use of an overcomplete set of basis vectors. The method yields very accurate ground-state energies, occupation numbers, and two-particle transfer amplitudes, as evidenced by comparison with the exact results for the case of the Ni isotopes.

NUCLEAR STRUCTURE Equations-of-motion method in pairing-force theory.

The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.

NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.

We have reanalyzed previous data on the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$($p$,$\mathrm{pd}$) quasifree scattering at 590 MeV incident energy, from which the authors deduce a momentum distribution of the clusters $\alpha$ and $d$ in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ with a full width at half maximum around 120 MeV/c. We find instead that the experimental results are compatible with a momentum distribution whose full width at half maximum is about 70 MeV/c, which is in agreement with other experimental findings and with the prediction of the cluster model.

NUCLEAR REACTIONS ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$($p$,$\mathrm{pd}$), $E=590\mathrm{}$ MeV; the FWHM of the momentum distribution deduced.

In a previous article, we gave a parametrization of a theoretical microscopic optical model potential for nucleon energies ranging from 10 to 160 MeV. However, it is not suitable for low-energy scattering. Reanalyzing our nuclear matter results, we propose a modification of the formula suitable for proton or neutron energies from 0 to 10 MeV.

NUCLEAR REACTIONS Parametric expression of a microscopic theoretical optical model potential for $p$ or $n$ with $0<E<\mathrm{}10\mathrm{}$ MeV.

The half-life of ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$ has been measured to be (4.08±0.24) × ${10}^{10}$ years.

RADIOACTIVITY ${}_{}{}^{176}{}_{}{}^{}\mathrm{Lu}$: Measured $T_{\frac{1}{2}}$. Ge(Li) detector.

The pion-nucleus optical potential in the isobar-doorway model is extended to isospin nonzero nuclei. Many-body effects in isobar propagation are parametrized in terms of an energy shift and width and an isobar nonlocality. Isospin dependence of these parameters is found to play an important role in determining pion charge exchange cross sections.

NUCLEAR REACTIONS Pion charge exchange, isobar-doorway optical potential model, isospin-dependent modification of isobar propagator.

Differential cross section angular distributions have been measured for the first few states in each residual nucleus in the ${}_{}{}^{124,126,128,130}{}_{}{}^{}\mathrm{Te}$($t$,$\alpha$)${}_{}{}^{123,125,127,129}{}_{}{}^{}\mathrm{Sb}$ reactions at $E_t=16\mathrm{}$ MeV. The angular distributions for the spin-orbit pair $\frac{5}{2^{+}}$ and $\frac{3}{2^{+}}$ have more structure at this energy than those at $E_t=12\mathrm{}$ MeV, but their shapes do not exhibit sufficient $J$ dependence to distinguish between the two spins. Distorted-wave Born approximation calculations reproduce the cross sections quite well. Relative spectroscopic factors, normalized to the sum rule limit, are obtained and these compare well with those obtained in other studies.

NUCLEAR REACTIONS ${}_{}{}^{124,126,128,130}{}_{}{}^{}\mathrm{Te}$($t$,$\alpha$)${}_{}{}^{123,125,127,129}{}_{}{}^{}\mathrm{Sb}$, $E_t=16\mathrm{}$ MeV, measured $\sigma (E_{\alpha },\theta )$, DWBA calculations, Spectroscopic factors.

The wave function representation of the half-shell functions is extended to include the channel with a bound state (${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ channel). The knowledge of the bound state is assumed a priori and a scheme is presented to construct the scattering states exploiting the known bound state. In our formulation only a small part of the half-shell function remains unknown which can then be suitably parametrized. We suggest a particular parametrization which yields the half-shell functions in a separable form. The effectiveness of the scheme is illustrated by presenting numerical results for simple potentials. Specific features of our scheme in relation to results from earlier investigations are discussed.

NUCLEAR REACTIONS Half-shell functions parametrization, triplet $S$ channel, wave function representation, separable form.

The $E2\mathrm{}$ transition rates and the quadrupole moment of the first $2^{+}$ state for $N=50\mathrm{}$ even $A$ nuclei and for even Zr isotopes are calculated using the structure wave functions of the broken pair approximation, assuming ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ as an inert core. The broken pair approximation results are in excellent agreement with the corresponding shell model results obtained by using identical input information. This fully demonstrates the usefulness of the broken pair approximation as a valid, reliable, and practical approximation to the shell model.

NUCLEAR STRUCTURE Shell model, broken pair approximation (BPA), generalized BPA, $E2\mathrm{}$ transition rates, quadrupole moment, $N=50\mathrm{}$ even $A$ nuclei, even Zr isotopes.

Comments on proton capture reactions involving isobaric analog states are summarized on the basis of experimental results.

NUCLEAR REACTIONS Fine structure of isobaric analog states.

Cross sections for the radiative capture of tritons by ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ have been measured in the incident energy range 0.8 to 3.3 MeV and found to be of order 200-300 nb/sr. The 90° excitation functions exhibit resonant structures for the transitions to the $\frac{5}{2^{+}}$ ground state of ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ and the $\frac{1}{2^{+}}$ (0.87-MeV) first excited state. Multilevel $S$-matrix fits of both excitation functions and angular distributions, on the assumption that dipole transitions dominate, permit $J^{\pi }$ assignments for the observed resonances to be limited to a very few possibilities; the best fit results, which are also most consistent with other relevant arguments, give the most likely assignments $\frac{3}{2^{-}}$, $\frac{5}{2^{-}}$, $\frac{1}{2^{+}}$, and $\frac{3}{2^{-}}$ for states at 19.76, 20.39, 20.58, and 21.05 MeV, respectively, although the parities cannot be individually ascertained. The lower limit for the radiative widths ${\Gamma }_{\gamma }$ ranges from 1 to 6 eV. An additional level also appears to be present at ∼19.3 MeV.

NUCLEAR REACTION ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$($t$,$\gamma$)${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$, $E=0.8-3.3\mathrm{}$ MeV; measured $\sigma (\theta ,E)$, ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ deduced levels, $J^{\pi }$, $\Gamma$, ${\Gamma }_t$. ${\Gamma }_{\gamma 0}$, ${\Gamma }_t$. ${\Gamma }_{\gamma 1}$. Natural nitrogen target.

Data are presented for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$+${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=60.2\mathrm{} \mathrm{and} 113.1$ MeV. Both angular distributions show pronounced backward angle peaking, largely due to single neutron exchange. Both optical model calculations including a Majorana exchange term and coupled reaction channel calculations including single neutron transfer provide a reasonable description of the experimental data but do have some difficulty reproducing the region of interference between the direct and exchange processes.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=60.2\mathrm{} \mathrm{and} 113.1$ MeV; Measured $\sigma \left(\theta \right)$; optical model and coupled reaction channel analyses.

The three-body variational wave functions resulting from two realistic nucleon-nucleon interactions featuring different deuteron $D$-wave probabilities have been used in the calculation of the three-body electrodisintegration of triton in the quasi-elastic region. The angular distributions of the coincidence cross section ${}_{}{}^3{}_{}{}^{}\mathrm{H}(e,e^{\prime }p)2n$ are found to depend sensitively upon the $D$-wave probability in the triton. In the case of the Reid soft core interaction a comparison of the $T=1\mathrm{}$ spectral functions corresponding to the Faddeev and variational wave functions reveals an appreciably larger high momentum content in the latter.

NUCLEAR REACTIONS ${}_{}{}^3{}_{}{}^{}\mathrm{H}(e,e^{\prime }p) 2n$, calculated spectral function $P(k,E_2)$, angular distributions of coincidence process, quasi-elastic peak, energy-weighted sum rule. Three-body variational wave functions; Reid and RHEL-1 nucleon-nucleon interactions.

Excitation functions and angular distributions of protons emitted from the reaction ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$p$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ have been measured in the energy range from 9 to 14 MeV. Some of the excitation functions show the presence of fluctuations that can be attributed to the statistical multistep compound emission. This effect explains also the shape and absolute value of the emitted proton spectrum measured at 13 MeV incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ beam. This comparison yields the value of the strength of the residual two-body interaction.

NUCLEAR REACTIONS ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$p$)${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, $E=9-14\mathrm{}$ MeV: measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, $\sigma \mathrm{}(E,Ep)\mathrm{}$, $\sigma (Ep,\theta )$. Deduced coherence energy $\Gamma$. Calculated residual two-body interaction strength.

Differential cross sections for proton elastic scattering by ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ were measured at several proton energies between 14 and 44 MeV. Previous data on ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ have also been considered. Evidence has been found for a strong enhancement in proton emission at backward angles for scattering by spherical nuclei at incident energies higher than 26 MeV. A phase-shift analysis of all the differential cross sections showed that the partial waves involved are those near grazing. Optical-model fits of good quality have been obtained for collective nuclei, while for spherical nuclei the cross sections at backward angles are not reproduced. The disagreement is not substantially modified when nonstandard radial dependences are given to the optical potential.

NUCLEAR REACTIONS Proton elastic scattering on ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$, $E_p=18.1-44.2\mathrm{}$ MeV; ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$, $E_p=14.7-44.1\mathrm{}$ MeV; ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, $E_p=35.2-44.1\mathrm{}$ MeV; ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, $E_p=20.9-44.1\mathrm{}$ MeV. Measured $\sigma \left(\vartheta \right)$. Comparison with phase-shift and optical-model analysis. Deduced optical-model potentials.

Differential cross sections for proton scattering on 61 nuclei with mass numbers between 9 and 70 were measured at 35.2 MeV incident energy. To extend previous measurements further data were collected at 29.7 MeV on 10 nuclei. From a detailed inspection of the data a definite correlation emerges between the elastic and inelastic cross section values at backward angles and the quadrupole deformation parameters ${\beta }_2$. Nuclear structure effects are also evident at forward angles at the filling of the $1p$ shell. A set of mass dependent optical-model parameters which produces acceptable fits at forward angles was derived. The imaginary part was found to contain terms connected with the above structure effects. The results of this and of a coupled-channels analysis are discussed.

NUCLEAR REACTIONS Proton scattering on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{10,11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12,13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14,15}{}_{}{}^{}\mathrm{N}$, ${}_{}{}^{16,17,18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$, ${}_{}{}^{20,22}{}_{}{}^{}\mathrm{Ne}$, ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{24,25,26}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28,29,30}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{32,34}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{35,37}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{39,41}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{40,42,43,44,48}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{46,47,48,50}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{50,52,53,54}{}_{}{}^{}\mathrm{Cr}$, ${}_{}{}^{55}{}_{}{}^{}\mathrm{Mn}$, ${}_{}{}^{54,56,58}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{58,60,61,62,64}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{63,65}{}_{}{}^{}\mathrm{Cu}$, and ${}_{}{}^{64,66,67,68,70}{}_{}{}^{}\mathrm{Zn}$; $E_p=35.2\mathrm{}$ MeV. On ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{50,53,54}{}_{}{}^{}\mathrm{Cr}$, and ${}_{}{}^{62,64}{}_{}{}^{}\mathrm{Ni}$ at $E_p=29.7\mathrm{}$ MeV. Measured $\sigma \left(\vartheta \right)$ for elastic and inelastic scattering to $2_1^{+}$ states. Optical-model and coupled-channel analysis. Deduced optical-model parameters and ${\beta }_2$ quadrupole deformation parameters.