A new effective range formula is derived using a conformal mapping variable that incorporates the knowledge of the left-hand cut. Our formula is valid up to higher energies and has good convergence and extrapolation properties. As an illustration, we use the formula for a study of the $S$ and $P$ waves in the $n-p$ scattering.

NUCLEAR STRUCTURE New effective range formula derived from analyticity using conformal mappings.

We have made accurate absolute differential cross section measurements for ground state ($p, t$) transitions on the targets ${}_{}{}^{40,42,43,44,48}{}_{}{}^{}\mathrm{Ca}$ in order to study their systematics. Our results are in good agreement with ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^2$ pickup in a pure ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^n$ model for these nuclei. At the extremes of the shell, very small admixtures, ≈ 0.5% ${\left(1\mathrm{}{d}_{\frac{3}{2}}\right)}^2$ pickup for ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ →${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ≈ 0.25% ${\left(2\mathrm{}{p}_{\frac{3}{2}}\right)}^2$ pickup for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ →${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$, are required.

NUCLEAR REACTIONS ${}_{}{}^{48,44,43,42,40}{}_{}{}^{}\mathrm{Ca}(p, t)$. $E_p=40\mathrm{}$ MeV; measured ${\sigma }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\left(\theta \right)$ for ground state transitions. DWBA analysis. Comparison with pure ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^n$ model.

The positions of zeros and poles of the optical model $S$ matrix are tracked for the case of antiproton scattering from ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. It is found that moderately rapid energy variations can arise from zeros near the real axis and that this is a likely occurrence for expected strengths.

NUCLEAR REACTIONS Scattering theory, antiproton-nucleus optical model, $S$-matrix analytic structure.

Previous low-temperature nuclear orientation and angular correlation data from the decay of ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$ are reanalyzed in order to determine more precise values for the ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$ magnetic moment and the ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}$ gamma-ray mixing ratios.

NUCLEAR STRUCTURE ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$; reanalyzed $\gamma \left(\theta \right)$, $\beta \gamma \left(\theta \right)$, $\gamma \gamma \left(\theta \right)$; ${}_{}{}^{103}{}_{}{}^{}\mathrm{Ru}$, deduced $\mu$; ${}_{}{}^{103}{}_{}{}^{}\mathrm{Rh}$ deduced $\frac{E2\mathrm{}}{M1\mathrm{}}$ $\delta$.

The vertex function of the quasipotential in scattering equations is spectral analyzed in terms of the strength eigenstates, and a criterion for its effectiveness established. A simple variational procedure is given to construct the strength eigenstates, by which vertex functions may be evaluated.

NUCLEAR REACTIONS Quasipotential method, convergence of the iteration series.

A previous analysis of high resolution measurements of the total cross sections for 25- to 1100-keV neutrons on ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ in terms of an $l$-dependent optical model is extended to obtain model-independent but still $l$-dependent average scattering matrix elements from the data. The particular optical model obtained here is essentially the same as that deduced in the previous paper but the matrix elements are more amenable to future analyses with different models.

NUCLEAR REACTIONS (${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(n, n)$, $E_n=25-1100\mathrm{}$ keV, average scattering matrix elements and optical model parameters for $l=0\mathrm{} \mathrm{and} 1$.

The effect of Coulomb distortion on the proton analyzing powers in elastic $p-d$ scattering is calculated by an effective two-body approximation that involves $n-d$ on-shell information only. Varying the $n-d$ input information hardly affects the charge symmetric $p-d$ predictions. The calculated difference of the neutron and proton analyzing powers is significant at all but the very backward angles. Around the peak value of the analyzing power the difference is mainly due to Coulomb distortion, whereas in forward direction pure Coulomb effects dominate. The agreement with the measured analyzing power difference at 10 MeV is good but only fair 14 MeV, where the experimental situation might not be fully settled.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(N, N)$, $E=5, 10, \mathrm{and} 14$ MeV. Coulomb corrections to nucleon analyzing powers; predicted proton analyzing powers from $n-d$ Faddeev amplitudes.

The longitudinal sum rule, computed from recent measurements of quasielastic longitudinal structure functions at high momentum transfers, is lower than the theoretical prediction by about a factor 2. Here it is shown, by comparison between the theoretical measured values of the ratio of the $f$ sum rule to the longitudinal sum rule, that any substantial fraction of missing longitudinal strength must lie at energies low enough to have been detected. This analysis is independent of any systematic experimental errors of overall scale.

NUCLEAR REACTIONS Quasielastic electron scattering; longitudinal response function; longitudinal sum rule and "$f$" sum rule.

Conservation of particle number in the number-operator approximation of Otsuka and Arima is shown to require a particular normalization for the pair-creation operator. Even with this normalization, two difficulties arise: (a) the average number of particles in a shell can easily violate the Pauli principle, and (b) the mean square fluctuation of the particle number can be negative. As a consequence of the tendency to Pauli violation, the approximate ground-state expectation of the single-particle energy per particle is too low and fails to increase with the number of particles.

NUCLEAR STRUCTURE Number conservation and Pauli principle in number-operator approximation for pairing.

The apparent differences between two analyses of the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}F_3^{}{}_{}{}^{}$ nucleon-nucleon amplitudes by VerWest and the present authors are resolved. In both analyses dynamical poles are present in the scattering amplitude. These poles are associated with fixed left hand singularities.

NUCLEAR REACTIONS Intermediate energy $\mathrm{NN}$. Scattering theory. $NN-N\Delta$ coupled separable potentials.

Precessions were measured of the $2_1^{+}$ states in ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$ in the enhanced transient field in thin cobalt foils and comparison made with similar recent studies of ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{194}{}_{}{}^{}\mathrm{Pt}$ ions in Fe foils. It is concluded that (i) the transient field acting on Pt in Fe is singularly anomalous, and (ii) recent contention by Levy et al. that the $g$ factors of even Pt $2_1^{+}$ states may be substantially lower than reported earlier cannot be sustained.

NUCLEAR REACTIONS ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$′) ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$($2_1^{+}$), ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$(${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$′)- ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$($2_1^{+}$), ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$(${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$′) ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$($2_1^{+}$), ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$(${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$′) ${}_{}{}^{198}{}_{}{}^{}\mathrm{Pt}$($2_1^{+}$), $E_{\mathrm{S}}=80\mathrm{}$ MeV, $E_{\mathrm{Ni}}=220\mathrm{}$ MeV, enriched targets; measured $W(\theta , H, T)$ in thin polarized Co. Deduced relative transient field strengths $\mathrm{Os}\mathrm{Co}$ and $\mathrm{Pt}\mathrm{Co}$, $\mathrm{Os}\mathrm{Fe}$ and $\mathrm{Pt}\mathrm{Fe}$ for $1.5\%<~\frac{v}{c}<~3.9\%$, deduced $g\left(2_1^{+}\right)$ even Pt isotopes.

We report the first charged particle exclusive data for 425 MeV/nucleon. Ne on NaF in a triggered streamer chamber. Ratios of deuteron to proton and triton to proton production as functions of angle and multiplicity in the projectile rapidity region have been obtained. A total event analysis based on "rigidity flow" is also presented.

NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ (NaF), $E_{\mathrm{lab}}=425\mathrm{}$ MeV/nucleon. Multiplicity dependence of $\frac{\sigma \mathrm{}\left(d\right)\mathrm{}}{\sigma \mathrm{}\left(p\right)\mathrm{}}$, $\frac{\sigma \mathrm{}\left(t\right)\mathrm{}}{\sigma \mathrm{}\left(p\right)\mathrm{}}$ measured. Full event analysis.

Differential cross sections for ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\gamma , {\pi }^{+}){}_{}{}^{13}{}_{}{}^{}\mathrm{B}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ at $E_{\gamma }=194\mathrm{}$ MeV ($T_{\pi }\cong 40$ MeV) were measured at seven angles from 30° to 150° encompassing the momentum transfer range $0.6<~q<~1.5$ ${\mathrm{fm}}^{-1\mathrm{}}$. These results are compared with several distorted-wave impulse-approximation calculations with and without core polarization. We observe serious discrepancies between theory and experiment and also among the various calculations.

NUCLEAR REACTIONS ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(\gamma , {\pi }^{+}){}_{}{}^{13}{}_{}{}^{}\mathrm{B}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$, $E_{\gamma }=194\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $\theta =30-150\mathrm{}°$, $\Delta \theta =20\mathrm{}°$. Enriched target. Results compared to DWIA calculations.

We have measured velocity spectra of evaporation residues from the reactions ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + Al, Ca, and Ni at bombarding energies of 8.8, 13.6, and 19.6 MeV/nucleon. Comparison with statistical model predictions shows clear evidence for the onset of incomplete momentum transfer at about 5 MeV/nucleon above the interaction barrier. To first order, the results are similar for all targets, suggesting that the missing momentum is mainly associated with the projectile. The fraction of transferred linear momentum appears to decrease linearly with increasing relative velocity of the colliding nuclei at the barrier.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + Al, Ca, Ni. $E\left({}_{}{}^{16}{}_{}{}^{}\mathrm{O}\right)=8.8, 13.6, \mathrm{and} 19.6$ MeV/nucleon. Measured residue velocity distributions. Deduced linear momentum transfer.

Neutron spectra have been obtained at various angles in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reactions leading to the ${}_{}{}^{170}{}_{}{}^{}\mathrm{Yb}$ compound nucleus between 4 and 11 MeV/nucleon above the Coulomb barrier. The energy and angular distributions can be fitted by a moving hot source model. However, this model does not consistently explain other systematic trends obtained by the analysis. The Boltzmann master equation model also does not provide an adequate fit to the data.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$, 4-11 MeV/nucleon, nonequilibrium neutron emission systematics.

A new method is presented for treating rotational motion up to very high spin in deformed nuclei. Going beyond the mean field approach by the generator coordinate method, we take into account additional corelations, in particular, the interaction between the yrast and the two quasiparticle bands.

NUCLEAR STRUCTURE Rotational motion; heavy nuclei; generator coordinate method.

The analyzing power $A_y\left(\theta \right)$ for elastic scattering of neutrons by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ has been measured for eight angles in the range $80°<{\theta }_{\mathrm{lab}}<150\mathrm{}°$ at 50.4 MeV. A polarized neutron beam ($p_n=0.50\mathrm{}$) was produced through bombardment of a high-pressure deuterium target by a 50 MeV polarized deuteron beam ($p_d=0.55\mathrm{}$) and by collimation of the neutrons in the 0° direction. A liquid-helium polarimeter placed in the neutron beam was used to measure asymmetries for left and right elastic scattering, with cyclic beam polarization reversal. Multiparameter methods of data acquisition and analysis were used to discriminate against backgrounds from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ breakup reactions and from interactions with the target-cell walls. The extracted $A_y$ values exhibit the large positive maximum at backward angles and the smaller negative minimum at more forward angles typical of $n$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering at lower energies. The $n$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ $A_y$ values are compared with $p$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ results at a nearby energy by means of a phase-shift analysis and are found to be in good agreement (except perhaps in the negative minimum) when Coulomb corrections to the phase shifts are taken into account.

NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}(\overrightarrow{n}, n){}_{}{}^4{}_{}{}^{}\mathrm{He}$, $E_n=50.4\mathrm{}$ MeV; measured $A_y$ vs $\theta$ for $80°<{\theta }_{\mathrm{lab}}<150\mathrm{}°$.