The recent identification of the [$1f_{\frac{7}{2}}{j}^{-1\mathrm{}}$] multiplets observed in ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$)${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ reaction enables us to calculate the energy separation between the $2{s_{\frac{1}{2}}}^{-1\mathrm{}}$ and $1{d_{\frac{3}{2}}}^{-1\mathrm{}}$ hole states in the odd potassium isotopes. The calculations predict a linear dependence of this separation energy on the mass number and reproduce the experimental results fairly well.

NUCLEAR STRUCTURE Separation energies between the $\frac{1}{2^{+}}$ and $\frac{3}{2^{+}}$ hole states of ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{43}{}_{}{}^{}\mathrm{K}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{K}$, and ${}_{}{}^{47}{}_{}{}^{}\mathrm{K}$ isotopes. Shell model effective interactions deduced from ${}_{}{}^{40,41}{}_{}{}^{}\mathrm{Ca}$($d$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) ${}_{}{}^{39,40}{}_{}{}^{}\mathrm{K}$ reactions.

We have measured the cross sections for the production of 57 keV and 202 keV $\gamma$ rays (corresponding to the ground state deexcitations of the first two excited states of ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$) in the inelastic scattering of 2.8 and 14.1 MeV neutrons. At 2.8 MeV, the cross sections for the 57 and 202 keV $\gamma$ rays are, respectively, 0.43±0.04 and 0.16±0.02 b; at 14.1 MeV the cross sections are 0.28±0.03 and 0.11±0.01 b.

NUCLEAR REACTIONS ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$($n$,$n^{\prime }\gamma$), $E_n=3, 14$ MeV, $E_{\gamma }=57, 202$ keV. Measured $\sigma \left(E_n\right)$.

The first incomplete moment of the proximity flux function, used in the one-body proximity friction and diffusion, is calculated exactly in a simple model. It is seen that the usual classical approximation underestimates appreciably the exact results. This shows the importance of the quantum tunneling. Good agreements to the exact calculation can be obtained by using the Wentzel-Kramers-Brillouin approximation.

NUCLEAR REACTIONS: Deep inelastic collisions, one-body friction, proximity flux function, transmission probability, tunneling.

Analyzing powers were measured in the reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(p,\alpha ){}_{}{}^{37}{}_{}{}^{}\mathrm{K}(J^{\pi }=\frac{3}{2^{+}},\frac{5}{2^{+}})$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}(p,\alpha ){}_{}{}^{57}{}_{}{}^{}\mathrm{Co}(J^{\pi }=\frac{7}{2^{-}})$, and ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}(p,\alpha ){}_{}{}^{59}{}_{}{}^{}\mathrm{Co}(J^{\pi }=\frac{3}{2^{+}},\frac{9}{2^{-}},\frac{11}{2^{-}})$ at 22.0 MeV. A strong $J$ dependence of the analyzing power has been observed for $L=2\mathrm{}$ transitions in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and $L=5\mathrm{}$ transitions in ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$. The data are well reproduced by the distorted-wave Born approximation using a triton-cluster form factor.

Nuclear Reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{60,62}{}_{}{}^{}\mathrm{Ni}$ ($\overrightarrow{p}$, $\alpha$), $E_p=22.0\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$, $A_y\left(\theta \right)$; enriched targets.

A value of (-5.2±6.4) μb has been obtained for the cross section of the two-quantum radiative thermal neutron capture in hydrogen for the energy region $330<\mathrm{}{E}_{\gamma 1},E_{\gamma 2}<1890\mathrm{}$ keV. Restriction of the evaluation to a $\gamma$ energy range from 700 to 1520 keV yields (-0.4±3.0) μb. The present results are weighted averages from several coincidence experiments performed with various types of detectors. In one experiment, using two NaI(Tl) detectors, special care was taken to cover also the region of lower $\gamma$-ray energies ($233<\mathrm{}{E}_{\gamma 1},E_{\gamma 2}<2017\mathrm{}$ keV), since here the most severe discrepancy to theoretical predictions is indicated by an earlier measurement. The existing data reject a hypothesis concerning nonorthogonality of the ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ neutron-proton capturing and the deuteron ground state. Due to use of a ${\mathrm{H}}_2$O target from the present measurements at the same time the total cross section for the reaction ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($n$,$\gamma$)${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$ could be determined as (187±10) μb.

NUCLEAR REACTIONS ${}_{}{}^1{}_{}{}^{}\mathrm{H}$($n$,$\gamma \gamma$), ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$($n$,$\gamma$), thermal $n$, measured ${\sigma }_{\gamma \gamma }$, ${\sigma }_{\gamma }$.

The angular distributions of charged particles from the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$($n$,$t$)${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($n$,$\alpha$)${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ were measured with monoenergetic neutron beams from a reactor. Silicon surface barrier detectors were used. The ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$($n$,$t$)${}_{}{}^4{}_{}{}^{}\mathrm{He}$ data were compared with previous results having poorer angular resolution and with an $R$-matrix calculation. The ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$($n$,$\alpha$) ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ data show a marked anisotropy at 2 and 24 keV for the ground state group and a lesser anisotropy for $\alpha$'s leading to the first excited state of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$. Branching ratios are measured at thermal, 2- and 24-keV neutron energies. The results are compared with the $R$-matrix calculation.

NUCLEAR REACTIONS Neutron capture, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$; measured($n$,$\alpha$)$\sigma \left(\theta \right)$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$ branching ratio, $E_n=th, 2,24$ keV. Comparison with $R$-matrix calculation.

It is proved that the $2^{N-1\mathrm{}}-1\mathrm{}$ Lippmann-Schwinger-Glöckle-Tobocman equations provide a unique solution to the $N$-body scattering problem and that they represent the minimum number of Lippman-Schwinger-type equations necessary and sufficient to ensure uniqueness.

NUCLEAR REACTIONS Scattering theory. The $N$-body problem. Lippmann-Schwinger-Glöckle-Tobocman equations.

Nuclear reactions involving large momentum transfers require strong correlations among target nucleons. To provide an improved treatment of these correlations, a modified multiple scattering theory is formulated in which a fully off-shell three-particle scattering operator is the driving term in the scattering integral equation. Extensions and applications of this result are discussed, and the eikonal approximation considered.

NUCLEAR REACTIONS Multiple scattering theory, three-particle amplitude $t_{\mathrm{ij}}$ as the driving term, two-particle correlations.

The role of $E1$ excitations in neutron inelastic scattering from ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ has been explored. In essence, we find that the excitation of $1^{-}$ levels does not reflect their $E1$ strength, even when the transitions are to particularly collective levels. By "collective" $1^{-}$ levels, we mean those which have substantial $E1$ photon widths. We have made definite spin assignments to two $J=1\mathrm{}$ levels, at 5805.0 and 5946.4 keV and observed scattering intensities to six of them. This includes all known dipole levels below 6-MeV excitation. The neutron excitation strengths of these levels are compared with those from photon scattering, and with statistical model expectations. Transition energies were measured with uncertainties less than 0.5 keV, to resolve some ambiguities associated with previous level energy determinations.

NUCLEAR REACTIONS ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$($n$,$n^{\prime }\gamma$), $E_n=5.2, 6.2, 7.0, \mathrm{and} 8.5$ MeV. Measured $E_{\gamma }$, $I_{\gamma }$ at 90° and 152° (lab), deduced levels, ${\sigma }_n^{\prime }$. Statistical model analysis.

Ratios of cross sections for elastic scattering of 30.3 MeV protons from ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$ have been measured using a method which should be free of most systematic uncertainties. Protons scattered from a mixed metallic target with a thickness of 100 μg/${\mathrm{cm}}^2$ were detected by a position-sensitive proportional counter in the focal plane of an Enge split-pole spectrograph. Resolution of 8-10 keV (full width at half maximum) permitted identification of the scatterer by the kinematic shift for angles as small as 30°. A standard optical model successfully reproduces the data.

NUCLEAR REACTIONS ${}_{}{}^{40,44,48}{}_{}{}^{}\mathrm{Ca}$($p$,$p$), $E=30.3\mathrm{}$ MeV; measured ratios of $\sigma \left(\theta \right)$. Technique using mixed target, kinematic shift in spectrograph. Performed optical model analysis.

States populated by the ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$($p$,$2n\gamma$) ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$ reaction were studied using in-beam $\gamma$-ray spectroscopy with standard techniques that included fast timing, coincidences, and angular distributions. We populate the previously well characterized bands built on the ground state and the 5.2-ms $8^{-}$ state at 1529.0 keV up to the ${12}^{+}$ and ${12}^{-}$ levels, respectively. In addition we identify the rotational band built on the 7.4-ns $K=2^{-}$ octupole vibrational state at 1006.4 keV up to the $J^{\pi }={11}^{-}$ member and we observe the decoupling of the octupole phonon from the core rotation. A state at 1634.6 keV is populated with moderate intensity. If this state is the one reported at 1637 keV in ($d$,$d$) excitation then it is most likely the $K=3^{-}$ octupole vibration. We observe the gamma-vibrational band up to the spin 7 member and also a new band built on a metastable state at 1639.8 keV. This state has a half life of 19.2±0.3 ns and most likely $J=5\mathrm{}$ with uncertain parity.

NUCLEAR REACTIONS ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$($p$,$2n\gamma$), $E=16\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coinc, $T_{\frac{1}{2}}\left(\gamma \right)$, $W{\left(\theta \right)}_{\gamma }$, deduced levels $E$, $J$, $K$, $\pi$.

Photoneutron cross sections, including $\sigma \left[\right(\gamma ,n)+(\gamma ,pn\left)\right]$, $\sigma \left[\right(\gamma ,2n)+(\gamma ,p2n\left)\right]$, and $\sigma (\gamma ,3n)$, were measured for ${}_{}{}^{188}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{189}{}_{}{}^{}\mathrm{Os}$, ${}_{}{}^{190}{}_{}{}^{}\mathrm{Os}$, and ${}_{}{}^{192}{}_{}{}^{}\mathrm{Os}$ from 7 to 30 MeV and for ${}_{}{}^{186}{}_{}{}^{}\mathrm{Os}$ from 11 to 20 MeV, with a photon energy resolution of about 300 keV. The source of radiation was the monoenergetic photon beam obtained from the annihilation in flight of fast positrons. The partial photoneutron cross sections were determined by neutron multiplicity counting, and the average neutron energies for each multiplicity were determined simultaneously with the cross-section data by the ring-ratio technique. Nuclear information extracted from the data includes parameters of the giant dipole and giant quadrupole resonances, integrated cross sections and their moments, nuclear symmetry energies, and nuclear deformation parameters and intrinsic quadrupole moments. No fewer than eight kinds of evidence point to a sudden change of behavior between ${}_{}{}^{189}{}_{}{}^{}\mathrm{Os}$ and ${}_{}{}^{190}{}_{}{}^{}\mathrm{Os}$, which could be interpreted as a phase transition from a statically deformed prolate nucleus to a $\gamma$-unstable one, in general (but not detailed) agreement with the prediction of a dynamic-collective-model calculation.

NUCLEAR REACTIONS ${}_{}{}^{186,188,189,190,192}{}_{}{}^{}\mathrm{Os}$($\gamma$,$n$,$2n$,$3n$), $E_{\gamma }=7-30\mathrm{}$ MeV; measured $4\pi$ neutron yield, multiplicities, average energies for monenergetic photons; $\sigma (E_{\gamma },1n)$, $\sigma (E_{\gamma },2n)$, $\sigma (E_{\gamma },3n)$, GDR parameters, nuclear shape parameters, integrated cross sections and moments, GQR parameters, nuclear phase transition.

A systematic study of all of the stable even germanium isotopes by the ($t$,$p$) reaction has been performed. The reaction protons were analyzed in a quadrupole-dipole-dipole-dipole spectrometer with a resulting energy resolution approximately 15 keV. Levels up to 3 MeV in excitation energy were measured and the angular distributions compared to distorted wave analysis. A number of new spin assignments are made in the heavier germanium nuclei. Examination of the systematic trend of the ground state as well as various excited levels strongly supports a transition in nuclear deformation between $N=40\mathrm{}$ and $N=42\mathrm{}$. The data also indicate the effects of the approaching shell closure at $N=50\mathrm{}$.

NUCLEAR REACTIONS ${}_{}{}^{70,72,74}{}_{}{}^{}\mathrm{Ge}$($t$,$p$), $E_t=17\mathrm{}$ MeV $\sigma \left(\theta \right)$, DW analysis.

The ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$ (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$d$) ${}_{}{}^{73}{}_{}{}^{}\mathrm{As}$ reaction has been investigated at a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ bombarding energy of 20 MeV. Nearly 25 new bound levels in ${}_{}{}^{73}{}_{}{}^{}\mathrm{As}$ have been observed beyond 3 MeV excitation. The relative spectroscopic factors for the bound states have been extracted and are compared with the predictions of the simple pairing theory. Several isobaric analog states of ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ have also been identified.

NUCLEAR REACTIONS ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}$ (${}_{}{}^3{}_{}{}^{}\mathrm{He}$,$d$)${}_{}{}^{73}{}_{}{}^{}\mathrm{As}$, $E=20\mathrm{}$ MeV; measured $\sigma (E;\theta )$, DWBA analysis; deduced ${}_{}{}^{73}{}_{}{}^{}\mathrm{As}$ levels, $l_p$, $S$. Enriched target.

The ($\alpha$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) breakup reaction on ${}_{}{}^{62}{}_{}{}^{}\mathrm{Hi}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ targets at incident $\alpha$-particle energies of 172.5 and 140 MeV respectively has been studied by a plane-wave spectator model. The results have been compared with the Serber model calculations as well as with those of the distorted-wave Born approximation. It is found that plane wave methods are not appropriate to describe this reaction correctly. Apart from the distortions in the $\alpha$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ channels, the proper consideration of the neutron target interaction is also very important. The validity of some of the assumptions of the Serber model has also been investigated. It is found that these assumptions are not valid for the reactions under investigation and consequently some of the conclusions drawn previously from the Serber model calculations for this reaction are not justified.

NUCLEAR REACTIONS ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ ($\alpha$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$), ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$($\alpha$,${}_{}{}^3{}_{}{}^{}\mathrm{He}$) breakup reactions, calculated ($\frac{d^2\sigma }{d\Omega \mathrm{dE}}$); $E_{\alpha }=140-172.5\mathrm{}$ MeV plane wave spectator model analysis; comparison with DWBA.

The cross section for electron scattering from natural cerium (89% ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$) has been measured with electrons of 80 and 92 MeV at 90 and 105° between 4 and 48 MeV excitation energy. The nine resonances or resonance-like structures identified at $E_x=6\mathrm{}\left(31\mathrm{}{A}^{-\frac{1}{3}}\right), 7.4\left(38\mathrm{}{A}^{-\frac{1}{3}}\right), 10\left(52\mathrm{}{A}^{-\frac{1}{3}}\right), 12\left(62\mathrm{}{A}^{-\frac{1}{3}}\right), 15.3\left(79\mathrm{}{A}^{-\frac{1}{3}}\right), 22\left(114\mathrm{}{A}^{-\frac{1}{3}}\right), 25\left(130\mathrm{}{A}^{-\frac{1}{3}}\right), 31\left(160\mathrm{}{A}^{-\frac{1}{3}}\right)$, and $37.5\left(195\mathrm{}{A}^{-\frac{1}{3}}\right)$ MeV were classified on the basis of their momentum transfer dependence and discussed in the framework of the shell model. Since some of the arguments used are intricate we refer for quantitative particulars to the text. It is shown that the $E2$ sum rule strength not exhausted in the excitation range of this experiment may contribute up to 50% of the classical dipole sum rule to the photon cross section between 50 MeV and the pion threshold. The resonance at 10 MeV might be due to a separate oscillation of the excess neutrons against the rest of the nucleus.

NUCLEAR REACTIONS ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$($e$,$e^{\prime }$, $E_0=50\mathrm{} \mathrm{to} 92$ MeV, Measured $\frac{d^2\sigma }{d\Omega d{E}_x}$, bound and continuum states (giant resonances). Deduced multipolarity, reduced matrix element $B\left(E\lambda \right)$, radiative width ${\Gamma }_y^{\circ }$, sum rule exhaustion of giant resonances, photon cross section to pion threshold, total width of continuum and clustered states.

A study of the ($t$,$p$) reaction on the two stable Ga isotopes has been performed. The reaction protons were analyzed in a quadrupole-dipole-dipole-dipole spectrometer with a resulting energy resolution approximately 18 keV. Levels up to about 3 MeV excitation energy in ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$ and 2.75 MeV in ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$ were measured with 11 new levels observed in the first case and 18 in the second. The angular distributions have been compared to pure distributions observed in the ${}_{}{}^{72,74}{}_{}{}^{}\mathrm{Ge}$($t$,$p$) reactions at the same energy and found to correspond mostly to pure angular momentum ($L$) transfer although mixing of $L$'s is allowed. A number of new spins assignments are made for Ga levels and the results are used to discuss the spin of ${}_{}{}^{73}{}_{}{}^{}\mathrm{Zn}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$. The striking splitting of the $L=0\mathrm{}$ strength in three approximately equal components, observed in ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ga}$, strongly supports a transition in nuclear deformation between $N=40\mathrm{} \mathrm{and} 42$.

NUCLEAR REACTIONS ${}_{}{}^{69,71}{}_{}{}^{}\mathrm{Ga}$($t$,$p$) $E_t=17\mathrm{}$ MeV $\sigma \left(\theta \right)$

Fragment mass numbers, charges, and kinetic energies were measured by time of flight and $\Delta E$ techniques for reactions of ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$ targets with ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ projectiles at laboratory bombarding energies of 440 and 720 MeV. Dispersions in kinetic energy and mass for fixed atomic number fragments are reported for strongly damped fragments; estimates of the primary dispersions in fragment excitation, kinetic energy, and mass are presented by using the statistical model to estimate broadening due to particle emission. The standard deviation in $Q$ value is found to be nearly a constant 13% of the $Q$ value at both bombarding energies. The experimental yield distribution are shown to be consistent with a division of excitation which is proportional to mass.

NUCLEAR REACTIONS Deep inelastic ${}_{}{}^{124}{}_{}{}^{}\mathrm{Sn}$ (${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$,$X$) measured distributions in energy and mass number versus fragment atomic number; deduced primary distributions.