We present a possible connection of a recent model for the nuclear motion with the renormalization group. We focus our attention on quantities which depend on the bulk properties of the two-body potential.

NUCLEAR REACTIONS Statistical theory in the frame of the renormalization group.

Decay energies for several mass-separated activities of Kr, Xe, and daughters have been reported previously. At the time of these measurements, the plastic scintillation detector used could be calibrated accurately only to 5 MeV. Using recently available decay energies for Rb and Cs fission products, the calibration curve for $\beta$ energies above 5 MeV has been redetermined. Redetermined $Q_{\beta }$ values are reported for 23 fission products, and comparison is made with various atomic mass predictions.

RADIOACTIVITY ${}_{}{}^{88,89,90,91,92,93}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{88,90,91,92,93}{}_{}{}^{}\mathrm{Rb}$, ${}_{}{}^{92}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{138,139,140,141,142}{}_{}{}^{}\mathrm{Xe}$, ${}_{}{}^{138,139,140,141,142}{}_{}{}^{}\mathrm{Cs}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Ba}$; measured $Q_{\beta }$. (Redetermination, based on an improved energy calibration.)

Time-differential $\beta -\gamma$ angular correlations perturbed by the nuclear quadrupole interaction in a zinc single crystal were used to extract a value of $y=+0.030\mathrm{}\pm 0.015$ for the ratio $\frac{C_V{M}_F}{C_A{M}_{\mathrm{GT}}}$ of Fermi to Gamow-Teller matrix elements in the allowed ${\beta }^{-}$ decay from the $\frac{5}{2^{+}}$ ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ ground state to the $\frac{5}{2^{+}}$, 197 keV state in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$. This leads to a figure of $M_F=(4.7\mathrm{}\pm 2.4)\times {10}^{-3\mathrm{}}$ for the isospin-forbidden Fermi matrix element. Other parameters which can be derived from this number are $\alpha =(2.7\mathrm{}\pm 1.4)\times {10}^{-3\mathrm{}}$ for the admixture of the analog of the ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$ ground state in the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ excited state and $\left|H_{\mathrm{CD}}\right|=20\mathrm{}\pm 10$ keV for the effective charge-dependent matrix element. A value of ${\omega }_0=+8.5\mathrm{}\pm 0.5$ μ${\sec }^{-1\mathrm{}}$ was determined for the nuclear quadrupole interaction of the ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ excited state in a zinc single crystal. The calibration provided by the pure Gamow-Teller decay to the $\frac{3}{2^{+}}$ 1.554 keV state in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ was used to remove effects of the implantation process, and data analysis was performed with a model which incorporated the effects of $\beta \text{'}\mathrm{s}$ backscattered by the thick crystal.

RADIOACTIVITY ${}_{}{}^{19}{}_{}{}^{}\mathrm{O}$; measured $\beta -\gamma$ ($\theta$) in Zn single crystal; deduced allowed $\beta$ decay matrix element, isospin mixing in ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ level, and ${\omega }_0$ sign for ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ level in Zn.

A polyisotopic sodium beam produced by reactions of 20 GeV protons in an uranium target, was illuminated with a tunable cw dye laser. The atomic beam is analyzed by a six-pole magnet, ionized, and detected after selection of one isotope by use of a mass spectrometer. From the optical $D_1$ resonance lines the hyperfine structure, magnetic moments, and isotope shifts of ${}_{}{}^{21-31}{}_{}{}^{}\mathrm{Na}$ have been determined. The nuclear spins of ${}_{}{}^{26-30}{}_{}{}^{}\mathrm{Na}$ have been measured by magnetic resonance. The results are discussed in terms of nuclear deformation. The analysis of isotope shifts shows the presence of an appreciable volume shift contribution.

NUCLEAR STRUCTURE ${}_{}{}^{26-30}{}_{}{}^{}\mathrm{Na}$; measured $J$. ${}_{}{}^{21-31}{}_{}{}^{}\mathrm{Na}$; measured isotope shifts; deduced $\mu$. Atomic beam laser spectroscopy and magnetic resonance.

The approximations of the interacting boson approximation of Iachello and Feshbach and the ability of this approach to describe the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ nucleus are tested. In the interacting boson approximation some "exchange" parts of many-boson matrix elements and violation of the Pauli principle in many-boson states are ignored. Matrix elements, two-boson wave functions and energies resulting from the interacting boson approximation are compared with exact two-hole two-particle calculations for the lowest 2+, 0 and the lowest excited 0+, 0 states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. It was found that neither of the above two approximations of the interacting boson approximation are valid. Calculations without these two approximations improve the approximate energies but not the wave functions.

NUCLEAR STRUCTURE ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$; calculated structure of lowest 0+ and 2+ excited levels. Interacting boson and shell model approaches.

Isotope shifts and hyperfine structure of the BaI $6s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-6s6p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ transitions ($\lambda =553.6\mathrm{}\mathrm{nm}$) in neutron deficient Ba nuclides ($N<\mathrm{}82\mathrm{}$) have been investigated by observing the resonance fluorescense in a well collimated atomic beam with a high resolution tunable CW dye laser. The experiments aimed at information on nuclear charge radii and on nuclear moments. Results are presented for the radioactive isotopes and isomers ${}_{}{}^{133}{}_{}{}^{}\mathrm{Ba}_{}^g{}_{}{}^{}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$, in addition to remeasurements of all stable Ba nuclides. The extracted values of $\delta 〈r^2〉$, the observed odd-even staggering and the nuclear moments are discussed in the light of other theoretical and experimental nuclear structure studies of the region $50\le (Z, N)\le 82$.

NUCLEAR STRUCTURE isotope shifts and hyperfine structure ${}_{}{}^{133}{}_{}{}^{}\mathrm{Ba}_{}^g{}_{}{}^{}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$, measured by laser spectroscopy, deduced $\delta 〈{\mathcal{r}}^2〉$ and nuclear moments.

A general hierarchy of approximations to the many-body Schrödinger equation is presented which reduces to the time-dependent mean-field approximation in lowest order and provides systematic corrections in subsequent orders. The theory is applied to two interacting systems described by the Lipkin model Hamiltonian. Comparison of the results of the lowest two orders of approximation with the exact solution demonstrates the practicality of the method and its potential for generalizing nuclear dynamics beyond the mean field theory.

NUCLEAR STRUCTURE Time-dependent approximation to nuclear dynamics. Corrections to time-dependent mean-field theory. Solution of Lipkin model for two interacting systems.

We apply the hyperspherical method to the $N$-body Schrödinger equation and solve for the bound states of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ with the center of mass motion correctly treated. It is shown how to construct antisymmetric hyperharmonic polynomials of definite $J$, $J_z$, $T$, and $T_z$ from Slater determinants with shell model coordinates. A set of coupled one dimensional differential equations are obtained and solved in $K_{min}$ approximation. A super-soft- core potential that provides a good fit to the two-nucleon scattering phase shifts is given a slight state dependence and is used for the two-nucleon potential. The proper handling of the potential energy matrix element with the center of mass motion excluded is detailed. A prescription for obtaining effective interactions for shell model calculations is presented. The difference in the potential energy matrix element of four $S_{\frac{1}{2}}$ nucleons in a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ nucleus or in a ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ nucleus is shown not to be zero. A $J$, $T=1, 1$ state of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ is calculated to have a binding energy of 15.245 MeV. This state may resemble a nuclear molecule of ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.

NUCLEAR STRUCTURE Many-body problem, hyperspherical method, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ bound states.

A study is made in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and infinite nuclear matter of the effects of mesonic and isobar degrees of freedom and the effect of the eikonal form factor in the meson-nucleon vertex of the nucleon-nucleon interaction. Three main effects are seen: First, the mesonic degrees of freedom are found to play a significant role by introducing additional density dependence, which results in a large improvement of the radius with a small change in the energy for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. Second, when the isobar and mesonic degrees of freedom are combined, repulsion is obtained in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ with a corresponding increase of the radius. These results are relatively insensitive to the replacement of part of the pionic form factors by the $\rho$ meson in the transition potentials to intermediate states with $\Delta$ resonances. Third, the use of the eikonal form factor, instead of phenomenological ones of the dipole type, results in additional attraction. This effect persists when the eikonal form factor is used in a potential that includes mesonic degrees of freedom.

NUCLEAR STRUCTURE Brueckner-Hartree-Fock in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, nuclear matter, mesonic degrees of freedom, one-boson-exchange potential with intermediate isobars.

In a "high-resolution" nuclear quadrupole experiment designed to detect nuclear hexadecapole interactions in solids, a series of ${}_{}{}^{185}{}_{}{}^{}\mathrm{Re}$/${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$ quadrupole moment ratios were also determined. The compounds included N${\mathrm{H}}_4$Re${\mathrm{O}}_4$, N${\mathrm{D}}_4$Re${\mathrm{O}}_4$, and KRe${\mathrm{O}}_4$ at a variety of temperatures. The weighted mean of our result is $\frac{Q\left(185\right)\mathrm{}}{Q\left(187\right)\mathrm{}}=1.056709\mathrm{}\left(17\right)\mathrm{}$ where the error indicated is the standard error.

Quadrupole moment ratio ${}_{}{}^{185}{}_{}{}^{}\mathrm{Re}$, ${}_{}{}^{187}{}_{}{}^{}\mathrm{Re}$.

Recent electron scattering results on the 0.850 MeV level of ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}$, when analyzed in terms of the interacting boson model, are inconsistent with the interpretation of this level as a pure $J^{\pi }\mathrm{}\left(K\right)=2^{+}\mathrm{}\left(0\right)\mathrm{}$ state. Very recent ($n, n^{\prime }\gamma$) work has shown this level to be a $1^{-}$, 2+ doublet. Assuming this level to be the band-head of a "$K^{\pi }=0^{-}$" octupole band, a simple model is used to predict electron scattering form factors for the 0.850 MeV state and a $3^{-}$ octupole level observed at 0.931 MeV. Comparison is made between these predicted form factors and recent electron scattering data.

NUCLEAR REACTIONS ${}_{}{}^{150}{}_{}{}^{}\mathrm{Nd}(e, e^{\prime })$, calculated 0+ → $1^{-}$; 0+ → $3^{-}$ octupole transition densities and form factors for comparison to measured form factors; small amplitude octupole vibration.

A search has been made for $\alpha$ particles that might stem from an isoscalar $E2\mathrm{}$ giant resonance in ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ near 9 MeV. Using 40 MeV electrons the spectra of protons and $\alpha$ particles emitted in the electrodisintegration of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ were measured. Peaks in the proton spectrum indicated that the target has an oxygen contamination. The less intense $\alpha$ spectrum contains $\alpha$ particles resulting from the electrodisintegration of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, a group that probably stems from ternary fission, and a higher energy feature which may be attributed to the electrodisintegration of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The integrated ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(e, \alpha )$ cross section is less than 1% of a recently suggested values.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(e, \alpha )$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(e, p)$, $E_e=40\mathrm{}$ MeV, particle spectra measured 4-24 MeV, deduced ternary fission cross section.

For the previously reported Gamow-Teller transition centered in ${}_{}{}^{90}{}_{}{}^{}\mathrm{Nb}$ at 8.4 MeV, two components are observed in the ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}({}_{}{}^3{}_{}{}^{}\mathrm{He}, t){}_{}{}^{90}{}_{}{}^{}\mathrm{Nb}$ reaction at 80 MeV. The first one of $M1\mathrm{}$ type is centered at 7.2 MeV, the other one of unknown multipolarity at 9.7 MeV.

NUCLEAR REACTIONS ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}({}_{}{}^3{}_{}{}^{}\mathrm{He}, t)$, $E=80\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$ IAS and Gamow-Teller states.

The $\gamma$-ray spectrum of a ${}_{}{}^{132}{}_{}{}^{}\mathrm{Te}$-${}_{}{}^{132}{}_{}{}^{}\mathrm{I}$ equilibrium source was measured with an 18% efficiency Ge(Li) detector to search for weak transitions in the ${}_{}{}^{132}{}_{}{}^{}\mathrm{I}$ decay. A more detailed study was made of an earlier spectrum taken with a Compton suppression system and a chemically purified source. The results are compared with all available data and average values of the energies and intensities are given.

RADIOACTIVITY ${}_{}{}^{132}{}_{}{}^{}\mathrm{I}$ separated and from ${}_{}{}^{132}{}_{}{}^{}\mathrm{Te}$; measured $E_{\gamma }$, $I_{\gamma }$ deduced levels.

Recent experimental results for $p$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering at 1 GeV are in fair agreement with the previous Saclay data, and also with the effective channel approach calculation, while a recent multiple diffraction analysis has found the $N^{*}$ effect important near the first diffraction minimum. In view of these, we comment on the role of the $N^{*}$ and other rearrangement channels within the effective channel approach, and show that the effective channel approach contains these effects collectively. The nonorthogonality and double-counting problems are discussed.

NUCLEAR REACTIONS Effective channels for proton-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ scattering, rearrangement channels, $N^{*}$ effects, nonorthogonality.

Riska and Brown have shown that an exchange-current correction of 10% to the total cross section for the threshold neutron capture $n+p\to d+\gamma$ can be obtained from one-pion-exchange terms. We investigate the sensitivity of the Riska-Brown calculation to the short-range behavior of the two-nucleon interaction by using unitary-equivalent transformations employed by the authors in an earlier study of the parity-violating circular polarization $P_{\gamma }$ in the same reaction. We find that some of the transformations, in fact those providing the greatest enhancement of $P_{\gamma }$, give exchange-current corrections in serious disagreement with the results of Riska and Brown. It is argued that enhancement of $P_{\gamma }$ caused by such transformations should be viewed skeptically.

NUCLEAR REACTIONS $p(n, \gamma )d$, thermal energy; sensitivity of exchange-current corrections to unitarily-equivalent short-range transformations, relation to parityviolation in $n-p$ system.

Data for the ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}(p, t)$ reaction to the $\frac{3}{2^{+}}$ state at 4.03 MeV excitation in ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ are consistent, both in angular distribution shape and cross-section magnitude, with calculations that assume a dominant 5p-2h configuration for this state.

NUCLEAR REACTIONS ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}(p, t)$, $E=40\mathrm{}$ MeV; measured $\sigma (E_t, \theta )$. ${}_{}{}^{19}{}_{}{}^{}\mathrm{Ne}$ levels deduced configuration. DWBA with microscopic wave functions.

The total neutron production cross sections for the ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}(p, n){}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(p, n){}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(\alpha , n){}_{}{}^{30}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}(\alpha , n){}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, and ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(\alpha , n){}_{}{}^{33}{}_{}{}^{}\mathrm{S}$ reactions have been measured for bombarding energies from threshold to 6.3 MeV. The neutron detector was a 60-cm diameter sphere of polyethylene with eight ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$${\mathrm{F}}_3$ counters and was insensitive to the angle and energy of the emitted neutrons. Cross sections for inverse reactions have been obtained using the principle of detailed balance. The data have been used to determine parameters for statistical model calculations to facilitate extrapolation of cross sections to higher bombarding energies. These reactions are relevant to problems of nucleosynthesis and stellar evolution and to studies of radiation damage. Nucleosynthesis reaction rates, $N_A\left(\sigma v\right)$, were determined for the reactions studied and are tabulated for temperatures ranging from 0.4 × ${10}^9$ to 10.0 × ${10}^9$ K.

NUCLEAR REACTIONS ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}(p, n)$, $E_p=5.0-6.5\mathrm{}$ MeV; ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}(\alpha , n)$, $E_{\alpha }=2.8-6.8\mathrm{}$ MeV; measured $\sigma \mathrm{}\left(E\right)\mathrm{}$. ${}_{}{}^{27}{}_{}{}^{}\mathrm{Si}(n, p_0)$, $E_n=0-0.55\mathrm{}$ MeV; ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}(n, {\alpha }_0)$, $E_n=0.4-0.9\mathrm{}$ MeV; ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{33}{}_{}{}^{}\mathrm{S}(n, \alpha )$, $E_n=0-2.3\mathrm{}$ MeV; deduced $\sigma \mathrm{}\left(E\right)\mathrm{}$ from measured $\sigma \mathrm{}\left(E\right)\mathrm{}$ and detailed balance. ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}(n, p)$, $E_n=0-3\mathrm{}$ MeV; calculated $\sigma \mathrm{}\left(E\right)\mathrm{}$. Deduced nucleosynthesis reaction rates.