We present a description, including relevant formulas and numerical estimates, of a set of polarization transfer experiments which appear to offer a feasible way to separate the deuteron charge and quadrupole form factors and measure the neutron and proton electric form factors. The experiments require a 2 to 4 GeV high-intensity, high-duty factor, longitudinally polarized electron beam and require that the polarization of the recoiling hadron be measured in a second, analyzing, scattering. The relevant asymmetries are fairly large, and our calculations show that they are sensitive to different models obtained from existing data. Attention is called to the fact that the proposed deuteron measurements will require new 10% measurements of vector and tensor analyzing powers of deuterons with kinetic energy from 150 to 450 MeV.

NUCLEAR STRUCTURE Analysis of electron polarization transfer experiments to measure $G_{\mathrm{Ep}}$, $G_{\mathrm{En}}$; separate $d$ monopole and quadrupole form factors.

A phenomenological model of the interactions between pions, nucleons, and $\Delta$ isobars is constructed. The mass operator is defined on a Hilbert space made up of $\mathrm{NN}$, $N\Delta$, and $\mathrm{NN}\pi$ states with the following interaction mechanism: (1) a $\Delta \rightleftarrows N\pi$ vertex in the $\pi N-P_{33}$ channel, (b) two-body $\pi N\to \pi N$ interactions in other $\pi N$ channels, and (c) two-body interactions for $\mathrm{NN}\to \mathrm{NN}$, $N\Delta \to N\Delta$, and $\mathrm{NN}\rightleftarrows N\Delta$ transitions. The model is Lorentz invariant and satisfies cluster separability. The interactions are parametrized by analytic separable forms with parameters determined by fitting the $\pi N$ scattering phase shifts for $l\le 1$ up to 300 MeV and $\mathrm{NN}$ scattering phase shifts for $l\le 4$ up to 800 MeV. In fitting parameters and in the applications, nonrelativistic approximations are used for the baryons in the $N\Delta$ and $\mathrm{NN}\pi$ channels. The model so determined gives a satisfactory description of pion absorption by deuterons and of elastic pion-deuteron scattering. Multiple rescattering of pions between $N$ and $\Delta$ as well as $\mathrm{NN}$ interactions in $\mathrm{NN}\pi$ intermediate states are found to be important in channels coupled to $N\Delta s$ waves. These effects enhance the cross sections for ${\pi }^{+}+d\to \mathrm{pp}$ by 40% in the resonance region. From the two-baryon Hamiltonian we construct a many-body Hamiltonian for nonrelativistic baryons.

NUCLEAR REACTIONS A model of interactions between $\pi$, $N$, and $\Delta$. Applications to the pion-deuteron system.

The elastic scattering of pions from ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is analyzed with a single-scattering optical potential, which is used in the solution of a relativistic integral scattering equation. Good agreement is obtained with available data near 1 GeV and choices are made for the nuclear and nucleon charge form factors and among the phase parameter sets at this energy.

NUCLEAR REACTIONS Scattering theory, pions on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, $E=1\mathrm{}$ GeV, calculate $\sigma \left(\theta \right)$, compare nuclear and nucleon form factors and phase shift sets.

Exact four-body calculations of the ${}_{\Lambda }{}^4{}_{}{}^{}\mathrm{He}-{}_{\Lambda }{}^4{}_{}{}^{}\mathrm{H}$ binding energy difference $\Delta B_{\Lambda }$ have been made using separable potential approximations to four of the $\mathrm{YN}$ potential models of Nagels, Rijken, and deSwart. The results indicate that two of the potential models are consistent with the $\mathrm{YN}$ charge symmetry breaking implied by the experimental $\Delta B_{\Lambda }$.

NUCLEAR STRUCTURE ${}_{\Lambda }{}^4{}_{}{}^{}\mathrm{He}$, ${}_{\Lambda }{}^4{}_{}{}^{}\mathrm{H}$, $\Delta B_{\Lambda }$, exact four-body calculation.

Differential cross sections for the reaction ${}_{}{}^2{}_{}{}^{}\mathrm{H}({\pi }^{\pm },p{\pi }^{\pm })n$ at incident pion momentum 340 MeV/c in a kinematically complete experiment are reported for eleven angle pairs. At neutron momenta ≲ 40 MeV/c the cross section peaks sharply and is described well by an impulse approximation corrected for entrance channel effects; the ratio of ${\pi }^{+}$ to ${\pi }^{-}$ cross section is approximately 9 to 1. For neutron momenta ≳ 40 MeV/c, the data are well fit by a combination of a $J^{\pi }=2^{+} N\Delta$ dibaryon resonance amplitude and an impulse approximation background; in some cases the ratio of ${\pi }^{+}$ to ${\pi }^{-}$ cross section is 1 to 1.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}({\pi }^{\pm },p{\pi }^{\pm })n$, $p=340\mathrm{}$ MeV/c; measured $\frac{d^3\sigma }{d{p}_{p}d{\Omega }_{p}d{\Omega }_{\pi }}$; model with DWIA, $p_n\lesssim 40$ MeV/c; model with $J^{\pi }=2^{+} T=1\mathrm{} N\Delta$ dibaryon resonance, $p_n\gtrsim 40$ MeV/c.

The Sternheim-Silbar linear transport model for calculating the effect of final-state charge exchange of the struck nucleon in ($\pi ,\pi N$) reactions has been reexamined. It is demonstrated that for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, the effect ranges from only 10% at low pion energies to 4% at the (3,3) resonance and plays a minor role in determining the magnitude of the inclusive cross sections. A semiclassical linear transport model is used to calculate the $\frac{{\pi }^{-}}{{\pi }^{+}}$ ratio for a clean, one-step nucleon knockout. Unlike the Sternheim-Silbar calculation these results are in very good agreement with intranuclear cascade model predictions.

NUCLEAR REACTIONS $\sigma (\pi ,\pi N)$ ratios, (3,3) resonance, final state interaction, nucleon removal, one-step quasi-free and intranuclear cascade calculations.

The effect of imposition of the Pauli principle for two-fragment elastic nuclear scattering is examined. It is shown that the antisymmetrized problem can be cast into the Lippmann-Schwinger form with an effective interaction in which the effect of the Pauli principle is entirely absorbed into the effective interaction potential operator. This result enables the formalism to be developed in analogy with the unsymmetrized formulation. Central to the approach is the choice of the off-shell extension of the transition operator. Comparison is made with a previously proposed treatment based on a different off-shell extension. It is shown that both the antisymmetrized transition operator and the associated optical potential proposed herein are readily expressed as spectator expansions in which the effect of the Pauli principle among the active fermions is incorporated in a physically appealing fashion at each stage of the expansion.

NUCLEAR REACTIONS Antisymmetrization incorporated in elastic scattering and optical potential theory. Multiple scattering series and spectator expansion.

Cross sections for the neutral current neutrino reactions $\nu +{}_{}{}^2{}_{}{}^{}\mathrm{H}\to p+n+\nu$ and $\overline{\nu }+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to p+n+\overline{\nu }$ are calculated by the use of form factors obtained from pion-photoproduction data by means of SU(2) commutation relations via the elementary particle model. The results are extrapolated from threshold to 150 MeV in the incident neutrino energy. Charged current cross sections for the reactions ${\nu }_e+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to p+p+e^{-}$ and ${\nu }_{\mu }+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to p+p+{\mu }^{-}$ are also obtained. Averaged cross sections for the reaction ${\nu }_n+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to p+p+e^{-}$ from neutrinos obtained from muon decay and for the reactions ${\overline{\nu }}_e+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to n+n+e^{+}$ and ${\overline{\nu }}_e+{}_{}{}^2{}_{}{}^{}\mathrm{H}\to n+p+{\overline{\nu }}_e$ from neutrinos obtained from the Savannah River reactor are also obtained and compared with recent experiments.

NUCLEAR REACTIONS Neutral and charged current neutrino disintegration cross sections of deuterium ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\nu ,\nu )np$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\overline{\nu },\overline{\nu })np$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\nu ,{\mu }^{-})pp$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\nu ,e^{-})pp$, ${}_{}{}^2{}_{}{}^{}\mathrm{H}(\overline{\nu },e^{+})nn$ are calculated using the elementary particle model.

Angular distributions and differential ranges at ${90}^0$ to the beam of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$, and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ emitted in the interaction of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with 0.8-400 GeV protons have been measured. The angular distributions of ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$ change from forward-peaked to sideward-peaked between 3 and 11.5 GeV, while those of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ are sideward-peaked and independent of bombarding energy in the above regime. Momentum distributions of all products are Gaussian at 0.8 GeV with a mean value increasing from 120 ${\left(\mathrm{M}\mathrm{e}\mathrm{V}\mathit{A}\right)}^{1/2}$ for ${}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$ to 139 ${\left(\mathrm{M}\mathrm{e}\mathrm{V}\mathit{A}\right)}^{1/2}$ for ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$. The momenta of the neutron-deficient products decrease by nearly a factor of 2 with increasing proton energy and the distributions broaden and become asymmetric. On the other hand, the momentum distributions of ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$ and ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$ are independent of proton energy. The results are analyzed with the two-step model and compared with the kinematics of the coherent interaction model. The implications of the results and comparisons for the reaction mechanism are considered.

NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}\mathrm{}(p,X)\mathrm{}{}_{}{}^{128}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Ba}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Ba}_{}^m{}_{}{}^{}$, ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ba}$. $T_p=0.8\mathrm{}-400$ GeV. Measured angular distributions and differential ranges at 90° to the beam, deduced two-step model parameters.

Nuclear pion single-charge exchange has been studied using a method of ${\pi }^0$ detection based on the spectroscopy of the back-angle $\gamma$-ray decay. Charge-exchange scattering from nuclei ranging from Be to Pb was studied for incident pion energies of 50 and 100 MeV. The angular distributions and ${\pi }^0$ energy spectra beyond 60° suggest effects characteristic of quasifree scattering. Total charge-exchange cross sections are larger than values suggested by optical-model calculations.

NUCLEAR REACTIONS ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}({\pi }^{\pm },{\pi }^0)$ $E_{\pi }=50\mathrm{} \mathrm{and} 100$ MeV, ${\theta }_{{\pi }^0}=25,40,60,90,120,150\mathrm{}°$; measured $\frac{d^2\sigma }{d\Omega \mathrm{dE}}$ for $0<\mathrm{}{E}_{{\pi }^0}<E_{{\pi }^{\pm }}$.

Neutrons from the interaction of ${\pi }^{-}$ at rest in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ were measured in coincidence with $\gamma$ rays which provided the identification of the resulting nuclei. Neutron energy spectra and neutron multiplicities were derived in discrete channels. A comparison is made with the interaction of 70 MeV ${\pi }^{+}$ with the same target investigated by protongamma coincidences. Despite their low detection efficiency, neutrons give information as valuable as protons and are an even better tool in the low-energy region under the experimental conditions. They give access to the study of all the secondary processes of the pion absorption.

NUCLEAR REACTIONS ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({\pi }^{-},n_{\gamma })$, $E_{{\pi }^{-}}=0\mathrm{}$; ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}({\pi }^{+},p_{\gamma })$, $E_{{\pi }^{+}}=70\mathrm{}$ MeV; neutron gamma and proton-gamma coincidences. Neutron and proton energy spectra, neutron and proton multiplicities for residual nuclei. Quasideuteron pion absorption model.

This study evauates the amplitude for the pion absorption reaction ${}_{}{}^4{}_{}{}^{}\mathrm{He}({\pi }^{-},n){}_{}{}^3{}_{}{}^{}\mathrm{H}$ to first order in the pion absorption operator for a pion laboratory kinetic energy of 290 MeV and the associated angular distribution of emitted neutrons is compared with recent experimental results. The pion absorption amplitude requires the full elastic scattering wave functions for the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ and $n-{}_{}{}^3{}_{}{}^{}\mathrm{H}$ systems and the bulk of this study is the generation of the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ full elastic scattering wave function in the effective channel approach. The effective channel approach expresses the ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ full elastic scattering state in terms of explicit elastic and inelastic channel wave functions. The input to the effective channel approach is a phenomenologica $\pi N$ separable interaction which satisfactorily accounts for the $\pi N$ 33 resonance and a complex local Gaussian potential which, in conjunction with the separable interaction, produces the approximate spin and isospin averaged $\pi N$ phase shifts and charge exchange cross section. A judicious choice of the form factor of the separable interaction allows an exact evaluation of the pion-nucleus potentials occurring in the application of the effective channel approach. These potentials are nonseparable and couple each partial wave to itself and to its two next neighbors as well as to the partial waves of the other channel. The complex local $\pi N$ Gaussian potential also allows the analytic construction of the associated terms of the effective channel approach. The resulting two-channel system of integrodifferential equations is solved by iteration. The parameters of the $\pi N$ potential are then varied to produce the observed total and inelastic ${\pi }^{-}-{}_{}{}^4{}_{}{}^{}\mathrm{He}$ cross sections and an angular distribution in reasonable accord with experiment to study pion absorption.

NUCLEAR REACTIONS ${\pi }^{-}{}_{}{}^4{}_{}{}^{}\mathrm{He}$ elastic scattering, ${}_{}{}^4{}_{}{}^{}\mathrm{He}({\pi }^{-},n){}_{}{}^3{}_{}{}^{}\mathrm{H}$ reaction at 290 MeV, effective channel approach.

Heavy particles emitted in the $\beta$ decay of ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ were studied by forming the activity in the ${}_{}{}^9{}_{}{}^{}\mathrm{Be}\mathrm{}(t,p)\mathrm{}{}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ reaction at $E_t=3.4\mathrm{}$ MeV and measuring the radiations by means of a helium-jet system together with Si and NaI(Tl) detectors. $\alpha$ particles and corresponding ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ recoil ions were observed both in singles and in coincidence with 478-keV $\gamma$ rays. It is deduced that ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ branches 2.9±0.4% by $\beta$-ray emission to the 9875-keV $J^{\pi }={\frac{3}{2}}^{+}$ excited state of ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, which then decays by $\alpha$ emission 87.4±1.2% to the ground state of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ and 12.6±1.2% to the 478-keV excited state. The experimental $log\mathrm{ft}$ of 4.04±0.08 for the ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$ $\beta$ branch to the 9875-keV state agrees with a theoretical estimate of ≃4.0, and the ambiguity in an earlier result is thereby resolved. The $\alpha$ branching intensity to the ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ 478-keV state is in reasonable agreement with a theoretical estimate.

[RADIOACTIVITY ${}_{}{}^{11}{}_{}{}^{}\mathrm{Be}$; measured delayed $\alpha$, ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$, and $\alpha -\gamma$ coin; He-jet system, Si and NaI(Tl) detectors; deduced $\beta$ and $\alpha$ decay branches; compared with theory.]

We are investigating the decay properties of even-even lead nuclei with $A\le 192$ in an effort to understand their anomalous $\alpha$-decay rates as reported by Hornshöj et al. Our results for ${}_{}{}^{192}{}_{}{}^{}\mathrm{Pb}$ were recently published. In this study ${}_{}{}^{190}{}_{}{}^{}\mathrm{Pb}$, $T_{\frac{1}{2}}=1.2\mathrm{}\pm 0.1$ min, was produced in the ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},6n)$ reaction and its decay was investigated with the use of an on-line isotope separator facility. Singles and coincidence $\gamma$-ray and conversion-electron data were accumulated. In addition, singles $\gamma$-ray and $\alpha$-particle spectra were taken with the detectors positioned in calibrated geometries. Twenty-three transitions were identified and placed into a scheme incorporating 16 levels in ${}_{}{}^{190}{}_{}{}^{}\mathrm{Tl}$. With this decay scheme information and the absolute photon and $\alpha$-particle intensities, the ${}_{}{}^{190}{}_{}{}^{}\mathrm{Pb}$ $\alpha$-decay branch was determined to be (9.0 ± 2.0) × ${10}^{-3\mathrm{}}$, a value about four times greater than that reported by Hornshöj et al. Our new results for ${}_{}{}^{190}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{192}{}_{}{}^{}\mathrm{Pb}$ indicate that the lead $\alpha$-decay reduced widths may show a dependence on neutron number observed for other elements.

RADIOACTIVITY ${}_{}{}^{190}{}_{}{}^{}\mathrm{Pb}$ measured $T_{\frac{1}{2}}$, $E_{\gamma }$, $I_{\gamma }$, $I_{\mathrm{ce}}$, $E_{\alpha }$, $I_{\alpha }$, $\gamma \gamma$, $\mathrm{ce}\gamma$ coin; ${}_{}{}^{190}{}_{}{}^{}\mathrm{Tl}$ deduced levels; ${}_{}{}^{190}{}_{}{}^{}\mathrm{Pb}$ deduced $\alpha$-decay reduced width. Mass separation.

The excitation of a many-body system by a one-body perturbation is considered. The stationary phase approximation to a functional-integral representation of the many-body evolution operator shows that the optimal mean field for describing the final expectation values of one- and two-body operators is that given by the time-dependent Hartree-Fock method. The forced Lipkin model is considered as a test of the mean-field approximation.

NUCLEAR REACTIONS Mean-field approximation, inclusive observables. Time-dependent Hartree-Fock.

The interacting boson approximation model of Arima and Iachello and co-workers has been used to make a schematic study of the tungsten isotopes. For each isotope of tungsten we determine the values of the five parameters in the interacting boson approximation Hamiltonian which yield the best fit to the experimental energy spectrum. Based on these values, we can extrapolate to isotopes for which no experimental data exist and can make predictions for future experiments. Using the same values of these parameters for each isotope, we can also obtain the $B\left(E2\mathrm{}\right)\mathrm{}$ transition rates, the $\rho \mathrm{}\left(E0\mathrm{}\right)\mathrm{}$ values, the quadrupole moments of the first two excited $2^{+}$ states, the two-neutron separation energies, and the isomer and isotope shifts. Where data exist our results, in general, agree very well with experiment, although more experimental information is needed for the isomer and isotope shifts and the quadrupole moments of the excited $2^{+}$ states. The long range goal is to understand the origin of the model parameters in terms of a microscopic theory, such as the nuclear shell model.

NUCLEAR STRUCTURE Interacting boson approximation model, investigation of the tungsten isotopes, energies, $B\left(E2\mathrm{}\right)\mathrm{}$ transition rates, and other properties. Model parameters as a smooth function of neutron number.

This paper reports the examination of the general problem of multiphoton processes which might occur at the nuclear level when one of the photons belongs to an intense radiation field of optical frequencies. Transition probabilities are reported which relate the rates for $\gamma$-ray transitions induced by the optical radiation to the Breit-Wigner cross sections for the absorption or emission of single $\gamma$ photons. In emission the induced processes of both anti-Stokes Raman scattering and two-photon emission are considered and both are found to lead to the generation of tunable $\gamma$ radiation. Transition probabilities are calculated to be large enough to support the production of usable spectral sources that could be tuned over a range of $\gamma$-ray energies approximately ${10}^3$ times greater than can be realized by conventional Mössbauer techniques. Analogous possibilities for the detection of nuclear reactions induced by intense optical fields also have been evaluated in this work.

NUCLEAR REACTIONS Calculated $B$ for multiphoton absorption; $\gamma$+ optical photon from laser.

We describe the nucleus by a system of mesons ($\pi ,\rho ,\dots$) and baryons ($N,N^{*},\Delta ,\dots$). Starting from a field theoretical Hamiltonian for the composite system we derive a Schrödinger equation in a subspace without mesons. In lowest order approximation we obtain a generalization of the one-boson-exchange formulation of the $\mathrm{NN}$ interaction for a general baryon-baryon interaction. We discuss two possible treatments of the many-body system: (i) nucleonic degrees of freedom only, and (ii) explicit inclusion of resonance degrees of freedom. In the case of nucleons and deltas the explicit form of the potentials is given together with a complete new fit of the Reid soft-core potential for the nucleonic part of the interaction. The coupled equations for the scattering states and the deuteron have been solved exactly using the complete baryon-baryon interaction in the one-boson-exchange limit. The deuteron $\Delta \Delta$ contribution is discussed in several limits of the general one-boson-exchange potential.

NUCLEAR STRUCTURE Meson and resonance degrees of freedom, calculated $N-N$ scattering, and deuteron properties.

An attempt has been made to generalize the U(6) boson model for nuclei introduced by Arima and Iachello by allowing the bosons to populate, in addition to the $L=0\mathrm{} \mathrm{and} 2$, the $L=4,6,\dots ,L_{max}$ excited levels. In this expanded space, a generalized boson degeneracy $g$ is defined. It is then shown that in the generalized space the interacting boson model will have the same simple features by explicitly looking at the rotational limit.

NUCLEAR STRUCTURE U(6) interacting boson approximation generalized. Odd-$K$ bands, band cutoffs predicted.

A shell-model calculation of the negative-parity states in the $A=36\mathrm{}-40$ nuclei is presented. The nucleus ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ is assumed to be an inert closed core. Active holes are restricted to the ($1d_{\frac{1}{2}},2\mathrm{}{s}_{\frac{1}{2}}$) configurations and an active particle is allowed to occupy the $1f_{\frac{7}{2}}$ or $2p_{\frac{3}{2}}$ orbit. The two-body effective interaction is assumed to be the modified surface-delta type. The energy spectra are calculated from a least-squares fit to the experimental data, varying the $T=0\mathrm{}$ and $T=1\mathrm{}$ strengths of particle-hole and hole-hole interactions and the three single-particle level splittings. Spectroscopic factors, $E2\mathrm{}$, $E3\mathrm{}$, and $M1\mathrm{}$ transition rates, and two-body matrix elements are also calculated and compared with the observed values and the previous theoretical results. The validity of the weak-coupling model is also tested.

NUCLEAR STRUCTURE $A=36\mathrm{}-40$, calculated effective interaction, energy spectra, spectroscopic factors and $\mathrm{EM}$ transition rates.