Effective two-body equations for the four-body problem are derived within the general $N$-body theory of Alt, Grassberger, and Sandhas. In contrast to usual treatments, the final expressions do not require separable (2 + 2) subamplitudes but incorporate these exactly. All four-body amplitudes can be calculated from the solution of a single integral equation for the reaction $\mathrm{}(3+1)\mathrm{}\to \mathrm{}(3+1)\mathrm{}$. With single-term separable approximations for the twoparticle and the (3 + 1) subsystem amplitudes the driving terms of the final equations are seen to reduce to those of the field-theoretical model by Fonseca and Shanley. Since our results are based on an exact and complete $N$-body theory, the investigation of subsystem reaction mechanisms is facilitated. As a consequence, we are led to a three-particle propagator which has the right pole behavior and includes exchange effects.

[NUCLEAR REACTIONS Four-body problem. Effective two-body equations with exact (2+2) subsystem contributions. Relation to field-theoretical model by Fonseca and Shanley. Three-body propagator with exchange effects.]

A nuclear structure effect in $A<\mathrm{}70\mathrm{}$ nuclei for elastic proton scattering, $25<E<\mathrm{}50\mathrm{}$ MeV, is identified with a strong channel coupling to known giant multipole resonances. Numerical studies reveal it as an effective $l$-dependent absorptive and repulsive optical model contribution. For an understanding in terms of microscopic optical potentials the connection between Brueckner-Hartree-Fock and nuclear structure approaches is discussed.

[NUCLEAR REACTIONS Proton elastic scattering on ${}_{}{}^{16,18}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, $E_p=21-48\mathrm{}$ MeV. Comparisons with optical model and coupled channel calculations. Deduced coupling strengths.]

A bound-state approximation when applied to certain operators, such as the many-body resolvent operator for a two-body fragmentation channel, in many-body scattering equations, reduces such equations to equivalent two-body scattering equations which are supposed to provide a good description of the underlying physical process. In this paper we test several variants of bound-state approximations in the soluble three-boson Amado model and find that such approximations lead to weak and unacceptable kernels for the equivalent two-body scattering equations and hence to a poor description of the underlying many-body process.

[NUCLEAR REACTIONS Test of bound-state approximations, soluble Amado model, Fredholm determinants calculated.]

Particle-particle coincidence measurements have been performed to study directly the particle decay modes of the isoscalar giant quadrupole resonance in ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$. The resonance was excited via inelastic alpha particle scattering at 160 MeV and decay protons, neutrons, and alpha particles were detected in coincidence at a number of angles. The importance of statistical processes in the decay of the giant quadrupole resonance is shown by the similarity of the measured branching ratios to statistical model predictions, which vary systematically across the Zn isotopes. This result is consistent with exciton model calculations which predict that the giant quadrupole resonance width in Zn isotopes is predominantly a spreading width rather than an escape width.

[NUCLEAR REACTIONS ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}(\alpha ,\alpha x)$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}(\alpha ,\alpha x)$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}(\alpha ,\alpha x)$, $x=p,n,\alpha$, $E_{\alpha }=160\mathrm{}$ MeV; measured $\frac{d^4\sigma }{d{\Omega }_{\alpha }d{\Omega }_{x}d{E}_{\alpha }d{E}_x}$; deduced giant quadrupole resonance branching ratios; compared with branching ratios calculated in statistical model.]

Singles $\gamma$-ray angular distributions obtained from the ($p,\gamma$) reaction on ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, and ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$ targets having a thickness of 3-5 mg/${\mathrm{cm}}^2$ are used to evaluate the statistical tensors for the alignment of the low-lying levels of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$, and ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$. The results show that these levels acquire a relatively strong alignment which depends only on the spin of the low-lying state. This fact makes the method suitable for spectroscopic investigation of odd mass nuclei. It has also been found that the observed Doppler shift of the transition in these nuclei can yield information on the lifetimes of the excited states upon the assumption of a side feeding time of 20 fs for the continuum $\gamma$ cascades. The method is illustrated with the examination of the level properties of the ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ nucleus.

[NUCLEAR REACTIONS ${}_{}{}^{56}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}$, ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$, ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}(p,\gamma )$, $E=2.0-4.0\mathrm{}$ MeV. Measured $I\gamma \left(\theta \right)$. ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}$, ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$, ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ deduced statistical tensors for alignment, side feeding time. ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ levels deduced $J$, $\delta$, $\tau$. Enriched targets, Ge(Li) detectors.]

Measurements of the tensor analyzing powers have been obtained for ($\overrightarrow{d},t$) reactions on ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$, ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ for deuteron energies both above and below the Coulomb barrier. The measurements are sensitive to the presence of $D$-state components in the triton wave function and allow the determination of a parameter $D_2$. This parameter is a measure of the importance of triton wave function components in which one neutron moves with orbital angular momentum $L=2\mathrm{}$ relative to the deuteron center of mass. Values of $D_2$ are extracted from the tensor analyzing power measurements by making use of distorted-wave Born approximation calculations. Analysis of the sub-Coulomb measurements leads to $D_2=-0.279\mathrm{}\pm 0.012$ ${\mathrm{fm}}^2$, which is somewhat larger in magnitude than recent theoretical predictions.

[NUCLEAR REACTIONS ${}_{}{}^{91}{}_{}{}^{}\mathrm{Zr}\mathrm{}(d,t)\mathrm{}$, $E_d=6.0,7.5\mathrm{}$ MeV, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}\mathrm{}(d,t)\mathrm{}$, $E_d=12.0\mathrm{}$ MeV, ${}_{}{}^{119}{}_{}{}^{}\mathrm{Sn}\mathrm{}(d,t)\mathrm{}$, $E_d=6.0,7.5,9.0\mathrm{}$ MeV, ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}\mathrm{}(d,t)\mathrm{}$, $E_d=10.0,12.3\mathrm{}$ MeV; measured polarization parameters $T_{20}\left(\theta \right)$, $T_{21}\left(\theta \right)$, $T_{22}\left(\theta \right)$; deduced $D_2$. Enriched targets, DWBA analysis.]

We have performed Monte Carlo calculations examining the sensitivity of the ${\Delta }_3$ statistic to missing levels for both single populations and two randomly mixed populations of neutron resonance data. Our results are presented in easy to use graphical form. By calculating ${\Delta }_3$ for the experimental data and then comparing it with the graphs, the most probable number of missed levels can be determined. We present results for 20, 60, and 100 observed single population levels and 20, 60, 100, 150, and 200 observed levels for two mixed populations and illustrate the use of these graphs by examining recently published neutron resonance data. We have also examined the sensitivity of the ${\Delta }_3$ statistic to spurious or added levels for both single and mixed populations and indicate how to estimate the number of spurious levels contained in a complete sequence of levels. Relations which express the average ${\Delta }_3$ and its standard deviation in terms of missing levels were found from our Monte Carlo results. They can be used to extend the range of the graphs, and have been found to apply under certain conditions to spurious levels as well. Finally, the results presented here are also useful when comparing the predictions of random matrix theory with experiment.

[NUCLEAR REACTIONS Statistical theory and fluctuations ${\Delta }_3$ statistic, Monte Carlo calculations, Dyson and Wigner's statistical theory. Effects of missing levels on the ${\Delta }_3$ statistic. Examination of experimental data.]

Predictions for statistical decay of highly deformed nuclei using the Hauser-Feshbach formulation are presented including emission of clusters up to ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. These calculatons use the rotating liquid drop model to estimate deformation versus angular momentum. The algorithms used to compute transmission coefficients for spherical and for deformed nuclei are presented, as well as results for several sets of calculations for $A=56\mathrm{} \mathrm{and} 148$ compound nuclei. Several different formulations are explored for computing decay rates of deformed nuclei. Large cluster emission amplification is predicted when deformation is considered, with consequent decrease in first chance fission. Qualitative comparisons are made with some heavy ion experiments which are consistent with these predictions, and types of experiments to verify the new cluster decay amplification mechanism are suggested. It is pointed out that the phase space dependence on deformation may prove valuable in interpreting some nonequilibrium heavy ion reaction results.

[NUCLEAR REACTIONS Model equilibrium decay clusters from superdeformed nuclei at high angular momenta. Discuss relevance new decay mode to incompletely equilibrated heavy ion systems. Compare predictions qualitatively with experimental results.]

We show that for large momenta the grand canonical ensemble is not an accurate enough approximation to the phase space integral to be used in calculating inclusive cross sections. In its place we propose a very general method based on the saddle point inversion of the Laplace transform integral. This method is shown to be quite accurate and is used to calculate deuteron inclusive spectra in conjunction with a two-fireball model.

[NUCLEAR REACTIONS Heavy ion collision; phase space; grand canonical ensemble; saddle point; inclusive cross section; finite number effect.]

The statistical properties of matrix elements which couple the collective (or shape) degrees of nuclear motion with the intrinsic degrees of freedom, are evaluated in the adiabatic representation. The results will be used in a future paper for the calculation of transport coefficients which describe the irreversible (dissipative) transfer of energy from the collective degrees of freedom to the intrinsic ones. As input we use a random-matrix model for the residual interaction, and salient properties of single-particle levels in nonspherical potentials.

[NUCLEAR REACTIONS Random-matrix model applied to heavy-ion reaction and fission.]

The energy density functional derived from the Negel effective interaction has been used to calculate the real part of the ion-ion interaction potential between several pairs of spherical nuclei in the framework of Brueckner's sudden approximation. We have found that the Negele realistic interaction produces a deeper ion-ion potential and shifts the barrier position outwards by about 0.3 fm compared with the potentials obtained using other simple effective nucleon-nucleon interactions. Our results for the positions and heights of interaction barriers are in good agreement with those obtained using Brueckner's phenomenological energy density formalism which compare very well with experimental results.

[NUCLEAR REACTIONS Negele two-body effective interaction, energy density, calculated ion-ion interaction potentials, and interaction barriers of spherical nuclei.]

Target fragment recoil properties were measured using the thick-target—thick-catcher technique for the interaction of 4.8 GeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and 5.0 GeV ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ with ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. The target fragment energies and momenta are very similar for the reaction of 4.8 GeV (400 MeV/nucleon) ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and 5.0 GeV (250 MeV/nucleon) ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ with ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. In the complex variation of fragment momenta with their $\frac{N}{Z}$ ratio, one finds evidence suggesting the existence of several mechanisms leading to the formation of the target fragments. Comparison of these results with the predictions of the intranuclear cascade model of Yariv and Fraenkel and the firestreak model shows that both model predictions grossly overestimate the target fragment momenta.

[NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},x)$, $E=4.8\mathrm{}$ GeV; ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},x)$, $E=5.0\mathrm{}$ GeV; measured target fragment recoil properties; deduced target fragment energies, momenta; relativistic heavy ion reactions; target fragmentation; spallation; fission; intranuclear cascade model; firestreak model; thick-target-thick-catcher technique; Ge(Li) gamma-ray spectroscopy.]

The reaction ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ is studied at 34 MeV ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ incident energy in the $5^{\circ }\le {\theta }_{\mathrm{lab}}\le {45}^{\circ }$ angular range in steps of 5°. Angular distributions are analyzed in terms of Hauser-Feshbach and exact finite range distorted-wave Born-approximation theories. The direct $\alpha$-transfer cross sections are evaluated in both the hypotheses of transfer to pure and mixed configurations. In the mixed configurations case good agreement between experimental and theoretical cross sections is found by using the empirical wave functions of Lawson, Serduke, and Fortune. Alpha-spectroscopic strengths are extracted for ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ states lying below 17.0 MeV excitation energy. Spins and parities are suggested for the 7.84, 8.9, 12.04, 14.6, and 17.0 MeV ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ levels. The existence and the structure of a positive-parity ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ rotational band is investigated.

[NUCLEAR REACTIONS ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}({}_{}{}^6{}_{}{}^{}\mathrm{Li},d){}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ $E=34\mathrm{}$ MeV; measured $\sigma \left(\theta \right)$; ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ levels deduced $J^{\pi }$ and $S_{\alpha }$. HF and EFR-DWBA analysis. EFR-DWBA analysis using empirical wave functions.]

Interactions between cascade particles were included in our intranuclear cascade calculation for high energy heavy ion collisions. This leads to better agreement between the calculated and experimental results for the inclusive pion cross sections and for two-nucleon correlations, without changing appreciably the calculated inclusive proton cross sections. The "single knockout" nucleons are shown to be a small fraction of the inclusive spectra.

[NUCLEAR REACTIONS Calculated effect of interactions between cascade particles in the intranuclear cascade model of high-energy heavy-ion reactions. Inclusive proton and pion cross sections and two-particle correlations. $E=400-1050\mathrm{}$ MeV/nucleon. ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$+${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$+${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$.]

We have measured the mass and kinetic-energy distributions of fragments from the spontaneous fission of a 1.5-s activity produced in bombardments of ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}$ with 95-MeV ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ ions. Its spontaneous fission decay exhibits a very symmetric, narrow (full width at half maximum = 12 mass units) mass distribution, a very high total kinetic energy of 234±2 MeV, and increasing total kinetic energy with increasingly symmetric mass division. Based on its half-life and the similarity of its fission properties to the unique fission properties so far only observed for ${}_{}{}^{258}{}_{}{}^{}\mathrm{Fm}$ and ${}_{}{}^{259}{}_{}{}^{}\mathrm{Fm}$, the most likely assignment of this activity is to the known ${}_{}{}^{259}{}_{}{}^{}\mathrm{Fm}$. However, assignment to some as yet undiscovered neutron-rich heavy element isotope such as ${}_{}{}^{260}{}_{}{}^{}\mathrm{Md}$ cannot be unequivocally excluded.

[RADIOACTIVITY, FISSION 1.5-s (sf) from ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}$ + 95-MeV ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$; measured $T$; measured fragment-fragment kinetic energies; total kinetic energy; deduced fragment mass distributions.]

The fission probability of ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$ has been measured as a function of excitation energy using the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}f)$ reaction with $E_a=152\mathrm{}$ MeV. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ spectrum in coincidence with fission exhibits a broad peak near the incident beam velocity. The deduced fission probability is the same as that obtained from the ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}\mathrm{}(n,f)\mathrm{}$ reaction. This suggests that the neutron transfers to the target forming a compound nucleus ${}_{}{}^{239}{}_{}{}^{}\mathrm{U}$, while the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, acting as a spectator, escapes with the incoming beam velocity.

[NUCLEAR REACTIONS ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\alpha ,{}_{}{}^3{}_{}{}^{}\mathrm{He}f)$ measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, fission probability to $E_x\sim 40$ MeV, discuss reaction mechanism.]

Neutron-induced angle-integrated fission cross sections of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ were measured from 1.3 to 1.8 MeV with a nominal neutron energy resolution of 0.15 ns/m. Data were taken for the angular intervals 0° to 23.4°, 0° to 33.7°, 0° to 51.7°, and 0° to 90°. The structure at ∼1.4, ∼1.6, and ∼1.7 MeV were interpreted in terms of rotational bands with $K=\frac{1}{2},\frac{3}{2},\mathrm{and}\ge \frac{5}{2}$. The approximate relative fission strengths for the $K$ bands are in the proportion 1.7:2.4:1.0, 0.0:2.6:1.0, and 1.0:2.8:0.0 for the three structures, respectively.

[NUCLEAR REACTIONS ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}\mathrm{}(n,f)\mathrm{}$, $1.3 \mathrm{MeV}<~E_n<~1.8 \mathrm{MeV}$, measured $\left(\frac{d{\sigma }_f}{d\Omega }\right)(0^{\circ }-{\theta }_m,E_n)$ for ${\theta }_m={23.4}^{\circ },{33.7}^{\circ },{51.7}^{\circ },\mathrm{and}{90}^{\circ }$. Determined $K=\frac{1}{2},\frac{3}{2},\mathrm{and}>~\frac{5}{2}$ components of the structures at ∼ 1.4, ∼ 1.6, and ∼ 1.7 MeV.]

Fission probability distributions of ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ compound systems have been measured with the (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$) reaction in the excitation energy range of 7-16 MeV using 65 MeV projectiles. Identification of ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ as two highly correlated alpha particles showed that under the conditions of this experiment ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$ can be separated from ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ in a simple $\Delta E-E$ system. The results are in good agreement with fission probabilities derived from neutron induced fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$.

[NUCLEAR REACTIONS, FISSION Measured fission probabilities for ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ with (${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^8{}_{}{}^{}\mathrm{Be}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$) reaction.]

The experimental cumulative yields of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Kr}_{}^m{}_{}{}^{}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, and ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$ and the independent isomeric yield of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$ in the thermal neutron fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ have been measured by the gas chromatographic method. The independent yields of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, and ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$ were deduced with the aid of ${}_{}{}^{133}{}_{}{}^{}\mathrm{I}$ and ${}_{}{}^{135}{}_{}{}^{}\mathrm{I}$ data. The isomeric yield ratios of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}$ have been computed and compared with theoretical values since they have the same high spin state $J=\frac{11}{2^{-}}$ and low spin ground state $J=\frac{3}{2^{+}}$. The influence of the shell effect on the fission isomeric yield ratio is discussed. From the measured independent yield of Xe isotopes plus the reported data, the Xe-isotopic distribution curve has been constructed. The curve is compared with the isotopic distribution curves of Xe isotopes formed in 11.5 GeV proton interactions with ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ and Cs isotopes formed in 24 GeV proton interactions with ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$. Upon fitting the yield curves we find that only those products with $\frac{N}{Z}\ge 1.48$ fit a curve typical of a binary fission process.

[NUCLEAR REACTIONS ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ (thermal neutron fission) ${}_{}{}^{85}{}_{}{}^{}\mathrm{Kr}_{}^m{}_{}{}^{}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{88}{}_{}{}^{}\mathrm{Kr}$, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, and ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$ cumulative yields, ${}_{}{}^{133}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$, ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^m{}_{}{}^{}$, and ${}_{}{}^{135}{}_{}{}^{}\mathrm{Xe}_{}^g{}_{}{}^{}$ independent yields and isomeric ratio.]

Experimental data on the isomer shelf in the photofission cross section of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ and the adequate theoretical description of this phenomenon are discussed.

[NUCLEAR REACTIONS, FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}(\gamma ,f)$, $E=3-6\mathrm{}$ MeV; analysis isomer shelf effect, calculated probability prompt and delayed fission by different theoretical models.]