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The intermediate and high-spin states of the $^{134}\mathrm{Ba}$ nucleus have been investigated up to spin ${I}^{\ensuremath{\pi}}=({20}^{\ensuremath{-}})$ using the $^{124}\mathrm{Sn}(^{13}\mathrm{C}, 3n)^{134}\mathrm{Ba}$ reaction at a beam energy of 48 MeV. The ${R}_{\mathrm{DCO}}$ and polarization asymmetry measurements were carried out to assign the spin and parity of the levels. Three ($\mathrm{\ensuremath{\Delta}}I=2$) negative parity bands were studied above the 1985.9 keV level having spin ${I}^{\ensuremath{\pi}}={5}^{\ensuremath{-}}$. The two quasiparticle $\ensuremath{\nu}[{h}_{11/2}\ensuremath{\bigotimes}({s}_{1/2}/{d}_{3/2})]$ configuration has been assigned to these bands based on the systematics of the $\mathrm{Ba}$ (even-$N$) isotopes and similarity in the behavior of signature splitting and $B(M1)/B(E2)$ ratios. Further, two ($\mathrm{\ensuremath{\Delta}}I=1$) dipole bands have also been observed starting at the 5677.9 and 5284.5 keV levels with spin ${I}^{\ensuremath{\pi}}={14}^{\ensuremath{-}}$ and ${15}^{+}$, respectively. The configuration of these bands was suggested from the systematics of the similar structure in the neighboring nuclei. Tilted axis cranking (TAC) calculations were carried out using the four quasiparticle $\ensuremath{\pi}[{h}_{11/2}({g}_{7/2}/{d}_{5/2})]\ensuremath{\bigotimes}\ensuremath{\nu}{[{h}_{11/2}]}^{2}$ and $\ensuremath{\pi}[{h}_{11/2}({g}_{7/2}/{d}_{5/2})]\phantom{\rule{4pt}{0ex}}\ensuremath{\bigotimes}\phantom{\rule{4pt}{0ex}}\ensuremath{\nu}[{h}_{11/2}{d}_{3/2}]$ configurations for bands D1 and D2, respectively. The TAC calculations and systematic studies of similar structures in the neighboring $N=78$ isotones suggest that the dipole band (D1) observed at 5677.9 keV level may have the magnetic rotation character.

The evolution of nuclear structure along the Xe and Ba isotopes with N{lt}82 is studied in comparison with that in the Pt-Os isotopes and with interacting boson approximation calculations. As is well known, the Pt isotopes from {sup 188{minus}196}Pt exhibit a stable structure very close to O(6), the lighter Pt isotopes and the Os nuclei evolve towards a rotor, and the heaviest Pt nuclei, {sup 198,200}Pt, show a tendency towards vibrational character. In contrast, we show that the Ba nuclei are best described by a trajectory from U(5) towards SU(3) that passes through an intermediate structure that resembles O(6) for N{approximately}72{endash}76. The Xe appears to evolve from U(5) to O(6)-like. {copyright} {ital 1998} {ital The American Physical Society}

Some aspects of the fluctuation part of the cross section at a doorway resonance are discussed. It is shown that in the strong absorption limit an inequality is derived for GAMMA/sup arrow-up/ namely GAMMA/sup arrow-down/> or = (2/N$sup 1$/$sup 2$-1) GAMMA/sup arrow-up/ where N is the number of open channels. In the strong absorption limit no doorway resonance appears in the average cross section. (AIP)

Compound nuclear processes should in fact exhibit all the resonances of the underlying compound nucleus. In intermediate resolution experiments where the energy resolution $\ensuremath{\Delta}E$ is considerably large compared to the width and spacing of compound nuclear states but small compared to those of optical model shape resonances, one observes the well-known intermediate structure. In the case of compound elastic processes a dynamically reasonable account of intermediate structure resonances was developed by various authors, where one assumes the existence of a doorway state through which the incident (or the final) state couples to the compound nuclear states. An energy average of the resultant amplitude exhibits intermediate structure. In the case of compound inelastic reactions the incident and the final states are different and the doorway states that relate the final state to the compound nuclear states will in general be different from the doorway states which relate the incident state to the compound nuclear states. The former doorway states will be referred to as the exit doorway states and the latter as the entrance doorway states. A dynamical theory is developed acknowledging the notion of these two kinds of doorway states. The energy averaged transition amplitude shows two sets of intermediate structure resonances corresponding to these two kinds of doorway states. It is expected that one of these sets of resonances will usually dominate a reaction in an energy domain. The present formulation can possibly explain the different sets of intermediate structure resonances observed in different exit channels of a nuclear reaction, for example, those observed in various exit channels of the $^{12}\mathrm{C}$+$^{16}\mathrm{O}$ system.

A projection operator method is presented for the calculation of low energy heavy ion inelastic scattering cross sections. The theory treats both gross and intermediate structure and is applied to the case of /sup 12/C+/sup 12/C..-->../sup 12/C(2/sup +/)+/sup 12/C(g.s.), where particle-vibration doorways of both 2/sup +/ and 3/sup -/ origin are included. The results are in reasonable agreement with experiment. A discussion of the possible effects of doorways of 0/sup +//sub 2/ origin is given.

The /sup 16/O+ /sup 16/O total reaction cross section has been deduced from the elastic data in the energy region from 15.5--18 MeV (c.m.) using the sum-of-differences method. It exhibits intermediate-width resonant structures which are attributed to quasimolecular resonances in the A = 32 system. Reduced partial widths of three resonances have been calculated. They indicate that the structure of the resonant states may not be that of a dinuclear molecule.

High resolution neutron transmission measurements have been performed on $^{204}\mathrm{Pb}$ in the energy interval $E=0.4\ensuremath{-}105$ keV. The transmission data were analyzed using a multilevel $R$-matrix code to deduce resonance parameters. Previously obtained neutron capture data were reanalyzed in the interval 2.6-86 keV. Values of $\frac{G{\ensuremath{\Gamma}}_{\mathrm{n}}{\ensuremath{\Gamma}}_{\ensuremath{\gamma}}}{\ensuremath{\Gamma}}$ were determined from the capture data. For those resonances where ${\ensuremath{\Gamma}}_{\mathrm{n}}$ could be determined from the transmission data, the capture data were analyzed to extract ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$. Our results yield an average capture for a stellar temperature $kT=30$ keV of 89.5\ifmmode\pm\else\textpm\fi{}4.5 mb. The $s$-wave level density for $^{205}\mathrm{Pb}$ corresponding to the neutron energy range investigated (i.e., $E\ensuremath{\sim}105$ keV) relative to that for $^{207}\mathrm{Pb}$ (which has about the same neutron separation energy) is greater by about a factor of 10. The average $s$-wave strength function in this energy region is determined as ${S}_{0}=0.93\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. This is an order of magnitude greater than that for a similar energy region in $^{206}\mathrm{Pb}$ + n where a doorway is observed at $E\ensuremath{\sim}500$ keV. However, the strength function in the initial $E=0\ensuremath{-}100$ keV in $^{204}\mathrm{Pb}$ + n is almost identical to the average value of that for $^{206}\mathrm{Pb}$ + n when the averaging interval for the latter is taken as ${E}_{\mathrm{n}}\ensuremath{\approx}0\ensuremath{-}1000$ keV (i.e., over the doorway state). This suggests that the $s$-wave doorway state observed in the higher mass lead isotopes is completely mixed with "background" states in $^{205}\mathrm{Pb}$, and most likely no intermediate structure will be observed in the $s$-wave strength function for the $^{204}\mathrm{Pb}$ + n reaction.

We study several statistical tests which can be used to determine whether experimental data, typically a sequence of partial widths, are compatible with the statistical model of nuclear reactions or, on the contrary, imply the existence of intermediate structure. These tests are applicable to cases where the data can be ascribed to a definite partial wave. We give a brief, but critical, discussion of the few known methods, and develop several new tests. These new tests involve the study of the following quantities: (a) the length of the longest unbroken sequence (run) of partial widths lying either above or below their median, (b) the length of the longest run about a value that we call the value of optimal run length, (c) the distribution of runs up or down, i.e., of unbroken sequences composed of increasing or decreasing values, (d) the number of large adjacent partial widths, and (e) the ratio of the mean-square successive difference to the variance. We apply these new tests and the previously known ones, and discuss their merits and drawbacks, in the examples $^{40}\mathrm{Ca}(p,{p}^{\ensuremath{'}})$, $^{56}\mathrm{Fe}(n,n)$, $^{244}\mathrm{Cm}+n$, $^{187}\mathrm{Re}(n,\ensuremath{\gamma})$, $^{115}\mathrm{In}(n,\ensuremath{\gamma})$, $^{90}\mathrm{Zr}+\ensuremath{\gamma}$, $\mathrm{Sn}+\ensuremath{\gamma}$, $^{70}\mathrm{Ge}(p,p)$, $^{239}\mathrm{Pu}(n,f)$, and $^{206}\mathrm{Pb}(n,n)$. We find reliable evidence for intermediate structure in all these cases, except in the reactions $^{187}\mathrm{Re}(n,\ensuremath{\gamma})$ and $^{115}\mathrm{In}(n,\ensuremath{\gamma})$.

Measurements made with a polarized neutron beam and a polarized target of /sup 235/U have been analyzed to obtain spin-separated fission cross sections of (/sup 235/U + n) below 25 keV neutron energy. Analysis of the cross section data in the resolved resonance region has been carried out to obtain a better estimate of average parameters than has been previously available. The average parameters have been used as the starting point for an extraction of energy-dependent average parameters in the unresolved resonance region. The results of this analysis show evidence for intermediate structure in the spin-4 component.

Nearly monochromatic photons from positron annihilation in flight have been used to measure photoneutron cross sections for $^{23}\mathrm{Na}$ and $^{25}\mathrm{Mg}$ in the giant-resonance region. The shape of the giant resonance of each of these nuclei is rather broad, with less striking intermediate structure than in most neighboring $\mathrm{sd}$-shell nuclei. In $^{23}\mathrm{Na}$ the total cross section rises to approximately 10 mb at 17.5 MeV and remains essentially constant up to 25 MeV. In $^{25}\mathrm{Mg}$ the total cross section reaches a peak of 28 mb at 23.1 MeV and falls to approximately half that magnitude at the upper energy limit of the experiment (29 MeV). In both nuclei the ($\ensuremath{\gamma},2n$) cross section appears to rise slowly above threshold but does not exceed 1 mb within the energy limits of the experiment. The integrated cross sections for $^{23}\mathrm{Na}$ and $^{25}\mathrm{Mg}$ are 119 and 249 MeV mb, respectively; the bremsstrahlung-weighted integrated cross sections are 5.7 mb for $^{23}\mathrm{Na}$ and 11.7 mb for $^{25}\mathrm{Mg}$.

Measurements have been made on the high-energy capture $\ensuremath{\gamma}$ rays associated with neutron resonances in the target nuclides ${\mathrm{Re}}^{185}$ and ${\mathrm{Re}}^{187}$ using an integral bias level of 4 MeV. The ${\mathrm{Re}}^{187}$ data show nonstatistical behavior, indicating the influence of at least one extremely narrow intermediate state, with a width of only about 30 eV.

A formal theory of scattering, including rearrangement processes, is presented. This theory is based on a model using completely antisymmetrized and orthogonalized channels. A detailed discussion of the ($p,2p$) reaction which emphasizes the sequential amplitude for this process is given as an application of the formal theory. The single-hole state generated upon the first collision is discussed using an extension of the theory of intermediate structure to doorway states which are not in a space orthogonal to the space of continuum channels. The theory developed here is able to properly include off-shell and Pauli principle effects in the description of the reaction. Some of the approximations necessary to obtain the standard results for the ($p,2p$) cross sections are also exhibited in the context of our general theory.