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-2- UCRL-18535 photoproduction at energies near 140 MeV. The:n: meson produced inside the nucleus was thought to be reabsorbed producing high excitation energy.Since this paper was published the same effect was observed in other isotopes and was always attributed to the onset of :n: meSon photoproduction. 5 ,8,9 Attempts we~e not usually made to consider separately the behavior of the fiss:1.onprobability as distinct from the interaction cross section, nor to take into account the energy deposition associated with each interaction process.In the present work these effects are taken into account separately and it is found that the variation in the photofission cross section as a function of energy for elements in the region of bismuth or lighter is essentially accounted for by the increase in fission probability with increasing excitation energy. On the other hand, since the fission prob..; ability in uranium is practically constant as a function of energy, the energy dependence of its photofission cross section is a reflection of the interaction cross section.· It seems also that the interaction described by the quasi-deuteron model lO is on the average much more efficient in transferring energy to the nucleus than is the mechanism involving :n: meson photoproduction. Consequently the former interaction process appears to be the dominant one in the excitations of sufficient energy to cause fission of lighter nuclei where the fission barriers are of large magnitude. On the other hand both processes are important in the fiSSion of heavier nuclei, such as uranium, which have small fission barriers.In the present :work we have measured the electron and Bremsstrahlung induced fission cross sections of the -3- UCRL-18535 cal expressions for the eBergy distributicn of the virtua~ photon spectrum associated with electrons, we have calculated the photofission cross sections from the electron-induced fission cross section data. Then the photofission cross sections calculated above have been integrated over the Bremsstrahlung spectrum and found to be in agreement with the measured Bremsstrahlung induced fission cross sections. This procedure has been followed assuming the virtual photon spectra corresponding to El, Ml, and E2 transitions, and some information about multipolarity has been obtained.The photofission cross sections have been subsequently analyzed in terms of , .the contributions due to photon interaction and to the fission.probability.The nature of the energy dependence of the photofission cross section has been establiShed. II. THEORETICAL RELATIONS A. Bremsstrahlung-Induced Reaction'Cross SectionsThe Bremsstrahlung-induced reaction cross sections are related to the photon-induced reaction cross sections through~the following expressionwhereO'B is the Bremsstrahlung induced reaction cross section, 0' (E) is y the photo reaction cross'section and KB(Eo:,E) is the energy distribution of the Bremsstrahlung from a thin radiator. This last q~antity is given by the following relation 11(1) -4-, UCRL-18535wher...

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The modern investigation of clusters, for which 1 N ∞, requires a generalization of the thermodynamics developed for infinite systems. For instance, in finite systems, phase transitions and phase coexistence become illdefined with ambiguous signals. The existence of phase transitions in nuclear systems, in particular of the liquid-vapor kind, has been widely discussed and even experimentally claimed. A consistent and unambiguous approach to this problem requires a connection between finite systems and the corresponding infinite systems. Historically, this has been achieved at temperature T = 0 by the introduction of the liquid drop model and the extraction of the volume term, which is a fundamental quantity of nuclear matter. This work extends this approach to T > 0, by determining the liquid-vapor coexistence line and its termination at the critical point. Since there is no known experimental situation where a nuclear liquid and vapor are in coexistence, we establish a relationship between evaporation rates and saturated vapor concentration and characterize the saturated vapor with Fisher's droplet model. We validate this approach by analyzing cluster concentrations in the Ising and Lennard-Jones models and extracting the corresponding first-order coexistence line and critical temperature. Since the vapor of clusters coexists with a finite liquid drop, we devise a finite size correction leading to a modified Fisher equation. The application of the above techniques to nuclear systems requires dealing also with the Coulomb force. Nuclear cluster evaporation rates can be corrected for Coulomb effects and can be used to evaluate the cluster concentrations in the 'virtual' equilibrium vapor. These cluster concentrations, determined over a wide temperature range, can be analyzed by means of a modified Fisher formula. This leads to the extraction of the entire liquid-vapor coexistence line terminating at the critical point. A large body of experimental data has been

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

The resilience to averaging over an initial energy distribution of reducibility and thermal scaling observed in nuclear multifragmentation is studied. Poissonian reducibility and the associated thermal scaling of the mean are shown to be robust. Binomial reducibility and thermal scaling of the elementary probability are robust under a broad range of conditions. The experimental data do not show any indication of deviation due to averaging. 25.70.PqThe complexity of nuclear multifragmentation underwent a remarkable simplification when it was empirically observed that many aspects of this process were: a) "reducible"; and b) "thermally scalable" [1][2][3][4][5][6]."Reducibility" means that a given many-fragment probability can be expressed in terms of a corresponding one-fragment probability, i.e., the fragments are emitted essentially independent of one another."Thermal scaling" means that the one-fragment probability so extracted has a thermal-like dependence, i.e., it is essentially a Boltzmann factor.Both "reducibility" and "thermal scaling" were observed in terms of a global variable, the transverse energy E t (defined as E t = i E i sin 2 θ i , i.e. the sum of the kinetic energies E of all charged particles in an event weighted by the sine squared of their polar angles θ), which was assumed (see below) to be proportional to the excitation energy of the decaying source(s) [1][2][3].In particular, it was found that the Z-integrated multiplicity distributions P (n) were binomially distributed, and thus "reducible" to a one-fragment probability p. With higher resolution, it was noticed that for each individual fragment species of a given Z, the n Z -fragment multiplicities P (n Z ) obeyed a nearly Poisson distribution, and were thus "reducible" to a single-fragment probability proportional to the mean value n Z for eachThe one-fragment probabilities p showed "thermal scaling" by giving linear Arrhenius plots of ln p vs 1/Similarly n-fragment charge distributions P n (Z) were shown to be both "reducible" to a one-fragment Z distribution as well as "thermally scalable" [5]. Even the two-fragment angular correlations P 1,2 (∆φ) were shown to be expressible in terms of a one-body angular distribution with amplitudes that are "thermally scalable" [6]. Table I gives a summary of the "reducible" and "thermal scaling" observables.TABLE I. Summary of reducible and thermal scaling observables in nuclear multifragmentation.Empirically, "reducibility" and "thermal scaling" are pervasive features of nuclear multifragmentation. "Reducibility" proves nearly stochastic emission. "Thermal scaling" gives an indication of thermalization.Recently, there have been some questions on the significance (not the factuality) of "reducibility" and "thermal scaling" in the binomial decomposition of Z-integrated multiplicities [7]. For instance, had the original distribution in the true excitation-energy variable been binomially distributed and thermally scalable, wouldn't the process of transforming from excitation energy E to transverse ene...