Total Interaction Cross Sections Research Articles

Fission-Excitation Functions in Interactions ofC12,O16, andNe22With Various Targets

The fission cross sections ${\ensuremath{\sigma}}_{f}$ in the bombardment of Cs, Pr, Tb, Ho, ${\mathrm{Er}}^{170}$, Tm, ${\mathrm{Yb}}^{174}$, Lu, ${\mathrm{W}}^{182}$, Au, and Bi with ${\mathrm{O}}^{16}$, Tm with ${\mathrm{C}}^{12}$, and Tb with ${\mathrm{Ne}}^{22}$ have been measured as a function of projectile energy. The technique consists of counting coincident fission-fragment pairs with two Au surface-barrier Si detectors. The results are given in units of the total interaction cross section ${\ensuremath{\sigma}}_{R}$, and as a function of the excitation energy $E$ of the compound nucleus. It is demonstrated that for a constant value of $E$ for a compound nucleus $\frac{{\ensuremath{\sigma}}_{f}}{{\ensuremath{\sigma}}_{R}}$ is a function of the mass of the ion used and thus of the angular momentum of the nucleus. Fission for the systems investigated takes place only for nuclei formed in a complete fusion of the ion and the target nuclei. The cross section of ${\ensuremath{\sigma}}_{\mathrm{CF}}$ for this process is shown to be nearly independent of $E$ and the target used. We find $\frac{{\ensuremath{\sigma}}_{\mathrm{CF}}}{{\ensuremath{\sigma}}_{R}}$ to be 0.70 and 0.45 for ${\mathrm{O}}^{16}$ and ${\mathrm{Ne}}^{22}$, respectively. From the ratio $\frac{{\ensuremath{\sigma}}_{f}}{{\ensuremath{\sigma}}_{\mathrm{CF}}}$, experimental $\frac{{\ensuremath{\Gamma}}_{f}}{{\ensuremath{\Gamma}}_{n}}$ values are obtained and compared to theoretical ones. The following values in MeV with a standard deviation of 2 MeV for the experimental fission threshold for a nonrotating nucleus are obtained: 34.9, 26.5, 25.1, 24.6, 24.2, 20.4, 19.8, 18.2, and 17.0 for the compound nuclei ${\mathrm{Eu}}^{149}$, ${\mathrm{Ho}}^{157}$, ${\mathrm{Ta}}^{175}$, ${\mathrm{Re}}^{181}$, ${\mathrm{Os}}^{186}$, ${\mathrm{Ir}}^{185}$, ${\mathrm{Pt}}^{190}$, ${\mathrm{Au}}^{191}$, and ${\mathrm{Po}}^{198}$, respectively. These values, when corrected for shell effects, fit well the formula for a nonrotating charged liquid drop: ${{E}_{f}}^{L}=6.76(0.75\ensuremath{-}x){A}^{\frac{2}{3}}$. Here, $x=\frac{(\frac{{Z}^{2}}{A})}{{(\frac{{Z}^{2}}{A})}_{\mathrm{crit}.}}$ and we obtain the value 48.0\ifmmode\pm\else\textpm\fi{}1.0 for ${(\frac{{Z}^{2}}{A})}_{\mathrm{crit}.}$. The ratio between the level-density parameters for fission and neutron evaporation $\frac{{a}_{f}}{{a}_{n}}$ is found to be 1.22\ifmmode\pm\else\textpm\fi{}0.05; this ratio is independent of nuclear type. In particular, the ratio is nearly the same inside and outside the region of the closed shell. Values for moments of inertia can not be evaluated from the analysis.

Deutron scattering in nuclear matter

The scattering of deuterons by density fluctuations in nuclear matter is considered. The relative contribution of elastic scattering and the process of disintegration to the total cross section for the deuteron-nuclear matter interaction is determined. The ratio of the imaginary part of the deuteron optical potential tothe of the nucleon optical potential is calculated.

Total neutron-proton interaction cross section at 5.5 GeV

Polyethylene and carbon targets 48.53 and 42.58 g/cm/sup 2/ thick were bombarded with up to 6.5-Bev protons. The energy spectrum of detected neutrons was limited by tue proton energy maximum and by tue threshold of the discriminator operation. The total cross section for the neutron-proton interaction at 5.5 Bev was found to be (41.2 plus or minus 1.7) mb. (R.E.U.)

Inelastic interactions of 11.4 GeV/c π--mesons in hydrogen

Production cross-sections and angular distributions of Λ and K° particles produced by 11.4GeV/c π-mesons in hydrogen have been measured. A systematic investigation was made of all two-body decays of unstable neutral particles. No events inconsistent with γ, Λ, or K° were found. Production cross-sections, angular distributions and effective mass distributions of π-mesons produced in 4-prong events were also measured. No evidence for dominance of any high-mass multi-pion resonance was found. Both the pion production and strange-particle production reactions demonstrated peripheral characteristics in that the baryon was strongly peaked backward in the center of mass. The average transverse momentum was observed to be a monotically increasing function of mass. The experimental total interaction cross-section was (25.3±1.5) mb. The effect of the pion-nucleon T=3/2 isobar was clearly observed.

Resonant Absorption of Neutrons by Crystals

A study has been made of the Doppler broadening of resonances in the total cross section for interaction of slow neutrons with nuclei bound in crystals. The resonance at 6.71 eV in Os metal and the resonance at 6.65 eV in U metal were chosen as examples of moderate crystal binding, while the 6.65-eV resonance in ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$, for which $k{\ensuremath{\theta}}_{0}=0.043$ eV, was chosen as an example of strong binding. The shapes of the resonance lines were determined as a function of temperature by measuring the neutron transmission of thin and thick samples by means of the Argonne fast chopper. These shapes were compared with theoretical line shapes calculated by means of Lamb's theory of Doppler broadening as applied to the spectra of lattice frequencies implied by simple models of the crystal lattices. For moderate binding, a simple Einstein model which reproduces the observed specific-heat behavior of the crystal above 40\ifmmode^\circ\else\textdegree\fi{}K gives accurate resonance-line shapes at all temperatures. However, for ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$ the line shape implies a generalized Nernst-Lindemann model of the lattice with a frequency spectrum $g(\ensuremath{\nu})=0.9\ensuremath{\delta}(h{\ensuremath{\nu}}_{1}\ensuremath{-}0.013 \mathrm{eV})+0.1\ensuremath{\delta}(h{\ensuremath{\nu}}_{2}\ensuremath{-}0.052 \mathrm{eV})$. The proportions of the high- and low-frequency components are quite different from the values resulting from specific-heat data. Possible interpretations of the ${\mathrm{U}}_{3}$${\mathrm{O}}_{8}$ results in terms of simple lattice models are presented.

Complex Angular Momenta and the Relation Between the Cross Sections of Various Processes at High Energies

Relations for the functions f(t), corresponding to the reactions, are obtained by the unitarity conditions on complex j(t), the moving pole of a partial wave in the annihilation channel. Simple connections between total interaction cross sections for various particles at high energies are discussed. (L.N.N.)

On processes in the interaction of γ-quanta with unstable particles

This paper deals with various inelastic processes occuring in the collisions of fast particles with the nuclei neither excited nor transformed. At q 2 = 0 ( q 2 being the invariant square of the momentum transfer to the nucleus) the amplitude of these processes has a pole involving virtual photons. Therefore at sufficiently small q 2 the virtual photon exchange makes a larger contribution to the amplitude than the exchange of strongly interacting particles. This makes it possible to connect at small q 2 the cross section of the process under study and that of the process at work between the γ-quantum and the incident particle. Given q 2 and E L ⪢ m ( E L being the energy of incident particle in the laboratory coordinate system and m its mass), the energy w of the particles produced in the reaction in their centre-of-mass system is restricted by the condition w 2 − m 2 < 2 E L √ q 2. The relation between the above-mentioned cross sections, equivalent to one following from the Weizsäcker-Williams method, is obtained in the present paper by a covariant method, and the conditions of applicability of this relation are discussed, in particular for strongly interacting particle processes. An appraisal is made of the contribution made by the processes involving the Coulomb nuclear field to the total cross section of interaction between the incident particle and the nucleus. The processes at work in the Coulomb field of the nucleus, such as the bremsstrahlung of π or K-mesons, the conversion of π-mesons into two π-mesons and the transformations of a Λ 0-particle into Σ 0-particle are analyzed in detail.

Recoil Studies of Nuclear Reactions Induced by Heavy Ions

The mechanism of nuclear reactions induced by heavy ions was investigated by measuring the recoil ranges of ${\mathrm{Tb}}^{149}$, ${\mathrm{At}}^{211}$ and other alpha-emitting isotopes of At and neighboring elements and by determining the cross sections for the formation of ${\mathrm{Tb}}^{149}$ and ${\mathrm{At}}^{211}$.Recoil ranges were consistent with compound-nucleus formation at all energies studied for the following reactions: ${\mathrm{Pr}}^{141}({\mathrm{C}}^{12}, 4n){\mathrm{Tb}}^{149}$, $\mathrm{Ce}({\mathrm{N}}^{14}, xn){\mathrm{Tb}}^{149}$, ${\mathrm{La}}^{139}({\mathrm{O}}^{16}, 6n){\mathrm{Tb}}^{149}$, ${\mathrm{La}}^{139}({\mathrm{O}}^{18}, 8n){\mathrm{Tb}}^{149}$, and $\mathrm{Ba}({\mathrm{Ne}}^{22}, pxn){\mathrm{Tb}}^{149}$. A similar result was obtained for the reaction ${\mathrm{Pr}}^{141}({\mathrm{O}}^{16}, 2p6n){\mathrm{Tb}}^{149}$ at 138 and at 146 Mev and for the reactions ${\mathrm{Au}}^{197}({\mathrm{O}}^{16}, 2pxn \mathrm{and} 3pxn)\mathrm{At}$, Po at energies below 100 Mev. The excitation functions of the $(\mathrm{HI}, xn){\mathrm{Tb}}^{149}$ reactions seem to be characteristic of an evaporation process but have smaller peak cross sections than do the excitation functions of the reactions $\mathrm{Ba}({\mathrm{Ne}}^{22}, pxn){\mathrm{Tb}}^{149}$ or ${\mathrm{Pr}}^{141}({\mathrm{O}}^{16}, 2p6n){\mathrm{Tb}}^{149}$. We conclude that most reactions probably involve charged-particle emission. The reaction $\mathrm{Ba}({\mathrm{Ne}}^{22}, pxn){\mathrm{Tb}}^{149}$ seems to occur with much greater probability than the reaction $\mathrm{Ba}({\mathrm{Ne}}^{20}, pxn){\mathrm{Tb}}^{149}$.In many cases the compound-nucleus mechanism cannot account for our results. Partial momentum transfer is observed in the reactions ${\mathrm{Au}}^{197}({\mathrm{O}}^{16}, 2pxn \mathrm{and} 3pxn)\mathrm{A}\mathrm{t},\phantom{\rule{0ex}{0ex}}\mathrm{P}\mathrm{o}$ at energies above 100 Mev. Partial momentum transfer also occurs when Bi is bombarded at energies 1.3 times the barrier energy or greater. Reactions of Bi with heavy ions (${\mathrm{Ne}}^{20}$ is possible exception) at energies near the Coulomb barrier produce ${\mathrm{At}}^{211}$ with greater recoil energy than expected from a compound-nucleus mechanism. Apparently, particles are emitted in the backward direction. Near the barrier the cross section for the production of ${\mathrm{At}}^{211}$ by ${\mathrm{C}}^{12}$, ${\mathrm{O}}^{16}$, and ${\mathrm{Ne}}^{20}$ bombardment comprises about \textonequarter{} the value calculated for compound-nucleus formation. Therefore, the cross section for all noncompound-nucleus reactions must comprise a large fraction of the total interaction cross section. The experiments with Pb as a target are also consistent with this conclusion.

Construction of the Adiabatic Nuclear Potential: Formalism

A new formalism is presented for the construction of the two-nucleon potential, whose salient characteristic is that it involves an expansion only in the number of mesons exchanged, the self-mesonic field of each nucleon being treated, in principle, exactly. Access to the potential is achieved through the intermediary of the scattering matrix. With the assumption that nonlinear meson propagation may be neglected, alternative versions of this matrix are derived, only one of which is exploited in this paper. The connection between the scattering matrix and the potential is discussed, and it is emphasized again that the transition between the two requires a knowledge of non-energy-conserving matrix elements of the potential, which can be obtained only if the underlying Schr\odinger equation is known. The potential involving the exchange of at most two $P$-wave mesons is computed and shown to depend on the renormalized coupling constant, the single-nucleon source function, and the total cross sections for pion-nucleon interaction. The numerical evaluation of these formulas is not here attempted.

Total Interaction Cross Section of Pions with Protons and Deuterons at 1.0 Bev

Total Interaction Cross Section of Pions with Protons and Deuterons at 1.0 Bev