Proton Reaction Cross Sections Research Articles

Theoretical Calculations of Proton Reaction Cross Sections in a Lead Target with Energy Ep ≤ 300 MeV

Various cross sections of the p+natPb reaction are calculated in the 5- to 300-MeV energy region based on nuclear reaction models, i.e., the optical, evaporation, and exciton models, and direct reaction theory. Comparison of the calculated results with the experimental data shows that our calculations are quite reasonable. Excitation functions of some long-lived radioactive nuclei and neutron multiplicity are predicted. For medium-energy, proton-induced natPb fission, an empirical formula is developed.

Activation of Structural Materials due to Recoil Protons in Light Water Reactor

The long-lived radioactivities of structural materials induced by recoil protons in BWR were estimated for land disposal of low level waste after reactor decommissioning. Reaction products of interest are 53Mn, 91Nb, 94Nb, 97, Tc, 125Sb, 173Lu and 174Lu. A method of calculating the proton spectrum in materials was presented. The program PEGASUS-P was developed by modifying the PEGASUS, a preequilibrium and multistep evaporation theory code, to calculate proton reaction cross sections. The proton-induced activities in stainless steel, Inconel and Zircaloy-2 were calculated under typical irradiation conditions in an operating BWR. It was shown that even the most dominant activity due to 91Nb from Zircaloy-2 did not exceed 1/1,000 of that of a typical neutron induced activity of 63Ni for cooling up to 1,000 yr after the irradiation of 40 yr. The results are believed to hold for the case of PWR as well.

Activation of structural materials due to recoil protons in light water reactor.

The long-lived radioactivities of structural materials induced by recoil protons in BWR were estimated for land disposal of low level waste after reactor decommissioning. Reaction products of interest are 53Mn, 91Nb, 94Nb, 97, Tc, 125Sb, 173Lu and 174Lu. A method of calculating the proton spectrum in materials was presented. The program PEGASUS-P was developed by modifying the PEGASUS, a preequilibrium and multistep evaporation theory code, to calculate proton reaction cross sections. The proton-induced activities in stainless steel, Inconel and Zircaloy-2 were calculated under typical irradiation conditions in an operating BWR. It was shown that even the most dominant activity due to 91Nb from Zircaloy-2 did not exceed 1/1,000 of that of a typical neutron induced activity of 63Ni for cooling up to 1,000 yr after the irradiation of 40 yr. The results are believed to hold for the case of PWR as well.

Nuclear mean free path in the relativistic sigma - omega model.

The nucleon mean free path in the intermediate energy region is estimated using various relativistic nuclear potential models. While the small effective mass in the relativistic models significantly enhances the theoretical values for the mean free path through Negele-Yazaki effect, it does not resolve the deviation from the experimental values extracted from the proton reaction cross sections on various targets.

Microscopic Description of Nucleon-Nucleus Total Reaction Cross Sections

Microscopic calculations of the total reaction cross sections for protons on $^{12}\mathrm{C}$, $^{27}\mathrm{Al}$, $^{40}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$, and neutrons on $^{27}\mathrm{Al}$ and $^{208}\mathrm{Pb}$ have been made, which provide for the first time an excellent description of the data for projectile energies from 15 MeV through 1 GeV. The calculations are based on the experimental nucleon-nucleon total cross sections and explicitly include the effects of the real nuclear potential, the Coulomb potential, Pauli blocking, and Fermi motion.

Measurements of the total reaction cross section for protons on Ti and B between 20 and 50 MeV

Using a variation of a standard attenuation technique, total proton reaction cross sections (σR) have been measured for Ti and B at eight incident proton energies between 20 and 50 MeV at the University of Manitoba Cyclotron Laboratory. The Ti cross sections are presented along with existing reaction cross section data and are compared with optical model predictions for σR. The B cross sections are compared with σR for the nearby elements Be and C. The B and Ti results are also compared to predictions of the opaque-nucleus model.

A technique for measuring proton total reaction cross sections at medium energies

Total proton reaction cross sections between 20 and 50 MeV have been measured at the UCLA 50 MeV Cyclotron Laboratory. Our method, a variation of the attenuation technique first proposed by Gooding and Eisberg, is described. Features include a tightly collimated and well defined beam, the ability to use either solid or gaseous targets, and rapid accumulation of the data.

Loss of protons in thin absorbers

Proton losses due to nuclear inelastic interactions have been measured in Al and Cu absorbers of thicknesses less than half the proton range, for incident proton energies of 250 and 560 MeV. It is shown that the data can be used to obtain absorption corrections in proton counter telescopes for other energies in this energy interval. The absorption correction would be found from the loss calculated from the proton reaction cross-sections by multiplying by an experimentally determined ratio which is given by the present measurement.

Reaction cross sections for protons in the energy range 220–570 MeV

Proton reaction cross sections have been measured for targets of natural isotopic abundance of the following elements and compounds: H, Be, C, Al, Fe, Cu, Ge, Sn, Pb, H 2O, B 4C and NaI. Data for proton energies between 220 and 570 MeV have been obtained with two types of transmission-counter assembly. The total errors are of the order of ± 3 %, which is a factor of three better than existing measurements in this energy region. A slight increase of the reaction cross sections with energy is observed for most of the elements studied. The results interpreted in terms of the semi-classical theory of reaction cross section as function of energy clearly demonstrate the onset of pion-production above 250 MeV.

Proton Total Reaction Cross Sections in the 10-20-MeV Range: Calcium-40 and Carbon-12

Total reaction cross sections for protons on $^{40}\mathrm{Ca}$ have been measured at 15 energies between 10.3 and 21.6 MeV by the beam-attenuation method. The total reaction cross section for $^{40}\mathrm{Ca}$ rises sharply at low energies, reaches a maximum value around 13 MeV, and reaches a minimum value around 16 MeV. The rise at the lower energies is a result of the Coulomb barrier. The dip at 16 MeV is probably associated with the ($p,n$) threshold for $^{40}\mathrm{Ca}$. A comparison is made between the present experimental values and preliminary optical-model predictions based on available elastic-scattering data and polarization data. The variation in the reaction cross section is also compared with the integrated partial cross sections for elastic scattering. Total reaction cross sections for protons on carbon have been measured at ten energies between 9.88 and 19.48 MeV. Resonances in the total reaction cross section are observed in the neighborhood of 10.4 and 13.8 MeV. Variations of 200 mb are seen in the cross sections with changes in energy of the incident protons of about 200 keV. A comparison is made of the present total reaction cross sections and the integrated partial cross sections for elastic scattering and inelastic scattering to the first excited state of $^{12}\mathrm{C}$.

An associated particle method for measuring total proton reaction cross sections at 15.8 MeV

Measurements of total proton reaction cross sections by the attenuation method involve the determination of the ratio of particles absorbed in the target to those transmitted. The associated particle technique has been adapted to enable total reaction cross section measurements for the 15.8 MeV protons from the 2H( 3He,p) 4He reaction. Detection of the 4He defines the spatial collimation and time of arrival of the associated proton. Anticoincidence and coincidence measurements between the 4He's and the associated proton after traversal of the absorbing target, are performed. The ratio of these measurements yield values for the attenuation of the proton beam in the target. Measurements were performed for targets of gold and natural copper and iron. The cross sections so obtained were measured to an accuracy of 10%. A number of improvements to decrease the uncertainty to better than 5% are also discussed.

Proton Total Reaction Cross Sections for 22 Isotopes of Ti, Fe, Ni, Cu, Zn, Zr, and Sn at 14.5 MeV

Total proton reaction cross sections have been measured at 14.5 MeV for 22 separated isotope targets to an accuracy of ±2% for Ti, Fe, Ni, Cu, Zn, and Zr isotopes and ±4½% for the Sn isotopes. A beam-attenuation technique employing a solid-state counter to detect elastically scattered protons at forward angles has been used. Use of the solid-state detector reduces the corrections due to inelastic processes to a negligible level. The total reaction cross sections for the Fe, Ni, Zn, and Zr isotopes increase more rapidly with increasing N than optical-model calculations based on 14.5-MeV elastic-scattering and polarization data predict. The measured values for Fe, Ni, Cu, Zn, and Zr isotopes were generally smaller than the optical-model predictions; the measured Sn values, however, were larger. The dip in σR near Ni, previously observed using elemental targets in a number of experiments, is reproduced by suitable averaging of the isotope reaction cross sections. The dip is shown to arise from a combination of a sharply rising σR with increasing N (for constant Z) and the relatively small average value of N for Ni due to shell closure.

The anomalous dip in total reaction cross sections in the nickel region

A dip in elemental reaction cross sections for protons, deuterons, and alpha particles has been observed previously in the vicinity of nickel. The present measurements on separated isotopes in the nickel region for 14.5 MeV protons reveal that the dip is associated with the relatively low average value of N for nickel.

Proton Reaction Cross Sections and Strength Functions

The average yields of neutrons from proton-induced reactions in thick targets have been measured for about 33 elements in the mass region $90\ensuremath{\lesssim}A<~209$ at incident proton energies between 5.5 and 9.5 MeV. In this region of energies and masses, the ($p, n$) reaction overwhelms competing reactions so that, except in a few cases, the average ($p, n$) cross sections deduced from the measured yields are equal to the total reaction cross sections for protons. Reduced cross sections, which are directly related to the proton strength function, were obtained from the measurements. These results, as well as the results of previous measurements for $A<90$, were compared with optical-model calculations. Proton reaction cross sections calculated from the optical potential of Perey are in remarkably good quantitative agreement with the measurements. The data are consistent with a resonance in the $P$-wave proton strength function at $A\ensuremath{\approx}105$, and with dominant contributions from $S$- and $D$-wave protons at $A\ensuremath{\approx}65$ and for $155<~A<~200$. The measured angular distributions for some of the nuclei showed symmetry about 90\ifmmode^\circ\else\textdegree\fi{} to about 2%, indicating no measurable direct-interaction component. The maximum anisotropy observed was about 7%.

Total proton and deutron reaction cross-sections in the energy range 8.5 to 11.5 MeV

Results of total proton reactions cross-sections are presented for Al, Fe, Co, Ni, 58Ni, 60Ni, Cu, 63Cu, 65Cu, Zn, Ag, Cd, In and Au in the energy range 8.5 to 11.5 MeV, and for the total deuteron reaction cross-section for Ni, 58Ni, 60Ni, Cu, 63Cu and 65Cu at 11 MeV. The method used is an attenuation technique in which the number of particles removed from the incident beam, during passage through a thin target, is determined by measuring the electric charge transferred to the target system as a result of absorption processes.

Elastic scattering of 10.5- and 14.5-MeV polarized protons from nuclei and the optical model potential at intermediate energies

The results of extensive measurements of the angular distributions and azimuthal asymmetries for elastic scattering of 10.5 and 14.5 MeV polarized protons, from a wide range of nuclei, are presented. Attention is focused on the general features of these angular distributions and certain deviations from the general trends. The interpretations of both these aspects of the data are discussed. In addition, results are presented from an extensive search program designed to obtain fits to the data with a six-parameter local “optical” potential. From these individual fits to each nuclide have been obtained a set of average parameters at 10.5 MeV and another set at 14.5 MeV. The predictions of the optical model with the average parameters are compared not only to the polarization data but also to elastic differential cross sections and reaction cross sections for protons. With a modification of the magnitudes of the refractive and absorptive central potentials, as required to fit 14.5 MeV neutron elastic scattering cross sections, the potential has been used to predict differential elastic cross sections, reaction cross sections, total cross sections, and polarizations for neutrons, and the results compared with available experimental data. A study has been made of the dependence of the refractive central potential depth on proton energy and on the nuclear symmetry parameter, (N−Z) A , obtaining reasonable agreement with the results of other workers.

Proton reaction cross sections at 8.8 MeV

Proton reaction cross sections at 8.8 MeV are given for Al, V, Fe, Co, Ni 58, Ni 60, Cu 63 Cu 65, Cu, Zn and Ga. An anticoincidence technique was used and the results are discussed in terms of optical model predictions.

The measurement of the total proton reaction cross-section of carbon in the energy region up to 50 MeV

Measurements are reported of the carbon total proton reaction cross-section at mean energies 22 MeV (420 ± 42 mb) and 42 MeV (405 ± 38 mb). A method is developed in which pulse-height spectra from plastic scintilator are carefully analysed to give the total number of low pulse-height events obtained with a mono-energetic incident beam. Theoretical analyses are made of the shape of the main peak to be expected for incident energies of 10 MeV, 30 MeV and 50 MeV.

Alpha-Particle Reaction Cross Sections at 40 MeV

We have measured the nonelastic cross section ${\ensuremath{\sigma}}_{R}$ for 40-MeV alpha particle for 19 target elements ranging in atomic, weight $A$ between 9 and 232. The results have been compared with the predictions of the optical model ${\ensuremath{\sigma}}_{I}$. The ratio $\frac{{\ensuremath{\sigma}}_{R}}{{\ensuremath{\sigma}}_{I}}$ deviates from unity in a systematic fashion being less than 1 for the lightest elements and greater than 1 for the heaviest. Superimposed on this trend, $\frac{{\ensuremath{\sigma}}_{R}}{{\ensuremath{\sigma}}_{I}}$ dips by 18% for elements where the nuclear charge is near 28. A similar effect had been noted earlier in proton-reaction cross-section data but not in deuteron-reaction cross-section data.

10-MeV Proton Reaction Cross Sections for Several Elements

We have obtained proton nonelastic cross sections at 10 MeV from Be, C, Al, Ti, Mo, Zr, Fe, Ni, Zn, Cu, V, Rh, Nb, Ag, Sn, Ta, Th, Au, and Pb. The most significant feature of the data is the appearance of two strong minima in the elements lighter than Cu. The data are compared with optical-model predictions. These calculations predict the right order for the reaction cross section when a surface absorption potential that fits existing elastic-scattering data is used. However, on the basis of our data, a volume absorption potential of the Woods-Saxon shape cannot be excluded. The data are compared with other measurements of non-elastic cross sections for 10-MeV protons.