Cascade Calculations Research Articles

Pion-induced spallation of copper across the (3,3) resonance

Cross sections for about two dozen radioactive spallation products have been measured for 50-, 100-, 190-, and 350-MeV ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ and for 200- and 350-MeV proton interactions with copper. Sums of measured pion-induced cross sections at 50 and 350 MeV are about the same as for protons of 200 and 590 MeV, respectively. However, at 100 and 190 MeV, nearer to the (3,3) pion-nucleon resonance, these pion-induced cross section sums are 50 to 75% greater than those for protons of similar total energy. Ratios of the ${\ensuremath{\pi}}^{\ensuremath{-}}$ to ${\ensuremath{\pi}}^{+}$ cross sections are greater than unity for neutron-rich products and less than unity for neutron-deficient products at all four energies, indicating that pion absorption is a substantial reaction mode, even at 190 and 350 MeV. At 100 MeV, and especially at 50 MeV, absorption appears to dominate over inelastic scattering and the $\frac{{\ensuremath{\sigma}}_{\ensuremath{\pi}}^{\ensuremath{-}}}{{\ensuremath{\sigma}}_{\ensuremath{\pi}}^{+}}$ ratios are noticeably changed from those at the higher energies. The intranuclear cascade plus evaporation codes reproduce the proton cross sections fairly well. The pion version of the intranuclear cascade code reproduces the pion results quite well at 350 MeV, but it underestimates them significantly at 50 and 100 MeV.NUCLEAR REACTIONS Cu (${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, spallation) and Cu ($p$, spallation), ${E}_{{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}}=50, 100, 190, 350$ MeV, ${E}_{p}=200, 350$ MeV. Production cross sections for radioactive residual nuclei. Comparison with intranuclear cascade plus evaporation calculations.

Helium ions from the interaction of 70-MeV pions with nuclei

He ions emitted in the interaction of 70-MeV pions with carbon, aluminum, nickel, silver, and gold were measured directly at $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}$. Cross sections and energy spectra are presented. Calculations of intranuclear cascades followed by evaporation reproduced the experimental data reasonably well. The results of the calculations imply that: (1) pion absorption in flight plays a major role in reactions in which $\ensuremath{\alpha}$ particles are emitted; and (2) one-"$\ensuremath{\alpha}$"-removal lines, observed in deexcitation $\ensuremath{\gamma}$-ray experiments, do not imply large probability for real $\ensuremath{\alpha}$ emission. The ${\ensuremath{\pi}}^{\ensuremath{-}}$ to ${\ensuremath{\pi}}^{+}$ ratio of cross sections was found to be about 1.4.NUCLEAR REACTIONS C, Al, Ni, Ag, Au (${\ensuremath{\pi}}^{\ensuremath{-}}, \ensuremath{\alpha}+\mathrm{anything}$), ${E}_{\ensuremath{\pi}}=70$ MeV; measured He energy spectra; $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}(90\ifmmode^\circ\else\textdegree\fi{})$. Natural targets; evaporation analysis.

The electromagnetic component of cosmic-ray extensive air showers

The electromagnetic component of EAS has been studied using unshielded scintillator detectors at Haverah Park. Data on the lateral distribution of the response are presented. A comparison of data from various arrays is undertaken and some disagreement is found. The predictions of model cascade calculations are also compared with the current experimental results. The problems of treating the low-energy components of the EAS are considered.

Deexcitation gamma rays from the interaction of 70-MeV pions withs−dshell nuclei

The interaction of 70-MeV positive and negative pions with $s\ensuremath{-}d$ shell nuclei was studied via measurements of the deexcitation $\ensuremath{\gamma}$ rays from residual nuclei produced in the reactions. Cross sections for producing specific levels in the residual nuclei were measured. The results are compared with Monte Carlo calculations of intranuclear cascades, followed by evaporation processes. In order to take into account the special features of the prompt $\ensuremath{\gamma}$-ray technique, the probability for leaving the residual nuclei at different regions of excitation, together with measured $\ensuremath{\gamma}$-ray branching ratios, are incorporated into the calculated cross sections. Good agreement is found between measured and calculated cross sections for reactions involving the removal of four or more nucleons. For such reactions, the calculations are dominated by pion absorption processes. The cross sections for the removal of an $\ensuremath{\alpha}$-equivalent cluster from T = 0 nuclei have about the same strength as those corresponding to the removal of a triton cluster from the neighboring $T=\frac{1}{2}$ nuclei. This suggests that the final nucleus, rather than the removed particle, is mainly responsible for the observed strength. The cross sections for single-nucleon-removal reactions do not agree with the calculations.NUCLEAR REACTIONS $^{23}\mathrm{Na}$, Mg, $^{27}\mathrm{Al}$, $^{28}\mathrm{Si}$, $^{31}\mathrm{P}$, $^{32}\mathrm{S}$, $^{39}\mathrm{K}$, $^{40}\mathrm{Ca}({\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}},\ensuremath{\chi}\ensuremath{\gamma})$, ${E}_{\ensuremath{\pi}}=70$ MeV, Ge(Li) detector, measured cross sections for producing specific levs in residual nuclei, calculated $\ensuremath{\sigma}$.

Rows on rows — A theory for collisions between heavy ions at high energy

The double differential cross section dσ/ dΩ dE is computed for protons and pions from collisions between nuclei at high energies (250 to 2100 MeV/nucleon). We derive the following within Glauber theory: At high energies the interaction between two nuclei reduces to a series of collisions between rows of target nucleons and rows of projectile nucleons. The scattering “rows on rows” can be obtained from a one-dimensional cascade calculation. We perform it in a simple approximation, using experimental nucleon-nucleon cross sections as the only input. The introduction of the Δ-degree of freedom leads to a satisfactory description of the proton and pion data at 2.1 GeV/nucleon. At 250 MeV/nucleon our agreement with experiment compares favourably with the one achieved in other approaches. A scaling law may be the reason why many simple approaches come already close to experiment. We discuss the question of thermalization.

Influence of nucleon mean-free paths on intranuclear cascade results

Results of the intranuclear cascade calculation are compared for 62 MeV protons on 89Y and 54Fe targets. Standard calculations and results with mean free paths increased fourfold are compared. The latter set gives poorer results versus experimental data due to an overestimate of nuclear transparency.

Optimization of antiproton fluxes from targets using hadron cascade calculations

A Monte Carlo method is described for calculating particle fluxes from an extended target as a function of the occupied phase volume. The calculation is used to optimize the antiproton flux from a tungsten target by considering variation of the target dimensions and the strength of an applied magnetic field.

Calibration calculations of hadronic cascades induced by high-energy muons in iron/plastic calorimeters

Calculations have been performed to determine the response of an iron-plastic calorimeter to muon-induced nuclear interactions. The calculated data include energy resolutions and average pulse-height signals as a function of energy transfer, energy-transfer angle, and spatial-interaction point.

(p, pxn) and (p, xn) reactions and mechanisms onCs133at 550 MeV

The mechanism of the (p,pn) reaction on /sup 133/Cs with 550 MeV protons was deduced by measuring the recoil angular distribution between 0/sup 0/ and 180/sup 0/, and the differential range distribution at 0/sup 0/ and 90/sup 0/, for /sup 132/Cs recoil nuclei. Similar measurements were made for the (p,p4n) and (p,3n) reaction products from /sup 133/Cs. Cross sections were also measured for the production of (p,pxn) and (p,xn) products. The experimental data were compared to predictions derived from Monte Carlo cascade and evaporation calculations, as well as from simple kinematic models of possible reaction mechanisms. The results indicate that about 80% of the (p,pn) reaction takes place by (p,p') events followed by neutron evaporation.

Neutron spectra from the capture of negative pions in carbon, oxygen and nitrogen

In April 1976, the Users Group at Kent State University (K.S.U.) used the negative pion beam at the Columbia University Cyclotron to measure the energy spectra of neutrons emitted following nuclear capture of negative pions stopped in various targets. One of the objectives of these measurements is to resolve discrepancies that exist among previous measurements. Another objective is to compare the spectral measurements with the predictions of Monte Carlo intranuclear cascade calculations in order to determine the degree of validity of these calculations. In Fig. 1, we show neutron spectra above 10 MeV from carbon measured by Anderson et al.’ and by Hattersley et aL3 These two measurements do not agree. The neutron yield per stopped pion reported by Hattersley et al. is lower below about 40 MeV and higher above 40 MeV than that reported by Anderson et al. The Monte Carlo calculated spectrum of Guthrie et al.’ does not agree with the measurements. This Monte Carlo calculation overestimates the production of neutrons below about 20 MeV and underestimates the production of higher energy neutrons. In Fig. 2, we present the spectrum from carbon measured by the K.S.U. Users Group. It agrees with the previous measurement of Hattersley et al. Fig. 3 is our spectrum from oxygen. Our spectra from oxygen, nitrogen, and carbon are identical within experimental errors. While there are no published spectral measurements from oxygen, Hattersley et al. reported that the spectrum from oxygen is the same as that from carbon. The Monte Carlo spectrum of Guthrie et al. for 5 _ E

Measurements and calculations of cascades produced by 300 GeV protons incident on a target inside a magnet

A thick aluminum block placed between the pole pieces of a magnet was irradiated with 300 GeV protons. Responses of activation foils and dosimeters placed around the magnet and inside the gap were measured to study the propagation of high-energy cascades. Predictions of two different Monte Carlo calculations agree well with these measurements.

Measurement of the Muonic X-Ray Cascade in Metallic Iron

The muonic x-ray cascade in Fe has been measured with Ge detectors. The intensities of 103 x-ray lines from the $K$, $L$, $M$, $N$, and $O$ series were determined and compared with cascade calculations. The best "initial distribution" at principal quantum number $n=20$ does not strongly depend on the angular momentum.

Possible correlations of electromagnetic transitions in exotic atoms, and their implication for cascade calculations

It is argued that if the atomic cascade is treated as a ‘coherent’, multi-quentum transition process, the population distribution of the atoms in the intermediate states differs significantly from results obtained by standard calculations, especially for exotic atoms with low Z number.

Neutron spectra at 0° from (p, n) reactions on 9Be, 12C, and 27Al at 647 and 800 MeV

The measured cross sections show a narrow high-energy peak (20–30 MeV/ c FWHM) and a broad bump at lower momenta associated with pion production. Comparison is made to an intranuclear cascade calculation.

Coulomb capture and x-ray cascades of muons in metal halides

Muonic x-ray yields have been measured for Al, ${\mathrm{AlF}}_{3}$, ${\mathrm{AlCl}}_{3}$, ${\mathrm{AlI}}_{3}$, KCl, KBr, KI, Cd, ${\mathrm{CdF}}_{2}$, ${\mathrm{CdCl}}_{2}$, ${\mathrm{CdBr}}_{2}$, ${\mathrm{CdI}}_{2}$, Sn, ${\mathrm{SnCl}}_{2}$, ${\mathrm{SnCl}}_{4}$, Sb, ${\mathrm{SbF}}_{3}$, ${\mathrm{SbCl}}_{3}$, and ${\mathrm{SbCl}}_{5}$. The yields were normalized with the total intensity of the Lyman series. The capture ratios between Coulomb capture in the anion and the cation were determined for all compounds listed. These ratios are not well reproduced by the Fermi-Teller $Z$ law. Chemical effects in the intensities were observed. All observed intensities were compared with cascade calculations assuming a modified statistical population of the levels with $n=20$. In a number of cases this procedure does not yield a satisfactory reproduction of the experimental data.

A General Method for the Calculation of an Ideal Cascade with Asymmetric Separation Units

A General Method for the Calculation of an Ideal Cascade with Asymmetric Separation Units

Intensitäten myonischer röntgenlinien in argon, in wasserstoff plus argon und in argon plus neon

Muonic X-ray spectra from Ar and H 2 + Ar have been measured with a high-pressure gas target. Strong differences between the observed intensities of corresponding lines were found for the two cases. The results are compared with cascade calculations. The ratio between Coulomb capture in Ar and in Ne for an Ar-Ne mixture (atomic ratio 1:1) was determined to be 1.11±0.14.

A Monte Carlo calculation of high energy hadronic cascade in matter

The technique and results of a Monte Carlo calculation of high energy cascades in heavy material are described. The results on hadronic penetration and radial distribution are compared whenever possible with experimental data. In particular the results are applied to the detection of muons produced in high energy collisions.

Fission of lead induced by 600 MeV protons

Absolute radiochemical fission yields have been measured for 12 nuclides of Rb, Ag, Cd and Cs and relative fission yields measured for seven Kr-isotopes and eight Xe-isotopes produced by fission of natural lead induced by 600 MeV protons. The relative Kr- and Xe-yields have been determined using the ISOLDE-facility at CERN. It is suggested that the production rate of a nuclide per m.b. of nuclear reaction cross section should be used as a figure of merit for on-line facilities like Isolde. During the present experiment 3·4 × 10 6 nuclei/sec. m.b. and 2·0 × 10 6 nuclei/sec, m.b. were obtained for Kr- and Xe-isotopes, respectively. Charge and mass distributions and charge dispersion for fission of lead with 600 MeV protons are determined using our measured fission yields and some yields measured by other groups. The most probable charge Z p , for a given mass and the width (FWHM) of the charge dispersion, both increase linearly with mass number. The integrated mass distribution curve gives a fission cross section of 149±6 m.b. Elemental yield distribution is constructed and shows a most probable atomic number of 40·0, giving Mercury as the most probable fissioning element. Assuming no proton evaporation from fission fragments, it is suggested that elemental yield distributions and isotopic yield distributions should be used rather than mass distribution and charge distribution and dispersion for the purpose of obtaining information on the fissioning nuclei. The elemental yield distribution is discussed on the bases of the liquid drop model for fission giving an average nuclear temperature at saddle point of 2·09 MeV, and a total number of neutrons evaporated after fission of about 13. Estimates of most probable cascade residuals for each residual element based on Monte Carlo intranuclear cascade calculations at 380 MeV together with presently observed most probable isotopes for each product Z, are used to predict average cascade deposition energies for events leading to specific products. The agreement with literature values from recoil experiments is good.

Experimental study on the (μ 4He) 2S + metastable system in helium gas

We report the results of an experimental investigation on the properties of the (μ 4He) 2S + metastable muonic system, which was performed stopping negative muons in a pure helium target at pressures ranging from 10 to 50 atm, and observing the total yield and the differential time distribution of the X-rays released in delayed coincidence with the arrival of muons. At each pressureP, information was obtained on the following quantities:a) the total disappearance rate λ2S,tot(P) of the (μ 4He) 2S + system,b) the disappearance rates λA(P) and λSt(itP) of the (μ 4He) 2S + system for external Auger effect and Stark-mixing collisions,c) the fractione 2S of muons stopped in helium which form the (μ 4He) 2S + system. The results obtained on λ2S,tot(P) are in agreement with the results of a cascade calculation, which was performed requiring consistency with previous experimental results; the present measurements show that the variation ofe 2S (P) with pressure in the range (7÷50) atm is small. Good agreement was found between the values for the two-quantum decay rate λ2X of the (μ 4He) 2S + system derived from the present data and the theoretical predictions. The results obtained on λ2S,tot(P), instead, are somewhat in conflict with the results of a recent calculation on λ2St(P). The possible reasons of such disagreement are discussed, referring to possible clustering effects of the helium atoms around the (μHe+ ion.