Mass-yield Curve Research Articles

Nuclear Reactions of Ti, Fe, Co, Ni, Cu, and Zn by 500-MeV Protons

Formation cross sections of product nuclides in the nuclear reactions of Ti, Fe, Co, Ni, Cu, and Zn targets by 500-MeV protons were measured with a Ge(Li) γ-ray spectrometer. The measured cross sections in the mass range between \(A\cong40\) and \(A\cong{A}_{\text{T}}-4\) were used in the charge-dispersion analysis, where A T is the mass number of the target nucleus. The N / Z ratio of the charge-dispersion peak was found to be consistent with those obtained in the same mass range of spallation products in the nuclear reactions of the same medium-mass targets with 12-GeV protons. The mass-yield curve falls sharply with decreasing masses of product nuclides in contrast to relatively flat distributions at higher energies.

Systematic behavior of mass-yield curves in low-energy fission of actinides

Mass yield curves of spontaneous fissions, thermal-neutron induced fissions, monochromatic-neutron and proton induced fissions of actinides are reviewed. Mean masses of light and heavy asymmetric mass yield peaks are listed. The subtle change of the shape of the asymmetric heavy peak is expressed in terms of the parameters of two Gaussians that fit the observed data well. One Gaussian is narrow in width and always peaks at A=133–136 while the other is broader and peaks at A=140−144. The FWHM of the heavy asymmetric peak becomes minimum for the fissioning mass A=240−245. An analysis of the projectile energy dependence of mass yield curves indicated, at least, two distinctively different behaviors, one for asymmetric products and the other for symmetric products. From the energy dependence of the peak-to-valley rations, the “extra-energy” required for symmetric mass division, or the difference in the fission barrier heights, in the nomeuclature of the two-mode hypothesis, is deduced for a wide range of fission nuclides.

Spallation of nickel by 9 GeV/c protons and deuterons

Cross sections for the production of radionuclides in the interaction of nickel with 9 GeV/c protons and deuterons were determined by an activation technique. These data were parametrised in terms of a six-parameter equation which reproduced the measured charge dispersions and mass-yield distributions. The similarity between the mass-yield curves in both investigations may be viewed as evidence for factorisation. The results were interpreted in the framework of the intranuclear cascade and abrasion-ablation models.

Systematic analysis of mass yield curves in low-energy fission of actinides.

Mass yield curves in low-energy proton-induced fissions of $^{233}\mathrm{U}$, $^{235}\mathrm{U}$, $^{238}\mathrm{U}$, $^{237}\mathrm{Np}$, $^{239}\mathrm{Pu}$, $^{242}\mathrm{Pu}$, $^{244}\mathrm{Pu}$, $^{241}\mathrm{Am}$, and $^{243}\mathrm{Am}$ were measured. The full widths at half maximum (FWHM) of the heavier asymmetric peak of the mass yield curves showed a sudden dip in the region of ${A}_{f}$=240--245. The correlation between the P/V ratio and the FWHM of the asymmetric mass yield peak was obtained as a function of proton energy. The FWHM values were independent of the incident proton energy as long as the P/V ratio was larger than 10 for all the fissioning systems studied. The excitation energy dependence of the mass yield curves was investigated. It was found that the excitation energy dependence of symmetrically divided fission products was apparently different from that of asymmetrically divided ones. With a simple assumption of the two-mode hypothesis, the observed mass yield curves could be decomposed into two mass yield curves. Asymmetric mass yield peaks could be best represented by the sum of two Gaussians, and their variation could be expressed by the variation of Gaussian parameters. The peak positions of the two Gaussians were always A=133--135 and A=140--142 for all the investigated fissioning nuclides. The preference of those fragment masses is discussed in terms of both the scission-point model and the saddle-point model.

New points of view on the nuclear properties of the fissile actinides

Some arguments are presented in favor of an interpretation of the asymmetric fission, in which the light fission fragments are considered as being formed from the valence shells of the fissile nuclei. E.g., the peak-to-peak distance of the mass yield curve for neutron-induced fission is found to vary linearly with the number N p + N n of valence nucleons of the system undergoing fission. A detailed description of the asymmetric fission can be given, e.g. of 240Pu, which is based on binding energy calculations (energy release = 216.868 MeV) and energy relations holding in the valence shells. The neutron-proton interaction energy within the valence shells is proportional to the number N p × N n of n-p couples. Two methods are proposed for the calculation of E np . For 240 Pu, E np is about 63 MeV, i.e. the interaction energy per n-p couple is 263.1 keV. Other interaction laws between valence nucleons are described: the n-2n and 2n-2n repulsion laws, and the p-2p and 2p-2p repulsion laws. In even-even nuclei, the energy binding all the valence proton pairs is p· \\ ̄ gs 2p , where p is the number of proton pairs and σ 2p a mean “from core” separation energy per proton pair. Its value is independent of the number of pairs of nucleons of the other kind. For 240Pu, the energy binding any one of the six proton pairs to the core is only 5050 keV, and the energy binding any one of the ten neutron pairs to the core is as great as 8358 keV. This means that the protons are farther from the core than the neutrons. As the energy binding the protons to the core decreases rapidly with Z, and could be zero for Z = 108, neutrons have to be seen as bridges binding to the core the protons of the valence shell in the heavy actinides. This situation, and the weakness of all the valence shell interaction energies, explain that a neutron can induce shell alterations permitting the onset of stronger nuclear forces and nuclear fission.

Spallation of Tantalum, Tungsten and Gold by 12-GeV Protons

Formation cross sections of spallation products in the nuclear reactions of tantalum, tungsten, and gold by 12 GeV protons were measured with the γ-ray spectroscopy for 58, 73, and 80 product nuclides, respectively. The present data were used to obtain the charge-dispersion and mass-yield curves by the least-squares analysis in the mass region of product nuclides from 40 to 110 for tantalum and tungsten and from 40 to 130 for gold. The N/Z ratio at the charge-dispersion peak was determined to be approximately 1.23 for all the three targets which have the average N/Z ratio of 1.49. This result is consistent with that obtained for medium-mass targets. The mass-yield curves are compared with results of Monte Carlo simulations of an intranuclear cascade-evaporation model. They are in qualitative agreement in the mass range of the spallation products greater than a half of the target mass.

Fertile-to-Fissile and Fission Measurements for Depleted Uranium and Thorium Bombarded by 800-MeV Protons

Axial distributions of fissions and of fertile-to-fissile conversions in thick depleted uranium and thorium targets bombarded by 800-MeV protons have been measured. The amounts of /sup 239/Pu and /sup 233/U produced were determined by measuring the yields of /sup 239/Np and /sup 233/Pa, respectively. The number of fissions was deduced from fission product mass-yield curves. Integration of the axial distributions gave the total number of conversions and fissions occurring in the targets. For the uranium target, experimental results were 5.90 +- 0.25 fissions and 3.81 +- 0.01 atoms of /sup 239/Pu produced per incident portion. Corresponding calculated results were 6.14 +- 0.04 and 3.88 +- 0.03. In the thorium target, 1.56 +- 0.25 fissions and 1.25 +- 0.01 atoms of /sup 233/U per incident proton were measured; the calculated values were 1.54 +- 0.01 fissions and 1.27 +- 0.01 atom/proton.

The quantum statistical model of fragment formation: Entropy and temperature extraction in heavy ion collisions

Quantum statistical model (QSM) calculations of nuclear fragment formation are presented. Various independent methods for extracting the temperature, T, and entropy, S A , from fragment- and pion yields in heavy-ion collisions are analysed. It is emphasized that stable and unstable medium mass fragments play an important role in determining T and S/ A: They alter the relation S/ A( R dp) dramatically and distort via feeding simple temperature measurements. However, these fragments allow by their very abundance for a variety of new, alternative methods to determine S/ A from data on multifragmentation (ratios of complex fragment yields, mass yield curves, and charged-particle multiplicities). Entropy values deduced from 4π plastic ball data exhibit a strong multiplicity dependence. For large multiplicities the entropy residing in nuclear fragments appears to be independent of the bombarding energy and low in absolute value, S/ A⋍3.5. The corresponding break-up temperatures of the fragment conglomerate are T = 12, 16, and 20 MeV at E lab = 400, 650, and 1050 MeV/ n, respectively. These values are much smaller (a factor 1 3 ) than the temperatures extracted from pion yields. This result can be understood only if the pions are created in the early, hot stage of the collision, while the fragments are formed after an isentropic expansion of the system at small densities where the temperature is low. This would imply that in the late stage of the reaction a large fraction (⋍80%) of the available center-of-mass energy resides in (possibly isotropic) flow.

Reproduction of the observed fission track distribution curves by calculation

Abstract Experiments with solid state detectors show a two peaked mass-yield curves for heavy and light fission products whereas the experimental track length distribution always show only a single peak. In this paper we explain the reasons for the observed fact and try to reproduce the observed track-distribution curves for 252 Cf fission fragments in mica, Lexan and cellulose acetate of suitable bunching of fission yields. A good correspondence has been observed between the theoretically constructed curves and the experimental ones in the case of Lexan and cellulose acetate whereas for mica the correlation show some disagreements.

Excitation functions for production of heavy actinides from interactions of 16O with 249Cf.

Excitation functions have been measured for the production of isotopes of Bk through Fm in bombardments of $^{249}\mathrm{Cf}$ with 90- to 150-MeV $^{16}\mathrm{O}$ ions. A comparison of the maxima of the mass-yield curves measured in this experiment with those for the reactions of $^{18}\mathrm{O}$ ions with $^{249}\mathrm{Cf}$ shows different shifts from those that have been measured for reactions of the $^{16}$,18O and $^{20}$,22Ne ion pairs with $^{248}\mathrm{Cm}$. However, the shifts appear similar to those recently measured for reactions of these ion pairs with $^{254}\mathrm{Es}$.

Variation of even-odd proton effects with excitation energy in fission of 252Cf: Confirmation of fine structure in v( A)

The existence of even-odd proton effects (fine structure) in νv( A) of individual fragments from 252Cf(sf) has been confirmed by analysis of previously reported data. The fine structure is seen to increase in amplitude as the fragment excitation energy decreases, a behaviour similar to the well-known behaviour of the mass yield curve. The present mass yield data also show these effects, as expected. Conversely, our total kinetic energy data TKE( A), not previously reported, show very little even-odd proton effect. It is shown that energy balance considerations, also, support the existence of even-odd proton effects in neutron emission from 252Cf(sf).

Absolute determination of the spontaneous fission yield of252Cf by radiochemical method

The distribution of mass in the spontaneous fission of252Cf has been investigated by the radiochemical determination of the absolute fission yields for 35 mass chains. A summation of the mass-yield curve gives a summed value of 199.4% which is in very good agreement with the value of 200% in fission. The mean masses of the light and heavy group are located at 106.39 and 141.82, respectively. The average number\(\bar \nu \) of neutron per fisson is 3.79±0.12. The peak-to-valley ratio is larger than 370. The width at one tenth of the maximum of the light and heavy group are 26.7 and 26.8 mass number, respectively. A comparison of previous investigators has resulted in “recommended” yields for 35 mass chains.

Photonuclear spallation reactions in Cu.

Yields of 24 radioactive nuclides formed by the interaction of bremsstrahlung with maximum end-point energies of 100 MeV--1 GeV with Cu have been measured by direct \ensuremath{\gamma}-ray counting of irradiated targets. The yields in the mass range of 42 to 60 (except for $^{60}\mathrm{Cu}$) were analyzed by a nonlinear least-squares fit to obtain the mass yield and charge dispersion curves in spallation reactions. From the parameter values obtained, the energy dependence of the slope of the mass yield curve and the relationship between target N/Z and the most probable product N/Z were investigated and compared with the results of proton, \ensuremath{\alpha}, and heavy-ion-induced spallation of Cu. The characteristics of photon-induced spallation are discussed.

Quantum molecular dynamics — A novel approach to N-body correlations in heavy ion collisions

We introduce a novel N-body approach to describe heavy ion collisions. The nucleons are represented as gaussian wave packets in configuration and momentum space. They interact via a combination of a Skyrme type potential and a Uehling-Uhlenbeck two-body scattering mechanism. This theory keeps track of the correlations and therefore allows for a selfconsistent theoretical description of the entire complex dynamics of heavy ion collisions, from the initial non-equilibrium penetration stage via the high density phase to the final formation of complex — stable and unstable — fragments. The cluster formation is caused by correlations and density fluctuations. We find that global equilibrium is not established in the course of the reaction. The form of the mass yield curve agrees with experimental findings. We also study the recently observed collective flow effects and find a strong dependence on the nuclear equation of state.

The nuclear lattice model of proton-induced multi-fragmentation reactions

A model of proton-induced multi-fragmentation reactions based on percolation theory is described and applied to experimental data. With only the simplest of assumptions the essential features of the mass-yield curves, such as their U-shape and their power-law dependence for low-to-medium masses, are reproduced. However, the model is, as will be demonstrated, flexible enough to allow for the inclusion of different physical mechanisms. The fits to mass-yield data are then quantitative over the whole mass range. The connection with real physics is made and some relevant experiments are suggested.

Variation of even-odd charge effects with excitation energy in ν(a) and mass yield for 252Cf(sf)

Abstract The existence of even-odd charge effects (fine structure) in ν(A) for 252Cf(sf) has been confirmed. The fine structure is seen to increase in amplitude as the fragment excitation energy decreases, a behaviour similar to that of the mass yield curve.

Spallation and Fission Yields in the Interactions of Tantalum, Tungsten, and Gold with 500-MeV Protons

Formation cross sections of spallation and fission products in the nuclear reactions of tantalum, tungsten, and gold with 500-MeV protons were measured with a Ge(Li) γ-ray spectrometer followed by computer analysis of the spectra. The measured results for gold are in good agreement with existing data measured with 490-MeV protons. The tantalum data are only in qualitative agreement with data measured previously at 340 and 450 MeV. The mass dependence of the cross sections of the fission products for tantalum seems to be in agreement with the mass-yield curves obtained at 340 and 450 MeV. The mass-yield distributions for fission products may indicate that the fission process takes place at the middle or near the end of the evaporation process in the two step mechanism of high-energy proton-nucleus interactions.

Monte Carlo Calculations on Nuclear Spallation Reactions with High Energy Protons above Several GeV

Monte Carlo calculations on nuclear spallation reactions with high energy protons were performed by using a model for intranuclear cascade reactions in the energy range up to 1000 GeV and a nuclear model for the evaporation process. The scale factor of the characteristic particle production distance δ and the nuclear density reduction factor D were used in the cascade model in order to simulate the energy dependence of particle production from heavy target nuclei and mass-yield distributions for spallation products in the incident proton energy range above several GeV. The general characteristics of calculated mass-yield curves were determined primarily by the two parameters δ and D and they are in reasonable agreement with experimental data.

Spallation of V induced by 1 GeV12C-ions and by 258, 350 and 910 MeV3He-ions

Cross Sections and thick target/thick catcher recoil properties have been measured for radionuclides formed in the interaction of 258, 350 and 910 MeV3He-ions and 1032 MeV12C-ions with V in order to study the systematics of their variation with product mass and energy and type of the incident projectile. The slope of the mass yield curves is observed to decrease with increasing bombarding energy. The dominant projectile variable determining the slope is the total kinetic energy, and the slopes are independent of the type of projectile.

Fission ofPu242with 15.1-MeV neutrons

The mass-yield distribution from the fission of /sup 242/Pu induced by 15.1-MeV neutrons was measured. Yields were measured for 65 fission products from /sup 85/Kr to /sup 151/Pm. From these data the total chain yields for 43 mass numbers were obtained and the mass-yield curve constructed. Fission product activities were measured by Ge(Li)= ..gamma..-ray spectrometry of the irradiated /sup 242/Pu target and by chemical separation of the fission product elements Pd, Ag, Cd, Sn, Sb, and Ce followed by ..beta.. counting or ..gamma..-ray spectrometry. The peak-to-valley ratio in the mass-yield distribution is about 9.5. The average masses of the light and heavy groups are 101.5 and 136.5, respectively.