Proton Reaction Cross Sections Research Articles

Combining nuclear reactions and structure with the dispersive optical model

A review of recent applications of the nonlocal dispersive optical model (DOM) is presented that allows a simultaneous description of nuclear structure and nuclear reactions. An assessment of the quality of the resulting potentials for 40Ca and 48Ca is discussed for the description of the (e, e′p) reaction to valence hole states and the possibility of interpreting the data in terms of absolute spectroscopic factors. The relevance of these results in the context of conflicting interpretations between transfer and knockout reactions is pointed out as well as the importance of proton reaction cross sections for isotopes with neutron excess. Application of the nonlocal DOM to 48Ca incorporates the effect of the 8 additional neutrons and allows for an excellent description of elastic scattering data of both protons and neutrons. The corresponding neutron distribution constrained by all available data generates a prediction for the neutron skin that is larger than most mean-field and available ab initio results. Results are presented for the most recent nonlocal DOM analysis of 208Pb.

Isotopically resolved neutron total cross sections at intermediate energies

The neutron total cross sections $\sigma_{tot}$ of $^{16,18}$O, $^{58,64}$Ni, $^{103}$Rh, and $^{112,124}$Sn have been measured at the Los Alamos Neutron Science Center (LANSCE) from low to intermediate energies (3 $\leq E_{lab} \leq$ 450 MeV) by leveraging waveform-digitizer technology. The $\sigma_{tot}$ relative differences between isotopes are presented, revealing additional information about the isovector components needed for an accurate optical-model description away from stability. Digitizer-enabled $\sigma_{tot}$-measurement techniques are discussed and a series of uncertainty-quantified dispersive optical model (DOM) analyses using these new data is presented, validating the use of the DOM for modeling light systems ($^{16,18}$O) and systems with open neutron shells ($^{58,64}$Ni and $^{112,124}$Sn). The valence-nucleon spectroscopic factors extracted for each isotope reaffirm the usefulness of high-energy proton reaction cross sections for characterizing depletion from the mean-field expectation.

Investigating the link between proton reaction cross sections and the quenching of proton spectroscopic factors in 48Ca

The nucleon self-energies of 40Ca and 48Ca are determined using a nonlocal dispersive optical model (DOM). By enforcing the dispersion relation connecting the real and imaginary part of the self-energy, scattering and structure data are used to constrain these self-energies. The ability to calculate both bound and scattering states simultaneously puts these self-energies in a unique position to consistently describe exclusive knockout reactions such as (e,e′p). The present analysis reveals the importance of high-energy proton reaction cross-section data in constraining spectroscopic factors required for the description of the (e,e′p) cross sections. In particular, it is imperative that high-energy proton reaction cross-section data are measured for 48Ca in the near future so that the quenching of the spectroscopic factors in the 48Ca(e,e′p)47K reaction can be unambiguously constrained using the DOM. Measurements of proton reaction cross sections in inverse kinematics employing rare isotope beams with large neutron excess will provide corresponding constraints on proton spectroscopic factors for exotic nuclei. Moreover, DOM generated spectral functions indicate that the quenching of spectroscopic factors compared to 40Ca is not only due to long-range correlation, but also partly due to the increase in high-momentum protons in 48Ca on account of the strong neutron-proton interaction. Single-particle momentum distributions of protons and neutrons in 48Ca calculated from these spectral functions confirm that neutron excess causes a higher fraction of high-momentum protons than neutrons.

Evaluation of the radiation hazard for ion-beam analysis with MeV external proton beams (X-IBA)

Abstract MeV ion beams which are extracted into air or He atmosphere are used in many labs for proton-induced X-ray emission (PIXE), proton induced gamma ray emission (PIGE) or Rutherford backscattering (RBS) to analyze samples which are difficult or impossible to handle in vacuum. When MeV proton beams are extracted into air through thin Kapton foils or nowadays thin silicon nitride membranes, the protons will interact with air, as well as elements present in the analyzed samples. Typically the range of MeV protons in air is several cm, in Helium atmosphere several 10 cm and in human skin around 100 µm. Besides the severe radiation hazard in case of a direct exposure of skin with protons, there are a manifold of nuclear reactions or inelastic proton scattering processes which may cause activation of air and target materials but also prompt radiation. The radiation hazard associated with the direct and scattered beam, nuclear reaction products and radionuclide production in air have been discussed in a publication by Doyle et al. in 1991 which was used as a reference in several later publications. I have reevaluated the radiation hazards for external proton beams with up to 4.5 MeV using proton reaction cross sections taken from the JANIS book of proton induced cross sections. The radionuclide production in air is about 3 orders of magnitude lower compared to values given in the 1991 publication. Radionuclide production as well as generation of prompt alpha, gamma and neutron radiation in target materials for elements up to molybdenum is also evaluated.

Activity computer program for calculating ion irradiation activation

A computer program, Activity, was developed to predict the activity and gamma lines of materials irradiated with an ion beam. It uses the TENDL (Koning and Rochman, 2012) [1] proton reaction cross section database, the Stopping and Range of Ions in Matter (SRIM) (Biersack et al., 2010) code, a Nuclear Data Services (NDS) radioactive decay database (Sonzogni, 2006) [2] and an ENDF gamma decay database (Herman and Chadwick, 2006) [3]. An extended version of Bateman’s equation is used to calculate the activity at time t, and this equation is solved analytically, with the option to also solve by numeric inverse Laplace Transform as a failsafe. The program outputs the expected activity and gamma lines of the activated material.Program summaryProgram title: ActivityCatalogue identifier: AFBS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBS_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU GPL v3No. of lines in distributed program, including test data, etc.: 688828No. of bytes in distributed program, including test data, etc.: 71056048Distribution format: tar.gzProgramming language: Fortran.Computer: PCs or HPCs.Operating system: Linux (tested on Debian).Has the code been vectorized or parallelized?: OpenMPIRAM: 250MB per process + 200MB overheadClassification: 2.2, 17.8.Nature of problem: To calculate the predicted activity of an ion irradiated target. The expected range of ion energies is between 1MeV and 200MeV; this is the range of the available ion cross section data.Solution method: The program loads cross section data from the TENDL database and trajectory data from a SRIM [1] simulation exyz data file. It uses this data to calculate the production/loss rate of each isotope in the simulated target. Radioactive decay equations are used to calculate the amounts and activity of each radioactive isotope at the set time.Running time: Typically the Activity program runs each input from seconds to no more than several minutes.

Application of the Continuum Discretized Coupled Channels Method to Nucleon-induced Reactions on 6,7Li for Energies up to 150 MeV

Nucleon-induced reactions on 6,7Li are analyzed systematically over a wide range of incident energies up to 150 MeV by using three-body continuum discretized coupled channels method (CDCC) capable of treating the breakup of 6,7Li. The diagonal and coupling potentials in the CDCC equation are obtained by folding the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction with transition densities. The normalization factors of the complex effective interaction are determined so as to reproduce experimental data on neutron total and proton reaction cross sections. Triton emission from 7Li breakup channel and p(n)+Li7→t+Li⁎5(He⁎5) channel is analyzed by the sequential decay model and final state interaction model, respectively. In most cases, the calculated results are in good agreement with experimental data except for the nucleon production double differential cross sections (DDX) at relatively low emission energies.

Systematic analysis of nucleon scattering from6,7Li with the continuum discretized coupled channels method

Nucleon scattering from ${}^{6,7}$Li is analyzed systematically over a wide range of incident energies up to 150 MeV with the continuum discretized coupled channels method (CDCC) capable of treating the breakup of ${}^{6,7}$Li. The continuum states of ${}^{6,7}$Li are discretized with the pseudostate method. Diagonal and coupling potentials in the CDCC equation are obtained by folding the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction with transition densities between corresponding bound and discretized continuum states of ${}^{6,7}$Li. The normalization factors of the complex effective interaction are determined so as to reproduce experimental data on neutron total and proton reaction cross sections for ${}^{6,7}$Li. CDCC calculations with the normalization factors reproduce experimental differential cross sections for nucleon elastic and inelastic scattering from ${}^{6,7}$Li well.

Microscopic optical potentials for nucleon–nucleus scattering at 65 MeV

Microscopic optical potentials for nucleon–nucleus scattering obtained from folding the calculated G-matrices with RMF densities of the target have been used to analyze the 65 MeV proton and neutron–nucleus scattering data over a wide mass region. The soft-core Argonne AV14, AV18 and the old hard-core Hamada–Johnston inter-nucleon potentials have been used to calculate the G-matrices in the Brueckner–Hartree–Fock approach. The calculated potentials have been used to analyze the differential elastic cross-section, analyzing power and spin-rotation function for neutron and proton scattering at 65 MeV from 12C to 208Pb. Our results are in satisfactory agreement with the experimental data. Comparison of our results with phenomenological optical model analyses is also presented. Mass number dependence of the mean square radii of real central optical potential 〈r2〉 pot. for the microscopic potentials used here is found to be in close agreement with each other as well as with empirical results. We also present our results for proton reaction cross-section from 12C to 90Zr in the energy region 20–200 MeV.

Global phenomenological optical model potential for nucleon-actinide reactions at energies up to 300 MeV

A set of new global phenomenological optical model potential parameters for the actinide region with incident nucleon energies from 1 keV up to 300 MeV is obtained. They are based on a smooth, unique functional form for the energy dependence of the potential depths and on physically constrained geometry parameters. The available experimental data including the neutron total cross sections, nonelastic cross sections, elastic scattering cross sections, elastic scattering angular distributions, and proton reaction cross sections and elastic scattering angular distributions of $^{232}\mathrm{Th}$ and $^{238}\mathrm{U}$ are used. The new nucleon global optical model potential parameters obtained are analyzed and used to analyze the experimental data of nucleon-actinide reactions. It is found that the present form of the global optical model potential could reproduce both the neutron and the proton experimental data.

Optical potentials for nuclear level structures and nucleon interactions data of tin isotopes based on the soft-rotator model

The soft-rotator model is applied to self-consistent analyses of the nuclear level structures and the nucleon interaction data of the even-even Sn isotopes, $^{116}\mathrm{Sn}$, $^{118}\mathrm{Sn}$, $^{120}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$. The model successfully describes low-lying collective levels of these isotopes, which exhibit neither typical rotational nor harmonic vibrational structures. The experimental nucleon interaction data---total neutron cross sections, proton reaction cross sections, and nucleon elastic and inelastic scattering data---are well described up to 200 MeV in a coupled-channels optical model approach. For the calculations, nuclear wave functions for the Sn isotopes are taken from the nonaxial soft-rotator model with the model parameters adjusted to fit the measured low-lying collective level structures. We find that the ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{3}$ deformations for incident protons are larger than those for incident neutrons by $~15%$, which is clear evidence of the deviation from the pure collective model for these isotopes.

A global dispersive coupled-channel potential for the A = 24–122 mass range up to 200 MeV

A global dispersive coupled-channel optical model potential for the mass range of A = 24–122 is constructed up to 200 MeV incident energies. The local parameters for seven individual nuclei are searched by using the coupled-channel method based on the rigid-rotator model. The global forms of potential parameters are obtained by fitting those local parameters with simple functional forms of the target mass number. The numerical calculations show good agreement with available experimental data for neutron total cross sections, proton reaction cross sections, neutron/proton elastic and inelastic angular distributions, and proton elastic and inelastic analyzing powers.

Proton Reaction Cross Sections as Measures of the Spatial Distibutions of Neutrons in Exotic Nuclei

Proton and neutron densities from Skyrme-Hartree-Fock calculations of a number of nuclei with masses ranging from 28 to 58 have been used to generate optical potentials for proton elastic scattering. Those potentials, generated by folding the structure functions with effective in-medium nucleon-nucleon (NN) interactions, have been used to evaluate proton total reaction cross sections; cross sections that reveal signatures of the structures.

Coupled-Channels Analysis of Nucleon Interaction Data of 28'30Si up to 200 MeV Based on the Soft Rotator Model

A consistent analysis for nuclear level structure and nucleon scattering data up to 200 MeV was performed for sd-shell nuclei, 28,30Si, using a unified framework of soft-rotator model and coupled-channels approach. The 28,30Si were assumed to be deformed nuclei having oblate shapes. The soft-rotator model parameters were determined so as to reproduce measured collective levels of 28,30Si up to an excitation energy of around 10 MeV. The relativistic kinematics and global optical potential form were taken into account in the coupled-channels optical model analysis, and the optical model parameters were derived. The calculation showed good agreement with experimental data for both collective levels and nucleon interaction data—neutron total cross sections, proton reaction cross sections, and nucleon scattering angular distributions.

Nucleon–nucleus real potential of Woods–Saxon shape between −60 and +60 MeV for the 40 ⩽ A ⩽ 208 nuclei

Nucleon differential elastic scattering cross sections, total proton reaction cross sections and single-particle energies of nucleon bound states for 40Ca, 90Zr and 208Pb nuclei are reanalysed in terms of the dispersive optical model at energy from −75 MeV to 60 MeV. The real effective Woods–Saxon potential, which corresponds to the real part of the dispersive optical model potential, is studied with respect to its dependence on A, Z, E and on projectile nature (proton or neutron). For the first time, a parametrization of the Woods–Saxon real part of the nucleon–nucleus optical potential is proposed for the 40 ⩽ A ⩽ 208 nuclei in an energy range from −60 MeV to +60 MeV, which obviously includes the Fermi energy range. The parametrization reflects the dispersion relation between the real and imaginary parts of the optical model potential through the energy dependence of the radius parameter of the real part of the potential. The method of determining the imaginary part of the optical model potential, which is symmetrical relative to the Fermi energy, is also proposed for the nuclei with 40 ⩽ A ⩽ 208. Differential elastic scattering cross sections, total neutron interaction cross sections, total proton reaction cross sections and single-particle energies of the nucleon bound states are calculated in terms of the proposed nucleon–nucleus potential parametrization for some of the (n + A) and (p + A) (40 ⩽ A ⩽ 208) systems and compared with the available experimental data, yielding a fairly good agreement.

Coupled-Channels Analysis of Nucleon Interaction Data of 28,30 Si up to 200 MeV Based on the Soft Rotator Model

A consistent analysis for nuclear level structure and nucleon scattering data up to 200 MeV was performed for sd-shell nuclei, 28,30Si, using a unified framework of soft-rotator model and coupled-channels approach. The 28,30Si were assumed to be deformed nuclei having oblate shapes. The soft-rotator model parameters were determined so as to reproduce measured collective levels of 28,30Si up to an excitation energy of around 10 MeV. The relativistic kinematics and global optical potential form were taken into account in the coupled-channels optical model analysis, and the optical model parameters were derived. The calculation showed good agreement with experimental data for both collective levels and nucleon interaction data—neutron total cross sections, proton reaction cross sections, and nucleon scattering angular distributions.

MASS DEPENDENCE OF p-NUCLEUS TOTAL REACTION CROSS SECTION AND GAMBHIR–PATIL NUCLEON DENSITY DISTRIBUTION

Total reaction cross sections for 50 and 100 MeV protons have been calculated for several nuclei using Gambhir–Patil semi-phenomenological nucleon density in the Coulomb modified Glauber model. It is shown that the semi-phenomenological nucleon density distribution provides quite satisfactory description of the observed A-dependence of the proton reaction cross sections.

Proton Reaction Cross Sections Measured in the BNL/AGS E943 Experiment

We have measured proton reaction cross sections over a wide mass and energy range at the Brookhaven AGS accelerator. The samples were elemental Be, C, Al, Cu, W, and Pb; the measurements were carried out at ten incident proton kinetic energies in the range 0.54 to 7.8 GeV. The experiment was similar to an earlier experiment in the 200- 550 MeV range by Renberg et al.1) The new results are in good agreement with those of Renberg et al. at the overlap point near 550 MeV. The combined results of the two experiments show an energy dependence expected from the behavior of the nucleon-nucleon cross sections. The results are reproduced by calculations based on variants of the impulse approximation and Glauber theory.

Proton reaction cross-section measurements on stable and neutron-rich nuclei as a probe of the nucleon–nucleus interaction

Proton reaction cross-section measurements on various stable and neutron-rich nuclei ( 4,6He, 7–9Li, 9–11Be, 21–24F, 22–26Ne, 25–29Na and 29–32Mg) were performed via the attenuation method at intermediate energies (∼35– 75 A MeV) and using a cryogenic hydrogen target. The results are discussed in the framework of different approaches of the nucleon–nucleus potential.

Measurement of neutron total cross sections up to 560 MeV

We have completed a new set of total cross section measurements of 31 elements and isotopes spanning the periodic table from A=1 to 238. We employed the same technique as in Finley et al. [Phys. Rev. C 47, 237 (1993)] with refinements intended to allow measurements on separated isotopes and improved systematic error control. The goal of the new measurement was 1% statistical accuracy in 1% energy bins with systematic errors less than 1%. This was achieved for all but the thinnest samples. Stringent checks of systematic errors in this measurement resulted in a reassignment of systematic uncertainties to the neutron total cross sections reported in Finley et al. Microscopic optical model calculations were carried out to interpret the results of the experiment. Two specific types of optical models were employed. The Jeukenne-Lejeune-Mahaux model was used in the range of 5--160 MeV, and a model based on the empirical effective interaction of Kelly was used from 135 to 650 MeV. These models are shown to be useful for predicting both neutron total cross sections and proton reaction cross sections. They are particularly important for light nuclei, for which standard global phenomenological parametrizations of the optical potential are insufficiently accurate.

Nuclear data for accelerator-driven systems

We review recent evaluations of neutron and proton reaction cross sections up to 150 MeV in the LA150 Library, for use in computer code simulations of accelerator-driven systems. An overview is provided of the nuclear theory together with measured cross section data used in the evaluations. The possible use of bismuth activation foils for high-energy neutron spectrometry is also discussed. We describe recent developments to the MCNPX radiation transport code, which merges MCNP and LAHET in one code and uses the LA150 evaluated data. A number of benchmark comparisons against integral experiments are described, for thick-target neutron production, neutron transmission through macroscopic slabs, and neutron kerma coefficients. The benchmarks help validate the transport code and the evaluated data for use in ADS simulations of neutron production in a spallation target (n/p), radiation shielding, heating, and damage. A brief summary is also given of future data needs for subcritical transmuters and spallation targets, in accelerator transmutation of waste technologies.