Inelastic Proton Scattering Research Articles

Elastic and Inelastic Scattering of Protons on 14N in the Energy Region of 10 to 15 MeV. II. Theoretical

Elastic and Inelastic Scattering of Protons on ¹⁴N in the Energy Region of 10 to 15 MeV. II. Theoretical

Analysis of Inelastic Proton Scattering fromN14Between 8.60 and 26.0 MeV

The elastic and inelastic proton differential cross sections for $^{14}\mathrm{N}$ have been measured at 8.6, 10.6, 12.6, and 14.6 MeV. The variation with energy of the cross sections, as well as the shape of the angular distributions, indicated that the contribution of compound processes to some of the inelastic cross sections was not negligible at these energies. Fits to the elastic scattering data yielded proton optical parameters, which were used in calculating transmission co-efficients for a Hauser-Feshbach calculation of the compound nuclear contribution to the inelastic cross sections. These data corrected for compound effects, and measurements for scattering to the 2.31- and 3.95-MeV levels at 18.0, 21.0, 23.0, and 26.0 MeV reported in the literature, were analyzed with a microscopic coupled-channel calculation. The purpose of the analysis was to find out how sensitive the calculations were to the wave functions used for $^{14}\mathrm{N}$, to the values of the effective two-body force, and to the channels coupled. The results were also compared to a simple distorted-wave Born-approximation (DWBA) calculation. Calculations for the 3.95- and 7.03-MeV level were also carried out assuming a weak-coupling model for $^{14}\mathrm{N}$, two ${p}_{\frac{1}{2}}$ nucleons coupled to a $^{12}\mathrm{C}$ core. This collective model gave over-all better agreement with the measured differential cross sections for these levels than the DWBA or the microscopic coupled-channel calculation.[NUCLEAR REACTIONS $^{14}\mathrm{N}(p,p)$, $^{14}\mathrm{N}(p,{p}^{\ensuremath{'}})$, $E=8.6,10.6,12.6, \mathrm{and} 14.6$ MeV; measured $\ensuremath{\sigma}(E,\ensuremath{\theta})$; $\ensuremath{\theta}=15\ensuremath{-}{165}^{\ensuremath{\circ}}$; coupled-channel analysis. $^{14}\mathrm{N}(p,{p}^{\ensuremath{'}})$, $E=18,21,23,26$ MeV, previous data compared with coupled-channel calculation.]

35-MeV Proton Inelastic Scattering from Low-Lying States inPb207

Differential cross sections for the excitation of the first four excited states in $^{207}\mathrm{Pb}$ via the inelastic scattering of 35-MeV protons have been compared with microscopic-model predictions. The effects of noncentral forces in a valence orbital model have been investigated and contributions from exchange and core polarization are important. Addition of an imaginary part to the microscopic form factor was also investigated and gave the best predictions of observed transition strengths.

Excitation of Giant Resonances inNi58via Inelastic Scattering of Polarized Protons

Measurements of the analyzing power and the differential cross section in the nuclear continuum for the reaction $^{58}\mathrm{Ni}(p, {p}^{\ensuremath{'}})$ initiated by 60-MeV polarized protons provide strong evidence for a quadrupole ($E2$) interpretation for the giant resonance at ${E}_{x}\ensuremath{\approx}\frac{63}{{A}^{\frac{1}{3}}}$ MeV. A resonance approximately 3 MeV lower in excitation energy has also been observed.

Determination of Fractional-Parentage Coefficients from Inelastic Scattering of Protons through Analog Resonances

Nuclear fractional-parentage coefficients, determined from inelastic proton scattering through isobaric analog resonances, are shown to be subject, in some circumstances, to a particular type of ambiguity. A simple linear transformation connects sets of such coefficients giving rise to indistinguishable resonance contributions to differential cross-section and analyzing power, if the relatively weak $j$ dependence of penetration factors, resonance mixing phases, and real optical-model phase shifts is neglected.

Spin-Flip Probability for Inelastic Proton Scattering from Carbon and Sulfur

Spin-Flip Probability for Inelastic Proton Scattering from Carbon and Sulfur

Elastic and Inelastic Scattering of Protons by Hydrogen Atoms

Glauber approximations for elastic and inelastic scattering of protons by ground state hydrogen atoms, comparing with measurements

Proton Inelastic Scattering from the Five Stable, Even-Mass Isotopes of Molybdenum

Elastic and inelastic scattering of 15-MeV protons, accelerated by the 90-in. cyclotron at Lawrence Radiation Laboratory, Livermore, from isotopically enriched targets of $^{92,94,96,98,100}\mathrm{Mo}$ were studied with an over-all resolution of 50 keV (full width at half maximum). The experimental angular distributions were analyzed using a coupled-channel calculation. The collective vibrational model was employed to describe the states of the nucleus. Fifty angular distributions of scattered particles were measured and all but three were fitted with theoretical curves. The results for $^{92}\mathrm{Mo}$, which has a closed neutron shell associated with the magic number $N=50$, are discussed separately. All the inelastic scattering to levels in $^{92}\mathrm{Mo}$ were fitted with single-step processes. The other even-mass isotopes of molybdenum were analyzed first by considering the main quadrupole and octupole vibrational states and then considering the states that can be described as possible mixtures of one- and two-quadrupole phonons. A high degree of single-phonon admixture was found to be present. Finally the weaker states were considered with the simple ${0}^{+}\ensuremath{-}{I}^{\ensuremath{\pi}}$ coupling scheme. Electromagnetic transition rates inferred from the deformabilities deduced in the present experiment. The results are compared with other experiments.

Enhancement of the 3 ^{4}He -> ^{12}C Reaction Rate by Inelastic Proton Scattering

The reaction 12C(p, p')12C*(7.65) has been studied in the energy range just above threshold. The measured total cross-section has been used to calculate the enhancement of the 3 4He 12C reaction rate by inelastic proton scattering. A resonance was found in the cross-section corresponding to a stellar temperature of about 2 X 10 K. The enhancement of the 3 4He H 12C reaction rate is found to be significant in certain high-density, high- temperature stellar environments.

Elastic and Inelastic Scattering of Protons on 14N in the Energy Region of 10 to 15 MeV. I. Experimental

The experimental results of the 14 N( p , p ') 14 N reaction in the energy region of 10∼15 MeV were analyzed from both points of view of direct and compound-nucleus formation processes. Although the direct reaction theory reproduces the experimental results fairly well, it is not satisfactory in some aspects, especially in its poor reproduction of the rapid changes of the cross sections and angular distribution shapes with proton energy. On the other hand the compound nucleus formation theory with reasonable choices of spins and parities of the levels of the compound nucleus 15 O can reproduce well not only this energy dependence but also various aspects of the experimental results. Some theoretical considerations on the symmetry natures of the wave functions of the 14 N and 15 O states are described.

Inelastic Scattering of Protons fromO16and the Spin-Dependent Part of the Effective Interaction

Angular distributions for the $^{16}\mathrm{O}(p,{p}^{\ensuremath{'}})^{16}\mathrm{O}$ reaction leading to the ${J}^{\ensuremath{\pi}}={2}^{\ensuremath{-}}$ state at 8.88 MeV and the doublet of states at 6.05 MeV (${0}^{+}$) and 6.13 MeV (${3}^{\ensuremath{-}}$) have been measured at 23.4, 24.5, 27.3, 30.1, 34.1, 36.8, 39.7, 43.1, and 46.1 MeV. In the distorted-wave approximation (DWA) with central forces, the transition to the unnatural-parity (${2}^{\ensuremath{-}}$) state can occur only through the spin-dependent part ${V}_{10}={V}_{\ensuremath{\sigma}}f(r){\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}}_{p}$ of the effective two-nucleon interaction. The experimental angular distributions were compared with DWA calculations assuming $f(r)$ has a Yukawa shape with a range of 1.0 F. Normalization to the measured cross sections determined the strength ${V}_{\ensuremath{\sigma}}$, which was found to decrease rapidly from a magnitude of 53 MeV to about 23 MeV between ${E}_{p}=17.0$ MeV and ${E}_{p}=30.1$ MeV, and then to decrease slowly to about 16 MeV at ${E}_{p}=46.1$ MeV. The shape of the experimental angular distributions for the inelastic scattering to the ${2}^{\ensuremath{-}}$ state are well represented by the DWA at the lower energies, but the agreement deteriorates as the energy increases. The forward peak in the higher-energy data occurs at larger angles than the DWA prediction. The cross section calculated using a pseudopotential derived from the impulse approximation is too small by a factor of about 4 at all energies. The possible contribution of other reaction mechanisms to the cross section for scattering to the ${2}^{\ensuremath{-}}$ state is discussed. An analysis of the transition to the 6.1- MeV doublet is used to estimate the strength ${V}_{c}$ of the spin-isospin-independent part ${V}_{00}$ of the effective two-nucleon interaction. The experimental angular distributions for the 6.1- MeV doublet were also compared with the predictions of the impulse approximation.

Inelastic Scattering of Electrons and Protons by the Elements He to Na

We have calculated discrete and continuum generalized oscillator strengths for all the occupied shells of He-Na and the $3s$ and $3p$ continuum generalized oscillator strengths for Ar. The calculations are done with a one-electron common-central-potential unrelaxed-core approximation. The generalized oscillator strengths were used to compute proton-excitation and -ionization cross sections and stopping power, electron-ionization cross sections, and neutral-neutral-ionization and -stripping cross sections. For proton ionization above 200 keV and electron ionization above 200 eV, the calculated cross sections are in better than 20% agreement with experiment. The calculated proton stopping power is lower than experiment by 25% at 100 keV and within 10% at 1 MeV. The computed He-He ionization cross section agrees with the measurement by Wittkower, Levy, and Gilbody, while the computed He-Ar ionization cross section is a factor of 5 higher than the measurement by Puckett, Taylor, and Martin.

Inelastic Scattering of 40-MeV Protons byNi58andNi60and Analysis in Coupled Channels

Data from the inelastic scattering of 40-MeV protons by ${\mathrm{Ni}}^{58}$ and ${\mathrm{Ni}}^{60}$ are presented and analyzed in terms of a coupled-channel approach. Previous discrepancies between the experimental and theoretical distributions of the first excited ${2}^{+}$ states are removed. The nature of coupled-channel calculations at this energy is discussed, with reference to absorptive strengths and form factors. ${4}^{+}$ states around 2.5-MeV excitation are shown to require one-phonon mixing in order to explain the observed cross sections. Spin-parity assignments are given for states at 3.2-, 5.1-, and 6.1-MeV excitation in ${\mathrm{Ni}}^{60}$.

11-MeV Proton Inelastic Scattering from Even-Even Medium-Weight Nuclei

The analysis of inelastic scattering of 11-MeV protons from quadrupole and octupole collective levels of 14 even-even nuclei between $^{48}\mathrm{Ti}$ and $^{76}\mathrm{Ge}$ is reported. The distorted-wave Born approximation is used to calculate the cross sections using the collective-model generalization of the optical model for inelastic scattering. The analysis is performed using both real and complex form factors for the model. A satisfactory description of all the data is obtained when a contribution due to compound-nucleus decay for most of the octupole levels and a few of the quadrupole levels is included.

Spin Flip in the Inelastic Scattering of Protons from 12C at Energies around 13.1 MeV Resonance

Proton spin-flip probabilities in the scattering of 12 C( p , p ') 12 C * (4.44 MeV) were measured in the energy range between 12 to 14 MeV. The differential cross sections in the elastic and inelastic scattering were also measured. The measurements were done in detail around the resonance in the elastic scattering cross section at 13.1 MeV. In this energy region, the spin-flip probability shows a remarkable energy dependence in contrast with a rather monotonous one of inelastic scattering cross section. The measurements were done by the ( p , p ' γ) coincidence technique due to Schmidt.

Elastic and Inelastic Scattering of Protons from Krypton

Elastic and inelastic scattering of protons from krypton has been investigated for the bombarding energy range 3.6-5.4 MeV. Resonances were observed in the elastic scattering and in the inelastic scattering to the first ${2}^{+}$ (0.877\ifmmode\pm\else\textpm\fi{}0.011 MeV) state in $^{84}\mathrm{Kr}$. The resonant energies are (as obtained from the inelastic scattering yield curves) 4.990\ifmmode\pm\else\textpm\fi{}0.017 and 5.277\ifmmode\pm\else\textpm\fi{}0.017 MeV. Resonance parameters obtained by the use of the optical model with an added isolated resonance term suggest that these resonances are due to isobaric analog states of hitherto unreported low-lying states of $^{85}\mathrm{Kr}$ with 1.23-MeV (${J}^{\ensuremath{\pi}}={\frac{3}{2}}^{+} or {\frac{5}{2}}^{+}$) and 1.52-MeV (${J}^{\ensuremath{\pi}}={\frac{1}{2}}^{+}$) excitation energies. These excitation energies have an associated maximum uncertainty of \ifmmode\pm\else\textpm\fi{}100 keV. Angular distributions of the inelastic protons from the $^{84}\mathrm{Kr}(p, {p}^{\ensuremath{'}})^{84}\mathrm{Kr}$ (0.877 MeV) measured on these resonance peaks show interference effects. Isobaric analogs of those states strongly excited via the $^{86}\mathrm{Kr}(d, t)^{85}\mathrm{Kr}$ neutron pickup reaction were not observed in the present investigation, thus confirming their "neutron-hole" nature. Inelastic scattering to the first ${2}^{+}$ (0.771\ifmmode\pm\else\textpm\fi{}0.011 MeV) and the second ${2}^{+}$ (1.470\ifmmode\pm\else\textpm\fi{}0.007 MeV) states of $^{82}\mathrm{Kr}$ was studied for the bombarding energy range 4.9-5.4 MeV. The yield of protons going to the first excited state resonates at 5.34 MeV. If one assumes that this resonance is a manifestation of an analog of a low-lying state of $^{83}\mathrm{Kr}$, the excitation energy is 1.89 MeV, again with a maximum uncertainty of about \ifmmode\pm\else\textpm\fi{}100 keV. No resonance is seen for the yield to the 1470-keV second excited state. The effect of the compound-nuclear-reaction mechanism on the inelastic cross sections has been investigated. Theoretical off-resonance inelastic cross sections calculated by the Hauser-Feshbach formalism of statistical compound-nuclear reactions agree with the experimental results quite satisfactorily.

Elastic and Inelastic Proton Scattering fromCa40and Two-Particle, One-Hole States inSc41

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Spin Flip in the Inelastic Scattering of Protons

Proton spin-flip probabilities and differential inelastic scattering cross sections were measured over a large angular region for the following ${2}^{+}$ excitations: 4.44 MeV in $^{12}\mathrm{C}$ at 12, 13, 14, 15, and 20 MeV; 1.45 MeV in $^{58}\mathrm{Ni}$ at 9.25, 10.46, 15, and 20 MeV; 1.33 MeV in $^{60}\mathrm{Ni}$ at 10.5 and 14 MeV; and 1.34 MeV in $^{64}\mathrm{Ni}$ at 10.5 and 14 MeV. The results were analyzed in the distorted-wave Born approximation, with collective-model form factors derived from the optical-model potential. The deformed spin-dependent part of the coupling potential was of the full Thomas form, and the data are best described when ${{\ensuremath{\beta}}_{2}}^{\mathrm{SO}}g{\ensuremath{\beta}}_{2}$. Good fits are obtained for elastic polarization data (obtained elsewhere) when the depth of the spin-orbit potential is determined from spin-flip probability measurements.

Neutron Particle-Hole States Observed by Inelastic Proton Scattering fromXe136

Neutron particle-hole states have been observed in the decay of isobaric analog resonances formed in the reaction $^{136}\mathrm{Xe}$ plus proton. Analysis of the on-resonance inelastic data has given inelastic proton partial widths, spectroscopic factors, spins, and parities of several of the observed particle-hole states.

Elastic and Inelastic Proton Scattering from Even Isotopes of Cd, Sn, and Te

Elastic and Inelastic Proton Scattering from Even Isotopes of Cd, Sn, and Te