s- and p-wave neutron spectroscopy Xc. Intermediate structure: 88Sr

Neutron total cross section measurements of natural Sr were made from 50–875 keV using a high resolution proton beam and the ⁷Li(p, n) reaction as a neutron source. These data were analyzed with the help of an R-Matrix code to extract resonance (energies and other) parameters up to about 850 keV. 2p-1h and particle-vibration doorway interpretation of the s-, p- and d-wave resonances is attempted in terms of the sum rule Σγ_n² = γ_d². Predictions based on both of these models agree with the experimental results. As expected the p-wave resonances are stronger than either s- and d-wave structure. Theory accounts for the p-wave strength remarkably well. Possible location of the p-wave s.p. resonance is reproduced with a real potential and its damping due to the imaginary potential is calculated.More fragmentation of the strong p-wave doorways is observed than was expected for a compound nucleus so near ⁹⁰Zr, but a larger strength function is observed apparently due to the p-wave giant resonance.     

s- and p-wave neutron spectroscopy Xf(i). Intermediate structure in the 28Si + n reaction: R-matrix interpretation of experimental data

A multilevel R-matrix analysis of Si neutron cross-section data measured at NBS has been performed up to about 4.5 MeV neutron energy. Only a small fraction of the p- and s-wave s.p. strength is observed, but both exhibit local concentrations of strength indicative of doorway structure around 1 and 0.2 MeV, respectively. Besides the well-known 180 keV, strong, $\text{1}\text{2}{}^{\mathrm{+}}$ resonance, the s-wave resonance structure is of moderate strength and widely distributed. The f- and d-wave assignments are not unambiguous, but J > 3/2 resonances show strong signs of intermediate structure for d-waves. A possible correlation between neutron and gamma decay channels and the connection between the states observed in (n, n), (d, p), (n, γ), and (γ, n) channels is discussed. A coreparticle doorway interpretation for s and p- waves is presented.     

Valence-doorway model for radiative capture

A model of radiative capture is presented in which the T-matrix for valence capture is expressed as the sum of three terms, viz., a direct capture term, a term that describes the coupling between a single-particle resonance and the many possible continuum channels, and a pure single-particle resonance term. Expressions for the target excitations are not explicitly included, and projection operators are used to break up the single-particle space into resonant and nonresonant parts. The spreading of single-particle resonances is described through the coupling to particle-vibration doorways. The model is applied to the cases of ⁹⁸Mo(n, γ) ⁹⁹Mo and ⁹²Mo(n, γ) ⁹³Mo for an energy range of 0–3 MeV. In these cases the single-particle resonance amplitude is overwhelmingly dominant, and doorway effects are found to be relatively unimportant. Radiative widths obtained from our calculated average cross sections are compared to the corresponding widths obtained by averaging over the detailed fine structure measurements of Chrien et al. for ⁹⁹Mo. Good agreement is obtained. The valence capture cross section in ⁹³Mo is considerably smaller than in ⁹⁹Mo. This is consistent with the measurements of Chrien et al. and in good agreement with a recent analysis by Soloviev and Voronov.     

The fine structure of the isoharic analogue resonances

The distribution of an isobaric analogue resonance over the numerous surrounding states of different isobaric spin is studied analytically in the frame of the Fano-Weidenmüller shell-model theory of nuclear reactions. The doorway state wave function is described byLane's coupled equations. The matrix element of the residual nuclear interaction between this doorway state and a complicated state of different isobaric spin exhibits a particular energy dependence. A sum rule is established: the sum of the fine structure widths is larger than the width of the doorway state, as calculated fromLane's model. The residual Coulomb interactions are neglected. When perturbation theory holds, the distribution of the fine structure peaks is shown to have a characteristic asymmetrical shape. The connection withRobson's R-matrix treatment is discussed.     

Resonant parameters of <Superscript>5</Superscript>He and <Superscript>5</Superscript>Li states and nucleon-α scattering

A new method of analysis of resonant parameters in the framework of the J-matrix inverse scattering formalism is proposed. The method is applied to analysis of Nα scattering in various partial waves. The obtained 1/2^? and 3/2^? resonance energies and widths in ⁵He and ⁵Li nuclei are in good agreement with the results of other approaches. The eigenenergies entering the J-matrix phase shift parameterization are shown to correlate well with the respective results of no-core shell model calculations, in particular, in the case of non-resonant s-wave scattering.     

Structure of doorway states in the40Ca+n reaction

A model including 2p-1h and collective states in⁴¹Ca is used to investigate the intermediate structure resonances seen in then+⁴⁰Ca reaction. With potential well parameters determined by a calculation of the bound states it is found that most of thes-wave strength can be accounted for by the inclusion of one main doorway state component.     

Resonances and Fluctuations in Nuclear Reaction Cross Sections

On the basis of the continuum shell model, an expression for the S-matrix is derived. The external mixing between shape resonances and resonance states of complicated nuclear structure is investigated. It is shown that the doorway properties of the shape resonances may lead to an l-dependent transparency of the optical potential and, consequently, to an energy dependence of large back angle scattering if the unitarity of the S-matrix is taken into account.     

Isobar-hole doorway states and π-16O scattering

We describe and apply the isobar-hole approach to intermediate energy pion-nucleus reactions. Pion propagation, nucleon and isobar binding, Pauli restrictions and Δ propagation are calculated explicitly within a shell model framework. Intermediate coupling to multihole channels, for example through pion absorption, is treated phenomenologically through an isobar spreading potential. We find strongly collective Δ-hole states, leading to a reformulation of the approach in an extended schematic model. This entails systematic construction of a Δ-hole doorway state basis within which the Δ-hole propagator is evaluated. We find that this doorway space can be truncated at very low dimensionality while preserving accuracy, thereby simplifying the calculations appreciably. We make a detailed comparison between the theoretical results and recent data for π⁺ — ¹⁶O scattering in the pion energy range 50–340 MeV. Nonresonant πN interactions and the π-nucleus Coulomb interaction are included in the calculations. The data is reproduced quite well both below and in the resonance region, and we discuss in detail the role of various dynamical mechanisms. Above the resonance, the calculations are far less successful. We discuss possible shortcomings, stressing the role of inclusive pion-nucleus reactions for revealing the important dynamics. As a test of the Δ spreading potential used for describing elastic scattering, we calculate the total cross section for pion absorption. The result agrees reasonably well with the available data.     

Electromagnetic decay of fragmented analogue states in 45Sc

The ⁴⁴Ca(p, γ) reaction was studied for 45 resonances for E_p = 1.6?2.2 MeV. The overall proton energy resolution was 300–350 eV; the γ-rays were detected with both NaI(T1) and Ge(Li) detectors. Partial and total γ-ray widths were measured for each of the fine structure states of the $\text{3}\text{2}{}^{\mathrm{?}}$ and $\text{1}\text{2}{}^{\mathrm{?}}$ analogue states at E_p = 1.65 and 2.04 MeV, respectively. The data are examined for correlations between the partial widths (Γ_p, Γ_p′, Γ_γi, Γ_γ^total) in different channels. The γ-ray intensities are compared with (τ, d) spectroscopic factors.     

Low energy spectrum and giant multipole resonances of12C (I)

In a consistent shell model approach excitation energies and electromagnetic transitions are calculated for the low energy part of the¹²C spectrum up to the giant resonance region within a (1p1h+2p2h) configuration space. Comparison with available experimental data shows that almost the complete spectrum up to 40MeV can be described consistently. Thereby it is found that whereas the low lying collective states remain nearly unchanged by the inclusion of (2p2h) configurations, the spreading widths of all (2?ω) giant resonances are influenced drastically. For serious discrepancies in a few levels (4p4h) configurations or mesonic and baryonic degrees of freedom might be responsible.     

Reaction rate of 24Mg(p,γ)25Al

The proton-capture reaction on ²⁴Mg has been investigated in the bombarding energy range of E_p=0.2–1.7 MeV. Resonance properties (strengths, branching ratios and lifetimes) of low-energy resonances have been measured. From the experimental results, accurate proton partial widths, γ-ray partial widths and total widths (Γ_p, Γ_γ, and Γ) have been deduced. The present experimental information establishes the ²⁴Mg+p reaction rates over the temperature range T=0.02–2.0 GK with statistical uncertainties of 5% to 21%. Our recommended reaction rates deviate from previous estimates by 18% to 45%. Based on our results, we can rule out the recent suggestion that the total width of the E_R=223 keV resonance has a significant influence on the reaction rates. We also discuss several effects that might give rise to systematic uncertainties in the reaction rates. The astrophysical implications for hydrogen burning of ²⁴Mg at low stellar temperatures are presented.     

Neutron radiative capture in Cu

Radiative neutron capture in natural Cu has been studied in the neutron energy range from 200 eV to 16.5 keV. An area analysis of the data yields information on resonance parameters: For large resonances (Γ _n ?Γ _γ ) with known isotopic assignments values ofΓ _γ or, if the spin of the resonance is unknown, 2g Γ _γ are obtained. In some cases, it was possible to assign the spin of the resonance from the measured 2g Γ _γ assuming a fairly constant radiation width. For a number of small resonances (Γ_n?Γ _γ ) with unknown isotopic assignment, values of 4agΓ _n (a=isotopic abundance) have been determined. The distribution of these values, including those of the stronger resonances known from literature, shows an excess of small widths which is attributed top-wave levels. From this, thep-wave neutron strength function for natural Cu is estimated to be $$S_1 = \left( {0.30_{ - 0.14}^{ + 0.18} } \right)10^{ - 4} $$ .     

Average neutron resonance parameters and radiative capture cross sectins for the isotopes of molybdenum

The neutron capture cross sections of the stable molybdenum isotopes have been measured with high energy resolution (ΔE/E ? 0.2 %), between 3 and 90 keV neutron energy, at the 40 m station of ORELA. Average resonance parameters are extracted for s- and p-wave resonances. The s-wave neutron strength function is close to 0.5 × 10^?4 for all isotopes, but the p-wave strength function exhibits a well defined peak near At~ 95.Both s- and p-wave radiative widths decrease markedly as further neutrons are added to the closed shell. The p-wave radiative widths are generally greater than the s-wave widths showing the presence of non-statistical γ-decay mechanisms.Valence neutron theory fails to explain the magnitude of the p- to s-wave radiative width disparity and doorway state processes are invoked. In particular, the data for ⁹⁸Mo appear to violate the usual valence theory, since the correlations between radiative and neutron strengths are small. Further, the radiative widths are smaller than can be explained on the valence model. An explanation for the loss of valence strength is advanced.Interpolated resonance parameters allow an estimate for the unknown cross section for ⁹⁹Mo(n, γ).     

A perturbation expansion in the tunneling problem of many particle systems

The fine structure observed at Duke University in the total neutron cross section of²⁰⁶Pb is analysed in terms of theK- andS-matrix parametrizations. The distributions of the resonance parameters are in fairly good agreement with the theoretical ones derived from a doorway state hypothesis, combined with the picket fence model. Attention is drawn to the fact that the average cross section usually allows only a very inaccurate determination of the parameters of the doorway state resonance.     

Virtual excitation of the GDR mode in the subbarrier23Na(p, γ)24Mg reaction

Differential cross sections for nonresonant radiative capture of low energy protons (E _p = 1,348 keV and 1,370 keV) by²³Na nuclei exhibit features pointing to the virtual excitation of the giant dipole resonance (GDR) mode. Theoretical analysis carried out within the framework of the direct — semidirect capture model reveals an enhanced coupling of the GDR with the incident protonf-wave consistent with the microscopic structure of the GDR in thes-d shell nuclei.     

Strength functions for fragmented doorway states

Coupling a strongly excited “doorway state” to weak “hallway states” distributes its strength into micro-resonances seen in differential cross sections taken with very good energy resolution. The distribution of strength is shown to be revealed by reduced widths of the K-matrix rather than by the imaginary part of poles of the S-matrix. Different strength functions (SF) constructed by averaging the K-matrix widths are then investigated to determine their dependences on energy and on parameters related to averages of microscopic matrix elements. A new sum rule on the integrated strength of these SF is derived and used to show that different averaging procedures actually distribute the strength differently. Finally, it is shown that the discontinuous summed strength defines spreading parameters for the doorway state only in strong coupling, where it approximates the indefinite integral of the continuous SF of MacDonald-Mekjian-Kerman-De Toledo Piza. A new method of “parametric continuation” is used to relate a discontinuous sliding box-average, or a finite sum, of discrete terms to a continuous function.     

The Jπ = 3− doublet at Ex = 6241 keV in 18F: Isospin mixing

The resonance previously observed at E_x = 6241 keV in the reactions ¹⁷O(p, γ)¹⁸F and ¹⁴N(α, γ)¹⁸F has been found to be a closely separated doublet (ΔE_x = 2.09±0.04 keV). Resonance strengths in ¹⁷O(p, γ)¹⁸F, ¹⁷O(p, α)¹⁴N and ¹⁴N(α, γ)¹⁸ have been measured and partial widths for the resonance states have been obtained. The doublet was further investigated by means of the ⁴He(¹⁴N, α)¹⁴N reaction using the differentially pumped gas target at CRNL. Analysis of these data using R-matrix theory yielded J^π = 3^? for both states and more precise values of the α-particle widths (Γ_α(lower) = 133 ±4 eV; Γ_α(upper) = 137 ±4 eV). The reduced α-particle widths and the E1 and M1 transition strengths indicate that the doublet arises from the nearly complete mixing of T = 0 and T = 1 eigenstates which in the absence of an isospin breaking interaction would have been separated by less than 40 eV. The α-particle scattering experiments included the J^π = 1⁺ resonance at E_x = 6257 keV and yielded the new values of Γ_α = 580±12 eV and Γ_p = 25⁺³⁵_?25 eV.     

The 16O + p → 17F (T = 32) resonances at Ep = 11.26,12.71 and 14.57 MeV

Excitation functions for ¹⁶O+p reactions have been measured with high energy resolution in the region of the first, second and seventh $\text{T =}\text{3}\text{2}$ resonances in ¹⁷F at extreme backward angles. The observed resonance shapes have been analyzed with a single-level resonance formula taking the off-resonance spin-flip amplitude into account. The resonance parameters of the ¹⁷F first $\text{T =}\text{3}\text{2}$ state studied with special emphasis are E_x = 11193.3 ± 2.3 keV, Γ = 200 ± 40 eV and Γ_p0 = 19 ± 3 eV. This result and other results are compared with previous studies and theoretical predictions. The comparison with data of the mirror nucleus ¹⁷O is discussed with respect to the observed charge asymmetry of the isospin-forbidden particle decay widths.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.