Nonstatistical Structure Research Articles

Low-lying dipole strength of the open-shell nucleus94Mo

The low-lying dipole strength of the open-shell nucleus ${}^{94}$Mo was studied via the nuclear resonance fluorescence technique up to 8.7 MeV excitation energy at the bremsstrahlung facility at the Superconducting Darmstadt Electron Linear Accelerator (S-DALINAC), and with Compton backscattered photons at the High Intensity $\ensuremath{\gamma}$-ray Source (HI$\ensuremath{\gamma}$S) facility. In total, 83 excited states were identified. Exploiting polarized quasi-monoenergetic photons at HI$\ensuremath{\gamma}$S, parity quantum numbers were assigned to 41 states excited by dipole transitions. The electric dipole-strength distribution was determined up to 8.7 MeV and compared to microscopic calculations within the quasiparticle phonon model. Calculations and experimental data are in good agreement for the fragmentation, as well as for the integrated strength. The average decay pattern of the excited states was investigated exploiting the HI$\ensuremath{\gamma}$S measurements at five energy settings. Mean branching ratios to the ground state and first excited ${2}_{1}^{+}$ state were extracted from the measurements with quasi-monoenergetic photons and compared to $\ensuremath{\gamma}$-cascade simulations within the statistical model. The experimentally deduced mean branching ratios exhibit a resonance-like maximum at 6.4 MeV which cannot be reproduced within the statistical model. This indicates a nonstatistical structure in the energy range between 5.5 and 7.5 MeV.

Modeling Multivariate Time Series on Manifolds with Skew Radial Basis Functions

We present an approach for constructing nonlinear empirical mappings from high-dimensional domains to multivariate ranges. We employ radial basis functions and skew radial basis functions for constructing a model using data that are potentially scattered or sparse. The algorithm progresses iteratively, adding a new function at each step to refine the model. The placement of the functions is driven by a statistical hypothesis test that accounts for correlation in the multivariate range variables. The test is applied on training and validation data and reveals nonstatistical or geometric structure when it fails. At each step, the added function is fit to data contained in a spatiotemporally defined local region to determine the parameters--in particular, the scale of the local model. The scale of the function is determined by the zero crossings of the autocorrelation function of the residuals. The model parameters and the number of basis functions are determined automatically from the given data, and there is no need to initialize any ad hoc parameters save for the selection of the skew radial basis functions. Compactly supported skew radial basis functions are employed to improve model accuracy, order, and convergence properties. The extension of the algorithm to higher-dimensional ranges produces reduced-order models by exploiting the existence of correlation in the range variable data. Structure is tested not just in a single time series but between all pairs of time series. We illustrate the new methodologies using several illustrative problems, including modeling data on manifolds and the prediction of chaotic time series.

Oscillating-Correlated Nonstatistical Structures, Slow Spin Decoherence, and Hyperdeformed Coherent Rotational States in24Mg+24Mgand28Si+28SiScattering

Nonstatistical structures observed in ${}^{24}\mathrm{Mg}{+}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}{+}^{28}\mathrm{Si}$ elastic and inelastic excitation functions produce channel-channel correlations and damped oscillations in the cross section energy autocorrelation functions. We present an interpretation of these nonstatistical effects assuming the formation of a highly excited dinucleus with strongly overlapping resonances in these scattering processes. We show that the essential features of the nonstatistical behavior of the excitation functions can be reproduced in terms of a slow spin decoherence of $\ensuremath{\simeq}(4:1)$ hyperdeformed coherent rotational states excited in ${}^{24}\mathrm{Mg}{+}^{24}\mathrm{Mg}$ and ${}^{28}\mathrm{Si}{+}^{28}\mathrm{Si}$ scattering.

Evidence of non-statistical structures in the elastic and inelastic scattering of58Ni+58Ni and58Ni+62Ni and intermediate dinuclear states

Excitation functions and angular distributions of58Ni+58Ni and58Ni+62Ni scattering at energies just above the Coulomb barrier have been measured aroundθcm=90° in energy stepsΔEcm=0.25 MeV fromEcm ⋍ 110 MeV toEcm ⋍ 120 MeV for58Ni+58Ni and fromEcm ⋍ 110 MeV toEcm ⋍ 118 MeV for58Ni+62Ni. Evidence for structure of non-statistical character has been found in the angle-summed excitation functions; this evidence is corroborated by the analysis of the angular distributions. This is the first time that non-statistical structure in elastic and inelastic scattering is reported with high confidence level for this mass and excitation energy ranges. Attempts are presented to understand the nature of this structure, including the presence of intermediate dinuclear states and virtual states in a potential well.

Photodissociation dynamics of state-selected resonances of HCO X̃ 2A′ prepared by stimulated emission pumping

Metastable resonances on the ground electronic state of the HCO radical have been prepared by stimulated emission pumping. The resonances have energies 5000 to 10 000 cm−1 above the dissociation limit of HCO and can be assigned by their vibrational and asymmetric-top rotational character. The transition linewidths of the resonances and the rotational and vibrational distributions of the CO dissociation products have been measured. The linewidths show a strong dependence on the vibrational character of the resonance rather than a monotonic dependence on energy, and thus provide an important example of nonstatistical behavior. CO(v=2) was produced in the decay of all six resonances studied, while only the three highest energy resonances produced measurable amounts of CO(v=3). CO rotational distributions with population in low-J states, which often showed nonstatistical structure, were characteristic of the products from all the resonances studied. The rotational distributions depend both on the vibrational character of the parent state and on the rotational state prepared in the HCO. The experimental results are compared and contrasted with previous quantum mechanical calculations and analyzed in the context of a modified Franck–Condon model for the dissociation.

Nonstatistical structures in12C(14N,4He)22Na reaction

The data on the θlab=7° excitation functions of12C(14N,4He)22Na reaction betweenEc.m.=10.15 and 15.88 MeV for 20 states of22Na up to an excitation energy of 5.800 MeV have been subjected to a statistical analysis consisting of the calculations of the distributions of fluctuating cross-sections, energy-dependent correlation function, deviation function, summed excitation function, and the coherence widths. The number of effective channels was calculated exactly. The analysis shows that, in addition to the statistical fluctuations, there are nonstatistical structures at 10.5, 11.62, 13.02, 13.3, 13.6 and 14.86 MeV.

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of20Ne(16O,12C)24Mg,20Ne(16O,12C)24Mg*(1.37, 2+),20Ne(16O,12C)24Mg*(4.12, 4++4.24, 2+) +20Ne(16O,12C*(4.44, 2+))24Mg,20Ne(16O,12C)24Mg*(6.01, 4++6.43, 0+),20Ne(16O,20Ne)16O,20Ne(16O,20Ne*(1.63, 2+))16O, and20Ne(16O,20Ne*(4.25, 4+))16O reactions atθlab=13° fromEc.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atEc.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atEc.m. =25.6 MeV.

Non-statistical structures in12C(15N,4He)23Na reaction

The data on theϑ lab=7° excitation functions of12C(15N,4He)23Na reaction betweenE cm=9.42 and 17.33 MeV for 28 states upto an excitation energy of 8.940 MeV in23Na have been subjected to statistical analysis. In addition to statistical fluctuations, the results of the analysis indicate the existence of non-statistical structures atE cm=10.66, 10.93, 11.38, 12.62, 13.16, 15.32 and 16.18 MeV.

C12(O16, α)Mg*24reaction in the energy regionEc.m.=26.6 to 42.9MeV

The $^{12}\mathrm{C}$+$^{16}\mathrm{O}$ resonance structure in the $^{28}\mathrm{Si}$ nucleus is examined by means of the $^{12}\mathrm{C}(^{16}\mathrm{O}, \ensuremath{\alpha})^{24}\mathrm{Mg}$ reaction excitation functions in the energy range ${E}_{\mathrm{c}.\mathrm{m}.}=26.6 \mathrm{to} 42.9$ MeV in 430 keV steps at ${\ensuremath{\theta}}_{\mathrm{lab}}=7.5\ifmmode^\circ\else\textdegree\fi{}$. We could identify 64 discrete states in $^{24}\mathrm{Mg}$ up to 31.7 MeV of excitation energy. The excitation functions show abundant structure over the entire energy range. The summed excitation functions, which tend to average out statistical fluctuations, show pronounced intermediate structure enhancement in the cross section at ${E}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\simeq}29.5$, 32.2, and 35 MeV and indicate the presence of a smaller peak at 37.3 MeV. The widths of these structures are about 1 MeV, which is intermediate between the value expected from ion-ion potential resonances and statistical fluctuations. The nonstatistical character of these structures is reinforced by some statistical tests and by the correlations in energy and width found in several exit channels. Our data also suggest a possible structural relationship between the $^{28}\mathrm{Si}$ resonances and certain $^{24}\mathrm{Mg}$ final states.NUCLEAR REACTIONS $^{12}\mathrm{C}(^{16}\mathrm{O}, \ensuremath{\alpha})^{24}\mathrm{Mg}^{*}$; measured $\ensuremath{\sigma}(E)$ to states up to 31.7 MeV of excitation energy for ${E}_{\mathrm{c}.\mathrm{m}.}=26.6 \mathrm{to} 42.9$ MeV in 430 keV steps, ${\ensuremath{\theta}}_{\mathrm{lab}}=7.5\ifmmode^\circ\else\textdegree\fi{}$. Nonstatistical structure observed.

Gamma-ray studies of theC12+C12system

Excitation functions for the yields of ten residual nuclides from the $^{12}\mathrm{C}$+$^{12}\mathrm{C}$ reaction have been measured over the range ${E}_{\mathrm{c}.\mathrm{m}.}=5.25\ensuremath{-}20.0$ MeV in steps of 125 keV, using $\ensuremath{\gamma}$-ray techniques. Nearly all of the reaction channels, including those with light-particle evaporation, showed strong narrow structures. A qualitative statistical analysis performed on the data gave useful information about the locations of possible nonstatistical structure, based primarily on the very strong cross-channel correlation observed in the data set.NUCLEAR REACTIONS $^{12}\mathrm{C}$ ($^{12}\mathrm{C}$, $x$); ${E}_{\mathrm{c}.\mathrm{m}.}=5.25\ensuremath{-}20.0$ MeV; measured $\ensuremath{\sigma}(E)$ for production of $A=16\ensuremath{-}23$ reaction products; statistical analysis presented; deduced evidence for nonstatistical structure.

Entrance channel effects by populating resonances in theAl26,Si29, andSi30systems

Excitation functions have been measured for the elastic, recoil, and alpha-particle exit channels for four reactions: /sup 17/O+/sup 12/C (E/sub lab/ = 30.0--57.0 MeV), /sup 16/O+/sup 13/C (E/sub lab/ = 29.5--52.6 MeV), /sup 17/O+/sup 13/C (E/sub lab/ = 30.0--57.0 MeV), and /sup 16/O+/sup 10/B (E/sub lab/ = 42.4--60.1 MeV). The alpha particles were detected at theta/sub lab/ = 10/sup 0/ while the elastic and recoil particles were detected at theta/sub lab/ = 34/sup 0/. Statistical analyses of the data are used to search for correlated, nonstatistical structures in the excitation functions. The resonant properties of three compound nuclei (/sup 26/Al, /sup 29,30/Si) are studied by comparing the excitation energies at which nonstatistical structures are seen when the nuclei are formed via different well matched (in terms of J/sub max/) entrance channels. These resonancelike structures seen in the various entrance channels (for a given compound nucleus) are found to be uncorrelated in excitation energy, thereby implying a dependence upon the properties of the entrance channel. The lack of entrance channel correlations and the short lifetimes of the structures seen are viewed as evidence that the reaction may proceed through a quasimolecule, or that the compound nucleus itself is so highly excitedmore » and deformed that its formation is entrance channel dependent.« less

Search for resonances in 12C( 9Be, α) 17O

Excitation functions at 7° (lab) have been measured from E c.m. = 5.1 to 11.4 MeV in approximately 114 keV steps for 15 groups of final states in 17O populated by the 12C( 9Be, α) reaction. Statistical tests have been used to locate possible non-statistical structure in the excitation functions. Possible anomalies were found near E c.m. = 6.3, 7.5, 8.9 and 9.7 MeV. Angular distributions were measured at E c.m. = 9.20, 9.71 and 10.23 MeV for the three lowest excited states in 17O. The data have been compared with Hauser-Feshbach calculations in addition to the following reaction mechanisms: compound plus a single resonance, compound plus interfering resonances and compound plus direct reactions.

Analyzing-power fluctuations in the 26Mg( [formula omitted]) 26Mg reaction

Excitation functions of the cross section and analyzing power for the 26Mg( p , p′ ) 26Mg reaction have been obtained for the ground state and the first two excited states of 26Mg in the incident energy range 5.5 to 17.5 MeV, and for the fourth excited state in the energy range 6.8 to 17.5 MeV, in 50 keV intervals at 120°, 140° and 160°. Angular distributions of the cross section and analyzing power have also been measured at many energies throughout this entire energy range. The data have been analyzed in terms of the statistical model and deviations from its predicted features have been observed. The analysis of autocorrelations and cross correlations was used to obtain the average compound nucleus width for the analyzing power throughout the 13.5–25.1 MeV excitation energy range in 27Al. In addition, distribution-free statistical tests (runs tests) were used to study apparent non-statistical structure in the excitation functions.

Nonstatistical structure inC12(N14, α)Na22

Correlated structure has been found in the forward-angle excitation functions of the $^{12}\mathrm{C}(^{14}\mathrm{N}, \ensuremath{\alpha})^{22}\mathrm{Na}$ reactions. An attempt is made based on the strong correlations observed to determine the origin of the structure. It is found that several explanations including statistical fluctuations, direct mechanisms, and the population of isolated high-spin yrast states are unlikely.NUCLEAR REACTIONS $^{12}\mathrm{C}(^{14}\mathrm{N}, \ensuremath{\alpha})^{22}\mathrm{Na}$; ${E}_{\mathrm{c}.\mathrm{m}.}=10.1\ensuremath{-}15.9$ MeV, $\ensuremath{\theta}=75\ifmmode^\circ\else\textdegree\fi{}$; correlated nonstatistical structure found; resonances discussed.

An analysis of runs tests as indicators of nonstatistical structure in the compound nucleus

Runs tests were applied to computer-generated elastic-scattering excitation functions in order to examine their sensitivity to nonstatistical structure in the compound nucleus. The scattering amplitudes were either purely statistical or else they included contributions from additional resonances about 1 MeV broad. Our aim was to determine whether the runs tests could distinguish between the two cases. The tests were successful once trends producing correlations between the datum points were removed. Spurious nonstatistical effects were thus eliminated, demonstrating that if the trend-reduction problem is dealt with propertly, runs tests are effective in searches for nonstatistical structure beneath the compound-nucleus fluctuations in experimental excitation functions.

Critical analysis of statistical methods used to detect resonances in nuclear reactions

The effectiveness of several existing statistical tests in locating resonances in compound nuclear reactions above the Coulomb barrier is examined, and a new test based on the number of maxima at any single bombarding energy in a set of excitation functions is introduced. It was found that only the three tests based on the deviation functions, summed cross sections, and the distribution of maxima were suitable for the detection of resonances, and that the latter test was the most sensitive. The various tests were used to analyze $^{12}\mathrm{C}$($^{12}\mathrm{C}$,$\ensuremath{\alpha}$)$^{20}\mathrm{Ne}$, $^{12}\mathrm{C}$($^{14}\mathrm{N}$,$\ensuremath{\alpha}$)$^{22}\mathrm{Na}$, and $^{12}\mathrm{C}$($^{15}\mathrm{N}$,$\ensuremath{\alpha}$)$^{23}\mathrm{Na}$ excitation functions. Evidence for nonstatistical structure was found in all three reactions by examining the distribution of maxima.NUCLEAR REACTIONS $^{12}\mathrm{C}$($^{12}\mathrm{C}$,$\ensuremath{\alpha}$)$^{20}\mathrm{Ne}$, ${E}_{\mathrm{c}.\mathrm{m}.}=18.0\ensuremath{-}25.5$ MeV; $^{12}\mathrm{C}$($^{14}\mathrm{N}$,$\ensuremath{\alpha}$)$^{22}\mathrm{Na}$, ${E}_{\mathrm{c}.\mathrm{m}.}=10.2\ensuremath{-}18.1$ MeV; $^{12}\mathrm{C}$($^{15}\mathrm{N}$,$\ensuremath{\alpha}$)$^{23}\mathrm{Na}$, ${E}_{\mathrm{c}.\mathrm{m}.}=9.5\ensuremath{-}17.3$ MeV. Statistical model predictions. Statistical tests examined. Nonstatistical structure observed.

New Resonances in the Low-EnergyC12-C12Spectrum

Angular distributions of transitions to low-lying states in $^{20}\mathrm{Ne}$ have been measured for the reaction $^{12}\mathrm{C}(^{12}\mathrm{C},\ensuremath{\alpha})$ in 62.5-keV steps for $6.5<~{E}_{\mathrm{c}.\mathrm{m}.}<11$ MeV. Two new nonstatistical structures are identified at ${E}_{\mathrm{c}.\mathrm{m}.}=7.71 \mathrm{and} 9.84$ MeV, with ${J}^{\ensuremath{\pi}}={4}^{+} \mathrm{and} {8}^{+}$, respectively. These observations support the quasimolecular interpretations of the low-energy structure in the $^{12}\mathrm{C}$-$^{12}\mathrm{C}$ interaction.

The influence of the isospin on the coherence widths in the compound nucleus 51V

The reactions 50Ti(p, p 0) 50Ti and 50Ti(p, α 0) 47Sc were investigated with proton energies between 9.5 and 10 MeV. From an autocorrelation analysis the mean coherence widths were determined for the compound nucleus 51V. In the proton channel and in the α-particle channel different coherence widths were measured: in the proton channel Γ p = 5.3 ± 1.3 keV and in the α-particle channel Γ α = 2.3 ± 0.4 keV. The direct reaction part in the proton decay was more than 93 %. In the measured cross sections non-statistical structures were present.

Structure in the Resonance Neutron Capture inIn115

Gamma rays from resonance neutron capture in $^{115}\mathrm{In}$ were detected in the neutron energy range 40 eV-1 keV. The resonance energy dependence of the radiative transition intensities to the low-lying levels shows a nonstatistical structure. This structure is found to be correlated with the local neutron strength function.