Amplitude correlations in nuclear resonance spectroscopy

Both magnitudes and relative signs of inelastic decay amplitudes have been measured for proton resonances in the compound nuclei ⁴⁵Su, ⁴⁷V, ⁴⁹V, ⁵¹Mn, ⁵⁵Co, and ⁵⁷Co. Resonances with orbital angular momenta 1,2 and 3 and five different values of J^π were studied. For l = 1 and l = 2 resonances, sample sizes are sufficient to perform statistical analyses: distributions of the reduced widths, distributions of the products of reduced width amplitudes, and both amplitude and widt correlations have been determined over energy ranges of ～ 1 MeV. The distributions are compared with the predictions of random matrix theory, and good overall agreement is obtained. These result have provided new tests of the statistical theory of resonances and of the theory of isobaric analogue states. In addition, these data give the first experimental confirmation of the channel coupling required by direct reaction theory. The linear correlation coefficients are often surprisingly large (for these data sets, the average value is >0.5 ), so large in fact that the traditional DWBA treatment of direct reactions must fail in some cases. This failure is discussed with the aid of a simplified model. Tests of the Gaussian nature of reduced width amplitudes are also examined.     

s- and p-wave neutron spectroscopy: Part VII. Widths of Neutron Resonances

Neutron reduced widths Γ_n⁰ and Γ_n¹ are reported for about 200 resonances observed in neutron total cross sections of Ca^{40, 44}, Ti⁴⁸, Cr^{50, 52, 54}, Fe^{54, 56}, Ni^{58, 60}, Sr⁸⁸, Y⁸⁹, Sn¹²⁴, Te¹³⁰, Ba^{136, 138}, and Pb^{206, 207, 208}, in the energy region 1 to 200 ^kev. Average parameters $\text{Γ}{}_{\mathrm{n}}{}^0$, $\text{Γ}{}_{\mathrm{n}}{}^0\text{D}$, and $\text{Γ}{}_{\mathrm{n}}{}^{\mathrm{(1)}}\text{D}$ have been derived and the Wigner distribution for local spacings and the Porter-Thomas distribution for reduced widths are verified for the resonances in the even-even nuclei Ca⁴⁰, Fe⁵⁶, Ni⁵⁸, and Ni⁶⁰. A simple method of area analysis which is less tedious and time consuming than the method reported before in Part III is also described.     

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.     

High resolution proton scattering from 42Ca

Differential cross sections were measured for ⁴²Ca(p, p) at four angles between E_p = 1.2 and 3.0 MeV, with an overall energy resolution of 325 eV. Spins, parities and proton widths were extracted for 170 resonances. Two analogue states were identified and spectroscopic factors determined. The nearest neighbor spacing distributions were analyzed. Proton strength functions were determined for $\text{1}\text{2}$⁺, $\text{1}\text{2}$^? and $\text{3}\text{2}$^? resonances.     

Fine structure of analogue states

This article reviews all the high-resolution data on fragmented analogue states taken at the Triangle Universities Nuclear Laboratory, over a period of ten years. There are fifty analogue states observed by proton scattering on targets of masses between 40 and 64, and mass 92. The number of fragments may be only two or three, or as many as fifty. Of the total, only 17 states have a sufficient fine structure pattern where an analysis is attempted. In a few cases, inelastic widths and photon and neutron widths are observed besides proton elastic ones. The article discusses the optimum method of analysis of the data with a view to extracting the physical parameters of the analogue: the energy, proton spectroscopic factor, spreading width, shift and asymetry parameter. The last three quantities are discussed from the viewpoint of the Robson model based on one-channel external mixing of the analogue by Coulomb forces. This model has qualitative success, particularly in describing the large asymmetry sometimes seen, but it is not quantitatively adequate. When the proton spectroscopic factors are compared to the neutron counterparts for the parent (as measured by (d,p) studies), after allowing for Coulomb effects, the proton ones are smaller by an amount which increases to 30% in the heavier nuclei (Ni,Mo). This is in line with the situation on ^{2 0 8}Pb. Thus it seems that the inadequacy of a Coulomb explanation of the analogue-parent energy shift (the Nolen-Schiffer anomaly) has a counterpart in the spectroscopic factors.     

Statistical tests applied to proton resonances in57Co

Statistical tests are applied to a sequence of 1/2⁺ resonances observed in⁵⁶Fe(p,p) and the results are compared with predictions of the random matrix model. The target nucleus and proton energy were chosen to yield favorable level densities, strength functions, and Coulomb penetrabilities. In addition, the TUNL high resolution system provides excellent sensitivity to small resonances. These points combine to yield a fairly pure and complete sequence, as indicated by the DysonF statistic and the Dyson-MehtaΔ ₃ statistic. Good agreement is found with the orthogonal ensemble predictions for the long and short range spacing correlations, and for the widths of thek-th nearest neighbor spacing distributions fork=0 to 10.

     

Analysis of PNC neutron resonance experiments with polarized targets

The analysis of parity mixing experiments with unpolarized neutrons on polarized targets is described. Expressions for the neutron total cross section are presented for targets withI=1/2, 3/2, 5/2 and 7/2. These results are compared with the corresponding expressions for polarized neutron beams and unpolarized targets.     

Inelastic proton amplitudes forf-wave resonances in55Co

The measurement of inelastic proton channel amplitudes has been extended tof-wave resonances. Ten resonances were studied in the⁵⁴Fe(p, p′γ) reaction, All were established to haveJ ^π = 5/2^?, and inelastic decay amplitudes were determined for these resonances. Elastic and inelastic spectroscopic factors were determined for the 5/2^? analogue state atE _p =3.80 MeV.     

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.