s- and p-wave neutron spectroscopy: Part VI. Level density and neutron excess

Neutron total cross-section curves for Ca⁴⁰, Ca⁴⁴, Cr⁵⁰, Cr⁵², Cr⁵⁴, Fe⁵⁴ and natural Fe, Ti, and Cr have been measured in the kev region. Level spacings have been estimated for the predominant isotope in each of the samples measured, and are compared to similar data found for even N, odd Z targets. After correcting for differences in the angular momenta and excitation energies, it is found that on the average (between A = 35 and 60) $\text{d [}\text{ln}\text{D}{}_0\text{(6}\text{Mev}\text{)] = (?}\text{ln}\text{D}{}_0\text{?Z}\text{)dZ + (?}\text{ln}\text{D}{}_0\text{?N}\text{) dN ? 0.3 dZ ? 0.3 dN}$, and hence D₀(6 Mev) is proportional to exp ?0.3(N ? Z). D₀(6 Mev) is the spin and energy independent spacing parameter. Except for slight signs of a maximum at N = 28, D₀ (6 Mev) appears (between A = 35 and 60) to be strongly dependent only on the neutron excess, N ? Z, and not on N, Z, or A; uncertainties in the correction for excitation are such that it is likely that the absolute value of the exponent, 0.3 (N ? Z) is a lower limit. Isotopic and J^π assignments of many resonances in the natural fluorine and chromium cross-section curves are suggested.     

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: Part V. Level Spacings in Heavy Nuclei

Total neutron cross sections were measured for natural rubidium and thallium and for the separated isotopes, Pb²⁰⁸, Pb²⁰⁷, Pb²⁰⁶, Tl²⁰³, and Rb⁸⁵. Approximate s-wave resonance spacings were estimated for Pb²⁰⁷, Y⁸⁹, Rb⁸⁷, Rb⁸⁵, Tl²⁰³, and Tl²⁰⁵. D₀ = D_J(2J + 1) = 2D_S(2I + 1) = 50, 24, 8, 4, and 30 kev, respectively, where D_s is the average (s-wave) level spacing for all channels. The spacings (D₀) of Pb²⁰⁶ and Pb²⁰⁸ were found to be of the order of hundreds of kew; there is also evidence that resonance spacings are very wide for Sr⁸⁶ and Ba¹³⁶. It is concluded that, in all compound nuclei with a neutron number silightly less than the magic numbers 50, 82, and 126, the resonance spacings are usually not much less than when the magic number is exceeded slightly. Since neutron excitation energies of these sub-magic nuclei are higher than the average, the observed wide level spacings below the magic numbers must be due to the properties of the nearly closed shells and can not possibly be caused only by low excitation energy of the compound nucleus. In considering these comparisons it is shown that, for s-wave resonances, the relation $\text{D}{}_{\mathrm{J}}\text{=}\text{D}{}_0\text{(2J + 1)}$ is a useful approximation in that a plot of D₀ is a much less erratic function of A than is the observed spacing. We also discuss the Bethe-Hurwitz effect, i.e., the influence on resonance spacing (apart from the 2J + 1 factor) of an unpaired nucleon in the target nucleus. We estimate that $\text{α ≧ 30}$ in the equation $\text{D}{}_0\text{(0)}\text{D}{}_0\text{(W)}\text{=}\text{exp}\text{(αW)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ where D₀(0) is the energy and spin independent spacing parameter, and W is the excitation energy of the compound nucleus.     

s- and p-wave neutron spectroscopy Xf(ii). Intermediate structure in the 28Si + n reaction: Doorway state calculation

A core-particle calculation developed to describe the low-lying structure of ²⁹Si is extended above neutron threshold energy to yield information on the structure of doorway states indicated by the ²⁹Si + n reaction. The recent experimental evidence for a $\text{J =}\text{3}\text{2}{}^{\mathrm{?}}$ doorway state common to the ²⁸Si + n and the ²⁹Si + γ channels is supported by the calculation which also reproduces correctly the magnitudes of the neutron escape widths and the E1 radiative strengths of the $\text{3}\text{2}{}^{\mathrm{?}}$ doorway states.     

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.     

S- and P-wave neutron spectroscopy Part Xd: Intermediate structure, particle-vibration states

The weak coupling particle-vibration model is extended to lowlying neutron resonances in certain even-even or odd-odd nuclei by coupling the extra particle to core excited states of the odd mass target. The odd hole or particle in the target is treated as a passive spectator. ²⁰⁸Pb and ²¹⁰Bi are studied as test cases and the calculated resonance quantities are in good general agreement with the average features of high resolution experiments. The resonances in ²⁰⁸Pb and ²¹⁰Bi are related to the same intrinsic doorway in ²⁰⁹Pb. The ²¹⁰Bi data is presented here for the first time.     

New source of decoupling of E1 strength from the GDR: boundary condition mixing for s- and p-wave neutron states near threshold

Non-statistical effects in neutron capture reveal that E1 strength of neutron orbits of low l-value is partially decoupled from the GDR. Particle-hole diagonalisations with realistic forces do not show this effect. We show that it can arise from a new source, boundary condition mixing, which operates when fine-structure states are introduced. This may also explain the ‘pygmy dip’ in E1 strength reported for masses ～ 195.     

Neutron capture gamma ray investigation of Sr88 level structure

The level structure of Sr⁸⁸has been investigated at the Karlsruhe research reactor FR2 using thermal neutron capture in Sr⁸⁷. A pure thermal neutron beam was obtained by Bragg reflection from a lead single crystal. The target was natural strontium which gives a cross section contribution of about 87% for the reaction Sr⁸⁷(n,γ) Sr⁸⁸. High resolution measurements of the capture gamma ray spectrum have been performed by means of a 4 cm² × 0.5 cm lithium-drifted germanium diode. 146 gamma lines have been observed. Cascade relationships were studied by a double and triple coincidence apparatus containing 4″Ø × 5″ NaI(Tl) crystals and XP-1040 photomultipliers. In several cases coincident background was subtracted utilizing the doublewindow technique. By application of the triple sum coincidence method capture gammas from isotopes other than the investigated Sr⁸⁸ nucleus could be eliminated. Several new levels were established. A transition scheme is proposed and discussed. The neutron binding energy of Sr⁸⁸ is determined to be 11111±4 keV.     

Intermediate structure in the neutron scattering cross sections of iron

Differential cross sections for the Fe(n, n), (n, n′), (n, n′γ) reactions were measured at incident energies between 1.43 and 2.15 MeV. Structure with intermediate widths was observed. The result was analysed by the doorway-state model, and the widths of the assumed doorway states were obtained. Spin and parity assignment of $\text{3}\text{2}$(⁺) was made to a doorway-state resonance at about 2.0 MeV.     

s- and p-wave neutron spectroscopy. Xe. Intermediate structure in 90Y and the generalized R-matrix theory

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross section measurements in the range of 0.3 to 1.2 MeV incident energy was investigated using the generalized R-matrix theory of nuclear reactions and the doorway interpretation of intermediate structure. The energies and wave functions of the doorway resonances were calculated in a 2-particle and 3p-1h basis of the shell model. The model space and the parameters of the model calculation chosen were consistent with other shell model calculations in the mass-90 region. Several strong p-wave doorways with J^π = 0⁺, 1⁺, and 2⁺ were predicted by the model in the energy range studied. This is due to proximity of p-wave giant resonance. The escape widths Γ^↑ and the spreading widths Γ^↓ for these states were evaluated using the model wave functions and the R-matrix formalism. The calculated energy dependence of the total cross section shows that most of the predicted doorways are in general agreement with the observed anamolies with similar relative strength. More significantly, the underlying p-wave gross structure representing a grand average is of very similar shape in both theory and experiment. As expected in the mass 90-region, the s- and d-wave doorways contribute less significantly to the calculated resonance structure.     

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr

We report the use of photoassociative spectroscopy to determine the ground-state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494 +/- 5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr.     

Parity violation at neutron p-wave resonances of238U and232Th and related questions

Parity violation effects have been studied at 40 neutron p-wave resonances of the even-even nuclei²³⁸U and²³²Th. Of these 11 show parity violation effects larger than 2 standard deviations, making parity violation a rather common phenomenon. Parity mixing up to 10% has been found. The root-mean squared matrix elements for parity violation derived from these resonances are M=0.58 (+0.50/-0.25) meV for²³⁸U, respectively 1.39 (+0.35/-0.38) meV for²³²Th.     

Effective charges for 88Sr and 90Zr closed-shell cores

Effective charges are calculated for protons and neutrons in the region of mass 90. It is found that their magnitudes differ appreciably depending on whether the proton p _1/2 shell is empty or full. The calculated values are compared with values deduced from nuclei with simple configurations, and from a fit to N=50 data. The empirical values are used in shell-model calculations of quadrupole moments of N=50-58 nuclei. Received: 16 February 1998     

Complexity and neutron star structure

We apply the statistical measure of complexity introduced by López-Ruiz, Mancini and Calbet (1995) [1] to neutron star structure. We continue the recent application of Sañudo and Pacheco (2009) [2] to white dwarfs. The interplay of gravity, the short-range nuclear force and the very short-range weak interaction shows that neutron stars, under the current theoretical framework, are ordered (low complexity) systems.