Interaction of slow neutrons with the isotopes of molybdenum

Coherent neutron scattering lengths and total cross sections were measured on samples of ordinary Mo and isotopically enriched samples. From the experiments with neutrons of 0.57 meV and 1.26 eV the following values have been obtained:

1. the coherent scattering lengths (in fm) of the bound atoms of Mo (6.715±0.020) and for the isotopes with the mass numbers 92 (6.93±0.08), 94 (6.82±0.07), 95 (6.93±0.06), 96 (6.22±0.06), 97 (7.26±0.08), 98 (6.60±0.07) and 100 (6.75±0.07);
2. the incoherent scattering cross section at zero-energy for ordinary Mo: σ_i=0.02 ± 0.02 barn;
3. the absorption cross sections (in barn) for Mo (2.48 ± 0.04) and for the isotopes with the mass numbers 95(13.4 ± 0.3), 97(2.5 ± 0.2) and 100(0.4 ± 0.2). The relation of the present results to the resonance parameters of the neutron — Mo interaction has been discussed.

     

Neutron scattering lengths and cross sections of the barium isotopes

Coherent neutron scattering lengths and total cross sections have been measured for barium compounds and on isotopically enriched samples for neutron energies from 0.5 meV up to 132 eV using different techniques. From the experimental data the following quantities were obtained:

the coherent scattering lengths (in fm) of Ba (5.07±0.03) and of the isotopes with mass numbers 130 (?3.6±0.6); 132 (7.8±0.3); 134 (5.7±0.1); 135 (4.66±0.10); 136 (4.90 ±0.08); 137 (6.82±0.10); and 138 (4.83±0.08).

the absorption cross sections σ_γ (at 0.025 eV in barn): of Ba (1.1±0.1) and of the isotopes: 130 (30±5); 136 (0.68±0.17); 137 (3.6±0.2); and 138 (0.27±0.14).

zero-energy scattering cross sections for Ba and the isotopes 136, 137 and 138. On the basis of these data, the isotopic- and spin-incoherent cross sections and the (s)-resonance contributions to the coherent scattering lengths have been determined and discussed.

     

Neutron scattering lengths of the isotopes of thulium,ytterbium and lutetium

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tm, Yb and Lu and on isotopically enriched compounds. From the experimental data for 0.57 meV neutron energy the following data were obtained: the coherent scattering lengths (in fm) of the bound atoms¹⁶⁹Tm (7.07+0.03);¹⁷⁰Yb (6.8±0.1);¹⁷¹Yb (9.7±0.1);¹⁷²Yb (9.5±0.1);¹⁷³Yb (9.56±0.10);¹⁷⁴Yb (19.2±0.1);¹⁷⁶Yb (8.7± 0.1); Yb (12.41±0.03);¹⁷⁵Lu (7.28±0.09);¹⁷⁶Lu (6.3±0.2) and Lu (7.21±0.03); the thermal absorption cross sections (in barn) for¹⁶⁹Tm (100±2); Yb (34.8±0.8) and Lu (74±2). In combination with the resonance parameters the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the permanently deformed and deformable nuclei in the rare-earth region.     

Neutron interactions with germanium isotopes and amorphous and crystalline GeO2

Coherent neutron scattering lengths and total cross sections have been measured on elemental and oxide samples of ordinary Ge and of isotopically enriched substances. From the experimental results the following values were obtained:

the coherent scattering lengths (in fm) of the bound atoms Ge(8.185±0.020);⁷⁰Ge(10.0±0.1);⁷²Ge(8.51±0.10);⁷³Ge(5.02±0.04);⁷⁴Ge(7.58±0.10) and⁷⁶Ge(8.2 ±1.5);

the absorption cross sections at 0.0253 eV (in barn) for Ge(2.20±0.04);⁷⁰Ge(2.9±0.2);⁷²Ge(0.8±0.2);⁷³Ge(14.4±0.4) and⁷⁴Ge(0.4±0.2);

the free cross sections for epithermal neutrons and the zero energy scattering cross sections.

On the basis of this data, the isotopic- and spin-incoherent cross sections and thes-wave resonance contributions to the coherent scattering lengths have been determined and discussed. Transmission measurements at 0.57 meV on amorphous and crystalline GeO₂ yielded for the amorphous sample an inelastic cross section eight times larger than for the crystalline samples. This effect corresponds to a clearly higher density of low energy states in the amorphous than in the crystalline substances.     

Interaction of slow neutrons with nuclides of scandium,titanium, vanadium and manganese

Total cross section measurements at various neutron energies were performed on metallic and oxide samples of natural Sc, Ti, V, and Mn. By means of the Christiansen filter technique the coherent scattering lengths were determined on natural and isotopically enriched samples of Ti-, V-, and Mn-compounds. From the measured values we deduced the following data:

? the absorption cross sections (at 0.0253 eV in barn) of^natTi (6.43±0.06) and of^natV (5.06±0.04);

? the bound coherent scattering lengths (in fm) of^natTi (?3.370±0.013),⁴⁶Ti (4.72±0.05),⁴⁷Ti (3.53±0.07),⁴⁸Ti (?5.86±0.02),⁴⁹Ti (0.98±0.05),⁵⁰Ti (5.88±0.10),^natV (?0.443±0.014), and Mn (?3.750±0.018);

? the free potential radii (in fm) of Sc (3.60 ±0.10),⁴⁶Ti (3.50±0.10),⁴⁷Ti (3.60±0.10),⁴⁸Ti (3.90±0.10),⁴⁹Ti (4.10 ±0.15),⁵⁰Ti (4.50±0.15),⁵¹V (5.20±0.20), and Mn (6.50±20).

On the basis of the well known resonance parameters in combination with new fits of bound levels the spin state scattering lengths, the spin incoherence, and the obtained potential radii are discussed. Total cross section calculations were performed by multi-level formalism and are compared with the measurements.     

Interaction of neutrons with zinc and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured for elemental Zn,Zn-compounds and on isotopicly enriched samples for neutron energies from 0.5 meV up to 143 keV using different techniques. From the experimental data the following quantities were obtained:

the coherent scattering lengths (b in fm) of Zn (5.689±0.014);⁶⁴Zn (5.23±0.04);⁶⁶Zn (5.98±0.05);⁶⁷Zn (7.58±0.08;b ₊=9.4±0.5/5.8±0.5;b _?=5.0±0.7/10.1±0.7);⁶⁸Zn (6.04 ±0.03);

the potential scattering radii (R′ in fm) of Zn (6.2±0.2),⁶⁴Zn (6.0±0.3) and⁶⁶Zn (6.2 ±0.3);

the absorption cross sections (σ _γ at 0.025 eV in barn) of Zn (1.11±0.02);⁶⁴Zn (1.1 ±0.1) and⁶⁶Zn (0.62±0.06).

Derived quantities are the “zero energy” scattering cross sections (σ ₀ in barn) for Zn (4.128±0.010) and⁶⁷Zn (7.8±0.3) and the incoherent bound cross sections of Zn (0.061 ±0.023) and⁶⁷Zn (0.6±0.4). In the epithermal region the Zn-cross section can be described by introduction of two strong bound levels of⁶⁷Zn+n for which estimated parameters are given.     

Interaction of slow neutrons with natural terbium,holmium and erbium and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tb, Ho and Er and on isotopically enriched Er-compounds. From the experiment the following data were obtained:

• - the coherent scattering lengths (in fm) of the bound atoms ¹⁵⁹Tb(7.34 ± 0.02), ¹⁶⁵Ho(8.44 ± 0.03), ^ordEr(7.79 ± 0.02), ¹⁶²Er(9.01 ± 0.11), ¹⁶⁴Er(7.95 ± 0.14), ¹⁶⁶Er(10.51 ± 0.19), ¹⁶⁷Er(3.06 ± 0.05), ¹⁶⁸Er(7.43 ± 0.08), and ¹⁷⁰Er(9.61 ± 0.06)
• - the thermal absorption cross sections (in b) ¹⁴¹Pr(12.7 ± 0.6), ^ordNd(58 ± 1), ¹⁵⁹Tb(30 ± 2), ¹⁶⁵Ho (65 ± 2), ^ordEr (145 ± 2), ¹⁶⁶Er (18 ± 2), ¹⁶⁷Er(568 ± 9), ¹⁶⁸Er(2.3 ± 0.3), and ¹⁷⁰Er(15 ± 1). In combination with the resonance parameters, the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the optical model theory.

     

Neutron scattering length of lithium and boron and their isotopes

Coherent neutron scattering lengths and free cross sections were measured in order to determine the spin dependent scattering lengths of the isotopes of Li and B. The transmission measurements on Li at neutron energies of 0.51 meV, 1.26 eV and 5.19 eV delivered data for the⁶Li-abundances in the samples and for the free scattering cross section of⁷Li. By means of experiments on 15 different samples of lithium compounds we obtained the complex spin state scattering lengths for the bound atoms to be: (ie81-01) Measurements on 3 boron samples with different enrichments led to (ie81-02) A review on slow neutron scattering and resonance data shows an over all consistency of all values.     

Interaction of slow neutrons with natural Rutenium,Rhodium, Cadmium and Thallium and some of their isotopes

By means of Christiansen filter technique the following bound coherent neutron scattering lengths were obtained:^natRu:b=7.02 ± 0.02 fm¹⁰⁸Cd:b=5.31 ± 0.24 fm¹⁰³Rh:b=5.90 ± 0.04 fm¹¹⁰Cd:b=5.78 ± 0.08 fm^natTl:b=8.773 ± 0.015 fm¹¹¹Cd:b=6.47 ± 0.08 fm²⁰³Tl:b=8.51 ± 0.08 fm¹¹²Cd:b=6.34 ± 0.06 fm²⁰⁵Tl:b=8.87 ± 0.07 fm¹¹⁴Cd:b=7.48 ± 0.05 fm¹¹⁶Cd:b=6.26 ± 0.09 fm In combination with some total cross section measurements with neutrons in the eV-energy range and with the compiled resonance parameters we deduced consistent sets of spin state scattering lengths and potential radii.     

Interactions of slow neutrons with the chromium isotopes

Neutron transmission experiments and determinations of coherent scattering lengths were performed on natural chromium and enriched samples of⁵⁰Cr,⁵²Cr,⁵³Cr and⁵⁴Cr. By means of the Christiansen-filter-technique we obtained new values for the scattering lengths of the bound atoms:b(^natCr)=3.635±0.007 fm,b(⁵⁰Cr)=?4.50±0.05 fm,b(⁵²Cr)=4.914±0.015 fm,b(53Cr)=?4.20±0.03 fm, andb(⁵⁴Cr)=4.55±0.10 fm. The transmission experiments with neutrons of 510 ΜeV, 1.26 eV and 5.19 eV energy resulted in data for the absorption cross sectionσ _a (^natCr) =3.05±0.08 b and for the scattering cross section at “zero energy”:σ ₀ (^natCr)=3.381±0.010 b. Data for incoherent and spin-state scattering and for the potential-scattering radius of the nuclei could be deduced from these results.     

Interactions of neutrons with gallium and its isotopes

Coherent neutron scattering lengths and total cross sections were measured on elemental Ga, Ga-compounds and on isotopically enriched samples at neutron energies from 0.5 meV up to 143 keV using different techniques. From the experimental data the following quantities could be obtained:

the coherent scattering length of Ga and the spin state scattering lengths of the isotopes.

the potential scattering radii (R′)

the absorption cross sections of Ga,⁶⁹Ga,⁷¹Ga and⁷⁵As.

As derived quantities are given the coherent and incoherent cross sections and the resonance spin scattering lengths for theJ=1 andJ=2 states of⁷⁰Ga and⁷²Ga. The physical meaning of these data and ofR′ and the comparison with the resonance parameters are considered.     

Slow neutron scattering lengths of the isotopes of silver and indium

By means of the Cristiansen filter method we measured on filters containing powder, filings or wires of silver or powder of indium oxide the coherent scattering lengths for the bound atoms of the following isotopes:b(¹⁰⁷Ag)=7.64±0.04 fm,b(¹⁰⁹Ag)=4.19±0.03 fmb(nat.Ag)=5.97±0.01 fm,b(¹¹³In)=5.39±0.06 fmb(¹¹⁵In)=4.00±0.03 fm andb(nat.In)=4.065±0.020 fm. From these values and taking account of incoherent and resonance data we deduced values for the fundamental spin state scattering lengths and incoherent cross sections. These zero energy scattering parameters and the resonance parameters for silver are consistent if bound levels of¹⁰⁸Ag and¹¹⁰Ag are assumed. No indications were found for bound levels of the In isotopes.     

Precision neutron total cross section measurements on gold and cobalt in the 40 μeV-5 meV range

The slow neutron absorption cross sections of gold and cobalt have been accurately redetermined by transmission measurements in the neutron wavelength range 4 to 47 Å. For the range 4 to 7.6 Å a new time-of-flight spectrometer at the FRM reactor was used which involves a system of three synchronized choppers and a 150 m long guide tube as flight path. Utilizing the high wavelength resolution of the spectrometer, the time-of-flight wavelength scale could be accurately calibrated (±2 · 10^?3 Å) by means of various Bragg cutoff breaks observed in transmission on polycrystalline samples. Supplementary transmission measurements on gold and cobalt were performed in the range 11–47 Å using the time-of-flight spectrometer for ultracold neutrons at the FRM reactor. The absorption cross sections were evaluated considering corrections for incoherent and inelastic scattering and for the slight deviation from 1/v of the absorption of gold due to the 4.9 eV resonance level. For the absorption at subthermal energies we obtainσ _a /gl=(54.35±0.06) b/Å for Au, (20.66±0.04) b/Å for Co. Evaluation of the absorption cross sections at 2200 m/s neutron velocity gives (98.68±0.12) b for Au, (37.15±0.08) b for Co.     

Bounds on the coupling parameters in field theoretical models of nuclear physics

Neutrons of energies within a 50 eV interval at 1970 eV have been selected from reactor neutrons by means of resonance scattering on a target of⁶³Cu and subsequently by the 1970 eV resonance of a⁸⁰Se target. Insertion of stationary filters and the technique of difference measurements with a resonance filter resulted in a high selectivity, which allowed the determination of cross sections for quasi-monoenergetic neutrons for the elements: H, C, O, F, Na, Mg, Al, Si, P, Cl, K, Ca, Sc, Ti, V, Mn, Co, Ni, Cu, Ga, Pb and Bi. The precision cross sections of Pb and H contribute to investigations of fundamental neutron interactions. The measured σ(Pb)=11.198±0.003 b was recently used to deriveα _n=(0.8±1)10^?3 fm³ for the electric polarizability of the neutron. The neutron-proton cross sectionσ(¹ H)=20.13±0.03 b and data at 143 keV, 〈1.3〉 MeV, 〈2.1〉 MeV and from the literature provide a refined set of the scattering parameters for the shape-independent effective-range approximation of the neutron-proton interaction.     

Photoneutron cross sections of 121Sb, 123Sb and natSb

The cross sections for the reactions ${}^{121}\text{Sb}\text{(γ,n)}$, ¹²³Sb(γ, χn) and ^natSb(γ, χn) have been measured. The ¹²¹Sb and ¹²³Sb photoneutron reaction cross sections are consistent with collective model predictions for negatively deformed nuclei.     

Thermal neutron scattering parameters for light nuclei (A=12 to 27)

Neutron scattering lengths and free scattering cross sections were measured for isolated isotopes and natural elements in the mass region fromA=12 toA=27. By means of the Christiansen filter technique values for the coherent scattering lengths were obtained for the bound atoms of^12C,^13C,^14N,^15N,^16O,^17O,^18O, Mg and¹⁹F. Transmission experiments with neutrons of 0.51 meV, 1.26 eV and 5.19 eV yielded data for the free scattering cross sections of^19F,²³Na, Mg and¹⁹F. From all these results and with previous data the fundamental spin state scattering lengths for the concerned light nuclei have been deduced. The comparison of these values with resonance parameters has shown that the resonance data are complete. Therefore, values for the potential scattering radii could be obtained and discussed.     

New methods for interferometric neutron scattering lengths measurements

A skew symmetric neutron interferometer has been used for tests of a nondispersive and phase contrast variation measuring technique of scattering lengths and for the measurement of anomalous scattering lengths of strongly absorbing substances. The following bound coherent scattering lengths have been obtained: b_c(Pt)=9.60 ± 0.01 fm, b_c(Te) =5.6 ± 0.1 fm and as real parts of anomalous scattering lengths at λ=l.86Å: b_c(Sm) =0.7 ± 0.2 fm, b_c(Eu)=5.3 ± 0.3fm, b_c(Gd)=5.1 ±0.4 fm, b_c(Dy)=16.9 ± 0.3 fm.     

Epithermal neutron diffraction from a gadolinium alloy (Gd0.9Y0.1)

The coherent nuclear scattering amplitude of natural Gd was determined by epithermal neutron diffraction with neutron energy of 1.4 eV to be 1.4 ± 0.1 × 10^?12 cm.