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.     

The scattering of slow neutrons by cobalt

Different techniques have been used to determine with slow neutrons the coherent scattering amplitude b_c and the total scattering cross-section σ_sc of Co. We found values for the bound atom b_c=2.78+0.04 fm and for the free nucleus σ_sc=5.95+0.05 barns.From these quantities, the spin state scattering amplitudes b₊ and b_? corresponding to the compound nucleus states of spin I+1/2 or I?1/2 have been determined as b₊=?2.78±0.04 fm and b_?=+9.91±0.06 fm. These results are not in agreement with previous data, but they are found to be consistent with data obtained from resonance parameters.     

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.     

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.     

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.     

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.

     

The neutron zero-energy total cross section and scattering lengths for tritium

New results for the neutron total cross section for tritium extrapolate to 1.70 ± 0.03 b at zero energy. With a theoretical constraint A₁/A₀=0.92 ± 0.04, the scattering lengths A₁=3.60 ± 0.10, A₀ = 3.91 ± 0.12, and A_c=3.68 ± 0.05 fm can be inferred independently of, but consistently with, the previous experimental value for the coherent length A_c=3.82 ± 0.24 fm.     

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.

     

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.     

Scattering of slow neutrons by arsenic and selenium isotopes

Coherent neutron scattering lengths and free cross sections were measured for arsenic, for ordinary selenium and its isolated isotopes. By means of the Cristiansen filter technique the following scattering lengths for the bound atoms were obtained (in fm):b(As) =6.58(1) [b ₊=6.04(5) andb _?=7.47(8)],b(Se)=7.970(9),b(⁷⁶Se)=12.2(1),b(⁷⁷Se) =08.25(8),b(⁷⁸Se)=8.24(9),b(⁸⁰Se)=7.48(3) andb(⁸²Se)=6.34(8). Transmission measurements with neutrons of 1.26 eV and 5.19 eV resulted in an energy independent free scattering cross section for arsenic ofσ _{s, t}=5.40(3)b (in the eV-region). For ordinary selenium energy dependent free cross sections ofσ _{s, t}(1.26 eV)=7.9(1)b andσ _{s, t} (5.19 eV)=7.55(3)b were found. The results were compared with the resonance parameters of the nuclei and with different sets of potential scattering radii. Thus it could be concluded that there is no evidence for a bound state of the neutron-nucleus compound⁷⁵As+n but a clear evidence for strong bound levels of⁷⁶Se+n and⁷⁷Se+n.     

Elastische Elektronenstreuung an14N,15N,16O und18O bei kleiner Impulsübertragung

Elastic electron scattering cross sections of¹⁴N and¹⁶O have been measured relative to the proton and of¹⁵N and¹⁸O relative to the lighter isotope (¹⁴N,¹⁶O resp.) using gas targets. The momentum transfer ranged from 0.22 to 0.48 fm^?1. The data were analyzed by phase shift calculations assuming harmonic oscillator shell model charge distributions. The following rms charge radii have been deduced: R_m(¹⁴N)=2.540±0.020 fm R_m(¹⁵N)=2.580±0.026 fm R_m(¹⁶O)=2.718±0.021 fm R_m(¹⁸O)=2.789±0.027 fm. The errors include statistical and systematic uncertainties and an estimate of effects due to the choice of the model. The radius differences of the isotopes are smaller than the values predicted by anA ^1/3 relation     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

Neutron scattering lengths of molten metals determined by gravity refractometry

Very accurate values of the coherent neutron scattering lengths of the heavy elements Bi and Pb are important quantities for the investigation of the electric interactions of neutrons with atoms. We performed, therefore, a series of experiments to determine accurate scattering lengths by means of neutron gravity refractometry on liquid mirrors of molten metals. The possible perturbations of the necessary reflection measurements have been discussed in details. After taking into account the uncertainties and corrections associated with observable pertubations we obtained the following values for bound atoms:b(Bi)=8.532±0.002 fm,b(Pb)=9.405±0.003 fm,b(Tl)=8.776±0.005 fm,b(Sn)=6.225±0.002 fm andb(Ga)=7.288±0.002 fm. These data are corrected for the local field effect occuring in the reflection on liquids. The recently reported results for the neutron's electric polarizability and the neutron-electron scattering length are supported by the Bi- and Pb-scattering length of this work.     

Nuclear charge radii of Al and Si from elastic electron scattering between 25 and 60 MeV

Elastic electron scattering cross sections of²⁷Al and Si (natural isotopic mixture) have been measured relative to carbon. The rms charge radiiR _m , deduced with partial wave calculations, are (3.01±0.05) fm for²⁷Al and (3.06±0.05) fm for Si, in good agreement with results from muonic X-ray energies. The values given are those for a Fermi charge distribution with skin thickness 2.5 fm; harmonic oscillator shell model distributions yield radii smaller by 0.03 fm. The ratioR _m (²⁷Al)/R_m(Si) is 0.984±0.016.     

Nuclear matter sizes and isoscalar octupole transition rates of204,206,208Pb from 104 MeV α-particle scattering

Differential cross sections for elastic and inelastic scattering of 104 MeVα-particles from^204,206,208Pb were measured with high angular accuracy. The experimental results were analysed on the basis of a semimicroscopic folding model in order to determine the matter distributions at the nuclear surface and the transition densities. Using phenomenological parametrizations of the densities the analyses of elastic scattering yield rms radii of 〈r ²〉^1/2=5.55±0.06 (²⁰⁴Pb), 5.57±0.06 (²⁰⁶Pb), 5.63±0.05 (²⁰⁸Pb) fm. Various sensitivities affecting the results were studied. From the inelastic cross sections for the 3 ₁ ^? -states octupole transition probabilities and transition radii were derived by using different methods proposed in literature.     

Determination of low-energy parameters of neutron-proton scattering on the basis of modern experimental data from partial-wave analyses

The triplet and singlet low-energy parameters in the effective-range expansion for neutron-proton scattering are determined by using the latest experimental data on respective phase shifts from the SAID nucleon-nucleon database. The results differ markedly from the analogous parameters obtained on the basis of the phase shifts of the Nijmegen group and contradict the parameter values that are presently used as experimental ones. The values found with the aid of the phase shifts from the SAID nucleon-nucleon database for the total cross section for the scattering of zero-energy neutrons by protons, σ ₀ = 20.426 b, and the neutron-proton coherent scattering length, f = ?3.755 fm, agree perfectly with experimental cross-section values obtained by Houk, σ ₀ = 20.436 ± 0.023 b, and experimental scattering-length values obtained by Houk and Wilson, f = ?3.756 ± 0.009 fm, but they contradict cross-section values of σ ₀ = 20.491 ± 0.014 b according to Dilg and coherent-scattering-length values of f = ?3.7409 ± 0.0011 fm according to Koester and Nistler.     

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.     

Kernradien von12C,13C,14N und16O aus Elektronenstreuung zwischen 30 und 60 MeV

Elastic electron scattering cross sections of¹²C,¹⁴N and¹⁶O relative to the proton, and of¹³C relative to¹²C have been measured. Using harmonic oscillator wave functions the followingrms charge radiiR _m were deduced by phaseshift calculations: 2.395 (28) fm for¹²C, 2.384 (47) fm for¹³C, 2.492 (33) fm for¹⁵N, 2.666 (33) fm for¹⁶O. The ratioR _m (¹³C)/R _m (¹²C) is 0.995±0.008. The errors given do not include uncertainties from the model dependence of the evaluation which may be of the same magnitude.