The bound coherent neutron scattering lengths of the lanthanoids Pr, Nd, Sm, Eu, Yb and several of their isotopes as determined by neutron Bragg powder diffraction

We have determined the bound coherent neutron scattering lengthsbcof nuclides¹⁴¹Pr,^isoNd (iso = 142, 143, 144, 145, 146, 148, 150),^isoSm (iso = 147, 148, 150, 152, 154),¹⁵³Eu,¹⁷⁰Yb and¹⁷⁴Yb as well as the natural elements^natEu and^natNd by using Bragg powder diffraction and analysing relative Bragg peak intensities with the Rietveld procedure. Some of these scattering lengths had never been determined before, to the best of our knowledge. Our investigations were carried out using different neutron diffractometers and different incident neutron energies (i.e. wavelengths) on chemically pure, crystalline, highly-enriched isotopic powder samples having different crystalline structures in order to ensure the consistency and robustness of the results and to reveal potential systematic errors. Our study led to final well-determined values ofbc(¹⁴¹Pr) = 4.44(4) fm,bc(¹⁴²Nd) = 7.24(4) fm,bc(¹⁴³Nd) = 17.51(6) fm,bc(¹⁴⁴Nd) = 3.06(7) fm,bc(¹⁴⁵Nd) = 10.40(12) fm,bc(¹⁴⁶Nd) = 8.56(9) fm,bc(¹⁴⁸Nd) = 4.44(13) fm,bc(¹⁵⁰Nd) = 6.87(5) fm.bc(¹⁴⁷Sm) = 6.68(5) fm,bc(¹⁴⁸Sm) = 6.67(7) fm,bc(¹⁵⁰Sm) = 10.05(10) fm,bc(¹⁵²Sm) = -6.14(12) fm,bc(¹⁵⁴Sm) = 9.34(9) fm,bc(¹⁵³Eu) = 8.33(11) fm,bc(¹⁷⁰Yb) = 4.83(3) fm,bc(¹⁷⁰Yb) = 22.02(7) fm,bc(^natNd) = 7.87(11) fm for thermal neutrons, and alsobc(^natSm) = 5.29(5) fm for an incident neutron energy of 330.3(9) meV andbc(^natEu) = 5.84(5) fm for an incident neutron energy of 168.10(5) meV. Based on the good precision and self-consistency of ourbcresults over so many isotopes, we advocate neutron Bragg powder diffraction as a method of choice for future studies to determine bound coherent neutron scattering lengths.