ALBERT

Notes: In the study reported here, unrestricted Hartree–Fock calculations were performed on the ground state and several soliton-like defect states of the model large polyene, trans-polyacetylene. The calculations included the use of the random phase approximation to obtain screened electron repulsion integrals and projection of the UHF eigenfunctions to obtain pure spin states. The trans-polyacetylene ground state geometry is characterized here by alternating double and single bonds with lengths of 1.456 and 1.369 A(ring), respectively. Calculations on model soliton-like defect states yielded functional forms for the bond alternation, spin density, and charge density defects which are consistent with the soliton model for trans-polyacetylene and are similar to those reported elsewhere. The average positive and average negative spin density on chains containing neutral kink defects are 0.045 and −0.011, respectively. These values are in fair agreement with the best experimental estimates of 0.06 and −0.02.

Notes: An ultrahigh precision coupling of the angular motion of the two axes in a double-crystal monochromator with constant exit height has been constructed. The coupling device is a double parallelogram similar to the kind used for drafting tables. Computer simulations have been used to minimize the angular motion in the joints of the parallelograms to less than ±5° for the entire Bragg-angle range from 10° to 71°. This allows the use of backlash-free and friction-free flexural pivots. The axis of the first crystal is controlled by a precision rotary table. The shaft of the second crystal stage is supported by a trolley riding on a translation stage. Bearings allow for free rotation of the shaft. The double parallelogram provides only for the exact angular position of the second axis but does not support any weight of the second crystal stage and freely follows the trolley. The trolley is positioned so that the beam from the first crystal is intercepted and reflected at the correct height. The device is ultrahigh vacuum compatible. This design, which fully separates the two demands for extremely precise angular tracking and for less precise positioning for constant exit height, has several advantages beyond its superior tracking accuracy. The stationary first axis allows efficient, in-vacuum cooling of the first crystal. A direct rotary drive can be used for the first axis thus providing direct linear Bragg-angle control. A heavy weight second crystal stage, e.g., for sagittal focusing, may be used without deforming the angular linkage mechanism since all weight is carried by the rugged translation stage. No high-precision machining such as grinding or lapping is needed for the double-parallelogram linkage. The arms of the parallelogram, i.e., the distance between the holes for the flexural pivots, need to be only of precisely the same length.Testing the linkage shows the expected high accuracy. The maximum nonrepeatable deviation between the two axes is less than 5×10−5 degree (=0.2 arcsec). The tracking error for a 10−4 degree step is less than 1×10−5 degree, for a 10−3 degree step it is less than 2×10−5 degree. The maximum total deviation at any point within an interval of 0.1° is less than 1×10−4 degree (=0.4 arcsec). Repeatable and smooth long range deviations of a few arcseconds are compensated by feeding a predetermined corrective voltage to a piezo translator.