Low-Lying Levels in Certain Actinide Atoms Export

@article{citeulike:2328492, abstract = {The problem of calculating the ordering and properties of low-lying levels in configurations of the type 5 f n 6 d falls into four parts: (a) the choice of a coupling scheme to define the basic eigenfunctions; (b) the evaluation of the matrix elements of the spin-orbit interaction and of the Coulomb interaction in the form of linear combinations of certain radial integrals; (c) the estimation of the radial integrals; (d) the diagonalization of the energy matrices. With regard to (a); the Jj coupling scheme is considered to be the most appropriate; this implies that the Coulomb interaction between the core; comprising the equivalent f electrons; and the d electron (to whose levels the respective symbols J and j refer) is weak compared with the interactions within the two systems. Part (b) is carried out by applying the tensor operator and group theoretical methods of Racah. For (c); values of the Slater integrals F k (5 f ; 6 d ) and G k (5 f ; 6 d ) are estimated for various atoms by assuming that they maintain the ratios one to another as they do in Th iii ; and that their variation along the actinide series parallels the variation of G 3 (5 f ; 7 s ). The last parameter is known for Th iii ; and analyses of U ii ; Pu ii ; and Am ii show that it decreases as one advances along the actinide series. This decline is interpreted as being due to the collapse of the 5 f shell; and the internal nature of the 5 f electrons allows some general statements to be made about the spin-orbit coupling constants. Additional information on the parameters is provided by an analysis of the properties of the four lowest levels of Cm i . Part (d) is accomplished for the very lowest levels of f 2 d ; f 3 d ; f 4 d ; f 8 d ; and f 10 d by the simple expedient of neglecting all off-diagonal elements; for U i f 3 d ; where extensive spectroscopic information is available; the interaction of the levels deriving from the Jj coupling of 4 I 9 / 2 to 2 D 5 / 2 with those deriving from the coupling of 4 I 11 / 2 to 2 D 3 / 2 is included. Where experimental data are available; agreement with the theory; both in respect to the positions of the levels and to their Land\'{e} g values; is good—often surprisingly so in view of the approximations made.}, author = {Judd, B. R.}, citeulike-article-id = {2328492}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.125.613}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v125/i2/p613_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v125/i2/p613_1}, day = {15}, doi = {10.1103/PhysRev.125.613}, journal = {Physical Review}, keywords = {judd, prb}, month = {January}, number = {2}, pages = {613+}, posted-at = {2008-02-04 07:03:00}, priority = {2}, publisher = {American Physical Society}, title = {Low-Lying Levels in Certain Actinide Atoms}, url = {http://dx.doi.org/10.1103/PhysRev.125.613}, volume = {125}, year = {1962} }

TY - JOUR ID - citeulike:2328492 L3 - citeulike-article-id:2328492 N2 - The problem of calculating the ordering and properties of low-lying levels in configurations of the type 5 f n 6 d falls into four parts: (a) the choice of a coupling scheme to define the basic eigenfunctions; (b) the evaluation of the matrix elements of the spin-orbit interaction and of the Coulomb interaction in the form of linear combinations of certain radial integrals; (c) the estimation of the radial integrals; (d) the diagonalization of the energy matrices. With regard to (a); the Jj coupling scheme is considered to be the most appropriate; this implies that the Coulomb interaction between the core; comprising the equivalent f electrons; and the d electron (to whose levels the respective symbols J and j refer) is weak compared with the interactions within the two systems. Part (b) is carried out by applying the tensor operator and group theoretical methods of Racah. For (c); values of the Slater integrals F k (5 f ; 6 d ) and G k (5 f ; 6 d ) are estimated for various atoms by assuming that they maintain the ratios one to another as they do in Th iii ; and that their variation along the actinide series parallels the variation of G 3 (5 f ; 7 s ). The last parameter is known for Th iii ; and analyses of U ii ; Pu ii ; and Am ii show that it decreases as one advances along the actinide series. This decline is interpreted as being due to the collapse of the 5 f shell; and the internal nature of the 5 f electrons allows some general statements to be made about the spin-orbit coupling constants. Additional information on the parameters is provided by an analysis of the properties of the four lowest levels of Cm i . Part (d) is accomplished for the very lowest levels of f 2 d ; f 3 d ; f 4 d ; f 8 d ; and f 10 d by the simple expedient of neglecting all off-diagonal elements; for U i f 3 d ; where extensive spectroscopic information is available; the interaction of the levels deriving from the Jj coupling of 4 I 9 / 2 to 2 D 5 / 2 with those deriving from the coupling of 4 I 11 / 2 to 2 D 3 / 2 is included. Where experimental data are available; agreement with the theory; both in respect to the positions of the levels and to their Landé g values; is good—often surprisingly so in view of the approximations made. IS - 2 JF - Physical Review TI - Low-Lying Levels in Certain Actinide Atoms PB - American Physical Society VL - 125 SP - 613 KW - judd KW - prb AU - Judd, BR PY - 1962/01/15/ UR - http://dx.doi.org/10.1103/PhysRev.125.613 ER -