Integrating actions and state constraints: A closedform solution to the ramification problem (sometimes)

Neodymium was extracted and isotopically fractionated in the liquidliquid extraction using a crown ether of dicyclohexano-18-crown-6. The maximum value in isotope enrichment factor was observed on the isotope pair (142)Nd-(150)Nd, and was epsilon(142,150)= 0.00084±0.00009: this was 0.00011±0.00001 in terms of the unit mass enrichment factor. The isotope enrichment factors showed breakdown of the conventional mass-dependent theory. We presented the advanced theory by use of the nuclear size and shape effect and the nuclear spin effect. The field shift effect was proved to give larger contribution than the nuclear mass effect. The predominance of the field shift effect in this study agreed with our previous studies on samarium and gadolinium.