Theoretical expressions for both the nonrelativistic and relativistic nuclear matrix elements for /3 transitions of arbitrary forbiddenness are derived by using the Nilsson model. The /3-decay operators are expressed in terms of irreducible spherical tensors. One-and two-particle intrinsic wave functions are used for odd-and even-mass nuclei, respectively. For even-mass nuclei, the results are found to be strongly dependent on the coupling of the two particles. The results are expected to be applicable to decays involving both intrinsic ground states and excited intrinsic states. The theoretical expressions are used to calculate matrixelement parameters for/? decays in Tm 170 and Re 186 . The theoretical values are compared with experimentally determined values of the Tm 170 and Re 186 parameters.
These two effects tend to compensate each other in cases where the spin of the bombarded nucleus is large.A complete expression for magnetic scattering by finite-size nuclei with a magnetic momentum was derived by Walecka and Pratt 8 ; the connection with Rosenbluth's formula is discussed there.From Fig. 5 it is seen that for light elements, where magnetic scattering is big and thus our error (due to subtracting the : charge cross section) is small, the experimental points follow the theory quite closely. 5 B 10 seems to be the only exception. Since it has a large spin, this might be due to contributions of higher multipoles which are not present in 5 B n . For heavier nuclei the errors are large, and there seem to be no major conflicts between theory and experiment. The H theoretical point is higher than the experimental because no recoil is assumed in formula (4) which makes an appreciable effect only in H, and removes completely the discrepancy when taken into account.For the case of Li 7 a calculation of the scattering cross section was made by Willey, 9 using known wave functions for the ground state of Li 7 . The calculations were made for a LS coupling and for an odd-proton model. J. D. Walecka and R. H. Pratt (private communication). R. Willey (private communication). EXPERIMENTAL PROCEDURE AND RESULTST HE 17-h Re 188 was purchased from the Oak Ridge National Laboratory as processed, high specific activity (^20 mC/ml) 91-h Re 186 . At the time of assay before leaving Oak Ridge the Re 188 activity was approximately one-third of the total activity. Sources were prepared by evaporation of the nitric acid solution of the HRe04 on 0.25-mil Mylar backing. The sources were transparent. They were grounded by a thin f Supported in part by a grant from the National Science Foundation (G6337).The results are listed below for 41.5 MeV:LS model 3.70 X 10~3 2 cm 2 /sr; Odd-proton model, 5,71X10 -32 cm 2 /sr; Formula (4), 7.1X10" 32 cm 2 /sr; Experiment, 5.6X10 -32 cm 2 /sr.Although the magnetic moment in Li 7 is in agreement with the predictions of the LS model, the old proton model is considerably better than the LS model in predicing the scattering results. The case of He 4 is very special because the absence of magnetic scattering can yield information on an electric dipole moment of the electron. It will be discussed in another publication. 10 Further work on the lighter nuclei with higher electron energies would be very interesting because of the expected sharp decrease in cross section due to the effect of the magnetic form factors.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.