Appendix A: Aspects of the shell model wave functions — Reduced matrix elements

2021 ◽  
pp. 405-417

2006 ◽  
Vol 73 (6) ◽  
Author(s):  
P. Navrátil ◽  
C. A. Bertulani ◽  
E. Caurier


1974 ◽  
Vol 49 (5) ◽  
pp. 443-446 ◽  
Author(s):  
L. Bimbot ◽  
I. Brissaud ◽  
Y. Le Bornec ◽  
B. Tatischeff ◽  
N. Willis ◽  
...  


1987 ◽  
Vol 65 (6) ◽  
pp. 691-698 ◽  
Author(s):  
O. Häusser

We present here recent [Formula: see text] results from TRIUMF that are relevant to the determination of spin-flip isovector strength functions in nuclei. Distortion factors needed for the extraction of nuclear-structure information have been deduced from cross sections and analyzing powers in elastic scattering for several energies and targets. Nonrelativistic optical potentials obtained by folding effective nucleon (N)–nucleus interactions with nuclear densities are found to overpredict both elastic and reaction cross sections, whereas Dirac calculations that include Pauli blocking are in good agreement with the data. Spin observables (Snn and Ay) for the quasi-elastic region in 54Fe[Formula: see text] at 290 MeV provide some evidence for the reduction of the effective proton mass predicted in relativistic mean-field theories as a consequence of the attractive scalar field in the nuclear medium. The energy dependence of the effective N–nucleus interaction at small momentum transfers has been investigated using isoscalar and isovector 1+ states in 28Si as probe states. We find that the cross sections for the isovector transitions are in good agreement with predictions for the dominant Vστ part of the Franey–Love interaction. Gamow–Teller (GT) strength functions have been obtained in 24Mg and 54Fe from measurements of both cross sections and spin–flip probabilities Snn. The spin-flip cross sections σSnn are particularly useful in heavier nuclei to discriminate against a continuous background of ΔS = 0 excitations. In the (s, d) shell where full shell-model wave functions are available, the GT quenching factors [Formula: see text] are in good agreement with those from recent (p, n) and (n, p) experiments. We show that a state-by-state comparison of (p, p′) and (e, e′) results has the potential of identifying pionic current contributions in (e, e′). The GT quenching factors in 54Fe are smaller than in the (s, d) shell probably because of severely truncated shell-model wave functions, particularly those of the nuclear ground state.



A method is derived for calculating matrix elements of a two-body interaction in wave functions which were classified in part I interms of the group U 2- . For simplicity, a Cartesian basis of intrinsic functions is introduced in which the one-dimensional oscillators in x, y and z are separately diagonal. An application to 24 Mg in L-S coupling shows very little mixing of the quantum number K but an appreciable (10 to 20 %) mixing of U 3 representations (λμ). Overall agreement with experiment is quantitatively only tolerable but the main pattern of the spectrum is undoubtedly given by the lowest representation (84). On this basis, suggestions are made concerning the type of spectra to be expected for even and odd parity levels of the even-even nuclei in the mass region 16 < A < 40.



1972 ◽  
Vol 39 (2) ◽  
pp. 176-178 ◽  
Author(s):  
G.R. Hammerstein ◽  
Duane Larson ◽  
B.H. Wildenthal


1972 ◽  
Vol 42 (2) ◽  
pp. 153-156 ◽  
Author(s):  
Duane Larson ◽  
S.M. Austin ◽  
B.H. Wildenthal


1993 ◽  
Vol 48 (6) ◽  
pp. 2673-2678 ◽  
Author(s):  
H. F. Wu ◽  
C. L. Song ◽  
H. Q. Song


1966 ◽  
Vol 82 (2) ◽  
pp. 337-353 ◽  
Author(s):  
S.N. Tewari ◽  
M.K. Banerjee


1960 ◽  
Vol 14 (3) ◽  
pp. 349-375 ◽  
Author(s):  
Th. Kanellopoulos ◽  
K. Wildermuth


2010 ◽  
Vol 81 (5) ◽  
Author(s):  
A. C. Hayes ◽  
A. A. Kwiatkowski


Sign in / Sign up

Export Citation Format

Share Document