Spectroscopic amplitudes for one-nucleon transfer between 1p0f-shell nuclei

Abstract

Abstract. Spectroscopic amplitudes are calculated for one-nucleon transfer between low-lying, normal-parity states of nuclei in the lower part of the 1p0 f-shell. Calculations are performed using shell-model wave functions obtained from the diagonalization procedure of a nuclear Hamiltonian in the space given by the complete set of states generated from the 1p 3/2 , 1p 1/2 , 0 f 7/2 and 0 f 5/2 orbits. The Hamiltonian contains one and two body interactions derived recently by Richter et al . Sum rules for one-nucleon pick-up and stripping reactions are given. The selectivity in excitation of the final states induced by one-nucleon pick-up or stripping is discussed.

The Path to Improved Reaction Rates for Astrophysics

“…Comparing (62) with (48) and (54) it is readily seen that the statistical model cross section is an averaged Breit-Wigner cross section for narrow resonances, when W = 1. Completely equivalently to the Breit-Wigner case, it can be shown that for the calculation of the stellar rate it is sufficient to replace T µ by T Aa in (62) and divide the resulting integral by the normalized partition function G A 0 , giving 13…”

“…Since they do not seem to be so well known in Nuclear Astrophysics and their implications also have to be interpreted in terms of stellar cross sections and astrophysical reaction rates, it is helpful to outline briefly the main points here. By comparison to (62) and (63) we find that (14) transforms to…”

“…In the absence of experimental data, the spectroscopic factor can be calculated microscopically from the overlap between initial and final state wave functions, e.g., in the shell model. 75,76,203,62,240,63 However, there is some ambiguity because this overlap is not well defined in different microscopic approaches. 60,77 It has been shown that the spectroscopic factors for depositing or picking up a single nucleon are related to the occupation factors of the participating quasi-particle states (see also Sec.…”

“…Both resonance energies and spectroscopic factors should, in principle, be predictable in the shell model (see, e.g., Refs. 62,63,64) or other microscopic theories but this is currently not feasible for all nuclei across the nuclear chart. Different approaches yield results which differ more than it is tolerable in the calculations of astrophysical reaction rates.…”

O18 -induced single-nucleon transfer reactions on Ca40 at 15.3<

“…where χ (±) α,β are the outgoing and incoming distorted waves in the entrance and exit partitions, V α,β is a suitable effective interaction potential, and ψ b |ψ a and ψ B |ψ A are the projectile-ejectile and target-residual overlap functions. The latter, assuming the fractional parentage decomposition B = A + x with x the transferred nucleon, can be written as [52]…”