Experimental Study of the Two-Body Spin-Orbit Force in Nuclei

Abstract

Energies and spectroscopic factors of the first 7=2 − , 3=2 − , 1=2 − , and 5=2 − states in the 35 Si 21 nucleus were determined by means of the (d, p) transfer reaction in inverse kinematics at GANIL using the MUST2 and EXOGAM detectors. By comparing the spectroscopic information on the 35 Si and 37 S isotones, a reduction of the p 3=2 -p 1=2 spin-orbit splitting by about 25% is proposed, while the f 7=2 -f 5=2 spin-orbit splitting seems to remain constant. These features, derived after having unfolded nuclear correlations using shell model calculations, have been attributed to the properties of the two-body spin-orbit interaction, the amplitude of which is derived for the first time in an atomic nucleus. The present results, remarkably well reproduced by using several realistic nucleon-nucleon forces, provide a unique touchstone for the modeling of the spin-orbit interaction in atomic nuclei. Introduction.-The spin-orbit (SO) interaction, which originates from the coupling of a particle spin with its orbital motion, plays an essential role in quantum physics. In atomic physics it causes shifts in electron energy levels due to the interaction between their spin and the magnetic field generated by their motion around the nucleus. In the field of spintronics, spin-orbit effects for electrons in materials [1] are used for several remarkable technological applications. In atomic nuclei, the amplitude of the SO interaction is very large, typically of the order of the mean binding energy of a nucleon. It is an intrinsic property of the nuclear force that must be taken into account for their quantitative description.An empirical one-body SO force was introduced in atomic nuclei in 1949 [2] to account for the magic numbers and shell gaps that could not be explained otherwise at that time. In this framework each nucleon experiences a coupling between its orbital momentum l⃗ and intrinsic spin ⃗ s. This ls coupling is attractive for nucleons having their orbital angular momentum aligned with respect to

Spin-orbit interaction in relativistic nuclear structure models

“…The isovector contribution is, of course, also responsible for the difference between the effective proton and neutron single-particle potentials, while the radial (density) profiles depend on the shell structure of occupied orbitals in the self-consistent solution for a particular nucleus. In this respect, especially interesting is the case of 34 Si, for which a possible central depletion of the proton density distribution has been analysed using a variety of theoretical approaches [26,27], and experimental constraints on the strength of the two-body spin-orbit interaction have been reported [15,28]. For the effective interaction DD-MEδ that explicitly includes contributions from both ρ and δ meson exchange in the direct term, the isovector channel of the spin-orbit potential is enhanced when compared to DD-ME2, although in both models the total isovector part of the spin-orbit potential is an order of magnitude weaker than the isoscalar contribution [20].…”

Spin-orbit splittings of neutron states inN=20isotones from covariant density functionals and their extensions

“…It is clearly stated in Refs. [19,20] that the results of these two experiments are ideal for a further theoretical investigation of the SO force deduced from the various nuclear density functionals. In particular, the extreme neutron-to-proton density asymmetry in the case of 34 Si and the subsequent large and abrupt reduction in the size of the p-spitting, can provide a better constraint of the SO force, since these results isolate the contributions coming mostly from its density and its isospin dependence.…”

“…state and compare its energy directly with the experimental results from Ref. [19], as shown in table VII. This is also done schematically in Fig.…”

“…For comparison we show the combined results from the experiments in Refs. [19,20]. This helps to distinguish amongst the various models.…”

“…[19] was conducted attempting to set an additional constraint on the strength of the spin-orbit force. Comparing these results with earlier experiments of nuclei within the N = 20 isotone chain such as in [22,23], one was able to evaluate a reduction in the 2p 3/2 −2p 1/2 splitting.…”