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Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in theisotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values werereported by using the major fragments of the states. An important reduction ofthe $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to astrong modification of the spin--orbit potential in the central region of thenucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings inthe $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ severalSkyrme and Gogny interactions, to reliably isolate pure spin--orbit andtensor--induced contributions, within the mean--field approximation. We useinteractions (i) without the tensor force; (ii) with the tensor force and withtensor parameters adjusted on top of existing parametrizations; (iii) with thetensor force and with tensor and spin--orbit parameters adjusted simultaneouslyon top of existing parametrizations. We predict in cases (ii) and (iii) a nonnegligible reduction of both $p$ and $f$ splittings, associated toneutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittingsare further decreased for the three types of interactions, going from $^{36}$Sto $^{34}$Si. This reduction is produced by the spin--orbit force and is notaffected by tensor--induced contributions. For both reductions, from $^{40}$Cato $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that themodification is more pronounced for $p$ than for $f$ splittings. Themeasurement of the centroids for neutron $2p$ and $1f$ states in the nuclei$^{36}$S and $^{34}$Si would be interesting to validate this predictionexperimentally. We show the importance of using interactions of type (iii),because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which arein agreement with the corresponding experimental values.

Neutron $2p$ and $1f$ spin--orbit splittings in $^{40}$Ca, $^{36}$S, and $^{34}$Si $N=20$ isotones: tensor--induced and pure spin--orbit effects