FIG. 4: Measured parallel momentum distributions for the ground state and the states at 4382, 4766, 4960 and 5096 keV (displayed in red in the level scheme) of \( ^ { 3 5 } \mathbf { P } \). The bottom panel shows that for \( ^ { 3 6 } \mathbf { P } \) nucleus, as produced from \( ^ { 3 6 } \mathrm { S } \). The verti-cal dashed line, crossing all panels, represents the centroid of the momentum distribution of \( ^ { 3 6 } \mathbf { P } \) nucleus, \( p _ { 0 } \), shifted by the evaporation of a neutron, i.e. \( p _ { 1 } \)=(A-1)/A \( p _ { 0 } \). It is seen that the distributions for all states labeled red in the level scheme are shifted relative to that of the \( ^ { 3 5 } \mathrm { P } \) ground state, that is produced via direct one-proton knockout.

section of about 2.5 mb was measured at similar beam energy for the sd-shell nucleus \( { } ^ { 2 2 } \mathrm { M g } \) [32]. It follows that the TS mechanism would have a rather low cross section, of the order of 0.10 mb, that is a factor of 20 lower than we observe for the sum over all states with shifted mo-mentum distributions. It is therefore likely that a more direct process is needed to account for the measured cross section.

Charge-exchange reactions occur more favorably with an allowed GT operator (\( \Delta L \)=0,\( \Delta J = \)=0 \( , \pm \) 1, \( \Delta \pi \)=no) that would lead to the production of \( 1 + \) states in \( ^ { 3 6 } \mathbf { P } \) starting from the \( 0 ^ { + } \) ground state of \( ^ { 3 6 } \mathrm { S } \). Higher momen-tum transfers are also observed when very strict kine-matic condition for the reaction as well as suitable target excitations cannot be selected, as in the present exper-iment. Moreover, having a closed neutron sd shell, the exchange of an sd proton to an sd neutron orbital that would lead to \( 1 ^ { + } \) states in \( ^ { 3 6 } \mathrm { S } \) is strongly hindered by Pauli blocking. Rather, transfer to the f p or to the high-est \( g - s d \) orbits must become largely competitive. The non-feeding of any of the known \( 1 + \) states in \( { } ^ { 3 6 } \mathrm { P } \) but the population of the negative parity states \( 4 ^ { - } \) (g.s.), \( 3 ^ { - } \) (250 keV) and of the tentatively assigned \( 2 ^ { - } \) (425 keV) through low-energy charge-exchange reactions of Ref. [33] are in line with the above assumptions. In the present experiment, several \( \gamma \) rays are observed in coin-cidence with \( ^ { 3 6 } \mathbf { P } \) (see Fig. 5). However, none of them arise from the deexcitation of the \( ^ { 1 + } \) states at 1303 keV and 2281 keV that were populated in the \( \beta \) decay of \( ^ { 3 6 } \mathrm { S i } \) to \( { } ^ { 3 6 } \mathrm { \mathbf { C } } \) [34] and whose decay occurs through \( \gamma \) rays of 878 keV and (934, 977, 1858 keV), respectively, as in Ref. [33]. Even if the present statistics does not allow ex-tracting \( \gamma \)-\( \gamma \) coincidences, the observation of transitions at 250 keV and about 170 keV suggest the feeding of the \( 3 ^ { - } \) and \( 2 ^ { - } \) states, respectively. Other transitions are ob-served, but none (except perhaps the 2020(20) keV from[35]) were reported in previous works. Interestingly, one transition is seen at 4050 keV, i.e. about 600 keV above the neutron emission threshold of 3.465 MeV. This state seems to decay preferentially through a \( \gamma \)-ray transition rather than neutron decay to the \( 1 / 2 ^ { + } \) ground state of \( ^ { 3 5 } \mathrm { P } \).

FIG. 5: Doppler-corrected \( \gamma \)-decay spectrum for the \( ^ { 3 6 } \mathrm { { P } } \) nu-cleus populated from \( ^ { 3 6 } \mathrm { S } \) in a nucleon-exchange reaction.

The last hypothesis is that these momentum-shifted distributions result from the proton knockout from a state excited in inelastic scattering. Such a TS reaction was discussed as one possibility to account for the obser-vation of a \( \gamma \)-decaying neutron-unbound state in \( ^ { 3 5 } \mathrm { S i } \) at 3.611 MeV (\( S _ { n } \)=2.470(40) MeV) populated in the \( ^ { 3 6 } \mathrm { S i } \)(−1n) reaction [22]. As shown in Fig. 4 of Ref. [22], the momentum distribution associated with the production of this unbound state appears to lie dominantly in the low-momentum tail of the \( ^ { 3 5 } \mathrm { S i } \) distribution, possibly in-dicating that its centroid is shifted to lower momentum. The production of such a state was evaluated in Ref. [22]to be of 0.8(2) mb, a value that is comparable to the par-tial cross sections for the states which are observed with a

shifted momentum distribution in our work. A total cross section of 2.4(4) mb is indeed obtained by summing over the four states represented in red in Fig. 2. Contrary to the case presented in Ref. [22], the states here possibly produced by the same TS mechanism are below the neu-tron separation energy. This could be due to the fact that the neutron emission threshold of \( ^ { 3 5 } \mathrm { P } \) (\( S _ { n } \)=8.380 MeV) is much higher than the one of \( ^ { 3 5 } \mathrm { S i } \) (\( S _ { n } \)=2.470 MeV).

# VI. CONCLUSIONS

The spectroscopy of \( { } ^ { 3 5 } \mathbf { P } \) was investigated with an intermediate-energy one-proton knockout reaction using a secondary beam of \( ^ { 3 6 } \mathrm { S } \) interacting with a \( ^ { 9 } \mathrm { B e } \) foil at 88 MeV/u mid-target energy. The \( { } ^ { 3 5 } \mathbf { P } \) nuclei were selected by the S800 spectrograph at NSCL and identified in the spectrograph’s focal plane in coincidence with prompt \( \gamma \) rays detected in the GRETINA segmented Ge array around the target. The level scheme of \( { } ^ { 3 5 } \mathrm { P } \) has been es-tablished up to about 7.5 MeV from \( \gamma - \)\( \gamma \) coincidences and relative \( \gamma \) intensities. Spins and parities for most of the populated states were proposed from a comparison be-tween calculated and measured \( \gamma \)-gated momentum dis-tributions for the population of individual final states in \( { } ^ { 3 5 } \mathrm { P } \). Spectroscopic factor values, \( C ^ { 2 } S , \), were derived from partial cross sections for the \( 1 / 2 ^ { + } \) ground state and the excited states \( ( 3 / 2 ^ { + } \),\( 5 / 2 ^ { + } \) and tentatively \( 1 / 2 ^ { - } \)) in \( { } ^ { 3 5 } \mathrm { P } \). An inclusive cross section of 51(1) mb was measured for

\[ ^ { 3 5 } \mathbf { P } \]

produced from

\[ ^ { 3 6 } \mathrm { S } \]

. The extracted summed \( \sum C ^ { 2 } S \) values agree with expected shell-model occupancies of the protons in the \( 2 s _ { 1 / 2 } \) (\( \sum C ^ { 2 } S = \) 2.2(\( 7 ) \)), \( 1 d _ { 3 / 2 } \) (0.7(3)), \( 1 d _ { 5 / 2 } \) (5.2(9)) or-bitals, while only a fraction (0.41(17)) of the strength corresponding to the deeply-bound \( 1 p _ { 1 / 2 } \) orbit is tenta-tively observed for two states above 5.6 MeV.

The present results were compared to those obtained for \( { } ^ { 3 5 } \mathrm { \mathbf { P } } \) using the \( ^ { 3 6 } \mathrm { S } ( d , ^ { 3 } \mathrm { H e } ) { } ^ { 3 5 } \mathrm { P } \) transfer reaction at low energy. Remarkable agreement is found for the proposed level scheme populated, the spin assignments (except for one state) and the deduced \( C ^ { 2 } S \) values. Since ob-tained from high-resolution \( \gamma \)-ray spectroscopy, the ex-citation energies of the presently identified states in \( { } ^ { 3 5 } \mathrm { P } \) are more accurate than those obtained in the \( ( d , { ^ { 3 } \mathrm { H e } } ) \) reaction [16]. They agree with the values obtained in a multi-nucleon transfer reaction [25], for which several states were observed in common. The present sensitiv-ity of the knockout reaction, with a projectile beam of 2 \( \cdot \bar { 1 0 ^ { 5 } } \) pps, matches the one obtained in the \( ( d , { ^ 3 } \mathrm { H e } ) \) reac-tion with a d beam on a stable \( ^ { 3 6 } \mathrm { S } \) target. This reinforces the enormous potential of this experimental technique in extracting level schemes, orbital angular momenta, and \( C ^ { 2 } S \) values.

Besides the observation of states that were expected to be produced in the knockout of protons from the \( p - s d \) shell, other states with likely high spin value (\( J \ge 5 / \) 2) and negative parity are observed as well, with a summed partial cross section of about 2.4 mb. Owing to the facts that these states were not observed in the \( ( d , { ^ { 3 } \mathrm { H e } } ) \)) re-action and that they exhibit parallel-momentum distri-butions that are down-shifted as compared to the ones from knockout, we propose that they are produced by an-other mechanism that could be either a charge-exchange or a two-steps mechanism in which a core excitation is followed by a proton knockout. While so far we can-not clearly identify which of these two mechanisms is the most probable, it interestingly leads to the production of states most likely corresponding to neutron-core excita-tions. This feature may be very interesting to single-out intruder states belonging to the so-called island of inver-sion, as evoked in Refs. [22, 37].

# Acknowledgments

This work is supported by the National Science Foun-dation (NSF) under Grant Nos. PHY-1102511 and PHY-1306297 and by the Institut Universitaire de France. GRETINA was funded by the US DOE - Office of Sci-ence. Operation of the array at NSCL is supported by NSF under Cooperative Agreement PHY-1102511 (NSCL) and DOE under grant DE-AC02-05CH11231 (LBNL). O.S wish to thank T. Duguet for fruitful dis-cussions. J.A.T acknowledges support of the Science and Technology Facility Council (UK) grant ST/L005743.