In-beam gamma-ray spectroscopy at the proton dripline: 23Al

We report on the first in-beam $\gamma$-ray spectroscopy of \nuc{23}{Al} using two different reactions at intermediate beam energies: inelastic scattering off \nuc{9}{Be} and heavy-ion induced one-proton pickup, \nuc{9}{Be}(\nuc{22}{Mg},\nuc{23}{Al}$+\gamma$)X, at 75.1 MeV/nucleon. A $\gamma$-ray transition at 1616(8) keV -- exceeding the proton separation energy by 1494 keV -- was observed in both reactions. From shell model and proton decay calculations we argue that this $\gamma$-ray decay proceeds from the core-excited $7/2^+$ state to the $5/2^+$ ground state of \nuc{23}{Al}. The proposed nature of this state, $[\nuc{22}{Mg}(2^+_1) \otimes \pi d_{5/2}]_{7/2+}$, is consistent with the presence of a gamma-branch and with the population of this state in the two reactions.

Since its discovery in 1969 [1], the neutron-deficient nucleus 23 Al has attracted much attention. 23 Al is four neutrons removed from stable 27 Al and is the last protonbound, odd-mass aluminum isotope known to exist. The low proton separation energy of S p = 122 (19) keV [2] made 23 Al an initial a candidate for a proton halo system. From the measurement of an enhanced reaction cross section, 23 Al was indeed proposed to have a proton-halo structure with a J π = 1/2 + assignment suggested for the spin and parity of the ground state [3,4]. However, a βNMR measurement clearly showed that the spin and the parity of the 23 Al ground state are J π = 5/2 + [5], in agreement with the mirror nucleus 23 Ne. Excited states of 23 Al have been studied in 24 Mg( 7 Li, 8 He) 23 Al reactions [6,7], in β-delayed proton decay [8], in Coulomb breakup [9] and most recently in 22 Mg+p resonant proton scattering [10]. None of these prior experiments was sensitive to γ-ray transitions in 23 Al. In the present paper we report on the first in-beam γ-ray spectroscopy study of 23 Al. Two complementary reactions were used to excite 23 Al: inelastic scattering off a 9 Be target at large momentum transfer and the heavy-ion induced one-proton pickup reaction, 9 Be( 22 Mg, 23 Al+γ)X.
Both measurements were performed with an exotic cocktail beam composed of 32% 22 Mg and 3% 23 Al. This secondary beam was produced in-flight by fragmentation of a 150 MeV/nucleon 36 Ar primary beam delivered by the Coupled Cyclotron Facility at NSCL on the campus of Michigan State University. The primary 9 Be production target (893 mg/cm 2 thick) was located at the midacceptance target position of the A1900 fragment separator [11]; an achromatic aluminum wedge degrader of 300 mg/cm 2 thickness and momentum slits at the dispersive image of the separator were used to select the secondary beam. The slits were restricted to ∆p/p=0.5% total momentum acceptance for the secondary beam.
The 9 Be( 23 Al, 23 Al+γ) 9 Be inelastic scattering and the 9 Be( 22 Mg, 23 Al+γ)X one-proton pickup reaction were induced by a 188(4) mg/cm 2 9 Be target placed at the target position of the S800 spectrograph [12]. The reaction target was surrounded by SeGA [13] in its "classic" configuration with nine and seven detectors, respectively, at central angles of 90 • and 37 • with respect to the beam axis. The SeGA high-purity germanium detectors are 32fold segmented and allow for an event-by-event Doppler reconstruction of the γ-rays emitted in-flight by the reacted nuclei. The emission angle that enters the Doppler reconstruction is determined from the location of the segment with the largest energy deposition relative to the target.
Event-by-event particle identification was performed in all entrance and exit channels with timing detectors before the reaction target and with the focal-plane detection system [14] of the S800 spectrograph. The time-of-flight difference measured between the two plastic scintillators located before the reaction target allowed for an unambiguous identification of all constituents of the incoming cocktail beam (see Fig. 2 of [15] and Fig. 1 of [16]). The reaction residues emerging from the 9 Be target were identified via their time-of-flight measured by plastic scintillators and their energy loss determined with the S800 ion chamber. A software gate on the incoming beam then allowed the selection of only those reaction residues induced by the projectile of interest (see also refs. [15,16]). Fig. 1(a) shows the particle identification spectrumenergy loss vs. time-of-flight -for the spectrograph setting that was optimized on the one-proton pickup channel. The particle identification spectrum only contains reaction products from 22 Mg. The one-proton pickup residue 23 Al can be clearly separated from the fragmentation products that enter the S800 focal plane as well. γ-ray spectrum in coincidence with 23 Al produced in the one-proton pickup reaction. A photopeak at 1614(9) keV is clearly visible and marks a γ-ray transition in 23 Al. FIG. 2: Doppler-reconstructed γ-ray spectrum detected in coincidence with 23 Al reaction residues produced in one-proton pickup (upper panel) and inelastic scattering (lower panel). The energy uncertainty is dominated by the uncertainty in the target position which is systematic and common for both measurements. Fig. 3(a) shows the particle identification of the inelastically scattered 23 Al. The spectrograph setting was optimized on the one-neutron knockout reaction 9 Be( 24 Si, 23 Si)X which is discussed in [16]. For a singleneutron knockout setting in this mass region, the magnetic rigidity of the spectrograph is more than 4% lower than for a setting centered on the projectiles passing through the target. Thus only the low-momentum tail of the scattered 23 Al projectiles can enter the spectrograph as displayed in Fig. 3(b). In coincidence with these scattered 23 Al nuclei, that must have been subject to a significant momentum transfer, to be found in the outmost low-momentum tail of the distribution, a γ-ray transition was observed at 1618(8) keV ( Fig. 2(b)). Due to the magnetic rigidity setting optimized on reaction residues with one neutron less than the projectile, only the low-momentum tail of scattered 23 Al enters the focal plane.
The observed γ-ray energy is consistent for the two measurements and implies an excited state at 1616(8) keV in 23 Al, 1494 keV above the proton separation energy. This state has a significant γ-ray branch to the proton-bound ground state. If this γ-ray transition were to originate from an even higher excited state it would either populate a proton-unbound excited state and could not have been observed here as a coincidence with 23 Al is required or would feed an excited state that also has a significant γ-ray decay branch which then should have been detected as well.
All excited states of 23 Al are reported to decay to 100% by proton emission, including the first excited state, E(1/2 + ) = 550(20) keV, with Γ p /Γ γ ∼ 10 8 [17]. Figure 4 compares the level schemes of the mirror nuclei 23 Al and 23 Ne below 2.3 MeV excitation energy. We tentatively assign spin and parity J π = (7/2 + ) to the excited state at 1616 (8) keV observed in the present work. There is a one-to-one correspondence for the states below 2.3 MeV. The energy difference of the 1/2 + first excited state can be explained by the Thomas-Ehrman shift [18] which influences ℓ = 0 orbits the most. In the following we discuss the structure of the proposed 7/2 + state, in particular the occurrence of a significant γ-ray branch, within the USD shell model and argue the consistency of this assignment with the reaction mechanisms that led to its observation. Shell-model calculations for the energies, spectroscopic factors and electromagnetic matrix elements were carried out with the USDB effective interaction (results with USDA were similar) [19]. The calculated half-life of the 7/2 + state, T 1/2 = 23 fs, corresponds to a γ width of Γ γ = 0.020 eV. The spectroscopic factor for the d 5/2 orbit connecting the 23 Al, J π = 7/2 + and 2 Mg, J π = 2 + levels is large indicating a dominance of the 22 Mg, [ 22 Mg(2 + 1 ) ⊗ d 5/2 ] 7/2 + configuration in the wavefunction. From the energetics summarized in Fig. 5, it follows that the Q-value for this decay is Q p = 244(21) keV. To quantify the proton decay of the 7/2 + state, the proton scattering cross section was calculated for ℓ = 2 at Q p = 244 keV with a Woods-Saxon potential and the resulting resonance width was used as the single-particle proton decay width, Γ sp p = 0.0024 eV. With the value S = 0.46 for the 7/2 + to [ 22 Mg(2 + 1 ) ⊗ d 5/2 ] spectroscopic factor, from the USDB shell-model calculations, this yields a proton decay width of Γ p = S × Γ sp p = 0.0011 eV for the decay of the 7/2 + state of 23 Al to the first excited 2 + state of 22 Mg. In conclusion, the proposed structure of the 7/2 + state, together with the energetics of the proton decay (see Fig. 5), results in Γ γ /Γ p ∼ 20 consistent with the observation of the γ-decay of this state. We note that proton detection was not possible with our experimental setup. Furthermore, 22 Mg residues populated by the proton decays of excited states of 23 Al could not be distinguished from 22 Mg produced by the fragmentation of the 23 Al projectiles, for example. Proton decay to the 22 Mg ground state could proceed by ℓ = 4. The singleparticle proton decay width from the potential scattering calculations for ℓ = 4 with Q p = 1.49 MeV is 10 eV. If we assume that the proton width is approximately less than or equal to the gamma width then S ≤ 0.002 for the g 7/2 spectroscopic fractor. Thus, the g-orbital admixture into the sd model space is very small.
In our experiment, the state at 1616 keV was excited in the inelastic scattering of 23 Al from a 9 Be target. In odd-A nuclei, core-coupled states are most likely excited in inelastic scattering processes or Coulomb excitation. This is consistent with the spin and parity assignment of J π = 7/2 + for this state and the proposed structure discussed above.
However, our analysis was restricted to scattering events with a large momentum loss, as only the lowmomentum tail of the scattered 23 Al nuclei was within the acceptance of the S800 spectrograph. To probe which states are excited in the scattering at the largest momentum transfer, the inelastic scattering of 22 Mg under identical conditions was analyzed. In the same reaction setting where the low-momentum tail of the 23 Al projectile distribution passing through the target was used to study the inelastic scattering, the low-momentum tail of the 22 Mg projectiles within the same cocktail beam entered the focal plane as well. The event-by-event Doppler reconstructed γ-ray spectrum in coincidence with these inelastically scattered 22 Mg projectiles is shown in Fig. 6. The photopeaks of the 2 + 1 → 0 + 1 and 4 + 1 → 2 + 1 γ-ray transitions are clearly visible. The intensities show that, predominantly, the 2 + 1 state of 22 Mg is excited in the inelastic scattering of 22 Mg projectiles from the 9 Be target. This is again consistent with the proposed structure of [ 22 Mg(2 + 1 ) ⊗ d 5/2 ] for the 1616 keV state excited in the inelastic scattering of 23 Al.
The proposed (7/2 + ) excited state in 23 Al was also populated in the one-proton pickup reaction 9 Be (  with fast exotic beams for spectroscopy has recently been investigated at the NSCL with the reaction 9 Be( 20 Ne, 21 Na+γ)X [21]. In that case, the pattern of the observed population of 21 Na single-proton states was found to be consistent with distorted wave transfer reaction calculations and shell-model theory. There also, a core-coupled 7/2 + state was observed in 21 Na, with a partial cross section of 0.20(5) mb from an inclusive cross section of 1.85(12) mb [21]. While unobserved feeding from higher-lying states could not be excluded, the direct population of this state with a complex structure would indicate the presence of higher-order processes, as for example the pickup onto 20 Ne in its 2 + 1 excited state. For the one-proton pickup to 23 Al, the subject of the present paper, an inclusive cross section of σ = 0.54(5) mb was measured for the 9 Be( 22 Mg, 23 Al)X reaction. From the γ-ray intensity, a partial cross section of σ(7/2 + ) = 0.07(2) mb was determined. The populations of the core-excited 7/2 + states in 21 Na [21] and 23 Al (present work), at about 11% and 14%, respectively, are consistent for the two measurements and suggestive of the proposed assignment in 23 Al. The low-momentum tail of the 23 Al one-proton pickup residue distribution (evident in Fig. 1(b)) is also indicative of the presence of multi-step or unbound 8 Li final state contributions in the reaction process. The population of other (single-proton) states in 23 Al, other than the 5/2 + ground and 7/2 + excited state could not be observed as these states decay by proton emission [17].
A reaction analysis of the present 9 Be( 22 Mg, 23 Al )X proton pickup data was performed within the finiterange, post form of the coupled channels Born approximation (CCBA) using the direct reactions code fresco [22]. Single-step 1d 5/2 proton transfer onto 22 Mg(J π ) core states was assumed (from 9 Be) according to the coupling scheme shown in Figure 7. It was also assumed (see Ref. [21]) that the final states were two-body. Thus the basic proton pickup mechanism is computed as 22 Mg( 9 Be, 8 Li(I + )) 23 Al(j π ) leading to the I π = 1 + , 2 + and 3 + states of 8 Li at 75.1 MeV per nucleon incident energy. The (absorptive) nuclear interactions were calculated, as in recent nucleon knockout reaction studies, by double folding the neutron and proton densities of 22 Mg (from Hartree-Fock calculations) and of 9 Be (assumed a Gaussian with rms radius of 2.36 fm) with an effective nucleon-nucleon (NN) interaction [23]. The 22 Mg was allowed to inelastically excite by deforming the entrance channel distorting potential, taking a deformation length δ 2 = 1.95 fm. This corresponds to an assumed 22 Mg mass β 2 value of 0.58; this is taken from the charge β 2 value 0.58 (11) of Ref. [24]. The (light) target-like vertices, [ 8 Li(I + ) ⊗ Φ j ] 3/2 − , were treated as in Ref. [21], making use of the Variational Monte Carlo (VMC) overlaps and spectroscopic amplitudes [25]. The required proton-core projectile overlaps, [ 22 Mg(J π )⊗π1d 5/2 ] j , and their spectroscopic amplitudes were guided by the USDB shell model calculations. As is noted in Fig. 7 there are interfering spectroscopic amplitudes α and β for population of the 23 Al(gs) via the [ 22 Mg(0 + ) ⊗ π1d 5/2 ] 5/2 and [ 22 Mg(2 + ) ⊗ π1d 5/2 ] 5/2 transfers, respectively. The 23 Al(7/2 + ) state is populated by [ 22 Mg(2 + ) ⊗ π1d 5/2 ] 7/2 . The USDB shell model spectroscopic factors of these overlaps are S=0.33, 0.84 and 0.46, respectively. The associated π1d 5/2 single particle states were calculated in real Woods-Saxon potential wells with radius and diffuseness parameters r 0 = 1.25 fm and a 0 = 0.7 fm and a spin-orbit interaction of strength 6 MeV with the same geometry parameters. The bound π1d 5/2 configurations used the physical separation energies. The very narrow resonant π1d 5/2 state, relevant to the 7/2 + transition with S p = −244 keV, was accurately described by a bound proton state with separation energy of S p = +5 keV.
The calculated yields, inclusive with respect to the three 8 Li(I + ) final state contributions, were as follows.
The cross section for direct population of the 23 Al(7/2 + ) state is 0.022 mb, underproducing the measured yield of 0.07(2) mb. The calculations were also sensitive to the relative phase of the spectroscopic amplitudes α and β that feed the 23 Al(gs), Fig. 7. The shell-model calculations for the spectroscopic amplitudes together with the electromagnetic matrix element, predicts that these paths interfere destructively to give 23 Al(gs) and inclusive cross sections of 0.26 and 0.28 mb, the latter to be compared with the experimental value of 0.54(5) mb. Inelastic 5/2 + → 7/2 + (single particle) coupling in 23 Al, shown in Fig. 7, was found to have negligible effect on the calculated 23 Al(7/2 + ) yield. We conclude that the relative yields of the 23 Al(5/2 + ) and 23 Al(7/2 + ) are reasonably reproduced by the model calculations. The inclusive cross section is a factor two smaller than that measured. These lower cross sections were not unexpected since we include only the three (lowest) 8 Li final states with summed spectroscopic factors of 0.97 (p 3/2 ) and 0.36 (p 1/2 ). Further consideration of strength leading to the 8 Li continuum is needed to assess the absolute cross sections. As was noted above, the low-momentum tail seen in the 23 Al distribution in Fig. 1 suggests a significant missing dissipative mechanism such as coupling to the 8 Li continuum.
In summary, the γ-decay of an excited state in 23 Al has been observed for the first time in (i) 23 Al inelastic scattering from 9 Be at large momentum transfer and (ii) in the heavy-ion induced one-proton pickup reaction 9 Be( 22 Mg, 23 Al+γ)X. The corresponding excited state at 1616(8) keV lies 1494 keV above the proton separation energy of 23 Al. The presence of the γ-ray decay branch and the population of this state in the two reaction mechanisms is consistent with the state being the 7/2 + coreexcited configuration, [ 22 Mg(2 + 1 )⊗d 5/2 ] 7/2 + , predicted by the shell model to be the second excited state. We have shown that the proton decay of this state, which will proceed by emission of a proton from the d 5/2 orbit to the first 2 + state of 22 Mg, is hindered by the small Q-value of Q p = 244(21) keV. A branching ratio of Γ γ /Γ p ∼ 10 is estimated from shell model and proton decay calculations.
This work was supported by the National Science Foundation under Grants No.
PHY-0606007 and PHY-0555366 and by the United Kingdom Science and Technology Facilities Council (STFC) under Grant EP/D003628.