Examining exotic structure of proton-rich nucleus 23 Al
D. Q. Fang, W. Guo, C. W. Ma, K. Wang, T. Z. Yan, Y. G. Ma, X. Z. Cai, W. Q. Shen, Z. Z. Ren, Z. Y. Sun, J. G. Chen, W. D. Tian, C. Zhong, M. Hosoi, T. Izumikawa, R. Kanungo, S. Nakajima, T. Ohnishi, T. Ohtsubo, A. Ozawa, T. Suda, K. Sugawara, T. Suzuki, A. Takisawa, K. Tanaka, T. Yamaguchi, I. Tanihata
aa r X i v : . [ nu c l - e x ] S e p Examining exotic structure of proton-rich nucleus Al D. Q. Fang ∗ , W. Guo, C. W. Ma, K. Wang, T. Z. Yan, Y. G. Ma, X. Z. Cai, W.Q. Shen, Z. Z. Ren, Z. Y. Sun, J. G. Chen, W. D. Tian, C. Zhong, M. Hosoi, T.Izumikawa, R. Kanungo, S. Nakajima, T. Ohnishi, T. Ohtsubo, A. Ozawa, T. Suda, K. Sugawara, T. Suzuki, A. Takisawa, K. Tanaka, T. Yamaguchi, and I. Tanihata Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, People’s Republic of China Department of Physics, Nanjing University, Nanjing 210008, People’s Republic of China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, People’s Republic of China Department of Physics, Saitama University, Saitama 338-8570, Japan Department of Physics, Niigata University, Niigata 950-2181, Japan TRIUMF, 4004 Wesbrook Mal, Vancouver, British Columbia, V6T 2A3, Canada Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan (Dated: November 2, 2018)The longitudinal momentum distribution ( P // ) of fragments after one-proton removal from Aland reaction cross sections ( σ R ) for , Al on carbon target at 74 A MeV have been measured. The , Al ions were produced through projectile fragmentation of 135 A MeV Si primary beam usingRIPS fragment separator at RIKEN. P // is measured by a direct time-of-flight (TOF) technique,while σ R is determined using a transmission method. An enhancement in σ R is observed for Alcompared with Al. The P // for Mg fragments from Al breakup has been obtained for the firsttime. FWHM of the distributions has been determined to be 232 ±
28 MeV/c. The experimentaldata are discussed by using Few-Body Glauber model. Analysis of P // demonstrates a dominant d -wave configuration for the valence proton in ground state of Al, indicating that Al is not aproton halo nucleus.
PACS numbers: 25.60.-t, 21.60.-n, 27.30.+t
Since the pioneering measurements of interaction crosssections ( σ I ) and observation of a remarkably large σ I for Li [1, 2], exotic structures like neutron halo or skin inlight neutron-rich nuclei have been found. Experimentalmeasurements of reaction cross section ( σ R ), fragmentmomentum distribution ( P // ) after one or two nucleonsremoval, quadrupole moment and Coulomb dissociationhave been demonstrated to be very effective methods toinvestigate nuclear halo structure. The neutron skin orhalo nuclei , He, Li, Be, C etc. [1, 2, 3, 4, 5, 6, 7],have been identified by these experimental methods.Due to Coulomb barrier, identification of a proton halois more difficult compared to a neutron halo. Thequadrupole moment, P // and σ R data indicate a protonhalo in B [8, 9, 10, 11, 12], whereas no enhancement isobserved in the measured σ I at relativistic energies [13].The proton halo in , P and S has been predictedtheoretically [14, 15]. Measurements of P // have showna proton halo character in , , P [16].Proton-rich nucleus Al has a very small separationenergy ( S p = 0 .
125 MeV) [17] and is a possible candi-date of proton halo. An enhanced σ R for Al has beenobserved in a previous experiment [18, 19]. To reproducethe σ R for Al within framework of Glauber model, adominating 2 s / component for the valence proton isshown [18]. A long tail in proton density distribution ∗ Corresponding author. Email: [email protected] has been extracted for Al which indicated halo struc-ture. The spin and parity ( J π ) for ground state of Alhas been deduced to be 5/2 + in a recent measurementof magnetic moment [20]. This result favors a d -waveconfiguration for the valence proton in Al. But it doesnot eliminate the possibility of a s -wave valence protonif its Mg core is in excited state. Therefore it will bevery important to determine configuration of the valenceproton for Al. As we know, P // of the fragment carriesstructure information of the projectile. However, thereare no such experimental data for Al up to now. In thispaper we will report simultaneously measurements of σ R and P // for Al and also σ R for Al.The experiment was performed at the RIken Projectilefragment Separator (RIPS) in RIKEN Ring CyclotronFacility. The experimental setup is shown in Fig. 1. Sec-ondary beams were generated by fragmentation reactionof 135 A MeV Si primary beam on a Be productiontarget in F0 chamber. In the dispersive focus plane F1,an Al wedge-shaped degrader (central thickness; 583.1mg/cm , angle; 6 mrad) was installed. A delay-line read-out Parallel Plate Avalanche Counter (PPAC) was placedto measure the beam position. Then the secondary beamwas directed onto the achromatic focus F2. Two delay-line readout PPACs were installed to determine the beamposition and angle. An ion chamber (200 φ × E ) of the secondarybeams [21]. An ultra-fast plastic scintillator (0.5 mmthick) was placed before a carbon reaction target (377mg/cm thick) to measure time-of-flight (TOF) from the FIG. 1: (Color online) Ex-perimental setup at the frag-ment separator RIPS.
PPAC at F1. The particle identification before the reac-tion target was done by means of Bρ − ∆ E − TOF method.After the reaction target, a quadrupole triplet was usedto transport and focus the beam onto F3 ( ∼ φ × E ) of the beam. To-tal energy ( E ) was measured by a NaI(Tl) detector. Theparticles were identified by TOF − ∆ E − E method. Anexample of typical particle identification spectra at F3for the fragment from Al breakup is shown in Fig. 2.In this spectrum, fragments with different nuclear chargewere already subtracted by TOF and ∆ E method.Under assumption of a sudden valence-nucleon re-moval, the momentum distribution of fragments can beused to describe that of the valence proton. The P // offragments from breakup reactions was determined fromthe TOF between the two plastic scintillators installed atF2 and F3. Position information measured by the PPACat F1 was used to derive incident momentum of the beam. Energy signal from NaI(Tl) (arb. units) T O F ( n s ) Mg Mg FIG. 2: (Color online) Particle identification at F3 by thebidimensional plot between TOF from F2 to F3 and energysignal from NaI(Tl) (corrected with TOF).
The momentum of fragment relative to the incident pro-jectile in laboratory frame was transformed into that inthe projectile rest frame using Lorentz transformation.In order to estimate and subtract reactions of the pro-jectile in material other than the carbon target, measure-ments without the reaction target were also performedand the beam energy was reduced by an amount cor-responding to the energy loss in the target. For one-proton removal reactions of Al, this background wascarefully reconstructed and subtracted based on ratio offragments to unreacted projectile identified in the target-out measurement and also broadening effect of the car-bon target on P // . The obtained momentum distribu-tion of Mg fragments from Al breakup in the carbontarget at 74 A MeV is shown in Fig. 3. We normalizedexperimental counts to the measured one-proton removalcross section ( σ − p ) so that P N ( p i)∆ p || equals σ − p . AGaussian function was used to fit the distributions. Thefull width at half maximum (FWHM) was determined tobe 232 ±
28 MeV/c after unfolding the Gaussian-shapedsystem resolution (41 MeV/c). The FWHM is consistentwith Goldhaber model’s prediction (FWHM=212 MeV/cwith σ = 90 MeV/c) within the error bar [22]. Sincemagnetic fields of the quadruples between F2 and F3were optimized for the projectile in the measurement,momentum dependence of transmission from F2 to F3for fragments was simulated by the code MOCADI [23].The effect of transmission on the width of P // distribu-tion was found to be negligible which is similar with theconclusion for neutron-rich nuclei [24, 25]. Using the es-timated transmission value, the one-proton removal crosssections for Al was obtained to be 63 ± σ R = 1 t ln (cid:18) γ γ (cid:19) (1)where γ and γ denote ratio of unreacted outgoing andincident projectiles for target-in and target-out cases, re-spectively; t thickness of the reaction target, i.e., numberof particle per unit area. -300 -200 -100 0 100 2000.000.050.100.150.20 d / dp // ( m b / ( M e V / c )) P // (MeV/c) FIG. 3: (Color online) P // distribution of fragment Mg afterone-proton removal from Al. The closed circles with errorbars are the present experimental data, the solid curve is aGaussian fit to the data.
The σ R of , Al at 74 A MeV were obtained to be1609 ±
79 mb and 1527 ±
60 mb, respectively. The errorsinclude statistical and systematic uncertainties. Proba-bility of inelastic scattering reaction was estimated to bevery small ( < Al which is much smaller than theerror of σ R .Results of previous and current experiments are shownin Fig. 4. Since the energy is different in two experi-ments, the previous σ R data at ∼ A MeV [18] werescaled to the present energy (74 A MeV) using a phe-nomenological formula [26]. First the radius parameter( r ) in this formula was adjusted to reproduce the σ R at ∼ A MeV, then the same r was used to calculate the σ R at 74 A MeV. As shown in Fig. 4, the σ R of , Alfrom present and previous experiments are in good agree-ment. And we observed a small enhancement in σ R for Al in our data again.To interpret the measured reaction cross sections andmomentum distributions, we performed a Few-BodyGlauber model (FBGM) analysis for P // of Al → Mgprocesses and σ R of , Al [27, 28, 29]. In this model, acore plus proton structure is assumed for the projectile.The total wavefunction of the nucleus is expressed asΨ = X ij ψ i core φ j , (2)where ψ core and φ are wavefunctions of the core andvalence proton; i , j denote different configurations for thecore nucleus and valence proton, respectively. For thecore, harmonic oscillator (HO) functions were used forthe density distributions. The wavefunction of the va-lence proton was calculated by solving the eigenvalueproblem in a Woods-Saxon potential. The separationenergy of the last proton is reproduced by adjusting thepotential depth. In the calculation, the diffuseness and
23 24 25 26 27 281400160018002000 R ( m b ) A Al isotope
FIG. 4: (Color online) The mass dependence of σ R for Al iso-topes. The solid circles are results of the present experiment( E = 74 A MeV), the solid triangles are the previous experi-mental data ( E ∼ A MeV) [18], and the open triangles arethe previous data scaled to 74 A MeV. radius parameter were chosen to be 0.67 fm and 1.27 fm,respectively [24].In the recent g -factor measurement using a β -NMRmethod, the spin and parity for ground state of Al isshown to be 5 / + . It gives a strong restriction on the pos-sible structure of this nucleus. Assuming Mg+ p struc-ture, three most probable configurations for J π = 5 / + of Al are: 0 + ⊗ d / , 2 + ⊗ d / and 2 + ⊗ s / [20]. The s -wave configuration is therefore possible for the core inthe excited state.The momentum distributions for the valence proton in s or d -wave configuration are calculated by using FBGM.In this calculation, the parameters α and σ NN in the pro-file function Γ( b ) = − iα πβ σ NN exp( − b β ) ( b is the impactparameter) are taken from Ref. [28]. The range parame-ter ( β ) is calculated by the formula which is determinedby fitting the σ R of C + C from low to relativisticenergies [30]. β is 0.35 fm at 74 A MeV. To fix the coresize, the width parameters in the HO density distributionof Mg were adjusted to reproduce the experimental σ I data at around 1 A GeV [31]. The extracted effectiveroot-mean-square matter radius ( R rms ≡ < r > / ) for Mg is 2 . ± .
09 fm. To see the separation energy de-pendence, the FWHM of P // is determined assuming anarbitrary separation energy in calculation of the wave-function for the valence proton in Al and shown inFig. 5. If we adopt a larger radius of R rms = 3 . Mg to see the core size effect on P // , we obtainedsolid and open squares of FWHM in Fig. 5. The oneproton separation energies for Mg in the ground andexcited ( J π = 2 + , E x = 1 .
25 MeV) states are taken as0.125 MeV and 1.375 MeV ( E x + 0 .
125 MeV). Those twovalues are marked by two arrows in Fig. 5. In this figure,we can see that the width for the s and d -wave are obvi-ously separated. The width for the s -wave is much lowerthan the experimental data, while that of the d -wave isclose to the experimental FWHM. With the increase of → → PSfrag repla ements Sp (MeV) F W H M ( M e V / ) Rrms=3.60 fm (s-wave)Rrms=2.89 fm (s-wave)Rrms=3.60 fm (d-wave)Rrms=2.89 fm (d-wave) P S f r ag r e p l a e m e n t s S p ( M e V ) F W H M ( M e V / ) R r m s = . f m ( s - w a v e ) R r m s = . f m ( s - w a v e ) R r m s = . f m ( d - w a v e ) R r m s = . f m ( d - w a v e ) FIG. 5: (Color online) The dependence of FWHM for the P // distribution after one-proton removal of Al on the sep-aration energy of the valence proton. The solid circles witherror bars is result of the present experiment, the shaded arearefers to error of the data. The solid and open squares arethe FBGM calculations for the d and s -wave configuration ofthe valence proton with the core R rms = 3 . R rms = 2 .
89 fm. Thelines are just for guiding the eyes. The two arrows refer tothe separation energy of 0.125 MeV and 1.37 MeV (the ex-citation energy for the first excited state of Mg plus theexperimental one proton separation energy of Al). S p , the width of P // increases slowly. It means that P // will become wider for Mg in the excited state. Theeffect of the core size on P // is negligible for the s -waveand small for the d -wave configuration. The larger sizedcore will give a little wider P // distribution. From com-parison of the FBGM calculation with the experimentaldata in Fig. 5, it is clearly shown that the valence protonin Al is dominantly in the d -wave configuration. Thepossibility for the s -wave should be very small. Further-more, it is possible to have an excited core inside Al.This is consistent with the shell model calculations andalso the Coulomb dissociation measurement [20, 32].From above discussions of P // , the valence protonin Al is determined to be in the d -wave configura-tion, which is used in the following calculations. Inthe calculation of σ R for Al using the FBGM, at first R rms = 2 . ± .
09 fm is used for its Mg core by repro-ducing the σ I data as described above. But the calcu-lated σ R is much lower than the obtained σ R data. Onereason may be due to the global underestimation of σ R found at intermediate energies in the Glauber model [33].Different method has been tried to correct this prob-lem [4, 30, 34]. These corrections are performed for al-most light stable nuclei. The σ R of Al is calculatedwith the size of its Mg core determined by fitting σ I at around 1 A GeV [31]. But the calculated σ R for Alis only 1430 mb which is ∼
10% lower than the presentdata. It was shown that scope of the discrepancy be-tween the Glauber model calculation and experimentaldata is large even for stable nuclei [33]. To correct the R ( m b ) R rms (fm) Rrms (fm) d e f o r m a ti on () FIG. 6: (Color online) The dependence of σ R at 74 A Mev onthe core size ( R rms). The horizontal line is the experimental σ R value, the shadowed area is the error of σ R . The trianglesdenote the FBGM calculations. The size of Mg obtained byfitting the σ I data at around 1 A GeV is marked by an arrow.The inset shows the relationship between the quadrupole de-formation parameter ( β ) and size of the core, for details seethe text. possible underestimation for nuclei with A >
20, we ad-justed the range parameter to fit the σ R of Al from thepresent measurement. And β = 0 . σ R of Al at 74 A MeV is reproduced. Using thisrange parameter, the calculated σ R value of Al is stillsmaller than the data. Similar puzzle is also encounteredfor some neutron-rich nuclei. The large σ I cannot be re-produced by the FBGM even for the valence neutron inthe s -wave for C and O. One way is to enlarge thecore size to reproduce the experimental σ R [35, 36]. Herewe changed the core size by adjusting width parametersin the HO density distribution of Mg. The dependenceof σ R for Al on the core size is calculated and shownin Fig. 6. The calculated results indicate that the coresize is 3 . ± .
18 fm when the experimental σ R data of Al is reproduced (8 ±
7% larger than the size of the bare Mg nucleus).In order to reproduce the σ R of Al from the currentwork, a larger sized core is deduced within the frameworkof the spherical Glauber model. It should be pointedout that this enlarged core may not necessarily reflectincreased physical size of the nucleus. The negligenceof some specific effects in the Glauber model could leadto the larger sized core. The possible reasons for theenlargement will be discussed qualitatively below. Theeffect of quadrupole deformation ( β , the parameter de-scribing the deformation) on the rms radius can be ex-pressed as R β rms = q (1 + π β ) R β =0 rms [37]. As shownin the inset of Fig. 6, R rms of the core changes quicklywith the increase of β . This simple relationship between R rms and β indicates that a deformed core inside Alwill give a larger sized Mg. In order to reproduce the σ R of Al, the lower limit of R rms for the core is 2.95fm as we can see from the calculated results in the fig-ure. If we assume that the shape of Mg as a nucleusis spherical and enlargement of the core is due to defor-mation, the lower limit of β = 0 . β = 0 . Mg core. Theexperimental and theoretical investigations have demon-strated the deformation for Mg. The experimental β is 0.566 [38], the calculated β by RMF and generalizedhybrid derivative coupling model are around 0.4 and 0.6,respectively [39, 40]. If the bare nucleus Mg is de-formed, the above analysis indicates that Mg as a corein Al may have larger deformation as compared with Mg as a nucleus. Additionally, the first excited stateof Mg was calculated within the RMF framework andits R rms is obtained to be around 2.4% larger than thatof the ground state [41, 42]. Thus the core excitationeffect may also contribute to the larger size for Mg. Asdemonstrated by the shell model calculations, the con-figuration of Mg (ground state) plus a d -wave protonis dominant in Al [20]. If deformation and excitationeffects exist in the core, the first one may be the maincomponent.In summary, the longitudinal momentum distributionof fragments after one-proton removal for Al and re-action cross sections for , Al were measured. An en-hancement was observed for the σ R of Al. The P // dis-tributions were found to be wide and consistent with theGoldhaber model’s prediction. The experimental P // and σ R results were discussed within framework of the Few- Body Glauber model. We determined the valence pro-ton to be a dominant d -wave configuration in the groundstate of Al. It indicates no halo structure in this nu-cleus. But a larger sized Mg core was deduced in or-der to explain both the σ R and P // distributions withinframework of the spherical Few-Body Glauber model. Itis pointed out that deformation and core excitation ef-fects may be two main reasons for the extracted largersized core. Further theoretical investigations are neededto extract more specific structure information for Alfrom the experimental data.
Acknowledgements
The authors are very grateful to all of the staff atthe RIKEN accelerator for providing stable beams dur-ing the experiment. The support and hospitality fromthe RIKEN-RIBS laboratory are greatly appreciated bythe Chinese collaborators. This work was partially sup-ported by the National Natural Science Foundation ofChina (NNSFC) under Grant No. 10405032, 10535010,10405033 and 10475108, Shanghai Development Foun-dation for Science and Technology under contract No.06QA14062, 06JC14082 and 05XD14021, the MajorState Basic Research Development Program in China un-der Contract No. 2007CB815004 and the Knowledge In-novation Project of Chinese Academy of Sciences underGrant No. KJCX3.SYW.N2. [1] I. Tanihata et al ., Phys. Rev. Lett. , 2676 (1985).[2] I. Tanihata et al ., Phys. Lett. B287 , 307 (1992).[3] I. Tanihata et al ., Phys. Lett.
B160 , 380 (1985).[4] M. Fukuda et al ., Phys. Lett.
B268 , 339 (1991).[5] D. Bazin et al ., Phys. Rev. Lett. , 3569 (1995).[6] T. Nakamura et al ., Phys. Rev. Lett. , 1112 (1999).[7] A. Ozawa et al ., Nucl. Phys. A691 , 599 (2001).[8] T. Minamisono et al ., Phys. Rev. Lett. , 2058 (1992).[9] W. Schwab et al ., Z. Phys. A , 283 (1995).[10] R. E. Warner et al ., Phys. Rev. C , R1166 (1995).[11] F. Negoita et al ., Phys. Rev. C , 1787 (1996).[12] M. Fukuda et al ., Nucl. Phys. A , 209 (1999).[13] M. M. Obuti et al ., Nucl. Phys. A , 74 (1996).[14] B. A. Brown, P. G. Hansen, Phys. Lett. B381 , 391(1996).[15] Z. Z. Ren et al ., Phys. Rev. C , R572 (1996).[16] A. Navin et al ., Phys. Rev. Lett. , 5089 (1998).[17] G. Audi, A. H. Wapstra, Nucl. Phys. A565 , 66 (1993).[18] X. Z. Cai et al ., Phys. Rev. C , 024610 (2002).[19] H. Y. Zhang et al ., Nucl. Phys. A707 , 303 (2002).[20] A. Ozawa et al ., Phys. Rev. C , 021301R (2006).[21] K. Kimura et al ., Nucl. Inst. Meth. A , 608 (2005).[22] A. S. Goldhaber, Phys. Lett. B53 , 306 (1974).[23] N. Iwasa et al ., Nucl. Instrum. Methods B , 284 (1997).[24] T. Yamaguchi et al ., Nucl. Phys.
A724 , 3 (2003).[25] D. Q. Fang et al ., Phys. Rev. C , 034613 (2004).[26] W. Q. Shen et al ., Nucl. Phys. A491 , 130 (1989).[27] Y. Ogawa et al ., Nucl. Phys.
A543 , 722 (1992).[28] Y. Ogawa et al ., Nucl. Phys.
A571 , 784 (1994).[29] B. Abu-Ibrahim et al ., Comput. Phys. Comm. , 369(2003).[30] T. Zheng et al ., Nucl. Phys.
A709 , 103 (2002).[31] T. Suzuki et al ., Nucl. Phys.
A630 , 661 (1998).[32] T. Gomi et al ., Nucl. Phys.
A758 , 761c (2005).[33] A. Ozawa et al ., Nucl. Phys.
A608 , 63 (1996).[34] M. Takechi et al ., Eur. Phys. J. A , s01, 217 (2005).[35] R. Kanungo et al ., Nucl. Phys. A677 , 171 (2000).[36] R. Kanungo et al ., Phys. Rev. Lett. , 142502 (2002).[37] J. A. Christley, J. A. Tostevin, Phys. Rev. C , 2309(1999).[38] S. Raman et al ., At. Data Nucl. Data Tables , 1 (1987).[39] G. A. Lalazissis et al ., Nucl. Phys. A628 , 221 (1998).[40] Parna Mitra et al ., Phys. Rev. C , 034329 (2002).[41] Z. Z. Ren et al ., Phys. Rev. C , 2752 (1998).[42] J. G. Chen et al ., Eur. Phys. J. A23