Measurement of two-halo neutron transfer reaction p( 11 Li, 9 Li)t at 3 A MeV
I. Tanihata, M. Alcorta, D. Bandyopadhyay, R. Bieri, L. Buchmann, B. Davids, N. Galinski, D. Howell, W. Mills, R. Openshaw, E. Padilla-Rodal, G. Ruprecht, G. Sheffer, A. C. Shotter, S. Mythili, M. Trinczek, P. Walden, H. Savajols, T. Roger, M. Caamano, W. Mittig, P. Roussel-Chomaz, R. Kanungo, A. Gallant, G. Savard, I. J. Thompson
aa r X i v : . [ nu c l - e x ] F e b Measurement of two-halo neutron transfer reaction p( Li, Li)t at 3 A MeV
I. Tanihata, ∗ M. Alcorta, † D. Bandyopadhyay, R. Bieri, L. Buchmann, B. Davids, N. Galinski, D. Howell, W. Mills,R. Openshaw, E. Padilla-Rodal, G. Ruprecht, G. Sheffer, A. C. Shotter, S. Mythili, M. Trinczek, and P. Walden
TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada
H. Savajols, T. Roger, M. Caamano, W. Mittig, ‡ and P. Roussel-Chomaz GANIL, Bd Henri Becquerel, BP 55027, 14076 Caen Cedex 05, France
R. Kanungo and A. Gallant
Saint Mary’s University, 923 Robie St., Halifax, Nova Scotia B3H 3C3, Canada
M.Notani and G. Savard
ANL, 9700 S. Cass Ave., Argonne, IL 60439, USA
I. J. Thompson
LLNL, L-414, P.O. Box 808, Livermore CA 94551, USA (Dated: (received on ))The p( Li, Li)t reaction has been studied for the first time at an incident energy of 3 A MeVdelivered by the new ISAC-2 facility at TRIUMF. An active target detector MAYA, build at GANIL,was used for the measurement. The differential cross sections have been determined for transitionsto the Li ground and the first excited states in a wide range of scattering angles. Multisteptransfer calculations using different Li model wave functions, shows that wave functions withstrong correlations between the halo neutrons are the most successful in reproducing the observation.
PACS numbers: 25.40.Hs, 27.20.+n, 24.10.Eq, 21.90.+f
The neutron-rich Li isotope Li has the most pronounced two-neutron halo. Presently the most important questionabout the halo structure concerns the nature of the interaction and correlation between the two halo neutrons. Ina halo, the correlation may be different from that of a pair of neutrons in normal nuclei for several reasons. Haloneutrons are very weakly bound and, therefore, the effect of the continuum becomes important. The wave functionof the halo neutrons has an extremely small overlap with that of the protons and, thus, may experience interactionsmuch different from those of neutrons in normal nuclei. The density of halo neutrons is very low compared withnormal nuclear density and, thus, may give rise to quite different correlations from that in stable or near-stable nuclei.So far, there have been several experimental attempts to elucidate the nature of these correlations between the haloneutrons in Li. For example, measurements of neutrons and Li from the fragmentation of Li have been used todetermine the momentum correlation between two halo neutrons [1]. However, the contribution of the Li resonance,which decays to Li+n immediately, made it difficult to reach definitive conclusions. Later, Zinser et al. [2] studiedhigh-energy stripping reactions of Li and Be to Li, and the analyses of the momentum distributions suggests thenecessity of considerable mixing of (1s / ) and (0p / ) configurations in the ground state of Li. The importance ofthe s-wave contribution is also seen in Coulomb dissociation measurements [3, 4]. Determinations of such amplitudeshave also been attempted from data associated with the beta-decay of Li; however, no definite conclusions could bereached.A recent measurement of the charge radius of Li and Li [5], when combined with the matter radii of Li and Li [6], provides unique information concerning the two-neutron distribution. The root-mean-square(rms) distancebetween two halo neutrons h r i / , as well as the distance between the two-neutron center-of-mass and the centerof the core h r i / , can be evaluated under two assumptions: a) that Li consists of a Li core plus two haloneutrons and b) that there is no angular correlation between the position vector connecting the two-halo neutronsand the position vector connecting the center of mass of the two-neutrons to the center of the core. Taking theseassumptions into account, and using experimental data from references [5, 6], we obtain h r i / = 7 . ± .
72 fmand h r i / = 6 . ± .
52 fm. This shows that the average opening angle of the two-halo neutrons, relative to thecore centre, is about 60 degrees. Similar analysis can be made for He, if again it is assumed: He → He + n + n.From this, and using measured matter and charge radii of , He [6, 7], we obtain h r i / = 3 . ± .
28 fm, and h r i / = 3 . ± .
06 fm. The average opening angle in this case is 54 degrees.In He case the wave function of the halo is known better than that of Li because it is mainly of a p / character.From three-body calculations two separate components (di-neutron and cigar shape) contribute almost equally tothe halo structure [8]. Experimental observations for the two-neutron transfer reaction, He + He → He + He,(backward elastic scattering included) yields results consistent with such theoretical calculations [9]. Although itseems that the relation between h r i / and h r i / is similar between Li and He, differences in the structure ofthe wave functions are expected because of the complexity of the Li wave function, namely a mixing of two differentorbitals (1s / and 0p / ). The mixing amplitude of these waves is an important factor that determines the bindingand the halo structure in Li.The newly constructed ISAC-2 accelerator at TRIUMF now provides the highest intensity beam of low-energy Li up to 55 MeV. This beam enabled the measurement of the two-neutron transfer reaction of Li for the firsttime. The reaction Q-value of Li(p,t) Li is very large (8.2 MeV) and, thus, the reaction channel is open at suchlow energies. The beam energy used in this experiment (33 MeV) is not as high as usually used in studies of directreactions, nevertheless due to the low separation energy of the two halo neutrons ( ∼
400 keV compared with about 10MeV in stable nuclei) and low Coulomb barrier ( ∼ Li was accelerated to energy of 36.9 MeV. Beam intensity on the target was about 2500 pps onaverage, and about 5000 pps at maximum. Measurement of the transfer reaction was made possible at this low beamintensity through the use of the MAYA active target detector brought to TRIUMF from GANIL. MAYA has a target-gas detection volume (28 cm long in the beam direction, 25 cm wide, and 20 cm high) for three-dimensional trackingof charged particles, and a detector telescope array at the end of the chamber. Each detector telescope consisted ofa 700 µ m thick Si detector and a 1 cm thick CsI scintillation counter of 5 × . The array consists of twenty setsof telescopes. MAYA was operated with isobutane gas first at a gas pressure of 137.4 mbar and then at 91.6 mbar.These two different pressure settings were used to cross check the validity of the analysis by changing the drift speedof ionized electrons and by changing the energy loss density. The coverage of center of mass angles was also differentunder these pressures - as will be discussed later. Reaction events were identified by a coincidence between a parallelplate avalanche chamber (PPAC), which is placed just upstream of MAYA, and the Si array. Li ions that did notundergo a reaction were stopped in the blocking material just before the Si array. Details of MAYA can be found inRef.[10].The two-neutron transfer reaction p( Li, Li)t was identified by two methods depending on the scattering angles.For forward scattering in the c.m., Li ions in the laboratory frame are emitted at small angles and have sufficientenergies to traverse the gas and hit the Si array, and so Li ions were identified by the ∆ E − E method. The ∆ E signal was obtained from the last 5 cm of the MAYA gas detector. Tritons emitted near 90 degrees have low energiesso that they stop within the gas detector and thus provide total energy signals. However tritons emitted in smallerangles, but larger than the angle covered by the Si array, punch though the gas volume and therefore only scatteringangles and partial energy losses in the chamber could be measured. The major background for such events came fromthe Li + p → Li + d → Li + n + d reaction. Fortunately, the kinematical locus in a two-dimensional plot betweenemission angles of Li and light particles, [ θ (Li) − θ (light)], of the (p,d) reaction is well separated from the punchthrough (p,t) events.For large angle scattering in the c.m., tritons were detected by the Si and CsI detectors and identified clearly bythe ∆ E − E technique. Under this condition, Li stops inside the gas detector volume and thus the total energy, therange, and the scattering angle were determined. Lithium ions can easily be identified from their energy loss alongthe track, but identification of the isotope mass number is more difficult. The largest background events are due toscattered Li with accidental coincidence that have higher energies and will hit the Si array. So rejection of such Li events was easily accomplished. Use again was made of a θ (Li) − θ (light) correlation plot for final identificationof the (p,t) reaction. To remove other sources of background, additional selections were applied. For forward angleevents, important correlations for these selections were: E (Li) − θ (Li), E (Li) − θ (H), and Q c (H) − θ (H), where E isthe energy of a particle determined by Si array and Q c is the total charge collected in the gas detection volume. Thelast correlation was effective for removing deuterons. For the large angle events, the most important correlation was E ( t ) − θ (heavy); here “heavy” means Z = 3 particles detected in the gas detector volume.Figure 1(a) shows θ (heavy) vs. θ (light) scatter plot after those selections. Two clear kinematic loci are seen. Thereaction Q -value spectra calculated from those angles are shown in the panel (b). The spectra show the transitionsto the ground state of Li as well as the transition to the first excited state Li (2.69 MeV). Mixing of ground statetransition into the first excited state spectrum is seen in the plot but, can easily be removed by the selection of the Q values. The tracking efficiency was determined by comparing the number of identified particles (by the ∆ E − E method) and the number of tracks that hit an array detector at consistent position; this comparison was undertakenseparately for Li and triton ions. The geometrical efficiency was estimated by a Monte-Carlo simulation that includesdetector geometries and energy losses of the charged particles in the gas.The number of incident Li ions was determined by counting the incident ions both by the PPAC and signals from
FIG. 1: (a) θ (Li) − θ (H) plot. Loci of (p,t) reactions are clearly seen. (b) Q -value histograms of (p,t) reactions. Blue pointsshow the spectrum for Li ground state transition and Red points are for the first excited state of Li. the first 7 cm of the gas detector. The position, direction, and energy loss along the track of an incident particlewere used to select good incident Li ions. The uncertainty of the incident beam intensity is < ± ◦ C. The center of mass scattering angles were calculated from the scattering angles of Li and the triton. The detection efficiencies are shown in the panel (b), as a function of the center of mass angle. Atthe 137.4 mbar, the detection efficiency drops to zero near θ cm = 110 ◦ ; this is because neither the Li nor the tritonions reach the array detector near θ cm = 110 ◦ . The efficiency of event detection near cm=110 was higher for the 91.6mbar setting; under this condition, either the Li ion or the triton will hit the array detector for all scattering angles.For any particular Li reaction event, the incident energy depends on the depth of the reaction point within thegas. In the present experiment cross sections were averaged over Li energies from 2.8 A to 3.2 A MeV. The deduceddifferential cross sections corresponding to the two different pressure settings were consistent within experimentaluncertainties. The averaged differential cross sections for transitions to the Li ground state are shown in Fig. 3,where the error bars on the figure include only statistical errors. The overall uncertainty in the absolute cross sectionvalues is about ± + or 2 + halo component is presentin the ground state of Li( − ) because the spin-parity of the Li first excited state is − . This is new informationthat has not yet been observed in any of previous investigations. Compound nucleus contribution should be small: atpresent energy, the angular distribution of compound decay must be essentially isotropic, and hence the deep minimaobserved in the angular distributions of the ground state and the first excited state exclude the strong contribution. Scattering angle in CM [degrees] D i ff e r e n ti a l c r o ss s ec ti on [ m b / s r] E ff i c i e n c y (a)(b) Fig. 2. (a) The comparison of the differential cross sections determined from the data sets at 137.4 mbar and 91.6 mbar. (cid:13)(b) The corresponding detection efficiency for each data set. B B B B B B B B B B B B B B B B B B B B B B B B BJ J J J J J J J J J J J J J J J J J J J J J J J J J J J J
BBBBBBBBBBBBBBBBBBBBBBBJJJJJJJJJJJJJJHHHHHHHHHHHHHHHHHHHHHHHHHHHHFFFFFFFFFFFFFF
FIG. 2: (a) The comparison of the differential cross sections determined from the data sets at 137.4 mbar and 91.6 mbar. (b)The corresponding detection efficiency for each data set.
TABLE I: Optical potential parameters used for the present calculations. V MeV r V fm a V fm W MeV W D MeV r W fm a W fm V so MeV r so fm a so fmp+ Li[15] 54.06 1.17 0.75 2.37 16.87 1.32 0.82 6.2 1.01 0.75d+ Li[16] 85.8 1.17 0.76 1.117 11.863 1.325 0.731 0t+ Li[17] 1.42 1.16 0.78 28.2 0 1.88 0.61 0
However, before a final conclusion can be made, detailed studies of coupled channels and sequential transfer effectsneed to be undertaken.Multistep transfer calculations to determine the differential cross sections to the ground state of Li have been made.For these calculations several of the three-body models from Ref.[11], recalculated using the hyperspherical harmonicexpansions of Ref.[12], with projection operators to remove the 0s / and 0p / Pauli blocked states, have been used.In particular, the P0, P2 and P3 models from [11], which have percentage (1s / ) components of 3%, 31% and 45%,respectively were used. The corresponding matter radii for Li are 3.05, 3.39 and 3.64 fm. For comparison, a simple(p / ) model based on the P0 case, but with no n-n potential to correlate the neutrons, was also investigated. Allmodels here do not include an excitation of Li core.The calculations reported here included the simultaneous transfer of two neutrons from Li to Li in a one stepprocess, as well as coherently the two-step sequential transfers via Li. The simultaneous transfers used a tritonwavefuction calculated in the hyperspherical framework with the SSC(C) nucleon-nucleon force [13], and a three-bodyforce to obtain the correct triton binding energy. The sequential transfers passed through both
12 + and − neutronstates of Li, with spectroscopic factors given by respectively the s- and p-wave occupation probabilities for Limodels of [11]. The spectroscopic amplitudes for h d | t i and h Li | Li i include a factor of √ ∼ Li distance in the Li models. The proton, deuteron and triton channel optical potentials used are shown in TableI. The differential cross sections were obtained using the FRESCO[14].Curves in Fig. 3 show the results of the calculations. The wave function (p / ) with no n-n correlation gives verysmall cross sections that are far from the measured values. Also the P0 wave function, with n-n correlation but witha small (s / ) mixing amplitude, gives too small cross sections. The results of the P2 and P3 wave functions fit theforward angle data reasonably well but the fitting near the minimum of the cross section is unsatisfactory. The resultsmay be sensitive to the choice of the optical potentials as well as the selection of the intermediate states of two-stepprocesses. Detailed analysis of such effects should be a subject of future studies.In summary, we have measured for the first time the differential cross sections for two-halo neutron transfer reactionsof the most pronounced halo nucleus Li. Transitions were observed to the ground and first excited state of Li.Multistep transfer calculations were applied with different wave functions of Li. It is seen that wave functions withstrong mixing of p and s neutrons which includes three-body correlations, provides the best fit to the data for themagnitude of the reaction cross section. However the fitting to the angular shape is less satisfactory. The populationof the first excited state of Li suggests a 1 + or 2 + configuration of the halo neutrons. This shows that a two-nucleontransfer reaction as studied here may give a new insight in the halo structure of Li. Further studies clearly arenecessary to understand the observed cross sections as well as the correlation between the two-halo neutrons.One of the authors, IT, acknowledges the support of TRIUMF throughout his stay at TRIUMF. The experiment issupported by GANIL and technical help from J. F. Libin, P. Gangnant, C. Spitaels, L. Olivier, and G. Lebertre aregratefully acknowledged. This work was supported by the NSERC of Canada through TRIUMF and Saint Mary’sUniversity. Part of this work was performed under the auspices of the U.S. Department of Energy by LawrenceLivermore National Laboratory under Contract DE-AC52-07NA27344. This experiment was the first experiment atthe new ISAC-2 facility. The authors gratefully acknowledge R. Laxdal, M. Marchetto, M. Dombsky and all otherstaff members for their excellent effort for setting up the beam line and delivering the high-quality Li beam. ∗ present address: RCNP, Osaka University, Mihogaoka, Ibaraki 567-0047, Japan. † present address: Institute de Estructura de la Materia, CSIC, Serrano 113bis, E-28006 Madrid, Spain. ‡ present address: NSCL, MSU East Lansing, MI 48824-1321, USA.[1] I. Tanihata et al., Phys. Letters B (1992) 307. FIG. 3: Differential cross sections of (p,t) reaction to the ground state of Li and to the first excited state (insert). Theoreticalpredictions using four different wave functions were shown by curves. See text for the difference of the wave functions. [2] M. Zinser et al., Nucl. Phys. A (1997) 151.[3] S. Shimoura et al., Phys. Letters B (1995) 29.[4] T. Nakamura et al., Phys. Rev. Letters (2006) 252502.[5] R. Sanchez et al., Phys. Rev. Letters (2006) 033002.[6] I. Tanihata et al., Phy. Rev. Letters (1985) 2676. A.Ozawa, T. Suzuki, and I. Tanihata., Nucl. Phys. A (2001) 32.[7] L. -B Wang et al., Phys. Rev. Letters (2004) 142501.[8] M. V. Zhukov et al., Phys. Rep. (1993) 151.[9] Y. T. V. Oganessian et al., Phys. Rev. Letters (1999) 4996.[10] C. E. Demonchy et al., Nuc. Instr & Methods A (2007) 145.[11] I.J. Thompson and M.V. Zhukov, Phys. Rev. C (1994) 1904.[12] I.J. Thompson et al., Phys. Rev. C , 24318 (2000).[13] R. de Tourreil and D.W.L. Sprung, Nucl. Phys. A (1975) 445.[14] I. J. Thompson, Computer Physics Report (1988) 167.[15] F. D. Beccehetti and G. W. Greenless, Phys. Rev. (1969) 1190.[16] W. W. Daehnick, J. D. Childs,and Z. Vrcelj Phys. Rev. C21