Multi-neutron transfer in 8 He induced reactions near the Coulomb barrier
MMulti-neutron transfer in He induced reactions near the Coulomb barrier
I. Martel ∗ Department of Physics, University of Liverpool, Liverpool L69 9ZE, United Kingdom † N. Keeley
National Centre for Nuclear Research, ul. Andrzeja So(cid:32)ltana 7, 05-400 Otwock, Poland
K. W. Kemper
Department of Physics, The Florida State University, Tallahassee, Florida 32306, USA ‡ K. Rusek
Heavy Ion Laboratory, University of Warsaw, ul. Pasteura 5A, 02-093 Warsaw, Poland (Dated: September 29, 2020)The measured inclusive He and He production cross sections of G. Marqu´ınez-Dur´an et al. , Phys.Rev. C , 034615 (2018) are reexamined and the conclusions concerning the relative importanceof 1n and 2n transfer to the production of He arising from the interaction of a 22 MeV He beamwith a
Pb target revised. A consideration of the kinematics of the 2n-stripping reaction whencompared with the measured He total energy versus angle spectrum places strict limits on theallowed excitation energy of the
Pb residual, so constraining distorted wave Born approximationcalculations that the contribution of the 2n stripping process to the inclusive He production canonly be relatively small. It is therefore concluded that the dominant He production mechanismmust be 1n stripping followed by decay of the He ejectile. Based on this result we present strongarguments in favor of direct, one step four-neutron (4n) stripping as the main mechanism for Heproduction.
Keywords: direct nuclear reactions; radioactive beams; DWBA; reaction mechanisms; 1n transfer; 2n transfer;4n transfer
I. INTRODUCTION
The existence of multi-neutron clustering in nuclei hasattracted considerable attention in recent years. Thesimplest such cluster, the dineutron, is unbound but adominant dineutron contribution to the He ground statehas been well established both theoretically [1] and ex-perimentally [2]. With a probable structure of an α coresurrounded by four “valence” neutrons, He provides theinteresting additional possibility of 3n and 4n clusteringas well as 2n, and early studies of the Ni( He, He) Ni[3] reaction suggested the presence of a strong one-stepprocess, which could be well described as transfer of a4n cluster. However, Wolski et al. [4], investigating elas-tic scattering of He from He, observed enhancement ofthe differential cross section at backward scattering an-gles that could be attributed to the sequential transfer ofneutron pairs from the He ground state.The very complete study by Lemasson et al. [5] of thedirect reactions induced by He on Cu at Coulomb bar-rier energies showed the dominance of neutron-transferreactions, suggesting the existence of important corre- ∗ [email protected] † Present position: Department of Integrated Sciences, Universityof Huelva, 21071 Huelva, Spain ‡ Heavy Ion Laboratory, University of Warsaw, ul. Pasteura 5A,02-093 Warsaw, Poland lations among the valence neutrons in the He groundstate. More recently, Marqu´ınez-Dur´an et al. [6] stud-ied the scattering of He from the doubly-magic nucleus
Pb at 16 and 22 MeV and, in addition to the elasticscattering, the energy distributions and cross sections for He and He events were obtained. The energy distribu-tion of the He events clearly pointed to the presence oftwo production mechanisms, one- and two-neutron trans-fer reactions. On the other hand, the energy distributionof the α particles suggested the presence of three- andfour-neutron stripping mechanisms.The five-body ( α + n + n + n + n) cluster orbital shellmodel approximation (COSMA) calculations of the Heground state by Zhukov et al. [7] seem to bear out theseconclusions, since of the three configurations of the fourvalence neutrons with maximum probability one resem-bles a 4n cluster and one a pair of 2n clusters (or possiblya more loosely correlated 4n cluster). The third config-uration corresponds to a more spatially symmetrical ar-rangement of the four neutrons around the α core. Thus,transfers of 2n and 4n clusters as well as single neutrontransfer should be possible according to this model.In this work we reexamine the inclusive He and He production data of Ref. [6] and revise our previ-ous conclusion that at an incident He energy of 22MeV the
Pb( He, He)
Pb single-neutron strippingreaction contributes approximately one third (33 ± He cross section, with theremaining two thirds almost exclusively due to the
Pb( He, He)
Pb two-neutron stripping reaction. A a r X i v : . [ nu c l - e x ] S e p more detailed consideration of the reaction kinemat-ics in connection with the experimental two-dimensional He total energy versus scattering angle spectrum placesstrict limits on the allowed excitation energy range of thestates in the
Pb residual that may be populated viathe two-neutron stripping reaction. Distorted wave Bornapproximation (DWBA) calculations of the two-neutronstripping process consistent with these limits are unableto reproduce the shape of the measured inclusive Heangular distribution, forcing the conclusion that directtwo-neutron stripping can make only a relatively minorcontribution to the observed He yield (of the order of16% of the total cross section). The small magnitudeof the initial 2n-stripping step in turn rules out sequen-tial 2n-2n transfer—the
Pb( He, He),( He, He)
Pbprocess—as a significant source of He production. Sincethis is the most likely sequential route we therefore ar-gue that the He production is dominated by direct 4nstripping. The good description of the measured inclu-sive He angular distribution by DWBA calculations isconsistent with this assumption.
II. ANALYSIS OF THE HE AND HE YIELDS
The inclusive He and He yields of Ref. [6] were mea-sured simultaneously with the elastic scattering at theSPIRAL facility of the GANIL laboratory in France us-ing the double-sided silicon strip detector array GLO-RIA [8]. Thanks to the excellent optical properties ofthe He beam, together with an on-target intensity of10 pps an elastic scattering angular distribution of com-parable quality to the best stable beam data was ob-tained, the different He isotopes being clearly separatedin the detectors. In this work we confine our atten-tion to the He and He data at 22 MeV since thesehave better statistical accuracy and clearly defined peaksin the angular distributions, thus providing more severeconstraints on their interpretation. The angular distri-butions for He and He production [6] were obtainedfrom the respective Energy vs. Angle plots after select-ing the corresponding isotope in the particle identifica-tion spectrum. Breakup and fusion-evaporation contri-butions were largely excluded by a careful considerationof the kinematics. Therefore, in the angular regions ex-amined in this study there should only be a backgroundcontribution from processes other than neutron transfer,adequately described with an exponential function. SeeRefs. [6, 8, 9] for further details of the experimental setupand data reduction procedures.
A. Analysis of the He yield
Before discussing the origin of the He production weconsider that of He in detail. The measured He yield [6]could result from the following four processes:1.
Pb( He, He+n → He+n+n)
Pb (1n breakup) 2.
Pb( He, He+2n)
Pb (2n breakup)3.
Pb( He, He → He+n)
Pb (1n transfer)4.
Pb( He, He)
Pb (2n transfer)In Ref. [6] we adduced arguments in favor of breakupprocesses providing an essentially negligible contributionto the inclusive He yield in the angular range consid-ered; there may be some small “background” from thesereactions that falls off approximately exponentially withscattering angle. This leaves us with 1n and 2n trans-fer reactions. It is possible to assess the relative 1nand 2n contributions via DWBA calculations since thesecan show the kinematic differences between the two re-actions. The one neutron transfer has an optimum Qvalue of around − . Pb with well known spectro-scopic factors, thus enabling quantitative DWBA calcu-lations. Since the entrance channel elastic scattering wasalso measured, in principle the only unknown is the exitchannel He +
Pb distorting potential. For the 2ncluster transfer, the optimum Q-value is − . Pb at energies around E x = 8 MeV, very close to the two-neutron binding energy(S n =9.1 MeV), in good agreement with the measured He energy spectrum [6]. At this high excitation energythe structure of
Pb is not known so that only qualita-tive DWBA calculations can be performed. However, therange of allowed excitation energies of the
Pb residualcan be fixed from the observed two-dimensional He totalenergy versus scattering angle spectrum purely by kine-matics.Figure 1 (a) clearly shows that if we assume direct 2nstripping as the He production mechanism then onlystates in
Pb with excitation energies in the range 7 ≤ E x ≤
13 MeV can be populated, with E x ≈
10 MeV,slightly larger than that corresponding to the calculatedQ opt value, being most likely.We therefore performed DWBA calculations of the
Pb( He, He)
Pb reaction subject to these con-straints in order to ascertain the angular position of thepeak of the predicted He angular distribution for com-parison with the measured inclusive He angular distri-bution at 22 MeV [6]. All DWBA calculations were per-formed with the code fresco [10]. The entrance channelpotential used the same parameters as in Ref. [6] and theexit channel He +
Pb potential used the 22 MeVparameters of Ref. [11]. The bound state potentials forthe 2n cluster bound to the He and
Pb cores wereof standard Woods-Saxon form, with r = 1 . × A / fm and a = 0 . (cid:10) He | He + 2 n (cid:11) overlap [12]and r = 1 . × A / fm and a = 0 . (cid:10) Pb | Pb + 2 n (cid:11) . The 2n cluster was assumed tohave spin-parity 0 + . Since these calculations were purelyqualitative the spectroscopic factors for both overlapswere set to 1.0. FIG. 1: (a) Experimental He total energy versus scatteringangle two-dimensional spectrum for 22 MeV He incident ona
Pb target. Superimposed are kinematic curves for Heejectiles produced by the
Pb( He, He)
Pb 2n-strippingreaction with the
Pb residual in states with E x = 7, 10and 13 MeV (reading from the top down). (b) Angular distri-bution of the differential cross section for inclusive He pro-duction at E lab = 22 MeV. The curves correspond to thedifferent contributions: dashed curve - one neutron transfer,dotted curve - 2n cluster transfer, dot-dashed curve - back-ground and solid curve - total. See text for details. Calculations were performed for transfers leading tostates in
Pb at excitation energies of E x = 7, 10 and13 MeV, covering the kinematically allowed range, andseveral values of the transferred angular momentum L for each E x . The dotted curve in Fig. 1 (b) denotes theresult of the DWBA 2n-stripping calculation for E x = 10MeV and L = 4 (cid:126) , approximately the best matched L value. The shape of the calculated angular distributiondoes not reproduce the measured one and it peaks at θ lab ≈ ◦ , about 10 ◦ larger than the measured He an-gular distribution. While the detailed shape of the cal-culated angular distribution depends slightly on L andthe choice of exit channel optical potential, the positionof the peak is essentially fixed by kinematics, i.e. thevalue of E x , variations due to different input choices be-ing of the order of 3 ◦ at most. The exit channel He +
Pb optical potentials are rather well determined sincethe relevant incident energy range is covered by the He +
Pb potentials of Ref. [11], which should not differsignificantly from those for a
Pb target. If α -particleoptical potentials are used instead in the exit channel—arather extreme assumption—the stripping peak is shiftedby about 3 ◦ to larger angles, i.e. making the descriptionof the data worse . This relative insensitivity to the choiceof exit channel optical potential is to be expected sincethe energies of the He recoils when populating the levelsof
Pb concerned are at or below the relevant Coulombbarrier. Reducing E x by a few MeV moves the peak crosssection to more forward angles but it is clear from Fig.1 (a) that the 2n-stripping cross section for such valuesof E x must be negligible, since little or no He are ob-served with the required energy. The shape is also notimproved. We therefore arrive at the inescapable conclu-sion that direct 2n stripping can only make a minor con-tribution to the He production on kinematical groundsalone , since no variation of the input parameters will en-able the shape of the measured angular distribution to bereproduced by DWBA calculations if E x remains withinthe kinematically allowed limits.Since we argue elsewhere [6] that breakup will onlymake a small contribution to the He yield in the angu-lar region considered here, essentially constituting an ap-proximately exponentially falling background, this leavesone neutron stripping as the main He production pro-cess. The one neutron stripping process can, at least inprinciple, be calculated quantitatively using a direct re-action theory since all of the inputs are reasonably wellknown from other sources with the exception of the He+
Pb exit channel optical potential. In Ref. [6] weperformed such calculations using a few “physically rea-sonable” choices for the exit channel potential, fixing theother inputs—the entrance channel distorting potentialand (cid:10) He | He + n (cid:11) and (cid:10) Pb | Pb + n (cid:11) overlaps—at values taken from the literature. The resulting crosssections accounted for about one third of the total Hecross section at 22 MeV, clearly a significant underesti-mate in the light of the kinematical considerations de-tailed in the preceding paragraph. We therefore per-formed new calculations in order to determine whetherit was in fact possible to account for most of the Hecross section by the one neutron stripping process whileremaining within the bounds of what is physically ac-ceptable with regard to the inputs.The potentials binding the transferred neutron to the He and
Pb cores were of standard Woods-Saxon formwith radius and diffuseness parameters r = 1 . × A / fm and a = 0 .
65 fm and the spectroscopic factors for the (cid:10) He | He + n (cid:11) and (cid:10) Pb | Pb + n (cid:11) overlaps wereset to 4 and 1 respectively, the theoretical maximumvalues under the conventions used by the fresco code.The entrance channel distorting potential was as in Ref.[6]. The exit channel distorting potential remains an un-known since He is unbound. In order to apply somephysical constraints to the choice of this potential we cal-culated the real part using the double-folding procedureand a theoretical He density [13]. This was then heldfixed and the three parameters of the standard Woods-Saxon form imaginary potential varied to give the largestpossible cross section. In the event, this was achievedwith a so-called “interior” potential, the parameters be-ing: W = 50 MeV, R W = 1 . × / fm, a W = 0 . He ejectiles (before decaying into He + n ) are relativelywell above the relevant Coulomb barrier, unlike for the2n-stripping. While the choice of the imaginary part ofthe exit channel potential merely affects the height of thepeak relative to the backward angle cross section the peakposition is sensitive to the choice of the real part, withshifts of up to 10 ◦ for a given imaginary potential. Thecalculation using the double-folded real potential basedon the He matter density of Ref. [13] gives the resultclosest to the measured He angular distribution. Usinga He real potential, either double-folded or the real partof the Woods-Saxon entrance potential, combined withthe “interior” imaginary potential gives a similar result,the peak cross section being shifted by approximately 2 ◦ to larger angles. Use of He, Li or Li real potentials asin Ref. [6] (but retaining the same “interior” imaginarypotential referred to above) shifts the peak of the calcu-lated angular distribution to even larger angles, by up toabout 10 ◦ .The measured inclusive He angular distribution wasfitted by summing the calculated one-neutron and two-neutron stripping cross sections together with a back-ground function (denoted by the dot-dashed curve onFig. 1 (b)), the magnitudes of the two-neutron strippingand background being varied to give the best agreementwith the data. The resulting sum is plotted on Fig. 1 (b)as the solid curve, approximately 67% of the total (812mb, cf. the experimental value of 871 ±
31 mb [6]) com-ing from one-neutron stripping, 16% from two-neutronstripping and 17% from the background (including anycontribution from breakup of He). An upper limit onthe two-neutron stripping contribution is reasonably welldefined by the measured backward angle He cross sec-tion. The maximum value of the calculated 2n-strippingcross section consistent with this is about one third ofthe total, with essentially no contribution from the back-ground. The lower limit on the two-neutron strippingcontribution is about 12% of the total, this being theminimum consistent with a good description of the mea-sured He angular distribution, with a corresponding in-crease in the background contribution. Assessing the un-certainty on the 1n-stripping contribution is more diffi-cult, but any variation greater than about ±
10% wouldlead to a significant degradation of the description of the He angular distribution.We therefore conclude that the measured inclusive Heangular distribution for the interaction of a 22 MeV He beam with a
Pb target is indeed consistent with one-neutron stripping as the dominant He production mech-anism, with two-neutron stripping playing a minor role,contributing at most about one third of the total. Thishas important implications for the He production mech-anism which we address in the following section.
B. Analysis of the He yield
We now turn to a detailed consideration of the Heproduction. In addition to neutron transfer processes themeasured inclusive He angular distribution will containany contribution from breakup of the He projectile, asin the He case, but may also include α particles arisingfrom fusion-evaporation events. In our analysis of theinclusive He production cross section these latter twoprocesses are subsumed into the background since theyare expected to be small compared to the transfer yield.The following neutron transfer processes could con-tribute to the inclusive He yield (we do not considertransfers with more than two steps):1.
Pb( He, He)
Pb2.
Pb( He, He → He+n)
Pb3.
Pb( He, He ∗ → He+2n)
Pb4.
Pb( He, He)
Pb( He, He)
Pb5.
Pb( He, He ∗ → ( He ∗ → He+2n)+n)
Pb6.
Pb( He, He)
Pb( He, He ∗ → He+2n)
Pb7.
Pb( He, He)
Pb( He, He)
PbWe may immediately rule out any significant contribu-tion from 4), the sequential transfer of two 2n clusters,since we have shown in the previous section that the ini-tial step must have a small cross section on purely kine-matic grounds. Processes 6) and 7) at first sight appearpossible significant contributors due to the strong popu-lation of the intermediate step, as demonstrated in theprevious section. However, they may be ruled out onstructural grounds: In process 6) the intermediate steppopulates low-lying single particle levels in
Pb below4 MeV in excitation energy which are unlikely to havesignificant overlap with levels in
Pb in the requiredexcitation energy range, around 8 MeV or so. For pro-cess 7) to contribute significantly the second step wouldrequire a significant overlap between the ground state of He and the α + 3n configuration, which seems unlikelygiven the accepted status of He as a He + n resonance(see, e.g., Ref. [14]). Process 5) is unlikely since thereappears to be little overlap between the ground state of He and excited states of He, see e.g. the He(p,d) workof Ref. [12], and in any case the known levels are broad,with widths of a few MeV [16]. Process 3) also seemsunlikely since the overlap between the ground state of He and at least the 1.8 MeV 2 + excited state of He issmall [12], although this need not necessarily be the casefor the other known low-lying levels of He at 2.6 and5.3 MeV [15]. However, test calculations of 2n strippingpopulating these levels in He found that not only wasthe cross section significantly smaller than for populatingthe ground state (even with the same spectroscopic fac-tor) but the angular distributions peaked at larger anglesas the excitation energy of the He resonance increased,moving the peak of the corresponding He distributionfurther away from the peak of the observed inclusive Heangular distribution. Finally, process 2) does not seema likely candidate since it would require a sizeable over-lap between the ground state of He and the He + 3nconfiguration in order to make a significant contributionand we are not aware of any structure calculations thatexplicitly mention significant 3n clustering in the groundstate of He.We are thus left with process 1), direct 4n stripping,as our candidate main mechanism for production of He.Transfer of four neutrons can in principle populate statesin
Pb from the ground state (Q = +14 .
99 MeV) up tothe four-neutron separation energy at E x = 18 .
08 MeV(Q = − .
11 MeV), or even beyond if resonant-like statesare considered. However, as discussed in Ref. [6], theoptimum Q value for this process is Q = − . He totalenergy versus scattering angle spectrum together withthe kinematics of the
Pb( He, He)
Pb reaction, as-sumed to be direct 4n transfer, enables us to fix the rangeof allowed excitation energies of the residual
Pb nu-cleus. Under this assumption only states in
Pb with14 MeV ≤ E x ≤
22 MeV can be populated, see Fig. 2(a).To test whether such a process, subject to these kine-matic constraints, can reproduce the shape of the mea-sured inclusive He angular distribution DWBA calcula-tions were performed for direct 4n transfer to states in
Pb at excitation energies of 14, 16, 18, 20 and 22 MeV,covering the observed energy range of He recoils, withangular momentum L = 6 (cid:126) relative to the Pb core,approximately the best matched L value. The shape ofthe angular distribution is only weakly dependent on thevalue of L . The potentials binding the 4n cluster to the He and
Pb cores were of Woods-Saxon form with pa-rameters r = 1 . × (4 + A / ) fm and a = 0 .
65 fm. Thespin-parity of the 4n cluster was assumed to be 0 + , thesimplest possibility consistent with the presence of such acluster in the ground state of He. The optical potentialin the entrance channel was the same as in the previoussection. The He+
Pb optical potential parameters ofRef. [17] were used in the exit channel. Since the calcu-lations were purely qualitative all spectroscopic factorswere set equal to 1.0. The form factors for the states at E x = 20 and 22 MeV were calculated assuming nominalbinding energies of 0.01 MeV for the 4n cluster with re-spect to the Pb core since these values of E x are above FIG. 2: (a) Experimental He total energy versus scatteringangle two-dimensional spectrum for 22 MeV He incident ona
Pb target. Superimposed are kinematic curves for Heejectiles produced by the
Pb( He, He)
Pb 4n-strippingreaction with the
Pb residual in states with E x = 14, 18,22 and 26 MeV (reading from the top down). (b) Angulardistribution of the inclusive He production for 22 MeV Heincident on a
Pb target. The filled circles denote the data ofRef. [6]. The various styles of broken curve denote the resultsof DWBA calculations of direct 4n transfer to states in
Pbat the labelled excitation energies and the background. Thesolid curve denotes the total (sum of all transfer calculationsplus background). See text for details. the 4n emission threshold of
Pb.The inclusive He angular distribution for 22 MeV Heincident on a
Pb target of Ref. [6] was fitted by adjust-ing the normalizations of the DWBA curves and the pa-rameters of an exponential background function (includ-ing any contributions from breakup of the He projectileand fusion-evaporation) to give the best description ofthe data. The data were obtained by integrating, foreach laboratory scattering angle, the energy distributionabove the 8.78 MeV alpha peak arising from the decay ofthe
Po ground state. To assist in fixing the parame-ters of the background function the angular range of thedata was slightly extended to more forward angles thanin Ref. [6]. Care was also taken to avoid unrealisticallylarge contributions from the calculations with E x valuesat the limits of the kinematically allowed range. The re-sults of this analysis are displayed in Fig. 2 (b). As in thecase of the 2n cluster transfer, the calculated shapes ofthe angular distributions were not very sensitive to thetransferred angular momentum but did depend on theexcitation energy of the recoil Pb nucleus, see Fig. 2(b).Our results suggest that the He yield can be well de-scribed by a combination of direct 4n transfer and anexponential background function, the transfer account-ing for 73% of the total (355 mb, cf. the experimentalvalue of 393 +10 − mb [6]). III. SUMMARY AND CONCLUSIONS
In a previous article [6] analyzing the measured in-clusive He and He yields for the He +
Pb sys-tem we concluded, with the aid of DWBA calcula-tions, that for an incident He energy of 22 MeV the
Pb( He, He)
Pb single-neutron stripping reactionwas responsible for about one third of the total measured He cross section, the remaining two thirds being mainlydue to the
Pb( He, He)
Pb two-neutron strippingsince kinematic considerations ruled out breakup as a sig-nificant contributor over the measured angular range. Inthis work we have revised this conclusion in favor of thesingle-neutron stripping mechanism, since a detailed con-sideration of the kinematics of the two-neutron strippingreaction in conjunction with the experimental He to-tal energy versus scattering angle spectrum places strictlimits on the range of possible excitation energies of the
Pb residual which, when applied to DWBA calcula-tions, exclude the possibility of the 2n-stripping provid-ing the main contribution to the measured inclusive Heangular distribution.The relatively small contribution to the inclusive Heyield from two-neutron stripping—estimated to be atmost about 30%—is a robust result, since it is mainlybased on kinematics. Distorted wave Born approxima-tion calculations of the 2n-stripping reaction were un-able to reproduce the shape of the measured He an-gular distribution while remaining within the kinemati-cally allowed values of the
Pb excitation energy, in-dependent of the choice of input parameters, the calcu-lated angular distributions being essentially insensitiveto the exit channel potential due to the low energiesof the He ejectiles relative to the respective Coulombbarrier. It was further demonstrated that the remain-der of the measured inclusive He yield can be ex-plained as mostly arising from the single-neutron strip-ping reaction—approximately 70% of the total—plus asmall exponential background representing the contribu-tion of breakup. However, the DWBA calculations of the single-neutron stripping are more sensitive to the choiceof exit channel optical potential, the energies of the Heejectiles (before decaying into He + n ) being above therespective Coulomb barrier, and a good description ofthe the He yield is dependent on the use of a particularpotential. Since He is unbound it is impossible to checkwhether this potential is consistent with the appropri-ate elastic scattering, although it is at least physicallyreasonable.Based partly on these results, but also on additionalkinematic and structural considerations, it was furtherargued that the inclusive He production was mostlikely dominated by direct 4n transfer. This conclusionwas borne out by DWBA calculations assuming onlythe
Pb( He, He)
Pb direct 4n transfer mechanismwhich, combined with a small background contribution,were able to describe very well the measured inclusive He angular distribution of Ref. [6]. These results areconsistent with the direct 4n transfer channel suggestedin Ref. [3]. This picture is also appealing in view of thestrong beta decay triton branch of He [18, 19], whichcould originate from the decay of the four-neutron skin.This process would be the 4-neutron equivalent to thedeuteron decay branch observed in Li [20]. However,this conclusion is less robust than that concerning the He production since at present nothing is known of thestructure of
Pb in the excitation energy region prefer-entially populated by the 4n stripping reaction, so thatthe DWBA calculations remain purely qualitative.The relative unimportance of 2n stripping does notnecessarily contradict the possibility of a significantdineutron condensate component in the ground state of He, as suggested by recent theoretical predictions ob-tained from Hartree-Fock-Bogoliubov calculations [21]and the alpha-dineutron condensate method [22]. Thecross sections of direct reactions are strongly dependenton kinematic matching conditions (Q value and angularmomentum transfer) as well as the structure of the nucleiinvolved so that different aspects of the structure may beemphasized by different reactions. Both the Q match-ing conditions and structure considerations combine inthis particular case to favor the (cid:10) He | He + n (cid:11) and, toa lesser extent, the (cid:10) He | He + 4 n (cid:11) components of the He ground state.
Acknowledgments
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