Investigation of the 6He cluster structures
ABSTRACT The 4He+2n and t+t clustering of the 6He ground state were investigated by means of the transfer reaction 6He(p,t)4He at 25 MeV/nucleon. The experiment was performed in inverse kinematics at GANIL with the SPEG spectrometer coupled to the MUST array. Experimental data for the transfer reaction were analyzed by a DWBA calculation including the two neutrons and the triton transfer. The couplings to the 6He --> 4He + 2n breakup channels were taken into account with a polarization potential deduced from a coupled-discretized-continuum channels analysis of the 6He+1H elastic scattering measured at the same time. The influence on the calculations of the 4He+t exit potential and of the triton sequential transfer is discussed. The final calculation gives a spectroscopic factor close to one for the 4He+2n configuration as expected. The spectroscopic factor obtained for the t+t configuration is much smaller than the theoretical predictions. Comment: 10 pages, 11 figures, accepted in PRC
- [show abstract] [hide abstract]
ABSTRACT: The nuclear break-up of 6He on a 208Pb target was studied at 20A MeV using a secondary beam of 6He produced by the SPIRAL facility at GANIL. -particles were detected in coincidence with two neutrons with a large angular coverage and the reaction mechanism was identified. From the distribution of the relative angles between the two neutrons the correlation function was extracted. It shows a strong correlation at small relative angles attributed to the contribution of the di-neutron configuration of 6He .European Physical Journal A - EUR PHYS J A. 01/2009; 42(3):441-446.
- [show abstract] [hide abstract]
ABSTRACT: . We have studied an effect of neutron and triton transfer reactions on the p +^6He elasticscatteringat25 MeVbymeansofcoupled - reaction - channelcalculations.Itisfoundthatwhenthetransferreactionsareexplicitlyincludedinthecalculationstheimaginarypartoftheinput$p + $6He optical model potential has to be reduced by 52 percent while its real part enhanced by 15 percent in order to fit the elastic-scattering data. The effect of transfer channels on the real part of this potential is somewhat weaker than that of 6He breakup reported previously. However, for the imaginary part, the effect of transfer channels is dominant. It is concluded that while the breakup contribution to proton elastic scattering mainly affects the real part of the bare potential, the contribution of transfer channels affects mainly its imaginary part.European Physical Journal A 01/2007; 32(2):159-163. · 2.04 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: Momentum correlations inherent to the 6He constituents in the ground state of this nucleus were studied in the quasi-free scattering (QFS) reaction 4He(6He, 2α)2n at 6He beam energy of 25 MeV/nucleon. A detailed study of nucleus structure was performed for the first time in QFS reactions with an unbound spectator. The Plane Wave Impulse Approximation was used in analyzing the experimental data. It was shown that the experimental data are described by model calculations in which the two neutron final state interaction is taken into account. t + t and t + d + n configurations were also studied in the 4He(6He, tα)t and 4He(6He, tα)dn QFS reactions.Bulletin of the Russian Academy of Sciences Physics 01/2010; 74(4):437-442.
arXiv:nucl-ex/0505007v1 4 May 2005
Investigation of the6He cluster structures
L. Giot,∗P. Roussel-Chomaz, C.E. Demonchy, W. Mittig, and H. Savajols
GANIL, BP 5027, 14076 Caen, France
N. Alamanos, F. Auger, A. Gillibert, C. Jouanne, V. Lapoux, L. Nalpas, E.C. Pollacco, J. L. Sida, and F. Skaza
DSM/Dapnia CEA Saclay, 91191 Gif-sur-Yvette,France
M.D. Cortina-Gil and J. Fernandez-Vasquez
Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain
Department of Physics and Astronomy, The Open University, Milton Keynes, MK7 6AA United Kingdom
University of Ioannina, 45110 Ioannina, Greece
PCC, College de France, 11 place Marcelin Berthelot, 75231 Paris, France
A. Rodin, S. Stepantsov, and G. M. Ter Akopian
Flerov Laboratory of Nuclear Reactions, JINR, Dubna 141980, Russia
Department of Nuclear Reactions,
The Andrzej Soltan Institute for Nuclear Studies,
Hoza 69, PL 00-681 Warsaw, Poland
I. J. Thompson
University of Surrey, Guildford,GU2 7XH, United Kingdom
The Henryk Niewodnicza´ nski Institute of Nuclear Physics PAN,
Radzikowskiego 152, PL-31-342 Cracow, Poland
(Dated: February 8, 2008)
The α+2n and t+t clustering of the6He ground state were investigated by means of the transfer
reaction6He(p,t)4He at 25 MeV/nucleon. The experiment was performed in inverse kinematics at
GANIL with the SPEG spectrometer coupled to the MUST array. Experimental data for the transfer
reaction were analyzed by a DWBA calculation including the two neutrons and the triton transfer.
The couplings to the6He →4He + 2n breakup channels were taken into account with a polarization
potential deduced from a coupled-discretized-continuum channels analysis of the
scattering measured at the same time. The influence on the calculations of the α+t exit potential
and of the triton sequential transfer is discussed. The final calculation gives a spectroscopic factor
close to one for the α+2n configuration as expected. The spectroscopic factor obtained for the t+t
configuration is much smaller than the theoretical predictions.
PACS numbers: 25.60.-t, 24.10.Eq, 27.20.+n, 21.10.Jx
In the vicinity of the neutron dripline, the weak bind-
ing of the nuclei leads to exotic features such as halos
. Furthermore, the two neutrons halo systems, such
∗Present address: GSI, D-64291 Darmstadt, Germany; Electronic
as6He,11Li and14Be, exhibit Borromean characteris-
tics, whereby the two-body subsystems are unbound .
Among these Borromean nuclei, the case of the6He nu-
cleus is of a special interest from both experimental and
theoretical points of view to study the halo phenomenon
and 3-body correlations, especially because the α core
can be represented as structureless.
of the dineutron and cigarlike α+2n configurations pre-
dicted for the6He ground-state wave function  was
investigated by means of a 2n transfer reaction or a ra-
diative proton capture [3, 4]. These two experiments give
opposite conclusions concerning the relative importance
of dineutron and cigarlike configurations.
An additional question arises whether the only contri-
butions to the6He ground-state wave function are the
cigar and di-neutron configurations, or if some t+t clus-
tering is also present. According to translational invari-
ant shell model calculations , the6He nucleus is ex-
pected to have a large spectroscopic amplitude for the
t+t configuration as well as for the α+2n configura-
tion, like the6Li nucleus for the configurations α+d and
3He+t. Microscopic multicluster calculations show also
that the binding energy of6He is better reproduced by
including some t+t clustering in the ground state wave
function . The spectroscopic factors predicted for the
t+t configuration by the different models range from 0.44
 to 1.77 .
Experimentally, this t+t clustering was investigated
for the first time by means of (t,6He) transfer reactions
on several targets and a spectroscopic factor St−tof 1.77
was proposed . Recently, Wang et al.
the charge radius of the6He nucleus by using a laser
spectroscopy method and compared the experimental ex-
tracted radius with those predicted by nuclear structure
calculations . The experimental radius is very close to
the predictions of the α+2n cluster models but far away
from those using a combination of α+2n and t+t clus-
ters. To determine the importance of the α+2n and t+t
configurations of the6He nucleus, Wolski et al. measured
at Dubna the intermediate angles of the
angular distribution , in analogy with the reaction
6Li(p,3He)4He used to study the relative importance of
the configurations α+d and3He+t for the6Li nucleus
. This reaction performed at 150 MeV can proceed
as the transfer of two neutrons or of a3H from the6He
nucleus. Several analyses leading to very different spec-
troscopic factors St−t were performed on these experi-
mental data within the distorted wave Born approxima-
tion (DWBA) framework. The DWBA analysis done by
Wolski et al. suggests a spectroscopic factor St−tof 0.42.
Rusek et al. also conclude to a small spectroscopic factor
St−tequal to 0.25 . The extreme case is the analysis
of Oganessian et al., which described the data in a four-
body three dimensional DWBA approach without any
t+t clustering . At the opposite, Heiberg-Andersen
et al. reproduced these data with a spectroscopic factor
St−tof 1.21 and took also into account the 2n sequential
transfer . All these calculations call for data covering
a wider range, especially at backward angles where the
dependence of the6He(p,t)4He differential cross section
with the value of the spectroscopic factor St−tis impor-
tant whereas the effect of the spectroscopic factor Sα−2n
is dominant at forward angles. Hence to clarify the sit-
uation between the different values of the spectroscopic
factor St−t, we measured at GANIL the complete angular
distribution for the6He(p,t)4He with a special emphasis
on the forward and backward angles which were never
The experiment was carried out at the GANIL coupled
cyclotron facility. The composite secondary beam was
produced by the fragmentation of a 780 MeV13C beam
of 5 µAe on a 1040 mg/cm2carbon production target
located between the two superconducting solenoids of the
SISSI device . The6He nuclei were selected with the
two dipoles of the α spectrometer and an achromatic Al
degrader located at the dispersive plane between these
two dipoles. The only contaminant was9Be at a level of
1%. The resulting 150 MeV6He beam with an average
intensity of 1.1 105pps impinged on a (CH2)3target, 18
mg/cm2thick, located in the reaction chamber. A sketch
of the experimental setup is shown on Fig. 1. Due to the
large emittance of the secondary fragmentation beam,
the incident angle and the position on the target of the
nuclei were monitored event by event by two low pressure
drift chambers . The angular and position resolutions
on the target were respectively 0.14◦and 2.4 mm.
FIG. 1: (Color online) Experimental setup.
The4He and3H from the6He(p,t)4He reaction for cen-
ter of mass angles between 20◦and 110◦were detected in
coincidence by the eight telescopes of MUST silicon de-
tector array . These detectors were separated in two
groups arranged to form two 12x12 cm2squares placed on
each side of the beam, one covering an angular range be-
tween 6◦and 24◦and the other one between 20◦and 38◦
with respect to the beam direction. The angular cover-
age in the vertical direction was ± 9◦. Each of the MUST
telescopes is composed of a doubled-sided silicon strip de-
tector backed by a Si(Li) and a CsI scintillator which all
give an energy measurement. The silicon strip detector
is 300 µm thick with 60 strips (1 mm wide) on each side
and provides X-Y position measurement, from which the
scattering angle is determined. The energy resolution in
the silicon strips detectors was 65 keV and the angular
resolution 0.15◦. The4He and3H nuclei were identified
by the standard ∆E-E technique. Due to a saturation
of the Si(Li) preamplifiers, we did not measure the total
energy of the α particles. The off-line identification com-
bined with a gate on the kinematical locus of the transfer
reaction on the3H plot, energy versus scattering angle,
reduced the background from the carbon component of
the target. Fig. 2 shows the angular correlation of the
4He and3H nuclei. The dotted line corresponds to the
calculated 2-body kinematical line for the (p,t) transfer
reaction towards the6He ground state. The remaining
backgound in the vicinity of this line was evaluated and
subtracted to the region of interest.
FIG. 2: (Color online) Scatterplot of the4He laboratory angle
versus the3H laboratory angle detected in coincidence in the
MUST array for the6He(p,t)4He reaction.
The forward and backward center of mass angles of the
angular distribution for the6He(p,t)4He reaction were
measured with the SPEG spectrometer  by detect-
ing respectively the high energy4He and the high energy
triton at forward laboratory angles. The particles were
identified in the focal plane by the energy loss measured
in an ionization chamber and the residual energy mea-
sured in plastic scintillators. The momentum and the
scattering angle were obtained by track reconstruction
of the trajectory as determined by two drift chambers
located near the focal plane of the spectrometer. The
spectrometer was also used to measure the elastic scat-
tering6He(p,p)6He angular distribution from 14◦c.m. to
To extract differential cross sections, data were cor-
rected for the geometrical efficiency of the detection in
SPEG or MUST. This efficiency was determined through
a Monte-Carlo simulation whose ingredients are the de-
tector geometry, their experimental angular and energy
resolutions, the position and the width of the beam on
the target. The error on the MUST detection efficiency
deduced from the Monte-Carlo simulation is estimated to
be 5 %. The absolute normalisation for the elastic scat-
tering data on the protons in the (CH2)3target and for
the transfer reaction was obtained from the elastic scat-
tering on12C which was measured simultaneously. Elas-
tic scattering calculations for the system6He+12C using
020 406080 100 120140160 180
Wolski et al.
tion. The full circles correspond to the present data. The
open circles are the data measured at Dubna .
Differential cross section for the6He(p,t)4He reac-
different optical potentials [19, 20] show that the angular
distribution at forward angles up to 7◦c.m. is dominated
by Coulomb scattering and is rather insensitive to the
potential used. Therefore the absolute normalisation of
the data was obtained from the measured cross section
on the first maximum of the6He(12C,12C)6He angular
distribution. The uncertainty on the normalisation is of
the order of 10 %. The same normalisation factor was
applied to the transfer data measured with the SPEG
spectrometer. In the overlap domain between 19◦c.m.
and 27◦c.m. for the transfer data obtained with SPEG
or MUST, the agreement was good. The final differential
cross section in this angular region is the statistical av-
erage value between the two sets of data. Fig. 3 displays
the transfer data obtained in the present experiment to-
gether with results measured previously at Dubna at the
same energy . The uncertainty of the dubna differen-
tial cross sections is estimated to be within a 30% limit,
mainly due to the beam monitoring errors. The error
bars displayed for the GANIL data are purely statisti-
cal. The data points between 120◦and 155◦could not
be obtained due to a lack of statistics in a set of runs
with the MUST array positionned in this angular region.
The main difference between the two sets of data ob-
tained at GANIL and Dubna is related to the width of
the second minimum around 90◦which is larger in our
case. The Dubna data were extracted from the energy
correlation between the α particles and the tritons de-
tected in coincidence in two telescopes. This energy cor-
relation presented a strong background, caused by the
breakup of the6He particles on the carbon component of
the target. The breakup background is not uniform and
could explain the difference observed between the two
sets of data in the angular range corresponding to the
deep minimum around 90◦. Here, the angular correlation
of the4He and3H nuclei combined with a selection on
the kinematical locus on the3H plot, energy versus scat-
tering angle, reduced strongly the breakup background
and improved the quality of the data, as shown on Fig.
2. Moreover, the oscillation widths of the GANIL data
are in better agreement with the new data measured at
Dubna by Stepantsov et al. .
III.ELASTIC SCATTERING AND THE6He + p
The6He + p elastic scattering data obtained here com-
plement the data measured at Dubna at the same energy
in two differents runs [10, 22]. Fig. 4 shows the three
sets of data which are in excellent agreement. These new
data allow to better determine the nuclear interaction po-
tential6He + p, which is an essential ingredient for the
analysis of the transfer reaction, since it is necessary for
the entrance channel in the DWBA calculation. Previ-
ous results obtained on6He + p elastic scattering in the
same energy range have shown that the nucleon-nucleus
optical models potentials used for stable nuclei have to
be modified in the case of loosely bound nuclei such as
6He [12, 23]. Coupling to the continuum and to the res-
onant states are expected to play a significant role since
the scattering states are much closer to the continuum
states than in stable nuclei. In this work, we tried two
approaches to take into account these couplings to the
continuum and thus the breakup effects. First, these ef-
fects were phenomenologically simulated by reducing the
real part of the potential or by adding a dynamical polar-
ization potential as discussed in Ref. . In this case,
the interaction potential6He + p was calculated within
the approach derived by Jeukenne, Lejeune and Mahaux
(JLM) . As seen in Fig. 4, this renormalization of the
real part of the JLM potential allows also to reproduce
the sets of data obtained at GANIL and Dubna reason-
In a second approach, the coupling to the contin-
uum was explicitly included by means of the coupled-
discretized-continuum-channels (CDCC) method. This
approach previously used by Rusek et al. [12, 25] assumes
a two body cluster model α+2n for the6He nucleus with
the spin of the 2n cluster set to s=0. The wave functions
Ψ0(r) and Ψ2(r) describing the relative motion of the
two clusters in the6He ground state and the6He(2+)
resonant state were calculated in potential wells whose
depths were varied to reproduce respectively the bind-
ing energy of 0.975 MeV and the excitation energy of
1.8 MeV. The parameters of these Woods-Saxon binding
potentials are listed in Table I. The continuum above
the6He → α+2n breakup threshold was discretized into
a series of momentum bins with respect to the relative
α-2n momentum k. The lowest bins were of ∆k=0.25
fm−1while all the others were of ∆k=0.2 fm−1. The
model space was truncated at the energies close to the
Stepantsov et al.
Wolski et al.
FIG. 4: Differential cross section for the6He(p,p)6He elastic
scattering compared to JLM calculations.
correspond to the present data.
crosses are the data measured at Dubna [10, 22].
The full circles
The open circles and the
t+t breakup threshold. The wave function Ψ(r) repre-
senting a bin is the average function over the bin width
of the cluster wave functions φ(r,k) in the bin,
where r is the4He-2n distance and N is the normal-
ization factor. All the spectroscopic amplitudes for the
couplings are assumed to be equal to one. The central
and coupling potentials Vi→f(R) used in the CDCC cal-
culations were derived from4He-p and 2n-p potentials by
means of the single-folding method,
Vi→f(R) = ?Ψf(r)|U2n−p(|?R + 2/3? r|)
+ U4He−p(|?R − 1/3? r|)|Ψi(r)?
where R is the distance between the6He nucleus and
the proton. The 2n-p potential was assumed to be the
same as for d-p. The parameters of the optical potentials
U2n−pand U 4He−p, listed in Table II, were obtained by
fitting the elastic scattering data of deuterons and alpha
particles from protons at the required energy [26, 27].
The results of the CDCC calculations for the6He+p elas-
tic scattering, performed using version FRXY-1c of the
code FRESCO , are plotted in Fig. 5 together with
the three sets of data measured at GANIL and Dubna.
These CDCC calculations reproduce, too, the values
and the slope of the differential cross section for the in-
elastic scattering exciting6He to its 2+resonant state
. The calculated value of the reduced transition prob-
ability B(E2;g.s.→2+)=7.08 e2fm4is larger than the
value of 3.21 e2fm4published earlier by Aumann et al.
. However, it should be noticed that the determi-
nation of B(E2) is strongly model dependent when the
0 204060 80 100 120 140
Wolski et al.
Stepantsov et al.
020406080 100 120 140
Stepantsov et al.
FIG. 5: a) CDCC calculations for the elastic scattering of6He
from1H. The experimental data are from this work (black cir-
cles) and from Ref. [10, 22]. b) CDCC calculations for the
inelastic scattering of6He from1H leading to the 2+resonant
state of6He at excitation energy of 1.8 MeV. The experimen-
tal data are from Ref. .
reaction is not dominated by the Coulomb interaction.
In particular, the value of B(E2) depends on the choice
of the neutron density distribution.
By inversion from the elastic channel S matrix, gener-
ated by the CDCC calculations, a local potential6He+p
including the breakup effects, is obtained. The inver-
sion is carried out using the iterative-perturbative (IP)
method [30, 31].The angular distribution calculated
within the CDCC approach or with the local potential,
named′Pot. IP′, can hardly be distinguished in Fig. 5.
The reaction cross sections calculated respectively with
the potential IP and the renormalized JLM potential are
respectively σR = 532 mb and 394 mb. The reaction
cross section for6He on proton has been measured at 36
MeV/nucleon using the transmission method and a value
of σR= 409±22 mb was obtained . Considering that
in the present energy domain, the reaction cross section
σRincreases when the energy of the projectile decreases
, the experimental value at 25 MeV/nucleon should be
closer to the value calculated with the IP potential. This
IP local potential and the renormalized JLM potential
will be tested in the next section as entrance potentials
for the DWBA calculation of the6He(p,t)4He.
IV.DWBA ANALYSIS OF6He(p,t)4He
DWBA calculation including both 2n and t trans-
fer from the6He ground state were performed on the
6He(p,t)4He data with the code FRESCO used in its fi-
nite range option. A sketch of the calculation is shown
in Fig. 6. The couplings to the continuum states were
He + p
α + 2n
(Color online) Scheme of the6He(p,t)4He DWBA
taken into account with the entrance channel potential
6He+p calculated, as described above within the JLM
or the CDCC framework. The effect of the triton se-
quential transfer (t=2n+p) was also investigated. The
wave functions describing the relative motion of the two
clusters α+2n, t+t, p+t and p+2n respectively in the
ground state of6He,
Woods-Saxon potentials with the well depth adjusted to
reproduce the corresponding binding energies, according
to the usual separation energy prescription. The remnant
potential Vp−twas taken from Ref.  and the remnant
potential Vα−pwas determined in the previous section.
All the potentials and the spectroscopic amplitudes used
in the calculation are listed in Table I and II.
Special care was taken in the choice of the potential for
the α+t exit channel and several potentials were consid-
ered [10, 12, 13, 34, 35, 36]. To obtain the α+t potential,
we used α+3He elastic scattering data at Ec.m. = 28.7
MeV  as the3H(α,α)3H reaction was not studied in
the energy range considered presently. Two approaches
were considered to extract the α+3He optical potential.
The process of one neutron transfer, which is not dis-
tinguishable experimentally from the elastic scattering,
was first explicitly taken into account in a DWBA analy-
sis of the3He(α,α)3He reaction. The dotted and dashed
curves on Fig. 7 show respectively the contribution of the
elastic scattering and the one neutron exchange to the
4He and3H were obtained from
3He(α,α)3He reaction. Hence, the potential A extracted
from the DWBA analysis represents only the elastic scat-
tering between the α and the3He. Next, we used the
potential B obtained in Ref. fitted on the complete
differential cross section of the3He(4He,4He)3He elastic
scattering. This fit on the α+3He data corresponds to
the solid line on Fig. 7. Although the fit is still far from
perfect, it reproduces the gross features of the measured
angular distribution. The values of these two exit poten-
tials A and B are given in Table II.
020 406080 100120140160 180
Ec.m. = 28.7 MeV
Elastic, Pot. A
+ n exchange, Pot. A
Elastic, Pot. B
FIG. 7: Differential cross section for the3He(α,α)3He reac-
tion compared with DWBA calculations assuming only the
elastic scattering and after the one neutron exchange. The
experimental data are from Schwandt et al. .
Both the direct and the sequential transfer of the triton
were included in a DWBA calculation, described on Fig.
6, and then in a coupled reaction channels calculation
(CRC) where the backcouplings were taken into account.
The proton transfer, which is the second step of the tri-
ton sequential transfer, can be seen as a proton exchange
between the two exit channels3H+α and α+3H and is
directly included in the DWBA calculation. Hence, the
exit channel potential α+3H has not to take into account
the proton exchange but only the elastic scattering. This
corresponds to the potential A, as determined above, for
the exit channel. A comparison between a DWBA cal-
culation with only the triton direct transfer and DWBA
and CRC calculations including the sequential transfer
t=2n+p is shown on Fig. 8. These calculations do not
allow to reproduce at the same time the experimental
data at forward and backward angles. Futhermore, the
amplitude and/or the position of the oscillation at 60◦is
Hence, we used Potential B for the exit channel of
the reaction, considering that the proton exchange in
6He(p,t)4He 150 MeV
Pot. IP and Pot. A
St-t = 0.08
Sα-2n = 1.
t direct transfer, DWBA
+ t sequential transfer, DWBA
+ t sequential transfer, CRC
(t=2n+p) on the6He(p,t)4He reaction.
Effect of the sequential transfer of the triton
the α+t partition, and consequently the sequential tri-
ton transfer, could be in some sense described by the
exchange term included in the Potential B. Only the
2n and the direct triton transfer are thus explicitly in-
cluded in the DWBA calculation. Fig. 9 compares the
6He(p,t)4He differential cross section obtained at GANIL
with the DWBA calculation using Potential IP for the
entrance channel and Potential B for the exit channel,
which gives actually the best description of the features
of the6He(p,t)4He angular distribution. The spectro-
scopic factors for the α+2n and t+t configurations were
adjusted to reproduce the data. The adjustment on Fig.
9 is a compromise between the experimental values at for-
ward and backward angles and the width of the second
oscillation. The dashed line on Fig. 9 corresponds to the
DWBA calculation where only the 2n transfer is taken
into account with a spectroscopic factor Sα−2nequal to
1, which is close to the predicted value. The spectro-
scopic factor St−t, determined from the comparison with
the data at backward angles, is equal to 0.08 with an
uncertainty of the order of 50%. The crosses on Fig. 9
correspond only to the triton transfer. The solid line is
the coherent sum of the two processes with these values
of their spectroscopic factors. Even if the spectroscopic
factor of the t+t clustering is small, the t-t component
is essential to reproduce the backward angles.
We tried to include the sequential transfer of the two
neutrons, processing via the5He+d channel. This calcu-
lation required the optical potential for the5He+d sys-
tem. Of course, no deuton elastic scattering data exist
for this unbound nucleus. A first potential was obtained
from the6He(p,d)5He reaction . The second poten-
tial was calculated from a method proposed by Keaton
0 204060 80100120140 160180
6He(p,t)4He 150 MeV
Pot. IP and Pot. B
Contributions of 2n and t transfer to the DWBA
0 2040 60 80100120140160 180
6He(p,t)4He 150 MeV
DWBA, Pot. B
FIG. 10: Dependence of the results of the DWBA calculation
on the choice of the6He + p entrance potential.
et al. convoluting the potentials5He+p and5He+n, de-
rived from the CH89 parametrization, with a deuteron
wave function [39, 40, 41]. These two potentials provided
a very poor reproduction for the one and two neutrons
transfer reactions. Therefore, we removed this channel in
the final caculation, due to the lack of a reliable potential
for the unbound nucleus5He.
Finally, both entrance potentials including breakup ef-
6He(p,t)4He 150 MeV
DWBA, Pot. IP and Pot. B
Sα-2n = 1
St-t = 1.77 Smirnov
St-t = 0.44 Arai
St-t = 0.08 This work
value of the spectroscopic factor St−t .
Dependence of the DWBA calculation with the
fects, obtained in the previous section, were also tested
in Fig.10. Obviously, the IP potential deduced
from a coupled-discretized-continuum-channels calcula-
tion, where the couplings to the continuum are explicitly
taken into account, improves the description of the data
compared to the JLM approach.
Fig. 11 shows the dependence of the DWBA calcula-
tion with the value of the spectroscopic factor St−tfor 3
cases: i) the value derived from the present work ii) the
value obtained in the 3-body cluster model by K. Arai
et al.  and iii) finally the value from a translational
invariant shell model calculation . It is clear that in
the present analysis, the two last values strongly over-
estimate the cross section measured at backward angles,
and that the largest value even affects the reproduction of
the most forward angles of the data. The theoretical val-
ues are considerably outside the range of the uncertainty
of the experimental data. The different approaches of
analysis performed within this work showed that the fi-
nal results somewhat depend on the potentials used in
the calculation, especially in the exit channel potential.
Considering the difficulties mentioned previously on this
potential, one can not exclude that another type of ap-
proach used to derive this potential could alter our con-
The6He(p,t)4He reaction at 150 MeV has been in-
vestigated at GANIL in order to provide insight on the
6He cluster structure: the α+2n and di-triton configu-
rations. The transfer differential cross section were mea-
sured with the SPEG spectrometer coupled to the MUST
array. The transfer data obtained at forward and back-
ward angles allowed to determine the spectroscopic fac-
tors Sα−2n and St−t and thus the contribution of the
configurations α+2n and t+t to the6He ground state
wave function. The6He(p,t)4He data were analyzed by
means of the DWBA and the coupled channels method
taking into account the direct 2n, the direct triton trans-
fer and also the sequential transfer of the triton. The
6He+p entrance channel optical potential of these cal-
culations was obtained by the inversion of the elastic
channel S matrix generated from a CDCC calculation
which took into account all the couplings to the con-
tinuum states. This CDCC calculation, where the con-
tinuum above the α+2n threshold is discretized, repro-
duced the elastic6He(p,p)6He, also measured in this ex-
periment, and the6He(p,p’)6He inelastic data available
at the same energy as the transfer reaction. A detailed
study of the exit channel was performed. The difficul-
ties encountered in this part of the analysis are related
to the lack of4He+t elastic scattering data in the en-
ergy range considered presently, and to the strong ef-
fects of the neutron exchange in the4He+3He system
which was used instead. The best description of the ex-
perimental data was obtained with a DWBA calculation
taking into account the 2n and t direct transfer. The
triton sequential transfer is assumed to be directly in-
cluded in the exchange term of the exit potential α+3H.
The present work shows that the DWBA analysis of the
transfer data is strongly dependent on the chosen poten-
tials. Nethertheless, the transfer data at backward angles
can only be reproduced with a spectroscopic factor St−t
which is much smaller than the theoretical values and
the t-t configuration is necessary for the description of
the6He ground state wave function.
The support provided by the SPEG staff of GANIL
during the experiment is gratefully acknowledged. We
would like to thank Y. Blumenfeld and N. K. Timo-
feyuk for fruitful discussions during the course of this
work. This work was financially supported by the IN2P3-
Poland cooperation agreement 02-106. Additional sup-
port from the Human Potential Part of the FP5 Euro-
pean Community Programme (Contract No HPMT-CT-
2000-00180) is also acknowledged.
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6Heg.s. = α + 2n
6He2+ = α + 2n
6Heg.s. = t + t
3Hg.s. = p + 2n
4Heg.s. = p + t
4Heg.s. =3He + n
TABLE I: Parameters of the binding potentials and the spectroscopic amplitudes.
d + p
α + p
α +3He, Pot. A
α +3He, Pot. B
TABLE II: Parameters of the input optical model potentials.