In flight production of a 8Li radioactive beam for Big Bang nucleosynthesis investigations at LNS Catania

ARTICLE IN PRESS

Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415 www.elsevier.com/locate/nima

In flight production of a 8Li radioactive beam for Big Bang nucleosynthesis investigations at LNS Catania C. Agodia, R. Albaa, L. Calabrettaa, S. Cherubinia,b, L. Cosentinoa, A. Del Zoppoa,, A. Di Pietroa, P. Figueraa, M. Gulinoa,b, A. Musumarraa,b, M.G. Pellegritia, R. Pizzonea, C. Rolfsc, S. Romanoa,b, C. Spitaleria,b, S. Tudiscoa,b, A. Tuminoa,b a INFN-Laboratori Nazionali del Sud, Via S.Sofia 44, I95123 Catania, Italy Dipartimento di Metodologie Fisiche e Chimiche per l’Ingegneria, Universita’ di Catania, I95123 Catania, Italy c Institut fur Physik mit Ionenstralen, Ruhr-Universitaet Bochum, Bochum, Germany

b

Received 15 February 2006; received in revised form 7 June 2006; accepted 7 June 2006 Available online 14 July 2006

Abstract The in flight production of a secondary 8Li radioactive beam using the existing beam transport lines at the SMP13 Tandem accelerator of the Laboratori Nazionali del Sud in Catania is studied. The method consists in the momentum filtering by a switching magnet of the 8 Li ions emitted backward in the centre of mass of the 2H(7Li,p)8Li reaction, followed by a time-of-flight tagging of the deflected ions. Details of the experimental procedures and preliminary results of the 8Li(4He,n)11B reaction study relevant for pregalactic nucleosynthesis are presented and discussed. r 2006 Published by Elsevier B.V. PACS: 29.27.Eg; 29.27.Fh; 25.60.
t; 26.35.+c Keywords: Radioactive ion beams; Big Bang nucleosynthesis

1. Introduction In the last decade, the availability of radioactive ion beams (RIBs) has made it possible to explore many new avenues in nuclear physics. Along with the discovery of new phenomena in nuclear structure (e.g. Refs. [1,2]) and reaction mechanisms (e.g. Refs. [3,4]), the availability of RIBs allowed the study of a variety of reactions having astrophysical interest (e.g. Ref. [5]). Various techniques with different degree of complexity have been used to produce these beams. In the intermediate energy (E410 MeV/nucleon) range, RIBs have been produced using the in flight fragmentation technique (e.g. Refs. [6–9]). A heavy ion beam impinges on a thin target where secondary reaction products following fragmentation reactions are created. These reaction proCorresponding author. Tel.: +39095542280; fax: +390957141815.

E-mail address: [email protected] (A. Del Zoppo). 0168-9002/$ - see front matter r 2006 Published by Elsevier B.V. doi:10.1016/j.nima.2006.06.053

ducts emerge from the production target with a velocity close to the one of the primary beam and with narrow angular and momentum distributions. Secondary beams of interest are then selected by a dedicated magnetic system and sent onto the secondary target. Low-energy RIBs have been produced using the twoaccelerator ISOL technique [10–14]. A primary stable beam is sent onto a thick target where the radioactive ions are produced by different reaction mechanisms and stopped. The produced radioactive ions diffuse out from the target and are ionized and preaccelerated. The secondary beam of interest is then selected by a proper magnetic system and accelerated by a second machine. This technique, used in dedicated accelerator facilities based on extremely complex technologies, allows to deliver to the final users radioactive beams with excellent optical quality equal to one of the stable beams. The EXCYT facility [15] under commissioning at Catania uses the ISOL technique.

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

2. 8Li production reaction In the inverted kinematics reaction 7

Li þ 2 H ! 8 Li þ 1 H

(1)

at bombarding energy up to a few MeV/nucleon, 8Li nuclei are produced in their I p ¼ 2þ ground state, mainly, or, if energetically allowed, in the only bound excited state I p ¼ 1þ at E  ¼ 0:980 MeV. 8Li nuclei formed in the excited state decay to the ground state with the time characteristic of the g transition and this decay leaves the linear momentum of the nucleus almost unchanged. The motion of the 8Li nuclei in the ground or in the excited state is completely determined by momentum and total energy conservation: for a given momentum of the primary 7Li beam in the laboratory system, the 8Li and the proton in the final state, two body reactions (1) have equal and opposite momentum vectors in the centre of mass and the momentum vector heads lie onto a spherical surface whose

Vf Vb

θb

θlab

θf

VCM

Fig. 1. Sketch of vector composition in velocity space.

1.2 1.0 momentum ratio

Low-energy RIBs have also been produced in a number of laboratories with in flight approaches (e.g. Refs. [16–21]) obtaining beams of sufficient quality to perform a selected class of experiments. A common idea in these methods, is to produce the radioactive species of interest using (d,n), (d,p) or (p,n) reactions in inverse kinematics. The radioactive nuclei of interest emerging from the target are then separated and refocused onto a secondary target by dedicated magnetic systems specially designed and built for this purpose which may have noticeable degrees of complexity [16–21]. With the RIB facilities and techniques mentioned above the typical intensity of exotic beams, close to the neutron or proton drip lines, is of the order of a few ions/s. On the other extreme, exotic beams in proximity of the stability valley are produced with much larger intensity, in the range 106–108 ions/s. This work is devoted to those applications with beams close to the stability valley where the requests of the largest intensity available and of high beam quality are not mandatory. For these cases, implementing low intensity RIB production at a stable beam accelerator facility using the existing beam transport devices could represent a helpful task. In such a context, in the present paper we report on the in flight production of a low intensity ðp104 =sÞ secondary 8Li beam in the inverse kinematics 7 Li þ 2 H ! 8 Li þ 1 H primary reaction at the Laboratori Nazionali del Sud Tandem accelerator facility in Catania. The activity we are going to discuss has been triggered by the specific aim of studying the 8Li(a,n)11B reaction, a possible and important way through the A ¼ 8 mass gap as in the inhomogeneous Big Bang nucleosynthesis [22] as well as in the r-process nucleosynthesis [23].

407

Pf / P7Li

0.8 Pb / P7Li

0.6 0.4 0.2 0.0 0.0

10.0 7Li

20.0 energy (MeV)

30.0

Fig. 2. FKS (continuous line) and BKS (dashed line) 8Li to momentum ratios at WLab ¼ 01 versus the primary 7Li kinetic energy.

7

Li

radius is 
pgsðexcÞ ¼ 2

 1=2 M 2H M 8 Li  M 1 H E 7 Li þ QgsðexcÞ M 2 H þ M 7 Li M 1 H þ M 8 Li (2)

where the reaction Q values are Qgs ¼
0.19 MeV and Qex ¼
1.170 MeV. Fig. 1 depicts the vector composition (not in scale) of reaction (1) in velocity space for a given 8Li entry state. Because of the inverted kinematics, the centre of mass velocity always exceeds that of 8Li in the centre of mass and, consequently, at a fixed allowed laboratory angle W, two 8Li groups exist with different laboratory velocities vf and vb, the former moving in the forward direction and the latter moving in the backward direction in the centre of mass system. This means that, depending on the bombarding 7Li energy, inside the forward cone determined by the geometrical acceptance Wmax of the following beam transport line, the 8Li linear momentum (and kinetic energy) is distributed according to a spectrum consisting of two or four lines, two lines of unequal intensities for each of the 8 Li entry states (i.e. ground state and first excited state). For small values of Wmax (Wmax 1 ) the kinematical spread is negligible and the mean linear momentum in each line is hPgsðexcÞ if  ðM 8 Li  vCM þ pgsðexcÞ Þ

(3a)

hPgsðexcÞ ib  ðM 8 Li  vCM
pgsðexcÞ Þ

(3b)

ARTICLE IN PRESS 408

C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

for forward and backward moving ions, respectively, with hPgs ib ohPexc ib ohPexc if ohPgs if and similarly for the kinetic energies. Fig. 2 shows a comparison between the 8Li to 7Li momentum ratios of both forward and backward ground state solutions calculated within the laboratory angular acceptance of the downstream set up Wmax  20 mr. The calculation is extended to low bombarding energies close the limit at which Wb ¼ Wf (E0.86 MeV) in the centre of mass frame. The forward (Wf  0) solution is always too much close in momentum to the very intense primary beam whereas the 8Li momentum of the backward solution (Wb  p) equals approximately 70% of the incident 7Li momentum. This fact provides us with the valuable opportunity that the separation of 8Li ions produced in the backward solution can be achieved simply using a deflecting dipole magnet. The practicability of such an opportunity is explored experimentally in the following. 3. 8Li production: set up and procedures The availability of a good quality primary beam in terms of emittance and momentum spread is the first crucial requirement of the method. In this respect the 7Li beam delivered by the SMP13 Tandem Van de Graaf accelerator of the Laboratory Nazionali del Sud in Catania, with typical emittance of 4p mm mrad and relative momentum uncertainty better than, 2  10
4 is well suited. The set up used to produce and separate the 8Li beam is sketched in Fig. 3. The primary 7Li beam impinges on the primary 2H target where 8Li ions are produced in reaction (1). After the target, the set up consists of focusing and deflecting magnetic sections and of scintillators and Faraday cup monitors which are permanently installed in the standard beam transport line used. For both 8Li groups, hereafter referred to as FKS or BKS (forward or backward kinematical solution) the beam transport line was tuned using a 7Li pilot beam having the same rigidity as the one of the 8Li ions to be transported. Specific detectors and monitors for charged particles and neutrons are located along the beam line as discussed in detail in the following. Primary targets consisting of solid CD2 foils with thickness up to 1200 mg/cm2 and a D2 gas cell with pressure values up to 200 mbar were used in the measurements. The CD2 foils were coated with 30 mg/cm2 carbon layers on both sides so that thicknesses in the range 150–1200 mg/cm2 could be irradiated for several hours with currents of the order of 500 pnA of 7Li. The gas target consisted of a cylindrical cell (6 mm diameter  100 mm length) with 0.5–2 mm thick entrance and exit Al windows. Target equivalence in terms of their content in 2H is regulated by the relation 1 mbar of 2H6.6 mg/cm2 of CD2. In order to determine their thickness uniformity, samples of CD2 and of Al foils were irradiated by 5.48 MeV alpha emitter 241Am source and the broadening of the transmitted peak was observed in a Si detector. The dispersion

Fig. 3. Sketch of the experimental setup. Q indicates quadrupole doublets, D the dipole magnet, MCP1 and MCP2 the microchannel plate detectors, n-det the neutron detector surrounding the 4He gas target. A DE
E removable telescope was inserted, when needed, at the MCP2 position. The 8Li intensity monitor is described in the text.

of the thickness uniformity was established with the help of straggling and energy loss calculations by assuming uncorrelated fluctuations on the two sample faces and subtracting the straggling effect. Typically, our CD2 targets exhibit a relative thickness dispersion of 15%–20% (standard deviation %) while a value of 5%–10% characterizes the thickness fluctuations of our Al windows. A focusing quadrupole doublet (Q2 in Fig. 3) is located between the production target and a switching dipole magnet. The beam emerging from the magnet output at 601 was refocused by the following beam line quadrupole doublet Q3 (Fig. 3) onto a 8Li intensity monitoring device which is not sensitive to (and it is not damageable by) beams of stable nuclei. The 8Li intensity monitor consists of a movable Ta catcher having the form of a disk (f ¼ 40 mm), which can be temporarily inserted into the beam axis, and of a 300 mm2, 30 mm thick, surface barrier silicon detector permanently located on a plane parallel to the Ta catcher with its centre at a distance of 100 mm from the beam axis (see inset in Fig. 3). Aluminium degrader foils of adjustable total thickness were inserted along the beam axis to implant the incoming 8Li ions very close to the Ta catcher surface. In its ground state, the unstable 8Li nucleus experiences a b
transition with mean life t ¼ 1211:9 1 ms [24] to the broad I p ¼ 2þ excited state at 3.040 MeV of 8 Be. This promptly disintegrates into two a particles having an energy spectrum [25] peaked at E1.5 MeV and with a high-energy tail extending up to about 5 MeV. The Ta catcher is mounted on a rotor shaft and moved cyclically between the beam axis, where it collects 8Li nuclei (position ‘‘IN’’), and the Si detector (position ‘‘OUT’’), which observes the b-delayed a particles from the decay of 8Li, with a waiting time Tw ¼ 1200 ms (approximately one 8Li mean life) at both positions and a transfer time T tr ¼ 150 ms. By denoting with T ¼ 2ðT w þ T tr Þ the period of each cycle, the link between the incident 8Li

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

409

x=3 mm; x′=20 mrad, DP/P=0, y=3 mm; y′=6 mrad Q3A Q3B

x(cm)

4

y(cm)

Q2A Q2B

2

60° bending magnet

R16 (cm/%)

2

4 1

2

3

4

5 [m]

6

7

8

9

10

Fig. 4. Transport set up optical scheme and beam envelope from the production target to the 8Li monitor. The dispersion curve (cm/%) along the trajectory is also shown. The size of the vacuum chamber radius at Q3 and that of the dipole magnet entrance aperture determine the geometrical acceptance along x and y, respectively.

intensity I and the actually monitored intensity Imon is (4)

where Tw/T is the fraction of the 8Li intensity which is caught by the Ta catcher at the position ‘‘IN’’, a fraction Z of which decays at the position ‘‘OUT’’ and a fraction e of this is observed in the silicon detector. The value of Z depends only slightly on the number of cycles under observation and even for a few cycles it is very close to its asymptotic value Zasympt ¼

∆P/P=0.8%, h=0.91, ∆M/M0=0.011 ∆P/P=2.0%, h=0.92, ∆M/M0=0.011 ∆P/P=6.0%, h=0.90, ∆M/M0=0.011 σ/P=0.2%, h=0.92, ∆M/M0=0.011 σ/P=3.0%, h=0.96, ∆M/M0=0.011

1

t ½eT w =t
1 2 e
ðT
T tr Þ=t . Tw ð1
e
T=t Þ

The silicon detector acceptance e was determined by a Monte Carlo calculation. The total efficiency (Tw/T)Ze of the 8Li monitor amounts to 0.035. Fig. 4 shows the ion optical trajectory of the largest accepted divergence (Wx p20 mr, Wy p6 mr) along both dispersion and the non-dispersive planes of the transport set up in Fig. 3. To allow a preliminary direct evaluation of the dispersion effects caused by the ion momentum spread also the curve R16 is shown. We measured the momentum acceptance of the transport set up at the 8Li monitor position in the case of an injected ‘‘pencil’’ beam. We removed the production target and then we injected into the magnet the low emittance 7Li tandem beam. By varying the magnet rigidity M and using Faraday cups we found a rectangular acceptance centred at the beam rigidity M0 having width DM pencil ¼ 0:012M 0 and height hpencil ¼ 1. This result was closely reproduced by pencil beam transport computer simulations using the TURTLE ray tracing code [26]. Using this code we have investigated the correlations which come into play when ions with spread in position, angle and linear momentum are injected into the transport line. As the kinematical momentum spread is of the order of 4  10
4 at E 7 Li X3 MeV for both FKS and BKS ions the small angle-momentum correlation introduced by reaction (1) was ignored. We simulated the transported intensity I(M) as a function of the magnet rigidity M for two types of injected distributions of great importance in the following: (a) rectangular test functions

0.8

I(M)/I0

I mon

Tw Z
¼I T

0.6

0.4

0.2

0

0

1

2

3 M-M0 /Σ

4

5

Fig. 5. Comparison between TURTLE simulations (symbols) and calculated I(M) spectra (curves), for rectangular and Gaussian injected functions characterized by the listed values of DP and s, respectively. The momentum shift jM
M0j on the horizontal axis is divided by S ¼ s or by pffiffiffiffiffi S ¼ DP= 12 to emphasize the cases with narrow injected distributions where large differences are observed. The accuracy on the effective acceptance parameters DM and h is 75%, typically.

versus both angle and momentum characterized by dispersions DW ¼ 40 mr (FW) and DP (FW), respectively; (b) Gaussian test functions versus both angle and momentum characterized by dispersions DW ¼ 40 mr (FWHM) and s (variance square root), respectively. Examples of simulated I(M) spectra divided by the ion intensity I0 injected into the geometric acceptance are reported in Fig. 5. In the cases regarding rectangular injected function the simulated I(M)’s provide an immediate evidence that the transport set up behaves as a rectangular momentum filter with the accepted width DM and the step height h determining the size of a regular trapeze

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

410

having the major basis equal to DP þ DM, the minor basis equal to jDP
DMj and the height given by IðMÞ=I 0 ¼ ðDM=DPÞh, if DMpDP, and IðMÞ=I 0 ¼ h, if DM4DP. Accordingly, and in order to check such a behaviour also with the injected Gaussian, we have calculated analytically the transported intensity I(M) simply by folding the normalized injected momentum test functions dI inj ðPÞ=dP with a rectangular momentum acceptance, i.e.

7000 Solid target

Deflected 8Li intensity (ion/(s pµA))

6000

D = 1.2×1019

2

H atoms/cm2

5000

4000 g.s.

Z

MþDM=2

IðMÞ ¼ I 0 h

3000

M
DM=2

2000

0.980 MeV

1000

0 365

370

375

380 385 M (MeV/c)

(a)

390

395

400

dI inj ðPÞ dP dP

(5)

and then we have fitted the simulated data with (5) leaving DM and h as free parameters. The satisfactory comparison between simulated and calculated I(M) as those reported in Fig. 5 supports a description in which the optical correlation modifies the pencil beam rectangular acceptance according to a decrease of both h and DM of at most 10% almost independent of the input function-type and momentum spread values in the range of interest in this work.

6000 gas target D = 4.9×1019

2H

atoms/cm2

4. 8Li beam transported intensity

Deflected 8Li intensity (ion/(s pµA))

5000 g.s.+0.980 MeV 4000

3000

2000 g.s. 1000 0.980 MeV 0 285

290

(b)

295

300

305 310 315 M (MeV/c)

320

325

330

335

Fig. 6. (a) 8Li transported intensity, scaled to the primary 7Li current, versus 8Li linear momentum for the forward solution tuning case and a 160 mg/cm2 solid CD2 primary target with a primary beam energy of 11 MeV. The solid curves through the experimental points are calculated as discussed in the text. The contributions of 8Li produced in the ground and first excited state 0.980 MeV are clearly resolved in the experimental data. (b) Same as (a) but for the backward solution tuning case and a gaseous deuterium target with a primary beam energy of 21 MeV. The contributions of 8Li produced in the ground and first excited state are not resolved experimentally but are clearly unfolded by the fit procedure.

For each value of the magnet rigidity M the intensity I mon ðMÞ averaged over a time interval of about 120 s, corresponding to 44 cycles of the 8Li monitor, was measured and then converted into I(M) according to Eq. (4). Two examples of measured deflected intensity are reported in Fig. 6 versus the magnet rigidity M expressed in linear momentum units. In the thin solid target FKS tuning case in Fig. 6a the two contributions associated to 8Li produced in the first excited state and in the ground state are clearly observed as well separated peaks in the linear momentum spectrum. These are centred about the kinematics values (4) Pf;ex and Pf;gs and the maximum transported intensity I max is reached at the linear momentum P ffi Pf;gs for the ground 8Li entry state, as expected. On the other hand, we notice that the shape of the two peaks in Fig. 6a is not the rectangular one having width DM ¼ 0:011Pf;gsðexÞ ffi 5 MeV=c which one would have expected by simply folding a sharp kinematics momentum line with the rectangular momentum acceptance of the transport set up determined in Section 3. Moreover, by increasing the thickness of the solid target the peaks become progressively broader and comparable in shape to those of the gas target cases in which the intense ground state contribution typically obscures the excited state one as in the example of Fig. 6b (Table 1).

Table 1 Basic information on the experimental settings concerning the 8Li production shown in Fig. 6a and b Kinematical setting

Target

E(7Li) (MeV)

i(7Li) (pnA)

E(8Li) (MeV)

I(8Li) (pps)

FKS

CD2 D ¼ 1:2  1019 atoms=cm2 D2 gas 4:95  1019 atoms=cm2

11

500

10.371

3200

21

500

BKS

6.370.6

2500

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

We have analysed the effects in the observed I(M) in terms of the linear momentum fluctuations caused by the production method. We have considered three sources of momentum dispersion:

(a) The straggling effect in the energy deposition traversing the target. It is assumed to be Gaussian and its variance square root ss can be calculated by using a suitable stopping power code. With the exception of very thin targets it has a negligible effect on the total momentum dispersion. (b) The thickness fluctuations in the solid target or in gas target windows determined in Section 3. The amount of this contribution depends on the quality of the targets or windows used. For the target used in this work, the dispersion sd is proportional to the thickness d in the case of a solid target and almost independent of d in the gas target case. (c) Interaction point fluctuations (IPFs), namely fluctuations of the depth x, 0pxpd, inside the target thickness d, at which reaction (1) takes place. These IPFs propagate into momentum fluctuations and are an intrinsic feature of the secondary beam in flight production methods. In fact, the production of a 8Li nucleus at the depth x is preceded by a decrease of the 7 Li initial energy along x and is followed by a decrease of initial 8Li energy (3) along d–x. Therefore, due to charge, mass and energy dependences of the stopping power, the momentum P of an emerging 8Li ion depends on x and the 8Li momentum spectrum can be described, to a good approximation, by a rectangular distribution with base DP ¼ Pðx ¼ dÞ
Pðx ¼ 0Þ. The pffiffiffiffiffi associated variance square root DP= 12 is proportional to the target thickness d and it is almost independent of the gas cell window thickness.

We then assumed that each value P0 inside DP is the centroid of momentum fluctuations induced by straggling and target thickness uniformity. For each P0 these fluctuations are assumed to be altogether Gaussian (GF). Accordingly, the 8Li differential intensity dI inj =dP injected into the magnet results from the convolution of the GF with the rectangular IPF P0 distribution, namely R P0 þDP=2
ðP
P0 Þ2 =2s2 0 dP dI inj ðPÞ P
DP=2 e ¼ R 1 0 R P þDP=2 0 2 0
ðP
P Þ =2s2 dP0 dP dP e 0

(6)

P0
DP=2

where 0pPp1, P0 ¼ Pðx ¼ 0Þ þ 12DP is the mean linear momentum value ffiof the 8Li ions emerging from the target qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi and s ¼ s2d þ s2s . In our set up, the link between the injected dI inj =dP and the transported I(M) is governed by the overlap between the differential intensity distribution (6) and the

411

rectangular momentum acceptance as in Eq. (5) with ds OfðbÞ rd (7) dO being the total 8Li intensity (ions s
1/(pmA of 7Li)) produced into solid angle OfðbÞ in the centre of mass frame as determined by the laboratory angular acceptance fWx p20 mr, Wy p6 mrg. In Eq. (7) I 7 Li is the intensity of the primary beam (ions s
1/pmA), r is the density of 2H (nuclei/cm3), d the target thickness (cm) and ds=dOfðbÞ ðcm2 =srÞ the differential cross-section in the centre of mass frame of reaction (1). In the comparison of the model prediction with the deflected intensity data we assumed incoherent contributions from ground and excited states and, accordingly, two functions of the type (5), one for each entry state, were summed. The relevant parameters P0;gs , P0;ex , DP and s in Eq. (6) can be calculated with the help of an energy loss computer code (e.g. Ref. [27]) whereas the 8Li intensities I 0;gs and I 0;ex were left as free parameters in a best fit of the distribution data. The examples in Fig. 6a and b show the excellent agreement between calculated and experimental momentum spectra. Shape and peak height Imax of the measured momentum distributions reflect the competition between GF and IPF. In particular, as the values of P0, DP and s fulfil the condition P0 bs þ 12DP it follows that the injected distribution (6) has the variance square root: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DP2 S  s2 þ : (8) 12 I 0 ¼ I 7 Li

The dependence of the scaled total dispersion S=D and thosepffiffiffiffiffi of its GF and IPF-scaled components s=D and DP= 12D, respectively, on the 2H content of the targets of this work are p shown ffiffiffiffiffi in Fig. 7. pffiffiffiffiffi If SpDM= 12, where DM= 12 is the variance square root of the rectangular acceptance function versus momentum, the whole injected 8Li intensity I0 is transported, i.e. ds OfðbÞ D (9) dO with D ¼ rd (target nuclei/cm2). Such a proportional regime with I max / D occurs with thin solid targets (Fig. 7a and b) and the optimum (i.e. the largest) peak intensity value I opt is reached at about Dprop ffi 2  1019ptarget ffiffiffiffiffi nuclei/cm2. On the other hand, pffiffiffiffiffi when S4DM= 12, a fraction of the order of DM=S 12 of the injected intensity I0 is transported, i.e., from Eq. (7),
 ds DM S
1 p ffiffiffiffiffi 7 OfðbÞ I max ffi I Li (10) dO 12 D I max ffi I 0 ¼ I 7 Li

and since DM / M can be considered almost constant within the momentum range spanned by intensity spectra (Fig. 6), from Eq. (10) I max / ðS=DÞ
1 . Consequently, in this regime, the smaller is the scaled total dispersion, the larger is the transported peak intensity. For solid targets

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

412

2H

CD2-FKS ∆M/(D•120.5) 1.0 Σ/D

0.8 GF

0.6 0.4 IPF

0.2 0.0 0.0

2.0

4.0

6.0

Σ/D

1.5 1.0

GF ∆M/(D•120.5)

0.5

IPF

8.0

D (atoms/cm2)/1019

0.0

Momentum spread/D ((MeV/c)/(atoms/cm2))1019

Σ/D IPF

0.8 0.6

6.0

8.0

10.0

12.0

D (atoms/cm2)/1019 2H

∆M/(D•120.5)

1.0

4.0

gas-BKS

2.0

1.4 1.2

2.0

(c)

CD2-BKS Momentum spread/D ((MeV/c)/(atoms/cm2))1019

2.0

0.0

(a)

GF

0.4 0.2

1.5 GF

1.0

Σ/D IPF

0.5 ∆M/(D•120.5) 0.0

0.0 0.0 (b)

gas-FKS

2.5 Momentum spread/D ((MeV/c)/(atoms/cm2))1019

Momentum spread/D ((MeV/c)/(atoms/cm2))1019

1.2

2.0

4.0 6.0 D (atoms/cm2)/1019

8.0

0.0 (d)

2.0

4.0 6.0 8.0 D (atoms/cm2)/1019

10.0

12.0

Fig. 7. Scaled dispersions versus the 2H content of the production target for the indicated target-tuning configurations. GF due to the thickness dominate the total momentum dispersion S in FKS tuning (a) and (c) and in thin and moderately thick gas target BKS tuning cases (d); the IPF dominate in solid BKS (b) and thick gas target BKS (d) cases. Due to the carbon atom in the CD2 molecule the IPF dispersion in the solid target case (b) is larger than that in gas target case (d). In BKS tuning (b) and (d), where the energy difference between the primary 7Li and secondary 8Li is large, the IPF are significantly larger than those of the FKS one (a) and (c) independently of the target type.

(Fig. 7a and b) the 8Li peak intensity remains almost constant and close to I opt in the proportional regime as given by Eq. (9) for D ¼ Dprop . For gaseous targets (Fig. 7c and d) the peak intensity is always regulated by Eq. (10) and increases with increasing D, with a tendency to become constant in the BKS case. Both the examples shown in Fig. 6 are near optimum configurations and are characterized by comparable values of the peak intensity. Though in the solid p target—FKS tuning case (shown in Fig. 6a) S ffi ffiffiffiffiffi DM= 12 and from Eq. (9) the measured value of the peak intensity I max ffi I opt ffi 7  103 s
1 =pmA coincides with the injected total intensity I0 whereas in the gas target pffiffiffiffiffi BKS configuration (shown in Fig. 6b) S ffi 5ðDM= 12Þ and, from Eq. (10), the value of the observed peak intensity I max ffi I opt ffi 5  103 s
1 =pmA represents approximately one fifth of the injected I0. It should be noted that the IPF curves pffiffiffiffiffiin Fig. 7 represent the ideal values ðS=DÞideal ¼ DP= 12D versus D in the case of perfectly uniform target or window thickness. A remarkable feature then follows: while in the FKS tuning cases the optimum (i.e. the smallest) ðS=DÞopt ffi ð324ÞðS=DÞideal , in the BKS tuning cases ðS=DÞopt ffi ðS=DÞideal . This means that in order to transport as large secondary beam intensity as possible,

while in the FKS option an extremely uniform solid or gas target assembly would be necessary, in the BKS tuning it is sufficient to use ordinary quality targets like those tested in this work. We performed our study at 7Li bombarding energy greater than 6 MeV, the lower value available with the accelerator in use. Then we explored the feasibility of the backward production–separation method at somewhat lower bombarding energy using the above formalism. For instance, at the bombarding energy of 2.8 MeV the differential cross-section in the centre of mass of the inverse kinematics reaction (1) assumes comparable values at Wf ¼ 0 and Wb ¼ p of the order of 10
26 cm2/sr [28]. We remark in passing that the peak intensities in Fig. 6a and b determine centre of mass cross-section values of this same order of magnitude, dsðWf ¼ 0Þ ¼ ð7 1:5Þ  10
27 cm2 =sr dO and dsðWb ¼ pÞ ¼ ð10 2Þ  10
27 cm2 =sr dO

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

at the primary beam energy of 11 and 21 MeV, respectively. 19:2 2 With the target pffiffiffiffiffi thickness D ¼ 1:2  10 H=cm , for which DM=S 12 ffi 0:06, and with the centre of mass solid angle Ob  12 msr the secondary beam peak intensity expected from Eq. (10) at 2.8 MeV bombarding energy is I max ffi 5  102 s
1 =pmA, a value which, depending on the application, still may represent a meaningful production rate of BKS 8Li ions at energy as low as about 1 MeV.

In the FKS tuning the momentum separation (P(8Li)
P( Li))/P(8Li) amounts to about 3.5%. Moreover, the primary beam emerging from the CD2 production target also exhibits a momentum spread caused by fluctuations in the target thickness uniformity and by straggling. The amount of the 7Li momentum spread is of the same order of that associated to the FKS bump of 8Li and from Fig. 7a and b we deduce that, in order to minimize this spread yet preserving the secondary beam intensity, an extremely thin solid target would be appropriate. However, even for a real thin solid target as that of Fig. 6a the width (FWHM%) is of the order of 1.2%, a value which is already sufficient to induce a strong contamination in the about 8–9 orders of magnitude less intense secondary beam. Furthermore, the primary beam is also unavoidably dumped inside the dipole magnet chamber. This generates, via multiple scattering, a 7Li beam emerging from the magnet with a continuous energy spectrum. On the contrary, in the case of the BKS tuning the momentum separation (P(7Li)
P(8Li))/P(8Li) amounts to about 30% and, therefore, it is worth to check experimentally the implications of such a convenient opportunity. To this aim, a detection system which allows element and isotopic identification as well as kinetic energy and intensity measurements was installed as indicated in Fig. 3. It consists of a microchannel plate detector (MCP1) and of a removable silicon detector telescope located about 4.5 m downstream at the MCP2 position. Clearly, attempting such an investigation in the case of FKS tuning, where the primary beam is only partially suppressed, could be fatal for the detectors. For this reason we abandoned definitely the FKS tuning and investigated the contaminants in the BKS tuning only. Fig. 8 shows the transported ion time-of-flight spectrum obtained in a solid target-BKS tuning case gated by the maximum occurring at approximately P0;gs in the associated 8Li intensity versus magnetic rigidity spectrum. The width of the peaks of 1.1% (FWHM%) reflects the transport line momentum acceptance DM=M ¼ 0:011. Since P0;ex
P0;gs ffi ð627ÞDM (see Fig. 6b) the 8Li peak is almost entirely due to the ground state contribution and exhibits a symmetric shape. The primary beam is almost completely suppressed by the BKS tuning. Leaky 7Li ions at approximately half the primary energy dominate the time spectrum. Nevertheless, the 8Li peak is only weakly contaminated by the 7Li tail and within a time gate of the 7

800 7

Li3+ x 1/10

700 8

Li3+

600 500 Counts

5. 8Li beam purification

413

400 7Be4+

300 200

4

He2+ 8 3+ B

100 0

11B5+

0

500

1000

1500 2000 TOF (channels)

11 4+ B

11B3+

2500

3000

Fig. 8. Time-of-flight spectrum of the secondary reaction products obtained by using a CD2 target in the BKS case. The 8Li beam is clearly separated from the contaminants.

order of 1 FWTM the residual impurity is of the order of 4%. Contamination of other nuclear species produced in the target assembly is irrelevant inside this gate. In order to keep such a degree of 8Li beam purification during the ‘‘real’’ experiment the Si telescope was replaced by a second microchannel plate detector, named MCP2 in Fig. 3. The ToF spectrum with two MCPs is very similar to that in Fig. 8 with the advantage that the MCP1 and MCP2 ToF meter is transparent to the detected ions. The MCP detectors used in this work were assembled in a common configuration with the emitting foil forming an angle of 451 with respect to the incident beam as described in Ref. [29]. The hardware was adjusted so as to get the same intrinsic efficiency value o ffi 0:9 on the two MCPs. This reduces by a factor o2 ffi 0:8 the tagged 8Li intensity. The MCP2 was chosen smaller than the MCP1 so that it defines an elliptical spot of maximum size p  1:0  0:7 cm2 on the experiment target located 50 cm downstream. Due to the MCP geometry and efficiency, the ToF tagging procedure implies an overall reduction factor p5 allowing a tagged 8Li intensity I tagg X103 s
1 pmA to be available in BKS tuning. Thus, for a value of the primary beam intensity I 7 Li p1 pmA the maximum expected projectile rate is R ffi 103 s
1 . With a typical FWHM value of the order of a few ns an efficient tagging of the detected 8Li peak can be performed with a less than 10 ns wide coincidence time gate. The dead time of the tagging procedure is primarily due to the time-of-flight itself of the order of a few hundreds of ns. This dead time is much smaller than the mean waiting time hti ¼ R
1 between successive ions and, therefore, does not affect the tagged beam rate.

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

414

6. Nuclear astrophysics investigation As an example of application with an extremely low intensity beam we have investigated the feasibility of the cross-section measurement of the 8Li(4He,n)11B reaction. This reaction is of crucial importance in the inhomogeneous Big Bang Model [22] since it represents the bottleneck for the possible production of ‘‘metals’’ (C,N,O,y) during pregalactic nucleosynthesis. As shown in Fig. 9, the state of the art evidences that large differences exist between excitation functions measured by various methods. Therefore, further investigations, in particular in the Gamow region, i.e. energy of 0.6–0.8 MeV in the centre of mass, are necessary. We afforded this cross-section measurement by a novel technique. Our approach is based on the fact that in the 8Li+4He reaction at centre of mass energy below 2 MeV the 11B+n is the only open neutron production channel and that, therefore, it is sufficient to count inclusively the neutrons by using a highly efficient detector. Details of the experimental procedure are reported elsewhere [30]. Here we only underline how the low beam rate R of at most 103 s
1 is well suited for our needs. Shortly, the transport set up sketched in Fig. 3 was reinstalled around a new dipole magnet designed to provide output beams at 461 and 661 with respect to the entrance direction. The 661–461 magnet output bending radius ratio of approximately 0.7 is very close to the secondary BKS to primary beam momentum ratio (Fig. 2). Both primary 7Li and secondary 8Li ions emerging from the primary target are almost exclusively in the 3+ charge 1000 8Li(4He,n)11B

900

7. Summary and conclusion

800

Cross section (mb)

700 600 500 400 300 200 100 0

state, so that when the BKS 8Li was deflected at 661 the intense 7Li beam was actually observed to be deflected towards the magnet output at 461. There the primary beam could be stopped and the associated neutron production was adequately shielded. BKS tuning with a primary 7Li beam at 23 MeV was selected and the energy of the secondary 8Li beam was adjusted to the near Big Bang centre of mass value of 1.2570.2 MeV using the Ni entrance window of the 4He target gas cell as a degrader (Fig. 3). At the same time the energy of the residual 7Li impurities was degraded well below the threshold of the 4He(7Li,n)10B reaction. The 4He gas target (20 cm long at 150 mb pressure) was located at the centre of the 4p thermalization neutron counter described in Ref. [31]. The neutron capture time distribution in this detector has an exponential shape characterized by the die away constant tda ¼ 87 ms. This feature allowed us to discriminate reaction neutrons from the background due to cosmic rays, radioactive contaminants in the detector and primary 7Li beam stopping, by looking at the time correlation between the neutron capture and the arrival of the tagged 8Li ion. Due to the large detection time scale and to the waiting time between successive tagged ions sequence which, at constant mean rate R, is a simple Markov process with probability density dq=dt ¼ Re
Rt , the tagged 8Li mean rate R was kept as low as 102 ions/s (i.e. Rtda ffi 0:01) allowing a simultaneous suppression of the uncorrelated background of the order of ðRtda Þ
1 ffi 100. Fig. 9 shows that even in a 70 h short bombardment the statistical error in our cross-section data is already comparable with the errors of the other data sets. We are confident to improve the quality of our cross-section data in future measurements.

0

1

2

3 4 Ecm (MeV)

5

6

7

Fig. 9. Excitation functions of the 8Li(4He,n)11B reaction obtained in the following references: closed circles [32], open squares [33], closed squares [34]. The dots are the data from the study of the inverse reaction 11 B(n,a)8Li [35]. The open circle is the cross-section measured in this work.

We have designed and tested a method to produce a secondary radioactive 8Li beam with mean rate up to 104 s
1. The beam has been produced via a 7Li(d,p) reaction in inverted kinematics using a deuterium production target placed in front of a switching magnet which selected 8Li ions moving backward in the centre of mass. The effects of the initial momentum spread on the deflected secondary beam current for BKS or FKS moving ions have been measured by a monitor device sensitive to the b-delayed a emission of 8Li. Two main causes which contribute to the 8Li momentum spread in the production target have been identified and discussed. One contribution, which is intrinsic to the secondary ion production method, reflects the propagation of the interaction point fluctuations. The other contribution is associated to the quality of the target assembly in terms of thickness uniformity. The contribution due to straggling in the energy deposition is of secondary importance. A momentum fluctuation model has been developed and used to

ARTICLE IN PRESS C. Agodi et al. / Nuclear Instruments and Methods in Physics Research A 565 (2006) 406–415

characterize the performances of the method versus the configuration of the production target. We have checked that BKS tuning is feasible using a gas production target as well as using a solid production target. Ordinary quality targets have been used and we have shown that better quality is not necessary. Moreover, in the BKS tuning of 8Li ions the separation from the primary 7Li beam can be easily achieved at an acceptable level. By coupling the production–separation set up with an appropriate tagging procedure we have selected 8Li ions with a mean rate of 103 ions/s and a residual 7Li impurity of at most 4%. Finally, the utility of such a low intensity beam has been demonstrated by performing a first test measurement of the total cross-section in a nuclear reaction relevant for Big Bang nucleosynthesis. The in flight RIB production, separation and transport approach adopted in this work is simple, cheap and easy to tune. It can be implemented in low-energy accelerator facilities to support compatible applications with a variety of secondary beams. Acknowledgements The authors wish to thank the LNS Tandem crew for the kind and patient collaboration and Mr. C. Marchetta for preparing the solid and gaseous primary targets. References [1] P.S. Hansen, et al., Ann. Rev. Nucl. Part. Sci. 45 (1995) 591. [2] T. Otsuka, et al., Eur. Phys. J. A 15 (2002) 151. [3] J.P. Bychowski, et al., Phys. Lett. B 596 (2004) 26 and references therein. [4] A. Di Pietro, et al., Phys. Rev. C 69 (2004) 044613. [5] M.S. Smith, K.E. Rehm, Ann. Rev. Nucl. Part. Sci. 51 (2001) 91. [6] A.C. Mueller, et al., Nucl. Instr. and Meth. B 56 (1991) 559. [7] D.J. Morrisey, et al., Nucl. Instr. and Meth. B 204 (2003) 90. [8] H. Geissel, et al., Nucl. Instr. and Meth. B 70 (1992) 286.

415

[9] T. Kubo, et al., Nucl. Instr. and Meth. B 204 (2003) 97; T. Kubo, et al., Nucl. Instr. and Meth. B 70 (1992) 309. [10] R. Baartman, et al., Proceedings of the Sixth European Particle Accelerator Conference, EPAC98, Stockholm, 1998. [11] M. Lindroos, Nucl. Instr. and Meth. B 204 (2003) 730. [12] D.W. Stracener, Nucl. Instr. and Meth. B 204 (2003) 42. [13] M. Loiselet, et al., Proceedings of the International Conference on Cyclotrons and their Applications, Cape Town, World Scientific, Singapore, 1995, p. 629. [14] M. Lieuvin, Proceedings of the Sixth European Particle Accelerator Conference, Stockolm, 1998. [15] G. Ciavola, et al., Nucl. Phys. A 701 (2002) 54c. [16] R.C. Haight, et al., Nucl. Instr. and Meth. B 10/11 (1985) 361. [17] X. Bai, et al., Nucl. Phys. A 588 (1995) 373c. [18] J.J. Kolata, et al., Nucl. Instr. and Meth. B 40/41 (1989) 503. [19] M.Y. Lee, et al., Nucl. Instr. and Meth. A 422 (1999) 536. [20] B. Harss, et al., Phys. Rev. Lett. 82 (1999) 3964. [21] J.J. Das, et al., Nucl. Instr. and Meth. B 241 (2005) 953. [22] E. Witten, Phys. Rev. D 30 (1984) 272; J.H. Applegate, et al., Phys. Rev. D 35 (1987) 1151; R.A. Malaney, W.A. Fowler, in: G.J. Mathew (Ed.), The Origin and Distribution of Elements, World Scientific, Singapore, 1988, p. 76; R.A. Malaney, W.A. Fowler, Astrophys. J. 333 (1988) 14; T. Kajino, R.N. Boyd, Astrophys. J. 359 (1990) 267. [23] M. Terasawa, et al., Astrophys. J. 562 (2001) 470; T. Kajino, Proceedings of Nuclei in the Cosmos, vol. 7, 2002; T. Kajino, Nucl. Phys. A 718 (2003) 295c; T. Sasaqui, et al., Astrophys. J. 634 (2005) 534. [24] K.E. Sale, et al., Phys. Rev. C 41 (1990) 2418. [25] L. Weissman, et al., Nucl. Phys. A 630 (1998) 678. [26] D.C. Carey, et al., TURTLE a computer program for simulating charged particle beam transport systems, SLAC-R-544, FermilabPub-99/232. [27] J.F. Ziegler, et al., The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985. [28] A.J. Elwin, et al., Phys. Rev. C 25 (1982) 2168. [29] J.L. Wiza, Nucl. Instr. and Meth. 162 (1979) 587. [30] S. Cherubini, et al., Eur. Phys. J. A 20 (2004) 355. [31] P.R. Wrean, R.W. Kavanagh, Phys. Rev. C 62 (2000) 055805. [32] Y. Mizoi, et al., Phys. Rev. C 62 (2000) 065801. [33] R.N. Boyd, et al., Phys. Rev. Lett. 68 (1992) 1283. [34] X. Gu, et al., Phys. Lett. B 343 (1995) 31. [35] T. Paradellis, et al., Z. Phys. A 337 (1990) 211.