Measurements of neutron-induced reactions in inverse kinematics
AAPS/123-QED
Measurements of neutron-induced reactions in inverse kinematics
Ren´e Reifarth and Yuri A. Litvinov
2, 3 Goethe-Universit¨at Frankfurt am Main, Max-von-Laue-Str.1, 60438 Frankfurt am Main, Germany GSI Helmholtzzentrum f¨ur Schwerionenforschung, 64291 Darmstadt, Germany Max-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany (Dated: November 6, 2018)Neutron capture cross sections of unstable isotopes are important for neutron induced nucleosyn-thesis as well as for technological applications. A combination of a radioactive beam facility, an ionstorage ring and a high flux reactor would allow a direct measurement of neutron induced reactionsover a wide energy range on isotopes with half lives down to minutes.
PACS numbers: 25.40.Lw, 26.20.+f, 28.41.-i, 29.20.db, 29.38.-c
I. INTRODUCTION
Knowledge of neutron-induced reaction rates is indis-pensable for nuclear structure and nuclear astrophysicsas well as for a broad range of applications, where theobvious example of the latter is the reactor physics. Innuclear astrophysics the neutrons with energies between1 keV and 1 MeV play the most essential role since thisenergy range corresponds to temperature regimes rele-vant for nucleosynthesis processes in stellar objects.In this context ( n, γ ) cross sections for unstable iso-topes are requested for the s -process [1], related to stellarhelium burning, as well as for the r - [2] and p -processes[3], related to explosive nucleosynthesis in supernovae.In the s -process, these data are required for analysingbranchings in the reaction path, which can be interpretedas diagnostic tools for the physical state of the stellarplasma [4]. Most of the nucleosynthesis reactions duringthe r - and p -processes proceed through nuclides outsidethe stability valley, thus involving rather short-lived nu-clei. Here, the challenge for ( n, γ ) data is linked to thefreeze-out of the final abundance pattern, when the re-maining free neutrons are captured as the temperaturedrops below the neutron separation energy [5]. Sincemany of these nuclei are too short-lived to be accessedby direct measurements [6] it is, therefore, essential toobtain as much experimental information as possible offthe stability line in order to assist theoretical extrapola-tions of nuclear properties towards the drip lines.Apart from the astrophysical motivation there is con-tinuing interest on neutron cross sections for technologi-cal applications, i.e. with respect to the neutron balancein advanced reactors, which are aiming at high burn-uprates, as well as for concepts dealing with transmutationof radioactive waste [7, 8].In general, the shorter the half life of the isotopes un-der investigation, the more difficult it will be to prepare aradioactive sample, to place the sample close to a detec-tor and to perform a reaction measurement. For protonand α -induced reactions, one solution to this problem isto invert the kinematics, namely to employ a radioactiveion beam hitting a proton or helium target at rest. Inthe case of neutrons, this approach would require a neu- e l e c t r on c oo l e r particledetectionSchottkypickup injectionrevolvingions reactorcore ISOL-typeradioactivebeam facility
FIG. 1: Schematic drawing of the proposed setup. Shown are:the facility to produce and separate exotic nuclei of interest(dark gray) and the main components of an ion storage ringwhich include the beam lines and focusing elements (gray),dipoles (dark blue), electron cooler (green), an intersectedreactor core (red), particle detection capability (black) andSchottky pick-up electrodes (brown). tron target, where the neutrons are themselves unstable.In this article, we describe a possible solution to thisproblem, which allows direct measurements of neutron-induced cross sections on radioactive isotopes. Nucleiwith half-lives as short as a few minutes or even belowcan be studied. Such short-lived isotopes can currentlynot be directly investigated. a r X i v : . [ nu c l - e x ] D ec II. CONCEPT
The idea presented in this article is to measureneutron-induced reactions on radioactive ions in inversekinematics. This means, the radioactive ions will passthrough a neutron target. In order to use efficiently therare nuclides as well as to enhance the luminosity, it isproposed to store the exotic nuclides in an ion storagering. The neutron target can be the core of a researchreactor, where one of the central fuel elements is replacedby the evacuated beam pipe of the storage ring. Suchgeometries are fairly common for research reactors, inparticular of TRIGA type. At least one fuel elementis typically replaced by an pipe, which can be loadedwith capsules containing sample material to be irradi-ated. Another possibility would be to add the beam piperight next to the reactor core. The core is usually sur-rounded be water and -in the case of research reactors-moderating water. The neutron densities at the edgeof the reactor core are typically one order of magnitudesmaller than in the center of the core. This can be takeninto account when planning such a setup. An evacu-ated beam pipe as needed for the proposed setup wouldtherefore not interfere with the operation of the reac-tor. More demanding might be the vacuum required forthe operation of the storage ring. Usually, it is neces-sary to bake the corresponding structural parts in orderto achieve UHV-conditions. However, it has been shownthat proton-induced reaction can be investigated in thiskinematics [9]. The revolving ions were penetrating ahydrogen jet-target [10], which has most likely a muchbigger impact on the vacuum conditions than the walls.The neutrons can easily penetrate the beam pipe creat-ing a kind of neutron gas, which the revolving ions haveto pass. The neutron density in the target is then onlydependent on the power output of the reactor and thetemperature of the reactor core. A schematic drawingof the proposed setup is given in FIG. 1. The schemeis quite flexible, but for practical reasons, we base ourdiscussion on the parameters of the existing rings. Adedicated design study could be performed in the future.Two storage ring facilities are presently in operationwhich offer stored exotic nuclides. These are the Exper-imental Storage Ring (ESR) [11] at GSI in Darmstadtand the experimental cooler-storage ring (CSRe) [12] atIMP in Lanzhou. Although these rings are capable ofslowing stored ions down to a few AMeV, these rings areprimarily designed to operate at energies around 200-400AMeV [13]. Therefore we consider a storage ring similarto the Test Storage Ring (TSR) [14] which was in oper-ation until 2013 at the Max-Planck Institute for NuclearPhysics in Heidelberg. Although this storage ring wasnot used to store radionuclides, there is a detailed tech-nical design report to move TSR to CERN where it shallbe coupled to the ISOLDE radioactive ion beam facil-ity [14]. The example parameters of the TSR are used inthe following discussion. Even lower beam energies canbe realized at cryogenically cooled rings, like the CSR injection
10 m e l e c t r on c oo l e r particledetectionparticledetection revolvingions c a v i t y f o r a cc e l e r a t i on o r de c e l e r a t i on experiment FIG. 2: Schematic drawing of the Test Storage Ring,TSR [14]. The injection, electron cooler, acceleration cavityand particle detector setups are indicated. A core of a reac-tor can be imagined at place for in-ring experiments. Adoptedfrom Ref. [14]. [15] or the CRYRING [16].The proposed storage ring shall have 4 straight sectionsas in the case of the TSR (see FIG. 2). One of thesestraight sections will go through the core of the reactor.The ion-optics of the ring will be set such that the beamsize is as small as possible in this section. The size ofthe beam in horizontal ( x ) and vertical ( y ) directionsis given as x = √ β x (cid:15) and y = (cid:112) β y (cid:15) , where the betafunctions β x and β y describe the envelope of the beamin x and y directions, respectively, along the beam axis,and (cid:15) is the beam emittance. Furthermore, in order tominimise the influence of the momentum distribution onthe beam size, the dispersion function has to be minimalin this section. Sufficiently small beta and dispersionfunctions are achieved, e.g., in the cooler section in thestandard operation mode of the TSR (see Figs. 34 and 36in Ref. [14]). In this case the size of the beam will be thesmallest (waist) in the middle of the reactor core. Thesize of the TSR beam pipe is 20 cm in diameter whichcan be taken here as a maximum size.One other straight section will be taken by the electroncooler. This is an essential component of the setup. Theelectron cooling is needed to achieve and to keep a smallbeam emittance, which is defined by the equilibrium be-tween the cooling force on the one side and effects actingagainst it, like intra-beam scattering or energy losses inthe rest gas, on the other side.The TSR is equipped with rf-cavities to acceler-ate/decelerate the stored beams which is not needed forour setup as it is much more efficient to inject and tostore the ions directly at the required energy.The straight section opposite of the neutron target willbe occupied by the injection hardware. The so-calledmulti-turn injection is employed at the TSR [14] and issuggested to be used here. In the multi-multi injectionthe horizontal acceptance of the storage ring is filled withions. With a help of septa magnets the ions are injectedinto the ring for several tens of revolutions ( ∼ µ sin case of the TSR). Afterwards, the ions are electroncooled which compresses the phase-space and emptiesa part of the ring acceptance. This emptied space canagain be used to inject new ions. The electron coolingrequires a few hundreds of milliseconds until the nextmulti-multi injection can be performed. This so-called“electron-cooling stacking” can be repeated continuouslyuntil an equilibrium is reached between the number ofions lost from the ring and the number of injected ions.There is an upper limit due to space charge effects. TheTSR holds a record by storing the 18 mA current of C ions, though a conservative limitation for a stable oper-ation is around 1 mA. However, in our case this limitmight become applicable only for ions with long lifetimesand large production rates. In the following we will as-sume a moderate intensity of stored ions of 10 particlesin the ring at any given time.Essential issue are the losses of the ions from the ring.Compared to other storage-ring based reaction measure-ments, where the internal target is the major source ofion losses, using neutrons as target means that no atomicreactions in the target have to be taken into account.Therefore, the two main loss mechanisms are atomiccharge exchange reactions of the ions with the residualgas atoms and electron capture in the electron cooler.The residual gas pressure of the TSR is 4 − · − mbar.Numerous measurements of the beam lifetimes exist inthe TSR for different ions, ionic charge states, and ener-gies [14].An ISOL-type radioactive ion beam facility can be asource of exotic nuclei. ISOL-beams combine high in-tensity and good quality. In particular all the isotopesdiscussed in the applications can be produced with suffi-cient rates [17]. The extracted low charged ions from thetarget will be trapped and charge-bred in an electron-ion beam trap/source, the scheme realised presently atISOLDE/CERN [14]. The highly charged ions can beextracted and post-accelerated to the required energy bya linear accelerator and then injected into the ring.Dependent on the momentum-over-charge change inthe neutron-induced reaction, the daughter nuclei canstay within the storage ring acceptance or not. In the for-mer case the number of daughter ions can be monitoredby a non-destructive Schottky spectroscopy [18, 19] or byusing a sensitive SQUID-based CCC-detectors [20]. Inthe latter case the reaction products will be intercepted by particle detectors located behind the first dipole mag-net downstream the reactor core (see Fig. 1). The feasi-bility of this has been demonstrated in the ESR this hasbeen demonstrated in the ESR by detecting the Rurecoil ions produced in the Ru( p, γ ) Ru reaction [9].The discussed concept requires the presence on site ofa reactor and an ISOL radioactive beam facility. One ofsuch locations could be the Petersburg Nuclear PhysicsInstitute in Russia (PNPI), where a new-generation reac-tor, PIK [21], is being constructed and an ISOL facility,IRIS, is in operation a few hundreds of meters away.
III. RATE ESTIMATES
The neutron flux through an arbitrary area in reactorsranges from φ neutron = 10 /cm /s in small researchreactors (TIRGA Mainz type [22]) to about φ neutron =10 /cm /s or more in modern research reactors (FRM-II Munich [23] or ILL Grenoble [24]). For the followingrate estimates, we will simply assume an averaged neu-tron flux of φ neutron = 10 /cm /s. This results in aneutron density in any given volume of ρ neutron = φ neutron v neutron (1)where v neutron = 2200 m/s denotes the average ve-locity of neutrons in a thermal reactor. Assuming aninteraction zone with a length of l = 0 . η neutron = ρ neutron · l = φ neutron · lv neutron (2)which gives η neutron ≈ · cm − .The number of ions passing the volume in a given timeis about I particle = 10 s − (10 stored ions circulatingin a ring with a revolution frequency of ∼ L = η neutron · I ≈ ·
1s cm (3)and gives number a reaction rate of R = Ltσ (4)or the number of counts per day: C daily = 20 · σ [mb] (5)which means, cross sections down to a few mbarns canbe measured with sufficient statistics within one day. Thebeauty of the method that it is applicable to compara-bly short-lived radioactive isotopes. The half-life limit ismostly determined by the production rate at the radioac-tive ion facility and the beam losses due to interactionswith the rest gas in the ring. IV. POSSIBLE REACTIONS TO BEMEASURED
In order to discuss the possible reactions, which couldbe investigated with a setup as proposed here, it is im-portant to understand the kinematics. The radius ( r ) ofa trajectory of a charged ( q ) massive ( m ) particle withvelocity ( v ) in a homogeneous, perpendicular magneticfield ( B ) follows immediately form the Lorentz force: qvB = mv r (6)hence r = mvqB = pqB (7)Equation 7 is even valid for relativistically moving par-ticles, if p and m are relativistic variables. Compared tothe revolving beam energy (energies above 0.1 AMeV),the neutrons (energies of 25 meV) can always be con-sidered to be at rest. For the purpose of this paper, allchannels can be viewed as a compound reaction. In afirst step, a nucleus X + n is formed and in a secondstep, particles or photons are emitted. This means, themomentum and the charge of the revolving unreactedbeam X and the compound nucleus X + n are the same,which means, both species will be on the same trajectory.However, the velocity, hence the revolution frequency, isreduced by the factor A/ ( A + 1). If the revolving ionshave charge Z = q/e and mass A = 12 · m/m C one findsthen for the ratio of radii: r D r P = Z P Z D p D p P = Z P Z D A P A P + 1 A D A P , (8)where indices D and P denote the produced daughterand unreacted parent nuclei, respectively. And finallywe obtain: r D r P = Z P Z D A D A P + 1 (9)It depends now on the actual exit channel under inves-tigation, which type of detection mechanism can and hasto be applied. A. Neutron captures (n, γ ) The neutron capture reaction can be viewed as a two-step process, where the neutron gets captured into a com-pound nucleus, which de-excites via γ -emission to theground state. AZ X + n → A +1 Z X ∗ → A +1 Z X + γ (10) The compound nucleus has the same total momentumas the primary beam. However, the velocity, hence therevolution frequency, is reduced by the factor A/ ( A + 1).The product will receive a small relative momentumspread of less than 10 − because of the γ -emission. Theappearance of the freshly synthesised ions can thereforebe detected via this frequency change by applying thenon-destructive Schottky detectors. It has been showneven single ions can be detected, even if the primarybeam is still present in the ring [25]. A rather sharp lineshould appear in the Schottky spectrum, centred around A/ ( A + 1) with respect to the primary beam (the veloc-ity, hence the frequency of the compound nucleus). TheSchottky method was already successfully demonstratedat the ESR at GSI [26, 27]. Since neither the charge northe momentum of the products are different from the un-reacted beam, the neutron capture can not be detectedwith particle detectors, see also Equation 9. B. Neutron removals (n,2n)
Similarly to the neutron capture reactions, also neu-tron removals at low energies can be viewed as a two-stepprocess: AZ X + n → A +1 Z X ∗ → A − Z X + 2 n + γ (11)The product ion has on average the same velocity asin the case of neutron capture, but the mass is reducedby two units. The momentum and hence the radius ina magnetic field of the produced ion compared to theunreacted beam is therefore reduced by (Equation 9): r ( n, n ) r P = A P − A P + 1 (12)In addition, the momentum spread is now in the or-der of 1 /A and it remains a matter of momentum ac-ceptance of the storage ring ( ≈ ± .
2% at the ESR and ≈ ±
3% at the TSR) and the isotope under investigation,if the measurement is feasible or not. Even for heavynuclei, a rather broad line should appear in the Schottkyspectrum, centred around A/ ( A + 1) with respect to theprimary beam (the velocity, hence the frequency of thecompound nucleus). C. Neutron-induced charged particle reactions ( n, Z ) Neutron-induced reaction with charged particles in theexit channel (like ( n, p ) or ( n, α )) are difficult to measurein conventional kinematics, even for long-lived or stableisotopes. The reasons are of technical nature: In orderto detect the charged reaction products, they have tobe able to leave the sample. This necessitates very thinsamples, which, in combination with small cross sections,results in a very limited number of successful measure-ments with fast neutrons.In inverse kinematics however, this difficulty does notexist, provided that it is possible to detect the producedions. The ratio of radii in case of a ( n, p ) reaction is(Equation 9): r ( n,p ) r P = Z P − Z P · A P A P + 1 (13)And for the (n, α ) reaction: r ( n,α ) r P = Z P − Z P A P − A P + 1 (14)This means, the separation of the trajectories of theproducts from the unreacted beam is huge and thereforethe products can easily be detected with charged-particledetectors placed at a place with a large dispersion outsidethe trajectory of the unreacted beam.The emission of the massive (charged) particle occursisotropically in the center of mass system. Therefore therecoil of the product leads to a momentum spread - lon-gitudinal as well as transversal. The momentum of theproduct p cmP in the center of mass is: p cmP = (cid:113) µE exitkin (15)where µ = mM/ ( m + M ) denotes the reduced mass. E exitkin denotes the kinetic energy released in the center ofmass and can have any value between zero and the someof the mass difference and the initial kinetic energy inthe center of mass:0 ≤ E exitkin ≤ Q + E initialkin (16)hence p cmP ≤ (cid:113) µ (cid:0) Q + E initialkin (cid:1) (17)The maximum relative momentum spread in the labo-ratory system is therefore:∆ p cmP p P = (cid:115) µM A Q + E initialkin E initialkin (18)If m << M , the equation can be simplified to:∆ p cmP p P = (cid:115) aA Q + E initialkin E initialkin (19)If one considers a typical case for a ( n, p ) reaction( a = 1), a sample mass of A = 100, E initialkin = 100 keV (corresponding to 0.1 AMeV beam energy) and a massdifference of Q = 1 MeV, the relative momentum spreadis 3%. This means, after 1 m of flight path, all the prod-ucts would still be within a 3 cm radius around the pri-mary, unreacted beam. The detection could be done forinstance with a pair of particle detectors even before thenext magnet. The detectors should be arranged suchthat they form a slit in the plane of the storage ring withthe unreacted beam in the center of the slit. This allowsthe optimization of the primary beam during injectionwithout interference with the detectors.If the Q-value is negligible, the relative momentumspread in the case of ( n, p ) is 1/ A , while it is 2/ A inthe case of ( n, α ). In this case, the products should beseparated from the primary beam in the field of the fol-lowing dipol magnet. D. Neutron-induced fission ( n, f ) As with the previously discussed reactions, alsoneutron-induced fission can be viewed as a process withseveral steps. At first, a compound nucleus is created.Secondly fission occurs, where the nucleus typically splitsinto two smaller nuclei. In a third process, promptneutrons are evaporated off the fission products. Atlast, comparably slowly, the fission products β − -decaytowards the valley of stability. The kinetic energy ofthe isotropically emitted fission products in the centerof mass is ≈ A/q ratio than the primarybeam. It would therefore be possible to detect the reac-tion products with charged particle detectors positionedjust outside the primary beam. The determination offission cross sections in inverse kinematics has been suc-cessfully proven, but not for neutron-induced fission [28].The chain of β − -decays will appear after the detection ofthe particles inside the detectors can be used for furtherinvestigation or discrimination against background.In order to estimate the momentum spread, we assumethe same mass for each the fission product. With a massof A = 250, a mass difference of Q = 190 MeV and abeam energy of 10 AMeV (corresponding to a neutron en-ergy of 10 MeV), the maximal momentum spread wouldbe: ∆ p cmP p P = (cid:115) A Q + E initialkin E initialkin = 20% (20)If the beam energy is sufficiently high and the Q-valuecan be neglected, the maximal relative momentum spreadis 1/ √ A ≈ V. APPLICATIONSA. Nuclear astrophysics
1. The s -process About 50% of the element abundances beyond ironare produced via slow neutron capture nucleosynthesis( s process) [1]. Starting at iron-peak seed, the s -processmass flow follows the neutron rich side of the valley ofstability. If different reaction rates are comparable, the s -process path branches and the branching ratio reflectsthe physical conditions in the interior of the star. Suchnuclei are most interesting because they provide the toolsto effectively constrain modern models of the stars wherethe nucleosynthesis occurs. As soon as the β − decay isfaster than the typically competing neutron capture, nobranching will take place. Therefore experimental neu-tron capture data for the s -process are only needed if therespective neutron capture time under stellar conditionsis similar or smaller than the β − decay time, which in-cludes all stable isotopes. Depending on the actual neu-tron density during the s -process, the ”line of interest”is closer to or farther away from the valley of β -stability.The modern picture of the main s -process componentproducing nuclei between iron and bismuth refers to theHe-shell burning phase in AGB stars [29]. The s processin these stars experiences episodes of low neutron densi-ties of about 3 · cm − , the C( α ,n)-phase, and veryhigh neutron densities, the Ne( α ,n) phase. The highestneutron densities during the latter phase reach values ofup to 10 cm − . FIG. 3 shows a summary of the β − decay times for radioactive isotopes on the neutron richside of the valley of stability, for the conditions duringthe main component of the classical s process, which isin between the two phases of the s process in AGB stars[4]. During the Ne( α ,n) phase, the lifetime versus neu-tron capture is much shorter resulting in isotopes withhalf-lives of just a few days forming the critical branch-ing points for the s -process reaction flow.Because of the smaller total neutron exposure, themass flow during the weak component of the s -processdoes not overcome the isotopes along the neutron shellclosure of N = 50 and is therefore restrictes to the massregion between iron and yttrium. It takes place duringconvective core-He burning in massive stars ( M > M (cid:12) )and the material is later reprocessed during a second neu-tron exposure during convective carbon shell burning ofmassive stars [30–32]. During the high temperatures ofthe carbon shell burning of T ≈ − cm − can be reached, similar to theconditions during the Ne( α ,n) phase during the heliumflash in AGB stars.The most crucial neutron-induced reaction during the s -process is the neutron capture reactions. TABLE Igives a small selection of interesting branch point nuclei,where direct determination of the neutron capture crosssection is desirable. Even though all of these isotopes are TE RR E S T R I A L HA L F L I V E [ d ]
40 60 80 100 120 140 160 180 200
ATOMIC MASS NUMBER
FIG. 3: Terrestrial β − live times for unstable isotopes onthe classical s -process path as a function of mass number.Shown are only isotopes where the neutron capture understellar conditions is faster than the stellar β − decay for aneutron density of 4 × cm − at a temperature of 30 keV,the conditions of the classical s process [4]. If the β -decay isfaster than the neutron capture, the s -process proceed to thenext higher element. very close to the valley of β -stability, none of them canbe investigated with current or upcoming neutron time-of-flight (TOF) facilities. The currently strongest TOF-facility used for measurements in the astrophysical energyregime is DANCE at the Los Alamos National Labora-tory [33]. At the sample position about 3 · n/s/cm are available between 10 and 100 keV. Upcoming facilitieslike FRANZ [34] or the upgrade of nTOF [35] are aimingat neutron fluxes around 10 n/s/cm . The last columnof TABLE I lists the minimum neutron flux in the keVregime necessary for a TOF measurement on the respec-tive isotopes. It is obvious that even with the upcomingfacilities, orders of magnitude are missing for a succesfulmeasurement. However, the setup proposed here, wouldallow the corresponding measurement. The productionof the corresponding nuclei in sufficient amounts is pos-sible, since the isotopes are very close to the stability[36].If charged particles are in the exit channel of a neu-tron induced reaction, the experimental determinationwith traditional methods is restricted to a few favourablecases. Since the charged particle has to leave the sample,its thickness is very limited resulting in a correspondinglylow reaction rate. The setup proposed here does not suf-fer from this requirement, since the resulting beam caneasily be detected. Very important reactions are (n, α )in particular on light nuclei, since they act as recyclingpoints of the mass flow. Interesting isotopes are S, Cl, , Ar, K and Ca [37].
2. The r -process The r -process synthesises roughly half the elementsheavier than A=70. It proceeds through neutron capture TABLE I: Interesting branchpoint nuclei in the s -process nu-cleosynthesis network, which can not be directly measuredwith current or upcoming facilities. The last column gives anestimate for the minimum neutron flux necessary in the keV-regime at the sample position for a traditional time-of-flightmeasurement using a 4 π -calorimenter to detect the emitted γ -rays [6].Isotope half-life neutron flux(d) (s − cm − ) Fe 45 10
Zr 64 10 Te m
109 5 · Nd 11 10 Pm m,gs
41, 5 10 and beta decay [38] at much higher neutron densities of10 − cm − . Therefore capture is much faster thanbeta decay, so that very neutron rich nuclei are createdwhich decay back towards the valley of stability as theneutron density drops marking the end of the r -process.The neutrino-driven wind model within core-collapse su-pernovae are currently one of the most promising can-didates for a successful r -process. These neutrino windsare thought to dissociate all previously formed elementsinto protons, neutrons and α particles before the seed nu-clei for the r -process are produced. Hence, the neutrino-driven wind model could explain the observational factthat the abundances of r -nuclei of old halo-stars are sim-ilar to our solar r -process abundances [39].During the freeze-out phase, when the neutron den-sity drops and the very short-lived nuclei decay, the( n, γ ) − ( γ, n ) equilibrium, which dominates the abun-dance distribution during most of the r -process episode,is interrupted. This means, neutron capture reactionscan modify the final abundances. The sensitivity of theabundances in the r -process abundance peaks to changesin the neutron capture cross sections have been inves-tigated [5]. The crucial reactions in range for the ex-perimental setup proposed here are neutron captures on − Sb with half lives between 2.8 and 40 min, and on − Sn with half lives between 40 s and 7 min).
3. The i -process Under certain conditions, stars may experienceconvective-reactive nucleosynthesis episodes. If unpro-cessed, H-rich material is convectively mixed with an He-burning zone, it has been shown in hydrodynamic simu-lations that neutron densities in excess of 10 cm − canbe reached [40, 41]. Under such conditions, which arebetween the s - and r -process, the reaction flow occurs afew mass units away from the valley of stability. These conditions are sometimes referred to as the i -process (in-termediate process). One of the most important, but ex-tremely difficult to determine rate, is the neutron captureon I. With an half-life time of around 6 h, this crosssection can not be measured directly. With the setupproposed here, this cross section could be investigateddirectly, suffcient production yields of
I provided.
B. Advanced Reactor Technology
The ratio of neutron capture to neutron induced fissionis most important for the estimation of the criticality ofnuclear reactors or other devices gaining energy via fis-sion of heavy elements. Most experiments determiningfission cross sections face the same problems like exper-iments determining reaction cross sections with chargedparticles in general. The short range of the charged fis-sion products limits the sample thickness and thereforethe reaction rate [42, 43]. Experiments determining smallneutron capture cross sections [44] in the presence of neu-tron induced fission have to deal with the γ -backgroundfollowing the deexcitation of the fission products [45]. Allof those measurements are therefore usually only pos-sible, if the investigated isotope is long-lived or stable.There are, however, a number of isotopes, which arevery important, but short-lived. Prominent examples ofimportant isotopes are m U (25 min),
U (6.75 d),
U (23.5 min). These isotopes can currently not beinvestigated directly. The setups proposed here wouldallow measurements in an energy regime, which is notof immediate importance for currently operating reac-tors, since the average energy of the neutron spectrum istoo low (thermal), but next generation reactors will notonly operate at much higher temperatures, but the neu-tron spectrum will also be less moderated. This requiresknowledge of the corresponding cross sections well intothe MeV-regime.
VI. SUMMARY
The combination of a modern storage ring with a neu-tron target consisting of a fission reactor allows the de-termination of a variety of neutron-induced cross sectionsin inverse kinematics. The luminosity of such a devicewould be sufficient to investigate cross sections down tomillibarns on isotopes with half-lives down to a few min-utes or may be even below. The energy in the centre ofmass, which corresponds to the neutron energy in regularkinematics, depends on the isotope under investigationand can be as low as 100 keV. This energy limit is onlygiven by the required life time of the beam, which mightbe improved in the future with new vacuum technologies.
Acknowledgments
We would like to thank F. K¨appeler and K. Sonnabendfor many fruitful discussions. This work was partly sup-ported by the HGF Young Investigators Project VH-NG- 327, the Helmholtz-CAS Joint Research Group HCJRG-108, the GIF project G-1051-103.7/2009, the BMBFproject 05P12RFFN6 and the EuroGenesis projectMASCHE. [1] F. K¨appeler, R. Gallino, S. Bisterzo, and W. Aoki, Re-views of Modern Physics , 157 (2011).[2] F.-K. Thielemann, D. Mocelj, I. Panov, E. Kolbe,T. Rauscher, K.-L. Kratz, K. Farouqi, B. Pfeiffer,G. Martinez-Pinedo, A. Kelic, K. Langanke, K.-H.Schmidt, and N. Zinner, International Journal of Mod-ern Physics E , 1149 (2007).[3] M. Arnould and S. Goriely, Physics Reports , 1(2003).[4] R. Reifarth, C. Arlandini, M. Heil, F. K¨appeler, P. Sedy-chev, A. Mengoni, M. Herman, T. Rauscher, R. Gallino,and C. Travaglio, Astrophysical Journal , 1251(2003).[5] R. Surman and J. Engel, Phys. Rev. C , 035801 (2001).[6] A. Couture and R. 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